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3D lip contour segmentation: initial (a,d) and final (b,e) contour, surface with added texture (c) and segmented lip area (f)
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Algorithms incorporating 3D information have proven to be superior to purely 2D approaches in many areas of computer vision
including face biometrics and recognition. Still, the range of methods for feature extraction from 3D surfaces is limited.
Very popular in 2D image analysis, active contours have been generalized to curved surfaces only recent...
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Citations
... Limited in topology and suffering from an ineffective evolution procedure, the method was reformulated as a level set method [3,5,28,22]. The level set method was generalized to volumetric 3D data [25]. The literature level set methods are mostly used for evolving a curve. ...
We present a new method for 3D shape reconstruction from a single image, in which a deep neural network directly maps an image to a vector of network weights. The network \textcolor{black}{parametrized by} these weights represents a 3D shape by classifying every point in the volume as either within or outside the shape. The new representation has virtually unlimited capacity and resolution, and can have an arbitrary topology. Our experiments show that it leads to more accurate shape inference from a 2D projection than the existing methods, including voxel-, silhouette-, and mesh-based methods. The code is available at: https://github.com/gidilittwin/Deep-Meta
... Looking at the body of literature on intrinsic image processing on surfaces, we can divide previous work into two approaches based on the representation of the surface. Implicit approaches (Krueger et al. 2008;Cheng et al. 2000) use an implicit surface (e.g. through the zero level set of a function), whereas explicit approaches (Lui et al. 2008;Stam 2003) construct a triangular mesh representation. ...
Event cameras or neuromorphic cameras mimic the human perception system as they measure the per-pixel intensity change rather than the actual intensity level. In contrast to traditional cameras, such cameras capture new information about the scene at MHz frequency in the form of sparse events. The high temporal resolution comes at the cost of losing the familiar per-pixel intensity information. In this work we propose a variational model that accurately models the behaviour of event cameras, enabling reconstruction of intensity images with arbitrary frame rate in real-time. Our method is formulated on a per-event-basis, where we explicitly incorporate information about the asynchronous nature of events via an event manifold induced by the relative timestamps of events. In our experiments we verify that solving the variational model on the manifold produces high-quality images without explicitly estimating optical flow.
... However, this approach has intrinsic disadvantages since the pre-image of the curve is used. In [18], drawbacks of this approach concerning the scaling behavior are discussed. Another drawback is the fact that the method does not allow to incorporate a balloon term [18]. ...
... In [18], drawbacks of this approach concerning the scaling behavior are discussed. Another drawback is the fact that the method does not allow to incorporate a balloon term [18]. ...
... The curve is represented by the intersection of the two zero level sets. This approach is used in [18,34] for image segmentation with geodesic active contours. A drawback of the method is that a one-dimensional curve evolution problem is extended to a three-dimensional problem. ...
In this article, a new method for segmentation and restoration of images on
two-dimensional surfaces is given. Active contour models for image segmentation
are extended to images on surfaces. The evolving curves on the surfaces are
mathematically described using a parametric approach. For image restoration, a
diffusion equation with Neumann boundary conditions is solved in a
postprocessing step in the individual regions. Numerical schemes are presented
which allow to efficiently compute segmentations and denoised versions of
images on surfaces. Also topology changes of the evolving curves are detected
and performed using a fast sub-routine. Finally, several experiments are
presented where the developed methods are applied on different artificial and
real images defined on different surfaces.
... Active shape 52 models and active appearance models are constructed around a training set of annotated cases and they also assume a 53 suitable initialisation. These methods have been explored mostly in two-dimensional images, although Krueger et al. (2008) 54 described the use of active contour models in three-dimensional facial settings. ...
Methods for capturing images in three dimensions are now widely available, with stereo-photogrammetry and laser scanning two common approaches. In anatomical studies, a number of landmarks are usually identified manually from each of these images and these form the basis of subsequent statistical analysis. However, landmarks express only a very small proportion of the information available from the images. Anatomically defined curves have the advantage of providing a much richer expression of shape. This is explored in the context of identifying the boundary of breasts from an image of the female torso and the boundary of the lips from a facial image. The curves of interest are characterised by ridges or valleys. Key issues in estimation are the ability to navigate across the anatomical surface in three-dimensions, the ability to recognise the relevant boundary and the need to assess the evidence for the presence of the surface feature of interest. The first issue is addressed by the use of principal curves, as an extension of principal components, the second by suitable assessment of curvature and the third by change-point detection. P-spline smoothing is used as an integral part of the methods but adaptations are made to the specific anatomical features of interest. After estimation of the boundary curves, the intermediate surfaces of the anatomical feature of interest can be characterised by surface interpolation. This allows shape variation to be explored using standard methods such as principal components. These tools are applied to a collection of images of women where one breast has been reconstructed after mastectomy and where interest lies in shape differences between the reconstructed and unreconstructed breasts. They are also applied to a collection of lip images where possible differences in shape between males and females are of interest.
... Another class of formulations based on Eulerian representation of the manifold where the surface is represented implicitly by embedding the manifold into a higher dimensional space using the level set method [22]. For example, a geodesic curvature flow model and an active contour model have been proposed in [23] and [24], respectively. Based on the intrinsic gradient and the work in [25], the Chan-Vese model [6] has been extended to manifolds in [26] by the closest point method [27]. ...
We propose a numerical approach to solve variational problems on manifolds represented by the grid based particle method (GBPM) recently developed in Leung et al. (J. Comput. Phys. 230(7):2540–2561, 2011), Leung and Zhao (J. Comput. Phys. 228:7706–7728, 2009a, J. Comput. Phys. 228:2993–3024, 2009b, Commun. Comput. Phys. 8:758–796, 2010). In particular, we propose a splitting algorithm for image segmentation on manifolds represented by unconnected sampling particles. To develop a fast minimization algorithm, we propose a new splitting method by generalizing the augmented Lagrangian method. To efficiently implement the resulting method, we incorporate with the local polynomial approximations of the manifold in the GBPM. The resulting method is flexible for segmentation on various manifolds including closed or open or even surfaces which are not orientable.
... Moreover, many image processes on surfaces are considered on implicit representations, which define a surface as a zero level set of a signed distance function on an Euclidean domain or a narrow band of the given surface. The differential operators on surfaces are approximated by combining the standard Euclidean differential operators with the projection along the normal direction [31,32]. In practice, it is not easy to obtain the implicit representation of a surface with complicated geometry or topology structure. ...
This paper considers the problem of decomposing an image defined on a manifold into a structural component and a textural component. We formulate such decomposition as a variational problem, in which the total variation energy is used for extracting the structural part and based on the properties of texture one of three norms, L2, L1 and G, is used in the fidelity term for the textural part. While L2 and G norms are used for texture of no a prior knowledge or oscillating pattern, L1 norm is used for structural or sparse texture. We develop efficient numerical methods to solve the proposed variational problems using augmented Lagrangian methods (ALM) when the manifold is represented by a triangular mesh. The contributions of the paper are two-fold: (1) We adapt the variational structure–texture image decomposition to manifolds, which takes the intrinsic property of manifolds into account. The non-quadratic fidelity terms with L1 and G norms are extended to 3D triangular meshes for the first time. (2) We show how to efficiently tackle the variational problems with non-linearity/non-differentiability terms by iteratively solving some sub-problems that either have closed form solutions or are to solve linear equations. We demonstrate the effectiveness of the proposed methods with examples and applications in detail enhancement and impulsive noise removal.
... To the best of our knowledge, there are, roughly speaking, two classes of approaches to study surfaces imaging, which reflect two different views of surface representations. One class of approaches is using implicit representation of surfaces by viewing a closed surface as a zero level set of a signed distance function in a Euclidean domain [6,7,8,9,10]. Then differential operators on surfaces can be approximated by combining the standard Euclidean differential operators with projection along the normal direction. ...
... In the Table 1, we give a brief comparison among different methods. method principle Advantage Disadvantage level set representation [6,7,8,9,10] view a surface as a zero level set of a function easy to handle topological changes when dealing with surface evolution all data need to be extended to the narrow band of the given surface, hard to adapt fast algorithms in Euclidean cases parametrization method [11,12,13,15,16] parameterize patches of a surface by Euclidean coordinates differential operators are easy to compute after finding parametrization not easy to obtain parametrizations for arbitrary surfaces, hard to handle topological change intrinsic geometry method [17,18,19,20,21] computation processed on the given surface itself by differential geometry techniques can deal with any surface without any preprocessing, easy to adapt fast algorithms in Euclidean cases hard to handle topological changes To clearly explain our intrinsic method to solve image processing on surfaces, we are here just focusing on total variation related image processing models on closed surfaces. As examples, we will mainly discuss ROF denoising model and the convexified CV segmentation model on surfaces by adapting two fast algorithms, the split Bregman iterations [28,29] and Chambolle's dual method [30,31]. ...
After many years of study, the subject of image processing on the plane, or more generally in Euclidean space is well developed. However, more and more practical problems in different areas, such as computer vision, computer graphics, geometric modeling, and medical imaging, inspire us to consider imaging on surfaces beyond imaging on Euclidean domains. Several approaches, such as implicit representation approaches and parameterization approaches, are investigated about image processing on surfaces. Most of these methods require certain preprocessing to convert image problems on surfaces to image problems in Euclidean spaces. In this work, we use differential geometry techniques to directly study image problems on surfaces. By using our approach, all plane image variation models and their algorithms can be naturally adapted to study image problems on surfaces. As examples, we show how to generalize Rudin–Osher–Fatemi (ROF) denoising model [1] and convexified Chan–Vese (CV) [2] segmentation model on surfaces, and then demonstrate how to adapt popular algorithms to solve the total variation related problems on surfaces. This intrinsic approach provides us a robust and efficient method to directly study image processing, in particular, total variation problems on surfaces without requiring any preprocessing.
... Deformable model based segmentation has been widely used throughout computer vision: in medical image analysis [1,2], surface reconstruction [3,4,5], feature extraction [6], visual tracking [7], and motion estimation [8]. As illustrated in Fig. 1, surface extraction techniques are essential to segment and quantify important structures of vol- Figure 1. ...
... Active surfaces, the three-dimensional generalization of two-dimensional active contours, are a popular approach for such surface extraction. The basic idea of active surfaces is to evolve a deformable model [6,9,10,11,12,13] under the influences of internal (prior) and external (measurement) energies to capture the surface of a 3D object. Typically, the internal energy maintains surface smoothness via some sort of elastic (thin-plate) constraint, whereas the external energy pulls the deformable model towards the desired object boundary, usually defined using an image gradient. ...
Identifying the surfaces of three-dimensional static objects or of two-dimensional objects over time are key to a variety of applications throughout computer vision. Active surface techniques have been widely applied to such tasks, such that a deformable spline surface evolves by the influence of internal and external (typically opposing) energies until the model converges to the desired surface. Present deformable model surface extraction techniques are computationally expensive and are not able to reliably identify surfaces in the presence of noise, high curvature, or clutter. This paper proposes a novel active surface technique, decoupled active surfaces, with the specific objectives of robustness and computational efficiency. Motivated by recent results in two-dimensional object segmentation, the internal and external energies are treated separately, which leads to much faster convergence. A truncated maximum likelihood estimator is applied to generate a surface consistent with the measurements (external energy), and a Bayesian linear least squares estimator is asserted to enforce the prior (internal energy). To maintain tractability for typical three-dimensional problems, the density of vertices is dynamically resampled based on curvature, a novel quasi-random search is used as a substitute for the ML estimator, and sparse conjugate-gradient is used to execute the Bayesian estimator. The performance of the proposed method is presented using two natural and two synthetic image volumes.
... Les variétés telles que les surfaces sont couramment utilisées que ce soit en synthèse d'images ou en vision par ordinateur. En vision, bien que la segmentation de données sur les surfaces a été récemment utilisée sur des représentations implicites telles que les level sets (voir par exemple [17,22]), ce problème n'a été que rarement traité dans le cadre de représentations explicites telles que les maillages triangulaires qui sont pourtant des représentations plus na-turelles et intuitives. Aussi, la représentation par maillage a été récemment très utilisée en reconstruction 3D ; voir par exemple [1,12,32]. ...
In this paper, we address the problem of segmenting data defined on a manifold into a set of regions with uniform properties. In particular, we propose a numerical method when the manifold is represented by a triangular mesh. Based on recent image segmentation models, our method minimizes a convex energy and then enjoys significant favorable properties: it is robust to initialization and avoid the problem of the existence of local minima present in many variational models. The contributions of this paper are threefold: firstly we adapt the convex image labeling model to manifolds; in particular the total variation formulation. Secondly we show how to implement the proposed method on triangular meshes, and finally we show how to use and combine the method in other computer vision problems, such as 3D reconstruction. We demonstrate the efficiency of our method by testing it on various data.
... Colbry et al. attempt to detect the mouth line in [6]. In [13], Krueger et al. [13] made a further step in this direction using 3D active contours [14] to segment 3D lips and eyes solely using surface curvature information. Yet, this approach is not efficient enough for some applications, the computations taking minutes rather than seconds. ...
3D face analysis is a field of growing interest in the applied Computer Vision community, its applications including face recognition, modelling and biometrics, virtual and augmented reality. While several works exist on the extraction of feature points from 3D face data, there is so far no automatic system for 3D face feature contour segmentation. This paper focuses on the later problem: we aim to fill this gap. Starting from a 3D range image, bounding boxes for the face features of interest are determined first. Then the feature boundaries are segmented accurately using globally optimal and quasi-optimal active contour (AC) methods. Both AC approaches incorporate shape priors to make features more robust under noise. Evaluation on a test database shows that the proposed system yields accurate segmentation results of lip and eye contours for 96% and 85% of the datasets, respectively.
