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Geometric shape priors for region-based active contours
Abstract
In this paper, we present a novel approach for incorporating geometric shape priors in region-based active contours in order to provide more robustness to clutter, noise and occlusions. We define shape descriptors based on Legendre moments and embed them in a recent Eulerian formulation of region-based active contours, which enables a rigorous mathematical treatment. An evolution equation that minimizes a function of the distance between the active contour and a reference shape is derived. Experimental results show the ability of the geometric shape prior to constrain an evolving curve to resemble a target shape. We finally introduce the new shape prior into a two-class segmentation functional and show its benefits on segmentation results, in presence of occlusions and clutter.
... Dans un premier temps, nous expérimentons notre algorithme sur une image de synthèse composée d'un objet ayant la forme de signe «plus» partiellement occulté et bruité (Fig.2.27). Nous proposons de comparer notre modèle à celui proposé par Alban Foulonneau dans [3]. La forme de référence est supposée connue à l'avance. ...
... La forme de référence est supposée connue à l'avance. Nous rappelons que le modèle présenté dans [3] présente une invariance des images médicales du coeur ainsi que sur des images réelles. ...
... Dans[3,4,5], il s'agit d'une approche permettant d'incorporer une contrainte géométrique de forme dans les contours actifs orientés région de façon à améliorer leur robustesse au bruit non gaussien, aux fonds d'images texturés et aux occultations. Pour cela, Foulonneau et al. ont définis un descripteur de forme à partir des moments de Legendre de la fonction caractéristique de la forme. ...
Active contours represent a particular segmentation’s technique that has pro- ven successful salient. They are used in many applications of image analysis like medical imaging, tracking of moving object, remote sensing etc. The introduction of shape constraint to improve the performance of these methods is of an
important issue.
In this work, we propose a shape constraint for two models of geometric active
contours based on the level set approach to improve their robustness in presence of
partial occlusions , noise and low contrast. Our first contribution considers that the
a priori information of the object of interest is obtained from a reference pattern, assumed to be known in advance after a registration step by phase correlation based
on the Analytical Fourier-Mellin transform to promote robustness of movement parameters’ estimation compared to the alignment methods. Our approach consists
in incorporating the a priori information only in the regions of variability between
the target shape and the reference one so that only some of the pixels in the image
will be invoqued in the detection process and promoting optimization in terms of
execution time. In a second work, we consider a multi-references case. We propose
a geometric approach based on a set of invariant shape descriptors for determining
the nearest template to the shape to be detected in the case where several references
are available.Experiments on sequences of moving object as well as medical images
have been made to show the advantages of the proposed approach for improving segmentation results obtained by conventional models.
Keywords : Segmentation, shape prior, active contours, phase correlation, invariant
descriptors.
... En effet, de nombreux travaux (Blake et Isard [9,52]) sont basés sur la modélisation de contour actif constitué d'une spline d'interpolation et mettent en oeuvre des propriétés de cette implémentation qui n'ont pas été présentées ici. Nous pourrions, par exemple, envisager d'introduire les résultats des travaux de Jacob et al. [51] sur le calcul des moments de régions intérieures et extérieures à un contour modélisé par une spline dans des méthodes nécessitant le calcul itératif de ces moments tels que la segmentation avec a priori de formes, proposée par Foulonneau et al. [38], ou les approches de segmentations basées régions manipulant des histogrammes (Jehan-Besson et al. [5] et Herbulot et al. [46]). Ces méthodes étant indépendantes de la modélisation du contour actif, cela permettrait de réduire le temps de calcul des moments de l'image dans les régions internes et externes au contour, de façon considérable. ...
... Le calcul des moments des régions internes et externes au contour est une des étapes clef dans de nombreux travaux utilisant des histogrammes (Jehan-Besson et al. [5] et Herbulot et al. [46]) ou considérant des a priori de formes (Foulonneau et al. [38]). ...
... Ces travaux de recherche permettent d'envisager de nombreux développements : -Une première perspective apportant un résultat immédiat, serait d'appliquer les résultats, obtenus par Jacob et al. [51], concernant « le calcul exact des moments pour des régions définies par des courbes splines et des courbes ondelettes » aux modèles paramétriques de contour actif proposés dans ce document. Le calcul des moments des régions internes et externes au contour est une des étapes clef dans de nombreux travaux utilisant des histogrammes (Jehan-Besson et al. [5] et Heerbulot et al. [46]) ou considérant des a priori de formes (Foulonneau et al. [38]). En utilisant les modèles paramétriques proposés, pour implémenter ces méthodes de segmentation, la réduction du coût calcul des moments représenterait donc une amélioration substantielle pour ces approches de segmentation par contours actifs basés régions. ...
Active contour modeling represents the main framework of this thesis. Active contours are dynamicmethods applied to segmentation of still images and video. The goal is to extract image regionscorresponding to semantic objects. Image and Video segmentation can be cast in a minimizationframework by choosing a criterion which includes region and boundary functionals. This minimizationis achieved through the propagation of a region-based active contour. The efficiency of thesemethods lies in their robustness and their accuracy. The aim of this thesis is triple : to develop (i) amodel of parametric curve providing a smooth active contour, to precise (ii) conditions of stable evolutionfor such curves, and to reduce (iii) the computation cost of our algorithm in order to providean efficient solution for real time applications.We mainly consider constraints on contour regularity providing a better robustness regarding tonoisy data. In the framework of active contour, we focus on stability of the propagation force, onhandling topology changes and convergence conditions. We chose cubic spline curves. Such curvesprovide great properties of regularity, allow an exact computation for analytic expressions involvedin the functional and reduce highly the computation cost. Furthermore, we extended the well-knownmodel based on interpolating splines to an approximatingmodel based smoothing splines. This latterconverts the interpolation error into increased smoothness?smaller energy of the second derivative.The flexibility of this new model provide a tunable balance between accuracy and robustness.The efficiency of implementating such parametric active contour spline-based models has beenillustrated for several applications of segmentation process.
... More recently shapes have been represented using Legendre moments in order to define shape priors for segmentation using active contours [16,17]. This representation can also be easily included in a variational setting [16,17,31]. ...
... More recently shapes have been represented using Legendre moments in order to define shape priors for segmentation using active contours [16,17]. This representation can also be easily included in a variational setting [16,17,31]. ...
... where Γ(z, τ) is the evolving curve, z a parameter of the curve, τ the evolution parameter, v(x, µ) the amplitude of the velocity in x = Γ(z, τ) directed along the normal of the curve N(x, τ). The evolution equation and more particularly the velocity v must be computed in order to make the contour evolve towards an optimum of the energy criterion (16). From an initial curve Γ 0 defined by the user, we will have lim τ→∞ Γ(τ) = µ at convergence of the process. ...
In this paper, we propose to consider the estimation of a reference shape from a set of different segmentation results using both active contours and information theory. The reference shape is then defined as the minimum of a criterion that benefits from both the mutual information and the joint entropy of the input segmentations. This energy criterion is here justified using similarities between information theory quantities and area measures, and presented in a continuous variational framework. This framework brings out some interesting evaluation measures such as the specificity and sensitivity. In order to solve this shape optimization problem, shape derivatives are computed for each term of the criterion and interpreted as an evolution equation of an active contour. A mutual shape is then estimated together with the sensitivity and specificity. Some synthetical examples allow us to cast the light on the difference between our mutual shape and an average shape. The applicability and robustness of our framework has also been tested for the evaluation of different segmentation methods of the left ventricular cavity from cardiac MRI.
... It then becomes necessary to include a combination of information into the segmentation algorithm in order to more accurately extract the target object. Methods have been proposed which incorporate prior information in terms of shape [12,13,20,21,25,35,36], topology [43], atlas information [2,14,19,22,33,59,64,70,73] (see [52] for details), and statistical information [44]. The exact technique and information to be incorporated should be chosen to best suit the specific application. ...
... While variations of level set techniques have been proposed to improve computation time [61], others have presented methods for improving upon the segmentation accuracy. In doing so, many techniques have been proposed which include a shape prior into the active contour segmentation framework [12,13,20,21,25,35,36,58]. In [35,36], Leventon et al. presented a method which includes statistical shape information into the geometric active contours energy function. ...
... [13] incorporated a different shape term into this model. Also, several approaches have been introduced which incorporate shape priors into the Chan-Vese model [12,21,25]. ...
... This framework includes a trade-off parameter which allows tuning the balance between the data fidelity term and the shape prior according to the level of noise and the confidence in the model. Most of the time, the shape prior is based on a similarity measure between the evolving shape and a reference one, which may be either a given silhouette (RiklinRaviv et al. 2004; Foulonneau et al. 2003) or the result of a (pre)segmentation stage (Zhang and Freedman 2003; Gastaud et al. 2003 ) or the outcome of some learning procedure (Staib and Duncan 1992; Cremers et al. 2003; Rousson and Paragios 2002; Tsai et al. 2003; Chen et al. 2002; Bresson et al. 2006). While several authors employ a parametric representation of curves (Staib and Duncan 1992; Székely et al. 1996; Cremers et al. 2003 ), or geometric differential representations (Joshi et al. 2005), a vast majority of recent papers consider non-parametric models. ...
... Pose parameters (rotation, translation and scaling) are generally taken into account in an explicit fashion (Leventon et al. 2000; Rousson and Paragios 2002; Riklin-Raviv et al. 2004; Tsai et al. 2003; Chen et al. 2002; Bresson et al. 2006), which increases the number of d.o.f. of the problem, and leads to systems of coupled partial differential equations (PDE's). To overcome these problems, intrinsic alignment was proposed: in Székely et al. (1996), Cremers et al. (2002 for explicit snakes implementations, in Cremers et al. (2006a), Foulonneau et al. (2003 for implicit representations in the case of translation and scale invariance, and extended in Foulonneau et al. (2006a) to the affine case. ...
... The approach reported in the present paper combines a compact , parametric representation of shapes (introduced by the authors in Foulonneau et al. 2003 Foulonneau et al. , 2006a for the modeling of single shapes) with curve evolution theory. More specifically , this parametric description is based on Legendre moments computed from the characteristic function of a shape. ...
In this paper, we present a new way of constraining the evolution of an active contour with respect to a set of fixed reference
shapes. This approach is based on a description of shapes by the Legendre moments computed from their characteristic function.
This provides a region-based representation that can handle arbitrary shape topologies. Moreover, exploiting the properties
of moments, it is possible to include intrinsic affine invariance in the descriptor, which solves the issue of shape alignment
without increasing the number of d.o.f. of the initial problem and allows introducing geometric shape variabilities. Our new
shape prior is based on a distance, in terms of descriptors, between the evolving curve and the reference shapes. Minimizing the corresponding
shape energy leads to a geometric flow that does not rely on any particular representation of the contour and can be implemented with
any contour evolution algorithm. We introduce our prior into a two-class segmentation functional, showing its benefits on
segmentation results in presence of severe occlusions and clutter. Examples illustrate the ability of the model to deal with
large affine deformation and to take into account a set of reference shapes of different topologies.
... The candidate result with the smallest shape difference is regarded as the extracted femur contour. Existing methods that also incorporate geometric constraints in the snake include [11, 14]. Shen et al. [11] embedded geometric information as attribute vector into a snake. ...
... So, this method may not reliably constrain the snake's shape. Foulonneau et al. [14] includes Legendre moments in the snake. The shortcoming of this method is that moments provide global description of a reference shape. ...
... Large local deformations such as size variations of parts of the femur and orientation variations of femurs in different images (Fig. 4) would change the moments significantly even though the overall shape remains roughly the same. Moreover, this method will become very complex if rotation invariance, left out in [14], is to be considered as well. In comparison, our method not only allows the snake to handle shape and size variations but also variations in the orientations of the femurs. ...
Extraction of bone contours from x-ray images is an important first step in computer analysis of medical images. It is more complex than the segmentation of CT and MR images because the regions delineated by bone contours are highly nonuniform in intensity and texture. Classical segmentation algorithms based on homogeneity criteria are not applicable. This paper presents a model-based approach for automatically extracting femur contours from hip x-ray images. The method works by first detecting prominent features, followed by registration of the model to the x-ray image according to these features. Then the model is refined using active contour algorithm to get the accurate result. Experiments show that this method can extract the contours of femurs with regular shapes, despite variations in size, shape and orientation.
... Most of the research used a database with a plain background that will be easy to segment, whereas it will be challenging to do so with a natural background. Therefore, this paper has considered cotton leaf images for the study, the database images created for the study by capturing the images from the field, and the method used for this research using deformable models [9,15,37,40]. In recent years, many authors used deformable models used for leaf segmentation [4,11,21]. ...
... Bilateral filtering [7,9]is defined as an edge-preserving smoothing method, and it is a noniterative scheme. In this average filter is used, and one among them is the median filter. ...
Segmenting the leaf images from the complex background is the current research topic. So, in this paper, we propose an algorithm to segment the leaf image from the natural background. Diverse methods exist in the literature, like region-based, edge-based, clustered-based, deformable models. Among these, deformable models are more advantageous, which leads to the use of the method for leaf segmentation. There are two types of deformable models, namely geometric and parametric models. The geometric model has many advantages over the parametric model; hence, we present the comparative study of the proposed model and other well-known algorithms. The proposed method combines the chan vese method with the level set method without re-initialization. It also uses bilateral filtering to remove the noise from the image for more vital image information, which helps in the fast evolution process. The main objective of the method is to segment a leaf from natural background. For our study, the model used the cotton leaf database with nearly 300 images. The results show that the proposed model modified chan vese method gives better results than other state-of-the-art performance parameters. The proposed method parameters Precision, Recall, Sensitivity, Specificity, Accuracy., Jaccard Index, F1 score values are 0.9685, 0.9949, 0.9949, 0.9817, 0.8897,0.9388 respectively.
... LM can also be used as shape descriptors for including geometric shape priors in region-based active contours, which will provide more robustness to noise, clutter, and occlusions (Foulonneau et al. 2003). Shape descriptors are used with a Eulerian formula for region-based active contours. ...
... Table 2 classifies the continuous orthogonal polynomials according to hyper-Geometric functions. face recognition, palm-print authentication, iris verification, classification of 2D polyacrylamide gel electrophoresis, texture analysis, 3D object images classification, histogram representation, vehicle recognition, image watermarking, line fitting in noisy image, incorporation of geometric shape priors in region-based active contours, image indexing and retrieval from image DB, finger crease pattern recognition, noise removal from ECG signals, reconstruction of noisy medical images (Annadurai and Saradha 2004), (Deepika et al. 2010b), (Sarmah and Kumar n.d.), (Marengo et al. 2005), (Sastry et al. 2012), (Arif et al. 2009), (Mandal et al. 1996, (Zhang et al. 2006), , (Qjidaa and Radouane 1999), (Foulonneau et al. 2003), (Ahmadian et al. 2003), (Luo and Lin 2007), (Kwan et al. 2006), (Hosny et al. 2013) (Chong et al. 2004;Hosny 2007Hosny , 2010Hosny , 2011aPapakostas et al. 2010b;Shu et al. 2000;Yang et al. 2006;Zhou et al. 2002) Gegenbauer moments ...
Orthogonal moments provide an efficient mathematical framework for computer vision, image analysis, and pattern recognition. They are derived from the polynomials that are relatively perpendicular to each other. Orthogonal moments are more efficient than non-orthogonal moments for image representation with minimum attribute redundancy, robustness to noise, invariance to rotation, translation, and scaling. Orthogonal moments can be both continuous and discrete. Prominent continuous moments are Zernike, Pseudo-Zernike, Legendre, and Gaussian-Hermite. This article provides a comprehensive and comparative review for continuous orthogonal moments along with their applications.
... The addition of a shape prior can then be crucial for many applications. In (Lecellier, Jehan-Besson, Fadili, Aubert, Revenu, & Saloux, 2006), we propose to combine our statistical data terms with a shape prior computed using its Legendre Moments based on the work of (Foulonneau, Charbonnier, & Heitz, 2003). Indeed, moments (The & Chin, 1988) give a region-based compact representation of shapes through the projection of their characteristic functions on an orthogonal basis such as Legendre polynomials. ...
... Indeed, moments (The & Chin, 1988) give a region-based compact representation of shapes through the projection of their characteristic functions on an orthogonal basis such as Legendre polynomials. Scale and translation invariances can be advantageously added as in (Foulonneau, Charbonnier, & Heitz, 2003) for their application to region segmentation, hence avoiding the registration step. To drive this functional towards its minimum, the geometrical PDE is iteratively run without the shape prior, then the shape prior term is updated, and the active contour evolves again by running the PDE with the shape prior. ...
In this chapter, we focus on statistical region-based active contour models where the region descriptor is chosen as the probability density function of an image feature (e.g. intensity) inside the region. Image features are then considered as random variables whose distribution may be either parametric, and then belongs to the exponential family, or non parametric and is then estimated through a Parzen window. In the proposed framework, we consider the optimization of divergences between such PDFs as a general tool for segmentation or tracking in medical images. The optimization is performed using a shape gradient descent through the evolution of an active region. Using shape derivative tools, our work is directed towards the construction of a general expression for the derivative of the energy (with respect to a domain), and the differentiation of the corresponding evolution speed for both parametric and non parametric PDFs. Experimental results on medical images (brain MRI, contrast echocardiography, perfusion MRI) confirm the availability of this general setting for medical structures segmentation or tracking in 2D or 3D.
... A new shape energy term, defined as the distance between moments calculated for the evolving active contour and the moments calculated for a fixed reference shape prior, is proposed and derived in the mathematical framework of [Aubert et al., 2003] in order to obtain the evolution equation. Initially, the method was designed for a single reference shape prior [Foulonneau, et al., 2003], but in the most recent version is able to take into account multi-reference shape priors. As a result, the authors have defined a new efficient method for region-based active contours integrating static shape prior information. ...
... Although Legendre moments and PCA are selected to build the shape space in this paper, other shape descriptors and dimensionality reduction techniques can be easily 'plugged' into the optimization framework as long as the shape reconstruction from the shape space is possible. It should be pointed out that, unlike derivative based optimization methods such as [Foulonneau, et al., 2003] and [Foulonneau, et al., 2009], the shape descriptors need not be differentiable in the proposed method. ...
For the last decade, Medical Image Analysis for Computer-Aided-Diagnosis (CAD) has been thecentral motivation of my research activity. With the constant increase of the imaging capabilities ofmedical devices and the huge amount of produced digital information, physicians are in real need for semiautomaticimage processing tools making possible fast, precise and robust analysis, including restoration,segmentation, pattern detection and recognition, quantitative analysis, etc. In this particular applicationarea, from an image processing perspective, my research work has mainly focused for the last 8 yearson two main tracks: (i) The study of the variational approach framework for image restoration andsegmentation which common point is the formalization of the related optimization problem under theform of a Partial Differential Equation (PDE); (ii) The development of embeddable pattern detectionand recognition methods based on statistical learning process for real-time in situ diagnosis.The main scientific contributions of my research activities have been since 2006: In image restoration:(i) The study of the stochastic resonance phenomenon in non-linear PDE for image restoration and (ii)The study of double-well potential functions for Gradient-Oriented-PDE in image restoration. In imagesegmentation: (i) An Active contour segmentation approach with learning-based shape prior information;(ii) An Alpha-divergence-based active contour image segmentation approach; (iii) A Fractional-entropybasedactive contour image segmentation approach. And finally in pattern recognition: The proposal of acomplete embeddable image processing scheme for in situ polyp detection in Wireless Capsule Endoscopyfor early colorectal cancer diagnosis.This manuscript proposes a detailed overview of these contributions as well as elements for my futureresearch activities.
... HOACs are a new generation of active contour models [5] allowing the incorporation of non-trivial prior knowledge about region geometry, and the relation between region ge- ometry and the data, via nonlocal interactions between tuples of region boundary points. They differ from most other meth- ods for incorporating prior geometric knowledge into active contours, for example [1,2,7], in not being based upon per- turbations of a reference region or regions. In consequence, they can detect multiple instances of an entity at no extra cost, a critical requirement for the current application. ...
... In addition, for the phase field model, ˜ α C is constrained. Thus both the HOAC and phase field 'gas of circles' models have three effectively 2 We ignore the normalization constant Z(R) = DI e −E I (I,R) since in our case it merely changes λ C and α C . free parameters, the same number as the CAC model. ...
The problem of extracting the region in the image domain corresponding to an a priori unknown number of circular ob-jects occurs in several domains. We propose a new model of a 'gas of circles', the ensemble of regions in the image do-main composed of circles of a given radius. The model uses the phase field reformulation of higher-order active contours (HOACs). Phase fields possess several advantages over con-tour and level set approaches to region modelling, in par-ticular for HOAC models. The reformulation allows us to benefit from these advantages without losing the strengths of the HOAC framework. Combined with a suitable likelihood energy, and applied to the tree crown extraction problem, the new model shows markedly improved performance, both in quality of results and in computation time, which is two or-ders of magnitude less than the HOAC level set implementa-tion.
... They are intrinsically Euclidean invariant . They differ from most other methods for incorporating prior geometric knowledge into active contours [2] [3] [6] in not being based upon perturbations of a reference region or regions. In consequence, they can detect multiple instances of an entity at no extra cost, a critical requirement for the current application. ...
... They are intrinsically Euclidean invariant . They differ from most other methods for incorporating prior geometric knowledge into active contours [2, 3, 6] in not being based upon perturbations of a reference region or regions. In consequence, they can detect multiple instances of an entity at no extra cost, a critical requirement for the current application. ...
We present a model of a 'gas of circles', the ensemble of regions in the image domain consisting of an unknown number of circles with approximately fixed radius and short range repulsive interactions, and apply it to the extraction of tree crowns from aerial images. The method uses the re- cently introduced 'higher order active contours' (HOACs), which incorporate long-range interactions between contour points, and thereby include prior geometric information without using a template shape. This makes them ideal when looking for multiple instances of an entity in an im- age. We study an existing HOAC model for networks, and show via a stability calculation that circles stable to pertur- bations are possible for constrained parameter sets. Com- bining this prior energy with a data term, we show results on aerial imagery that demonstrate the effectiveness of the method and the need for prior geometric knowledge. The model has many other potential applications.
... community was the first to use shape constrained deformable models as it has to deal with images frequently distorted by noise, occlusions and poor contrast of organs to be segmented [1, 2, 3, 4]. The application of these model-based schemes was later extended to manufactured and natural scenes objects as well as object tracking from video sequences [5, 6, 7, 8, 9, 10, 11]. The prior shape constraint can be derived from a single or a collection of reference shapes. ...
... Further works towards shape energy independent from Ω and the extension to shape prior with multiple components can be found in [10] with the formulation of a symmetric pseudo-distance. In [7] Foulonneau et al. formulate a distance between high order geometric moments of the evolving curve and the shape prior to apply the constraint. The moments are projected on a Legendre polynomial basis to decrease the redundancy of the shape representation. ...
This paper exposes a novel formulation of prior shape con- straint incorporation for the level set segmentation of objects from cor- rupted images. Applicable to variational frameworks, the proposed scheme consists in weighting the prior shape constraint by a function of time and space to overcome local minima issues of the energy func- tional. Pose parameters which make the prior shape constraint invariant from global transformations are estimated by the downhill simplex algo- rithm, which is more tractable and robust than the traditional gradient descent. The proposed scheme is simple, easy to implement and can be generalized to any variational approach incorporating a single prior shape. Results illustrated with different kinds of images demonstrate the efficiency of the method.
... The evolution equation is generally deduced from a general criterion that includes both region integrals and boundary integrals. The combination of those two terms in the energy functional allows the use of photometric image properties, such as texture [3, 27, 39, 42] and noise [20, 32, 35] , as well as geometric properties such as the prior shape of the object to be segmented [15, 19, 21, 33, 34, 45], see also the review in [14]. RBACs have proven their efficiency for a wide range of applications such as medical image segmentation [9, 30], video object segmentation or tracking [40] . ...
... which corresponds to the MLE of the parameter θ 2 given by: (19) 3. ...
In this paper, we focus on statistical region-based active contour models where image features (e.g. intensity) are random
variables whose distribution belongs to some parametric family (e.g. exponential) rather than confining ourselves to the special
Gaussian case. In the framework developed in this paper, we consider the general case of region-based terms involving functions
of parametric probability densities, for which the anti-log-likelihood function is a special case. Using shape derivative
tools, our effort focuses on constructing a general expression for the derivative of the energy (with respect to a domain),
and on deriving the corresponding evolution speed. More precisely, we first show by an example that the estimator of the distribution
parameters is crucial for the derived speed expression. On the one hand, when using the maximum likelihood (ML) estimator
for these parameters, the evolution speed has a closed-form expression that depends simply on the probability density function.
On the other hand, complicating additive terms appear when using other estimators, e.g. method of moments. We then proceed
by stating a general result within the framework of multi-parameter exponential family. This result is specialized to the
case of the anti-log-likelihood function with the ML estimator and to the case of the relative entropy. Experimental results
on simulated data confirm our expectations that using the appropriate noise model leads to the best segmentation performance.
We also report preliminary experiments on real life Synthetic Aperture Radar (SAR) images to demonstrate the potential applicability
of our approach.
... Reconnaissance faciale, authentification par empreinte palmaire, vérification de l'iris, classification de l'électrophorèse sur gel de polyacrylamide 2D, analyse de texture, classification d'objets 3D, représentation d'histogramme, reconnaissance de véhicule, tatouage d'image, ajustement de ligne dans une image bruyante, incorporation de formes géométriques a priori dans contours actifs, indexation et récupération d'images à partir de la base de données d'images, reconnaissance des formes de plis des doigts, suppression du bruit des signaux ECG, reconstruction d'images médicales bruitées [66], [116], [117], [118], [119], [120], [121], [36], [122], [123], [124], [125], [126], [127] [128], [56] GMs ...
Signal representation is an important topic in computer vision and pattern recognition. It plays a fundamental role in a range of applications towards understanding auditory and visual contents. Signal representation based on discrete orthogonal moment transforms has been reported to be effective in satisfying the core conditions of semantic description due to its beneficial mathematical properties, especially discriminability and robustness. The objective of this thesis is to propose approaches for the representation, characterization and analysis of signals and images multi-component using the discrete orthogonal moment transforms.
The first approach will focus on the compact and holistic representation of multi-component signals/images. In this context, we propose for the first time a new family of discrete orthogonal transforms, called octonion transforms, based on octonion theory and moment theory, to represent and describe multi-signal information in a compact and holistic way. These transforms generalize standard moments and quaternion moments and have been used to represent multi-signals such as color stereoscopic images and grayscale multi-images.
The second approach will focus on the development of a new set of discrete orthogonal moments called fractional discrete orthogonal moments. These new moments have additional parameters called fractional orders where different values of these fractional orders give different coefficients in the transform domain, which allows to optimize accuracy, robustness/invariance, and privacy in applications where these transforms are used.
The third approach will focus on developing a new signal/image watermarking method and ensuring its requirements by using the proposed fractional order transforms instead of the conventional integer order orthogonal transforms. We adjust the fractional orders in the transform domain, then select the optimal fractional orders and the corresponding moment coefficients are used as host coefficients to integrate the watermark.
The fourth approach will focus on extracting the invariants of discrete orthogonal transforms. In this framework, we have proposed a new approach for the fast and accurate computation of the 3D Charlier moment invariants by translation and uniform/non-uniform scaling directly from Charlier polynomials. This direct method significantly reduces the computation time of the invariants and eliminates the need for numerical approximation of the geometric moment invariants (conventional method). The performance of these descriptors is tested on 3D pattern classification and compared with other existing methods in the literature.
The fifth approach will focus on the parallelization of time-consuming algorithms based on moment transforms and their implementations on an embedded system cluster. We parallelized the intensive and repetitive steps of these algorithms in order to implement them simultaneously on the available physical cores of an embedded system cluster. In order to build a low-cost, low-power cluster with a large quantity of physical cores, we combined several Raspberry Pis and the communication between them is ensured by the MPI library. The adopted Raspberry Pi cluster is also characterized by its portability and mobility, which are desired in smart city applications.
... To avoid the problem of shapes alignment, many approaches adopt the use of invariant descriptors to define prior knowledge on shape. Foulonneau et al. [10] proposed an energy functional based on Legendre descriptors of the target object and the evolving front. This shape constraint was incorporated into a region based active contour [2]. ...
... The main approach for hand posture characterization is based on moments which are invariant to several image transformations. A review of such moments is available in [3,4]. Among those moments, Zernike [5] and Legendre [6] moments are based on orthogonal polynomials. ...
This paper deals with hand posture recognition. Thanks to an adequate setup, we afford a database of hand photographs. We propose a novel contour signature, obtained by transforming the image content into several signals. The proposed signature is invariant to translation, rotation, and scaling. It can be used for posture classification purposes. We generate this signature out of photographs of hands: experiments show that the proposed signature provides good recognition results, compared to Hu moments and Fourier descriptors.
... (1.42) L'avantage de cette mesure de distance est, premièrement, qu'elle ne dépend pas de l'aire de la région considérée en raison de la normalisation, et, deuxièmement, qu'elle est symétrique : d(φ 1 , φ 2 ) = d(φ 2 , φ 1 ). Foulonneau et al. (2003) proposent des descripteurs de forme, λ ref p,q , p + q ≤ N jusqu'à l'ordre N, invariants aux translations et aux facteurs d'échelle, à l'aide de moments de Legendre normalisés. Ils introduisent un terme d'a priori dans le cadre des régions actives géodésiques (Paragios et Deriche, 2002a), fonction de la distance quadratique entre les moments du contour à un instant donné et les moments du contour de référence : ...
This thesis addresses the question of how to introduce prior knowledge about the shape of an object to be detected in the general framework of object recognition from images. We illustrate this idea with the problem of line network extraction from satellite and aerial images. We use the framework of active contours and we introduce a whole new class of active contours, named "higher-order active contours". This class allows us to define new models that incorporate sophisticated prior geometric knowledge describing, rather than a specific shape, a general family of shapes. We first study a particular case of a geometric quadratic energy that favours network structures composed of arms of roughly constant width joined at junctions. This energy demonstrates the modelling possibilities offered by the new class of active contours. The geometric quadratic energy is added to the linear terms length and area, and is used as a geometric prior for the line network extraction models we propose. Several image terms are defined, one of them being a quadratic term linking the geometry of contour points and the data. A model for extraction in presence of occlusions is also presented. In order to minimize these energies, we develop an algorithm based on the level set methodology. The non-local forces of the gradient descent equation are computed on the extracted contour, before being extended to the whole domain. Finally, in order to solve certain difficulties with both standard active contours and the new models, we propose to use phase field models to model regions. They offer an advantageous alternative to classical techniques and we define line network extraction models similar to higher-order active contours in that framework. All proposed models are tested on real satellite and aerial images.
... En pratique, la présence de bruit et les données manquantes nécessitent d'intégrer des contraintes géométriques : on parle alors d'énergie de forme. Cette information a priori peut être injectée de différentes manières dans le cadre variationnel, par exemple l'utilisation des moments de Legendre d'une forme de référence [8]. L'intérêt du cadre variationnel est d'associer différentes contraintes (énergies contour, région et forme). ...
... où Ω désigne la forme. Dans [Foulonneau et al., 2003], ce vecteur est dénommé descripteur de forme. ...
Image reconstruction from first time arrival is a difficult task due to its ill-posedness nature and to the non linearity of the direct problem associated. In this thesis, the purpose is to use a deformable model because it enables to introduce a global shape prior on the objects to reconstruct, which leads to more stable solutions with better quality. First, high level shape constraints are introduced in Computerized Tomography for which the direct problem is linear. Secondly, different strategies to solve the image reconstruction problem with a non linearity hypothesis are considered. The chosen strategy approximates the direct problem by a series of linear problems, which leads to a simple successive minimization algorithm with the introduction of the shape prior along the minimization. The efficiency of the method is demonstrated for simulated data as for real data obtained from a specific measurement device developped by IFSTTAR for non destructive evaluation of civil engineering structures.
... A planar object shape can be characterized through twodimensional moment invariants, obtained for instance with Hu [6], Zernike [7,30], or Legendre [31] moments. One-dimensional moment invariants can also be used as signatures to characterize contours, for instance Fourier descriptors [8,9], which are obtained by Fourier transform of the arclength parametrization, in complex coordinates, of a closed contour. ...
Hand posture recognition is generally addressed by using either YCbCr (luminance and chrominance components) or HSV (hue, saturation, value) mappings which assume that a hand can be distinguished from the background from some colorfulness and luminance properties. This can hardly be used when a dark hand, or a hand of any color, is under study. In addition, existing recognition processes rely on descriptors or geometric shapes which can be reliable; this comes at the expense of an increased computational complexity. To cope with these drawbacks, this paper proposes a four-step method recognition technique consisting of (i) a pyramidal optical flow for the detection of large movements and hence determine the region of interest containing the expected hand, (ii) a preprocessing step to compute the hand contour while ensuring geometric and illumination invariance, (iii) an image scanning method providing a signature which characterizes non-star-shaped contours with a one-pixel precision, and (iv) a posture classification method where a sphericity criterion preselects a set of candidate postures, principal component analysis reduces the dimensionality of the data, and Mahalanobis distance is used as a criterion to identify the hand posture in any test image. The proposed technique has been assessed in terms of its performances including the computational complexity using both visual and statistical results.
... A planar object shape can be characterized through twodimensional moment invariants, obtained for instance with Hu [6], Zernike [7,30], or Legendre [31] moments. One-dimensional moment invariants can also be used as signatures to characterize contours, for instance Fourier descriptors [8,9], which are obtained by Fourier transform of the arclength parametrization, in complex coordinates, of a closed contour. ...
In this paper, we consider an issue of hand posture classification. We improve a recently proposed signature, a matrix containing the distance of all contour pixels to an arbitrary reference point. Adequate pre-processings ensure the invariance properties of the signature. Candidate postures are pre-selected with a surface criterion, and Principal Component Analysis (PCA) reduces the dimensionality of the data, which improves the classification process.
... The parametric active contour formulation is chosen because it is considerably faster than the level set approach. Besides, shape data is explicitly encoded in its energy components (Hicks et al., 2002; Foulonneau et al., 2003). Contour evolution can be formulated as an iterative energy minimization process. ...
In this work, we discuss the problems of automatic segmentation of Arabidopsis thaliana epidermal cell patterning in images captured using a Differential Interference Contrast (DIC) microscope. These images are difficult to analyze due to the non-linear nature of DIC optics. The border of objects appear as a combination of bright and dark shadows with variable thickens and contrast levels. Our segmentation approach exploits prior knowledge on the optical properties of A. thaliana cell walls. A set of matching filters and a scale space line detector are used to generate an enhanced image that shows a single response at the location of cellular walls. To reduce the uncertainty in low contrast cellular walls several images are captured at different orientations. After image fusion, we obtain a single image that can be segmented using well established algorithms. Experiments on a manually annotated DIC image data set demonstrated the effectiveness of the proposed scheme.
... ty given the prior shape model. Chen et al. (2001) define an energy functional depending on the gradient and the average shape of the target object. The prior shape term evaluates the similarity of the shape of the contour to that of the reference shape through the computation of a distance function using the Fast Marching method of Sethian (1996). Foulonneau et al. (2003) define shape descriptors with Legendre moments and introduce a geometric prior in the framework of region-based active contours, with a quadratic distance function between the set of moments of the contour and the set of moments of the reference object. In an interesting piece of work, Steiner et al. (1998) use a regularized inverse dif ...
We introduce a new class of active contour models that hold great promise for region and shape modelling, and we apply a special
case of these models to the extraction of road networks from satellite and aerial imagery. The new models are arbitrary polynomial
functionals on the space of boundaries, and thus greatly generalize the linear functionals used in classical contour energies.
While classical energies are expressed as single integrals over the contour, the new energies incorporate multiple integrals,
and thus describe long-range interactions between different sets of contour points. As prior terms, they describe families
of contours that share complex geometric properties, without making reference to any particular shape, and they require no
pose estimation. As likelihood terms, they can describe multi-point interactions between the contour and the data. To optimize
the energies, we use a level set approach. The forces derived from the new energies are non-local however, thus necessitating
an extension of standard level set methods. Networks are a shape family of great importance in a number of applications, including
remote sensing imagery. To model them, we make a particular choice of prior quadratic energy that describes reticulated structures,
and augment it with a likelihood term that couples the data at pairs of contour points to their joint geometry. Promising
experimental results are shown on real images.
... In [4], Poupon et al. proposed to use geometric moments to constrain the variation of a deformable model. In [5], Foulonneau et al. encoded the shape model with Legendre moments. The approach consists in defining a shape distance between the descriptors of both the evolving curve and the reference shape. ...
Region growing has become a popular method for 3D segmentation. Starting from a seed, this approach allows one to extract a region by merging all its neighbors and comparing the extracted region to a reference. Here, we present an alternative approach to constrain the evolution of the region growing method in respect to a fixed reference shape. This approach is based on a shape description by the Tchebichef moments. The evolution equation minimizes a function that represents the distance between the evolving region and the reference shape. Experimental results show the ability of our method to drive the segmentation towards a desired shape in 2D and 3D data. Finally, we apply our shape prior conjointly to a bimodal segmentation functional, showing its benefits on segmentation results.
... There is a large body of work that does this implicitly, via a template region or regions to which R is compared, e.g. [3,4,5,6]. However, such energies effectively limit R to a bounded subset of region space close to the template(s), which excludes, inter alia, cases like tree crown extraction in which R has an unknown number of connected components . ...
A central task in image processing is to find the region in the image corresponding to an entity. In a number of problems, the region takes the form of a collection of circles, e.g. tree crowns in remote sensing imagery; cells in bio- logical and medical imagery. In (1), a model of such regions, the 'gas of circles' model, was developed based on higher-order active contours, a recently devel- oped framework for the inclusion of prior knowledge in active contour energies. However, the model suffers from a defect. In (1), the model parameters were ad- justed so that the circles were local energy minima. Gradient descent can become stuck in these minima, producing phantom circles even with no supporting data. We solve this problem by calculating, via a Taylor expansion of the energy, pa- rameter values that make circles into energy inflection points rather than minima. As a bonus, the constraint halves the number of model parameters, and severely constrains one of the two that remain, a major advantage for an energy-based model. We use the model for tree crown extraction from aerial images. Experi- ments show that despite the lack of parametric freedom, the new model performs better than the old, and much better than a classical active contour.
... Active contours introduced by Kass with a model called Snake [16] had drawn attention due to their performance in various problems. Segmentation and shape modeling in single images proved effective by integrating region-based information, stochastic approaches and appropriate shape constrains [17,18]. Active contours merge image data and shape modeling through the definition of an linear energy function consisting of two terms: a data driven component (external energy), which depends on the image data, and a smoothness-driven component (internal energy) which enforces smoothness along the contour. ...
In this paper we present an approach to perform automated analysis of nematodes in population images. Occlusion, shape variability and structural noise make reliable recognition of individuals a task difficult. Our approach relies on shape and geometrical statistical data obtained from samples of segmented lines. We study how shape similarity in the objects of interest, is encoded in active contour energy component values and exploit them to define shape features. Without having to build a specific model or making explicit assumptions on the interaction of overlapping objects, our results show that a considerable number of individual can be extracted even in highly cluttered regions when shape information is consistent with the patterns found in a given sample set. Espol
... In [1], we addressed this problem using 'higher-order active contours' (HOACs) [2], a new generation of active contours [3] allowing the incorporation of non-trivial prior knowledge about region geometry. Unlike most methods for incorporating prior geometric knowledge into active contours456 , HOACs do not necessarily constrain region topology, thereby allowing the detection of multiple instances of a single entity at no extra cost, a critical requirement for the current application. To extract tree crowns, the HOAC model was analysed theoretically to find parameter values favouring regions composed of a number of approximate circles of approximately a given radius, by making such regions minima of the energy. ...
We describe a model for tree crown extraction from aerial images, a problem of great practical importance for the forestry
industry. The novelty lies in the prior model of the region occupied by tree crowns in the image, which is a phase field version
of the higher-order active contour inflection point ‘gas of circles’ model. The model combines the strengths of the inflection
point model with those of the phase field framework: it removes the ‘phantom circles’ produced by the original ‘gas of circles’
model, while executing two orders of magnitude faster than the contour-based inflection point model. The model has many other
areas of application e.g. , to imagery in nanotechnology, biology, and physics.
... Active contours introduced by Kass with a model called snake [16] has drawn attention due to their performance in various problems. Segmentation and shape modeling in single images proved effective by integrating region-based information, stochastic approaches and appropriate shape constrains [17,18]. ...
In this paper we study how shape information encoded in contour energy components values can be used for detection of microscopic organisms in population images. We proposed features based on shape and geometrical statistical data obtained from samples of optimized contour lines integrated in the framework of Bayesian inference for recognition of individual specimens. Compared with common geometric features the results show that patterns present in the image allow better detection of a considerable amount of individuals even in cluttered regions when sufficient shape information is retained. Therefore providing an alternative to building a specific shape model or imposing specific constrains on the interaction of overlapping objects. Department of telecommunication and information processing, Ghent University, St-Pieters Nieuwstraat 41, B-9000, Ghent, Belgium Centro de Vision y Robotica, Facultad de Ingenieria en Electricidad y Computación, ESPOL University, Km 30.5 via perimetral, 09015863, Guayaquil, Ecuador
... There is a large body of work that does this implicitly, via a template region or regions to which R is compared, e.g. [3,4,5,6]. However, such energies effectively limit R to a bounded subset of region space close to the template(s), which excludes, inter alia, cases like tree crown extraction in which R has an unknown number of connected components . ...
We present a model of a 'gas of circles': regions in the image domain composed of a unknown number of circles of approximately the same radius. The model has applications to medical, biological, nanotechnological, and remote sensing imaging. The model is constructed using higher-order active contours (HOACs) in order to include non-trivial prior knowledge about region shape without constraining topology. The main theoretical contribution is an analysis of the local minima of the HOAC energy that allows us to guarantee stable circles, fix one of the model parameters, and constrain the rest. We apply the model to tree crown extraction from aerial images of plantations. Numerical experiments both confirm the theoretical analysis and show the empirical importance of the prior shape information.
... They are also intrinsically Euclidean invariant. They differ from most other methods for incorporating prior geometric knowledge into active contours (Chen et al., 2001; Leventon et al., 2000; Foulonneau et al., 2003; Paragios and Rousson, 2002; Cremers et al., 2003) in not being based upon perturbations of a reference region or regions. Using this new framework, Rochery et al. (2003) proposed a model that goes a long way towards capturing the prior geometric knowledge we have of network regions, as well as the complex dependencies between image values associated with networks. ...
One of the main difficulties in extracting line networks from images, and in particular road networks from remote sensing images, is the existence of interruptions in the data caused, for example, by occlusions. These can lead to gaps in the extracted network that do not correspond to gaps in the real network. In this report, we describe a higher-order active contour energy that in addition to favouring network-like regions composed of thin arms joining at junctions, also includes a prior term that penalizes network configurations containing ‘nearby opposing extremities’, and thereby makes their appearance in the extracted network less likely. If nearby opposing extremi- ties form during the gradient descent evolution used to minimize the energy, the new energy term causes the extremities to attract one another, and hence to move towards one another and join, thus closing the gap. To minimize the energy, we develop specific techniques to handle the high-order derivatives that appear in the gradient descent equation. We present the results of automatic extrac- tion of networks from real remote-sensing images, showing the ability of the model to overcome interruptions. Key-words: road extraction, shape, prior, continuity, gap, closure, quadratic, higher-order, active
... As a result, recent work has developed models incorporating more sophisticated knowledge of region geometry . Most of this work models an ensemble of regions as perturbations of one or more reference regions, for example (Cremers et al., 2003, Rousson and Paragios, 2002, Srivastava et al., 2003, Foulonneau et al., 2003). This is an intuitive and useful approach, but it is inappropriate when the region sought can have arbitrary topology, since such an ensemble of regions cannot be described as perturbations around a finite number of reference regions . ...
We propose a new algorithm for network segmentation from very high resolution (VHR) remote sensing images. The algorithm performs this task quasi-automatically, that is, with no human intervention except to fix some parameters. The task is made difficult by the amount of prior knowledge about network region geometry needed to perform the task, knowledge that is usually provided by a human being. To include such prior knowledge, we make use of methodological advances in region modelling: a phase field higher order active contour of directed networks is used as the prior model for region geometry. By adjoining an approximately conserved flow to a phase field model encouraging network shapes (i.e. regions composed of branches meeting at junctions), the model favours network regions in which different branches may have very different widths, but in which width change along a branch is slow; in which branches do not come to an end, hence tending to close gaps in the network; and in which junctions show approximate ‘conservation of width'. We also introduce image models for network and background, which are validated using maximum likelihood segmentation against other possibilities. We then test the full model on VHR optical and multispectral satellite images.
Dans cet article, nous proposons une méthode originale pour incorporer un a priori de forme dans un modèle de contours actifs basé région afin d'améliorer sa robustesse aux similitudes, bruit et occultations. Nous définissons un a priori de forme à partir du recalage des fonctions level set associées au contour actif et une forme de référence. Le recalage que nous proposons se base sur la corrélation de phase par la transformée de Fourier-Mellin analytique (TFMA). Cette représentation, dédiée aux images à niveaux de gris, permet de gérer simultanément plusieurs objets. Nous illustrons expérimentalement les capacités de ce nouvel a priori de forme à contraindre l'évolution du contour actif vers une forme cible. Enfin, nous mettons en évidence, sur des images de synthèse et réelles, son apport pour la segmentation d'images en présence de similitudes, d'occultations et de bruits. ABSTRACT.
In this paper, we propose new method to incorporate geometric shape prior into region-based active contours in order to improve its robustness to noise and occlusions. The proposed shape prior is defined after the registration of the level set functions associated with the active contour and a reference shape. The used registration method is based on phase correlation by the Analytical Fourier-Mellin Transform (AFMT). This representation, dedicated to gray levels images, makes it possible to manage several objects simultaneously. Experimental results show the ability of the proposed geometric shape prior to constrain an evolving curve towards a target shape. We highlight on synthetic and real images, the benefit of the new shape prior on segmentation results, in presence of occlusions and noise. MOTS-CLÉS : contours actifs, a priori de forme, transformée de Fourier-Mellin analytique. Extended abstract Active contours have been introduced in 1988 (Kass et al., 1988). The principle is to move a curve iteratively minimizing energy functional. The minimum is reached at object boundaries. These methods can be classified into two families: parametric and geometric active contours. The first family, called also snakes, uses an explicit representation of the contours while the second one uses an implicit representation of the front via Level Set approach. These models typically manage the evolution of the active contour based on local information of the image (gray level). The lack of global information about the target object prevents these approaches to be robust in presence of textured background, occlusions or even noise. Several studies have proposed to introduce prior knowledge on the shape to detect into the active contour model. In the context of statistical shape prior, Leventon et al. (2000) proposed to associate a statistical model on the learned shape to the geodesic active contours (Caselles et al., 1997). Chen et al. (2001) defined an energy functional based on the quadratic distance between the evolving curve and the average shapes of the target object after alignment. This term is then incorporated into the geodesic active contours. Foulonneau et al. (2004) introduced an additional geometric shape prior into region-based active contours. Prior knowledge is defined as a distance between shapes descriptors based on Legendre moments of the characteristic function. An extension of this work in case of affine transformation is performed in (Foulonneau et al., 2006) and in (Foulonneau et al., 2009), a multi-references shape prior is presented. Charmi et al. (2008) introduced geometric shape prior into the snake model. A set of complete and locally stable invariants to Euclidean transformations (Ghorbel. 1998) is used to define new force which makes the snake overcome some well-known problems. In (Charmi et al., 2010), we defined new geometric shape prior for region-based active contours (Chan, Vese, 2001). The new added term was based on the property of signed distance function associated with the evolving contour which assigns negative values for points inside the contour and positive values for those outside. In fact, given two level set functions associated with the active contour and the template, variability between shapes can be formulated using the Heaviside of the product function of these two level set functions. Hence the proposed shape prior is the integral of this function on the image domain. This term is then incorporated into the evolution's equation of the active contour. If one takes a reference shape which is not necessarily defined in the image reference, it is necessary to apply a transformation to align it with the shape to segment (rotation, translation, scaling factor). Then, we used a shape alignment method based on Fourier descriptors. This shape prior introduced into region-based active contours has been successful in case of single object in the image in presence of noise and occlusion. It is well known that the level set approach solves the problem of topology changing of the snake model. However, shape prior in several works (Leventon et al. (2000), Chen et al. (2001), Chan et Zhu (2005), Fang et Chan (2007) and Charmi Contours actifs avec a priori de forme basé sur la TFMA 125 et al. (2010)) based on contours alignment constrain these approaches to segment only one object in the image. Thus our goal in this paper is to extend the work done in Charmi et al. (2010) to manage the case of several objects that may be partially occluded and possibly noisy. We were based on the property of distance maps of level set functions and associated binary image for every distance map. Then the problem amounts to the registration of these images. We used the method of phase correlation in Fourier space that is appropriate to estimate the translation vector and phase correlation in the space of Fourier-Mellin for estimating the rotation and the scaling factor knowing that the Fourier-Mellin transform applied to grayscale images is a mathematical tool known for its performance in objects description and features recognition. It was also pointed out that numerical estimation of the Mellin integral brings up crucial difficulties. A solution for the convergence of the integral was given in (Ghorbel, 1994) by using the analytical Fourier-Mellin transform (AFMT). In (Derrode, Ghorbel, 2001), three approximations of the AFMT were proposed. We adopt the fast algorithm based on fast Fourier transform (FFT) and log-polar sampling of the image. Hence to introduce the shape prior we proceed as follows:-we start by segmenting the target object with the Chan and Vese's model without prior knowledge;-then, after convergence of the evolving contour, we register the binary images associated with the level set functions of the evolving contour and the template;-having the parameter of the rigid transformation between shapes, we calculate the proposed shape prior;-finally, the proposed model evolves under Chan-Vese and the prior knowledge terms with big weight assigned to the shape prior energy to constrain the active contour to be similar to the template; Experiments have shown the ability of the new added term to improve the robustness of the segmentation process in presence of textured background, missing parts and partial occlusions of the target object. The addition of shape prior has not increased significantly the execution time of the algorithm given that the proposed approach does the registration only once and it is done by the Fast Fourier Transform (FFT2) unlike Foulonneau et al. (2004) and Charmi et al. (2008) where at each iteration, shape descriptors are calculated for a given order. As future perspectives, we are working on extending this approach to more general transformations such as affine transformations and manage the case where many references are available and thus the model must be able to choose the most suitable shape according to the evolving contours.
Some of the most difficult image segmentation problems involve an unknown number of object instances that can touch or overlap in the image, e.g. microscopy imaging of cells in biology. In an important set of cases, the nature of the objects and the imaging process mean that when objects overlap, the resulting image is approximately given by the sum of intensities of individual objects; and, in addition, the objects of interest are `blob-like' or near-circular. We propose a new model for the segmentation of the objects in such images. The posterior energy is the sum of a prior energy modelling shape and a likelihood energy modelling the image. The prior is a multi-layer nonlocal phase field energy that favours configurations consisting of a number of possibly overlapping or touching near-circular object instances. The likelihood energy models the additive nature of image intensity in regions corresponding to overlapping objects. We use variational methods to compute a MAP estimate of the object instances in an image. We test the resulting model on synthetic data and on fluorescence microscopy images of cell nuclei.
Some of the most difficult image segmentation problems involve an unknown number of object instances that can touch or overlap in the image, e.g. microscopy imaging of cells in biology. In an important set of cases, the nature of the objects and the imaging process mean that when objects overlap, the resulting image is approximately given by the sum of intensities of individual objects; and, in addition, the objects of interest are `blob-like' or near-circular. We propose a new model for the segmentation of the objects in such images. The posterior energy is the sum of a prior energy modelling shape and a likelihood energy modelling the image. The prior is a multi-layer nonlocal phase field energy that favours configurations consisting of a number of possibly overlapping or touching near-circular object instances. The likelihood energy models the additive nature of image intensity in regions corresponding to overlapping objects. We use variational methods to compute a MAP estimate of the object instances in an image. We test the resulting model on synthetic data and on fluorescence microscopy images of cell nuclei.
Introduction Stochastic approaches Variational approaches Bibliography
Dans cet article, nous proposons une méthode originale pour incorporer un a priori de forme dans un modèle de contours actifs basé région afin d’améliorer sa robustesse aux similitudes, bruit et occultations. Nous définissons un a priori de forme à partir du recalage des fonctions level set associées au contour actif et une forme de référence. Le recalage que nous proposons se base sur la corrélation de phase par la transformée de Fourier-Mellin analytique (TFMA). Cette représentation, dédiée aux images à niveaux de gris, permet de gérer simultanément plusieurs objets. Nous illustrons expérimentalement les capacités de ce nouvel a priori de forme à contraindre l’évolution du contour actif vers une forme cible. Enfin, nous mettons en évidence, sur des images de synthèse et réelles, son apport pour la segmentation d’images en présence de similitudes, d’occultations et de bruits.
Résumé – L'objectif de cette étude est la segmentation du muscle pectoral sur une mammographie. Ce travail a pour but de faciliter le recalage géométrique de paires d'images mammographiques par l'extraction fiable de points de repère. La sémantique de l'image est exploitée pour extraire des points de repère basés sur l'anatomie. La technique d'extraction utilisée est basée sur les contours actifs pour lesquels nous proposons de construire différentes énergies. Abstract – The aim of this paper is the segmentation of the pectoral muscle on a mammography, in order to improve the registration using geometrical features of pairs of mammographic images by reliable landmarks extraction. Thereby, image semantics is used to extract landmarks based on anatomical features. The developed methodology is based on active contours, where various energies are proposed.
A novel adaptive B-Spline deformable model is presented in this paper for object segmentation. Comparing with other B-Spline models, the proposed model has the following advantages. First, a fully automatic and affine-invariant strategy is proposed for landmark point assignment. Second, contrary to other B-Spline models that rely on predetermined number of control points, an automatic scheme for control point insertion is designed to enhance the adaptivity and the flexibility of B-Spline model for segmenting shapes with high complexity. Thirdly, a statistical framework is embedded for modeling the shape distribution and appearance characteristics of landmark points in the training samples. Fine deformation can be achieved through the minimum mean square error approach that allows the model to accurately adapt to the desired object boundaries in the image. Experiments on medical image segmentation are carried out to validate the performance, and comparison has been made with respect to the traditional Snake and ASM. It turns out that the proposed adaptive B-Spline model can attain more accurate object segmentation. Copyright © 2010 John Wiley & Sons, Ltd.
Lack of temporal coherence in video segmentation algorithms often leads to flickering or to discrepancies on the segmentation mask boundaries. Active contour video segmentation algorithms can lead to very smooth segmentation masks when they are defined in three dimensions (two spatial and one temporal). In this paper, we use an active contour method to attract an active surface toward a non-smoothed segmentation mask boundary. This active surface produces a new segmentation mask which is smoother than the first one. To achieve this task, we introduce a new region-based term for active contour segmentation in the variational framework. This term attracts the evolving curve to a reference contour. The energy criterion and the evolution equation are defined in n-dimension and we investigate the particular case of two regions. The use of active surfaces to smooth video segmentation masks appears to be a very powerful tool for video postprocessing. The resulting masks are smoother than the original ones, the discrepancies of the segmentation masks are removed and the flickering on the boundary of the segmentation masks are considerably reduced
The global shape prior knowledge has been exploited by many image segmentation approaches in order to improve segmentation results when there are such problems as occlusion, cluttering, low contrast edges, etc. We propose a global shape prior representation and incorporate it into a level set based segmentation framework. This global shape prior can effectively help remove the cluttered elongate structures and island-like artifacts in the segmentation. We experimentally compare the performance of our global shape prior with an extensively used global shape prior introduced in [3]. The experimental results show that our global shape prior averagely achieves 15% higher precision rates with comparable recall rates, which demonstrates the efficacy of the proposed shape prior.
In this paper, a novel recognition-driven variational framework, toward multiple building extraction from aerial and satellite images, is introduced. To this end, competing shape priors are considered, and building extraction is addressed through an image segmentation approach that involves the use of a data-driven term constrained from the prior models. The proposed framework extends previous approaches toward the integration of multiple shape priors into the level-set segmentation. In particular, it estimates the number of buildings as well as their pose from the observed data. Therefore, it can address multiple building extraction from a single optical image, a highly demanding task of fundamental importance in various geoscience and remote-sensing applications. Furthermore, it can be easily extended to deal with other remote-sensing data through a simple modification of the image term. Very promising experimental results and the performed qualitative and quantitative evaluation demonstrate the potential of our approach.
A novel method of parametric active contours with geometric shape prior is presented in this paper. The main idea of the method consists in minimizing an energy function that includes additional information on a shape reference called a prototype. Shape prior introduced through a similarity measurement between evolving contour and Procrustes mean shape of desired object. This similarity measurement is full Procrustes distance between these two contours that is invariant with respect to similarity transformations (translation, scaling, and rotation). This extra shape knowledge enhances the model robustness to noise, occlusion and complex background. We also use gradient direction information in addition to gradient magnitude for more robustness to complex background. In this paper we introduce one important application of this new snake "3D object tracking". We obtain promising results for 3D object tracking which show the robustness of our method against noise, complex background, similarity transformations, occlusion, and changing viewpoint of 3D object.
In delay tolerant network, message delivery can be inspired by biological communication models in realizing encountering and delivering. One way of communications can be through "thrown box" where the messages can be left and collected by different nodes in mimicking pheromone-based communications. In thrown box based model, the box is viewed as message relay and the delivery rate is enhanced by spreading a message at as many boxes as possible. Both the life time of message left at the boxes and message leaving preference will have a significant influence on the latency and delivery ratio in message dissemination. In this paper, we model the latency problem as discrete time Markov Chain and further derive the time distribution of first contact between the message and collector. By varying the parameters of message leaving probability and initial environment condition, the latency related results are studied.
In this paper, we present a novel method to incorporate geometric shape prior into region-based active contours. Prior knowledge is obtained from a reference shape. This shape reference is used to define a new energy term obtained through a Fourier-based shape alignment. The new energy is invariant with respect to Euclidean transformations. Experimental results show the ability of the geometric shape prior to constraint an evolving curve to meet target shape and to show the new method benefits on segmentation results in presence of occlusion and noise.
We present a new way of constraining the evolution of a region-based active contour with respect to a set of reference shapes.
The approach is based on a description of shapes by the Legendre moments computed from their characteristic function. This
provides a region-based representation that can handle arbitrary shape topologies. Moreover, exploiting the properties of
moments, it is possible to include intrinsic affine invariance in the descriptor, which solves the issue of shape alignment
without increasing the number of d.o.f. of the initial problem and allows introducing geometric shape variabilities. Our new
shape prior is based on a distance between the descriptors of the evolving curve and a reference shape. The proposed model naturally extends to the case where multiple reference shapes
are simultaneously considered. Minimizing the shape energy, leads to a geometric flow that does not rely on any particular representation of the contour and can be implemented with
any contour evolution algorithm. We introduce our prior into a two-class segmentation functional, showing its benefits on
segmentation results in presence of severe occlusions and clutter. Examples illustrate the ability of the model to deal with
large affine deformation and to take into account a set of reference shapes of different topologies.
This paper describes a novel method for shape detection and image segmentation. The proposed method combines statistical shape
models and active contours implemented in a level set framework. The shape detection is achieved by minimizing the Gibbs energy
of the posterior probability function. The statistical shape model is built as a result of a learning process based on nonparametric
probability estimation in a PCA reduced feature space formed by the Legendre moments of training silhouette images. The proposed
energy is minimized by iteratively evolving an implicit active contour in the image space and subsequent constrained optimization
of the evolved shape in the reduced shape feature space. Experimental results are also presented to show that the proposed
method has very robust performances for images with a large amount of noise.
Experiments on model organisms are used to extend the understanding of complex biological processes. In Caenorhabditis elegans studies, populations of specimens are sampled to measure certain morphological properties and a population is characterized based on statistics extracted from such samples. Automatic detection of C. elegans in such culture images is a difficult problem. The images are affected by clutter, overlap and image degradations. In this paper, we exploit shape and appearance differences between C. elegans and non-C. elegans segmentations. Shape information is captured by optimizing a parametric open contour model on training data. Features derived from the contour energies are proposed as shape descriptors and integrated in a probabilistic framework. These descriptors are evaluated for C. elegans detection in culture images. Our experiments show that measurements extracted from these samples correlate well with ground truth data. These positive results indicate that the proposed approach can be used for quantitative analysis of complex nematode images.
We present a variational integration of nonlinear shape statistics into a Mumford—Shah based segmentation process. The nonlinear statistics are derived from a set of training silhouettes by a novel method of density estimation which can be considered as an extension of kernel PCA to a stochastic framework.
The idea is to assume that the training data forms a Gaussian distribution after a nonlinear mapping to a potentially higher-dimensional feature space. Due to the strong nonlinearity, the corresponding density estimate in the original space is highly non–Gaussian. It can capture essentially arbitrary data distributions (e.g. multiple clusters, ring- or banana–shaped manifolds).
Applications of the nonlinear shape statistics in segmentation and tracking of 2D and 3D objects demonstrate that the segmentation process can incorporate knowledge on a large variety of complex real—world shapes. It makes the segmentation process robust against misleading information due to noise, clutter and occlusion.
We consider the problem of segmenting an image through the minimization of an energy criterion involving region and boundary functionals. We show that one can go from one class to the other by solving Poisson's or Helmholtz's equation with well-chosen boundary conditions. Using this equivalence, we study the case of a large class of region functionals by standard methods of the calculus of variations and derive the corresponding Euler-Lagrange equations. We revisit this problem using the notion of shape derivative and show that the same equations can be elegantly derived without going through the unnatural step of converting the region integrals into boundary integrals. We also define a larger class of region functionals based on the estimation and comparison to a prototype of the probability density distribution of image features and show how the shape derivative tool allows us to easily compute the corresponding Gâteaux derivatives and Euler-Lagrange equations. We nally apply this new functional to the problem of regions segmentation in sequences of color images. We briey describe our numerical scheme and show some experimental results.
Two-dimensional image moments with respect to Zernike polynomials are defined, and it is shown how to construct an arbitrarily large number of independent, algebraic combinations of Zernike moments that are invariant to image translation, orientation, and size. This approach is contrasted with the usual method of moments. The general problem of two-dimensional pattern recognition and three-dimensional object recognition is discussed within this framework. A unique reconstruction of an image in either real space or Fourier space is given in terms of a finite number of moments. Examples of applications of the method are given. A coding scheme for image storage and retrieval is discussed.
In many applications of dynamic scene analysis, the objects or structures to be analyzed undergo deformations that have to be modeled. In this paper, we develop a hierarchical statistical modeling framework for the representation, segmentation, and tracking of 2D deformable structures in image sequences. The model relies on the specification of a template, on which global as well as local deformations are defined. Global deformations are modeled using a statistical modal analysis of the deformations observed on a representative population. Local deformations are represented by a (first-order) Markov random process. A model-based segmentation of the scene is obtained by a joint bayesian estimation of global deformation parameters and local deformation variables. Spatial or spatio-temporal observations are considered in this estimation procedure, yielding an edge-based or a motion-based segmentation of the scene. The segmentation procedure is combined with a temporal tracking of the deformable structure over long image sequences, using a Kalman filtering approach. This combined segmentation-tracking procedure has produced reliable extraction of deformable parts from long image sequences in adverse situations such as low signal-to-noise ratio, nongaussian noise, partial occlusions, or random initialization. The approach is demonstrated on a variety of synthetic as well as real-world image sequences featuring different classes of deformable objects.
We devise new numerical algorithms, called PSC algorithms, for following fronts propagating with curvature-dependent speed. The speed may be an arbitrary function of curvature, and the front also can be passively advected by an underlying flow. These algorithms approximate the equations of motion, which resemble Hamilton-Jacobi equations with parabolic right-hand sides, by using techniques from hyperbolic conservation laws. Non-oscillatory schemes of various orders of accuracy are used to solve the equations, providing methods that accurately capture the formation of sharp gradients and cusps in the moving fronts. The algorithms handle topological merging and breaking naturally, work in any number of space dimensions, and do not require that the moving surface be written as a function. The methods can be also used for more general Hamilton-Jacobi-type problems. We demonstrate our algorithms by computing the solution to a variety of surface motion problems.
The shape variation displayed by a class of objects can be represented as probability density function, allowing us to determine plausible and implausible examples of the class. Given a training set of example shapes we can align them into a common co-ordinate frame and use kernel-based density estimation techniques to represent this distribution. Such an estimate is complex and expensive, so we generate a simpler approximation using a mixture of gaussians. We show how to calculate the distribution, and how it can be used in image search to locate examples of the modelled object in new images.
A snake is an energy-minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges. Snakes are active contour models: they lock onto nearby edges, localizing them accurately. Scale-space continuation can be used to enlarge the capture region surrounding a feature. Snakes provide a unified account of a number of visual problems, including detection of edges, lines, and subjective contours; motion tracking; and stereo matching. We have used snakes successfully for interactive interpretation, in which user-imposed constraint forces guide the snake near features of interest.
We propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by the gradient. We minimize an energy which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a "mean-curvature flow"-like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. We give a numerical algorithm using finite differences. Finally, we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable. Also, the initial curve can be anywhere in the image, and interior contours are automatically detected.
A novel method of incorporating shape information into the image segmentation process is presented. We introduce a representation for deformable shapes and define a probability distribution over the variances of a set of training shapes. The segmentation process embeds an initial curve as the zero level set of a higher dimensional surface, and evolves the surface such that the zero level set converges on the boundary of the object to be segmented. At each step of the surface evolution, we estimate the maximum a posteriori (MAP) position and shape of the object in the image, based on the prior shape information and the image information. We then evolve the surface globally, towards the MAP estimate, and locally, based on image gradients and curvature. Results are demonstrated on synthetic data and medical imagery, in 2D and 3D.
In this paper a theory of two-dimensional moment invariants for planar geometric figures is presented. A fundamental theorem is established to relate such moment invariants to the well-known algebraic invariants. Complete systems of moment invariants under translation, similitude and orthogonal transformations are derived. Some moment invariants under general two-dimensional linear transformations are also included. Both theoretical formulation and practical models of visual pattern recognition based upon these moment invariants are discussed. A simple simulation program together with its performance are also presented. It is shown that recognition of geometrical patterns and alphabetical characters independently of position, size and orientation can be accomplished. It is also indicated that generalization is possible to include invariance with parallel projection.