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Flow structure behind the backward facing step in a narrow channel was studied in details. The step height was 25% of the channel width. The structure of the region just behind the step forming the back-flow region is studied in details using stereo PIV technique. Time-mean 3D structures behind the step are evaluated and shown in the paper. (© 2012...
Citations
... Lin [167] proposes a framework for summation invariants, along with four important summation invariant classes. These invariants are used to define a format representation for several applications, one of which is the 3D object recognition. ...
... Additionally, some works demonstrated their results according to the receiver operating characteristics (ROC) and cumulative match characteristic (CMC) [273] curves. Others evaluated their results based on classification/recognition error and on the equal error rate (EER) [167]. Independently of the method used to demonstrate and evaluate the results, a large part of the analyzed works compared their results against other methods, considered state of the art on that moment, to demonstrate their work strengths and abilities. ...
In this paper, we present a systematic literature review concerning 3D object recognition and classification. We cover articles published between 2006 and 2016 available in three scientific databases (ScienceDirect, IEEE Xplore and ACM), using the methodology for systematic review proposed by Kitchenham. Based on this methodology, we used tags and exclusion criteria to select papers about the topic under study. After the works selection, we applied a categorization process aiming to group similar object representation types, analyzing the steps applied for object recognition, the tests and evaluation performed and the databases used. Lastly, we compressed all the obtained information in a general overview and presented future prospects for the area.
Link for the publication:
https://link.springer.com/epdf/10.1007/s10044-019-00804-4?author_access_token=paE7wTbqwKN7oCwVliHwLve4RwlQNchNByi7wbcMAY7uL2tJzq0UXA0O13kX7wvxz98EQWbRDi2uT7G5KxVe0WzCAoagCbJhmkFlrCPdZIPfyyYkaSt_0zAEiJJc2cojH9AajAmYQ5BT1LV4EonJMg%3D%3D
... There is a long history in the multimedia and computer vision society to employ geometric invariants that reflect intrinsic geometric properties of an object under different transformation groups [21], [22], [23]. The audio watermarking scheme using a geometric invariant achieves high quality in both objective and subjective quality assessments [24]. ...
Robustly localizing facial landmarks plays a very important role in many multimedia and vision applications. Most recently proposed regression-based methods prevailing in the community lack explicit shape constraints for faces and require a large number of facial images to cover great appearance variations. To address these limitations, this paper introduces a novel projective invariant named characteristic number (CN) to $explicitly$ characterize the intrinsic geometries of facial points shared by human faces. It can be verified that the shape priors from CN are inherently invariant to pose changes. By further developing a shape-to-gradient regression framework, we provide a robust and efficient landmark detector for facial images in the wild. The computation of our model can be successfully addressed by learning the descent directions using point-CN pairs without the need of large collections for appearance training. As a nontrivial byproduct, this paper also builds a face data set, where each face has 15 well-defined viewpoints (poses) to quantitatively analyze the effects of different poses on localization methods. Extensive experiments on challenging benchmarks and our newly built data set demonstrate the effectiveness of our proposed detector against other state-of-the-art approaches.
... There is a long history in the multimedia and computer vision society to employ geometric invariants that reflect intrinsic geometric properties of an object under different transformation groups [21]- [23]. The audio watermarking scheme using a geometric invariant achieves high quality in both objective and subjective quality assessments [24]. ...
Automatic extraction of fiducial facial points is one of the key steps to face tracking, recognition and animation as well as video communication. In this paper, we present a method to localize 8 fiducial points in a face image with cross ratio (CR), a fundamental projective invariant. We derive strong shape priors, which characterize the intrinsic geometries shared by human faces, from CR statistics on a moderate size (515) of frontal upright faces. We combine these shape priors with Gabor textural features and edge/corner into a convex optimization. The Gabor features of local patches and geometric constraints from CR are insensitive to global perspective transformations. Thereafter, the proposed approach renders the robustness to great pose or viewpoint changes. Extensive experiments on facial images from several data sets with great variations on expressions, illuminations and poses demonstrate the effectiveness of the proposed approach.
... Gu and Kanade present a regularized shape model [36] and Zhang et al. learn a sparse representation for shape variations [37]. These models are robust to noise and low It has been a long history in computer vision to use geometric invariants that reflect the intrinsic geometries of an object under different transformation groups [39], [40]. The cross ratio (CR) on 5 coplanar points is a fundamental invariant to projective transformations. ...
Automatic extraction of fiducial facial points is one of the key steps to face tracking, recognition and animation. Great facial variations, especially pose or viewpoint changes, typically degrade the performance of classical methods. Recent learning or regression based approaches highly rely on the availability of a training set that covers facial variations as wide as possible. In this paper, we introduce and extend a novel projective invariant, named the characteristic number (CN), which unifies the collinearity, cross ratio, and geometrical characteristics given by more (6) points. We derive strong shape priors from CN statistics on a moderate size (515) of frontal upright faces in order to characterize the intrinsic geometries shared by human faces. We combine these shape priors with simple appearance based constraints, e.g., texture, edge and corner, into a quadratic optimization. Thereafter, the solution to facial point extraction can be found by the standard gradient descent. The inclusion of these shape priors renders the robustness to pose changes owing to their invariance to projective transformations. Extensive experiments on the Labeled Faces in the Wild (LFW), Labeled Face Parts in the Wild (LFPW) and Helen database, and crossset faces with various changes demonstrate the effectiveness of the CN based shape priors compared with the state-of-the-art.
... It is a key mathematical tool for 3D reconstruction from multiple views [1]. Furthermore, there has been a long history for object recognition to use geometric invariants that reflect the geometries of an object under different transformation groups [2,3]. The cross-ratio on five coplanar points is a fundamental invariant under projective geometry. ...
Geometric invariants are important for shape recognition and matching. Existing invariants in projective geometry are typically defined on the limited number (e.g., five for the classical cross-ratio) of collinear planar points and also lack the ability to characterize the curve or surface underlying the given points. In this paper, we present a projective invariant named after the characteristic number of planar algebraic curves. The characteristic number in this work reveals an intrinsic property of an algebraic hypersurface or curve, which relies no more on the existence of the surface or curve as its planar version. The new definition also generalizes the cross-ratio by relaxing the collinearity and number of points for the cross-ratio. We employ the characteristic number to construct more informative shape descriptors that improve the performance of shape recognition, especially when severe affine and perspective deformations occur. In addition to the application to shape recognition, we incorporate the geometric constraints on facial feature points derived from the characteristic number into facial feature matching. The experiments show the improvements on accuracy and robustness to pose and view changes over the method with the collinearity and cross-ratio constraints.
... It is a key mathematical tool for 3D reconstruction from multiple views [1]. Furthermore, there has been a long history for object recognition to use geometric invariants that reflect the geometries of an object under different transformation groups [2,3]. The cross-ratio on five coplanar points is a fundamental invariant under projective geometry. ...
Geometric invariants are important for shape recognition and matching. Existing invariants in projective geometry are typically defined on the limited number (e.g., five for the classical cross-ratio) of collinear planar points and also lack the ability to characterize the curve or surface underlying the given points. In this paper, we present a projective invariant named after the characteristic number of planar algebraic curves. The characteristic number in this work reveals an intrinsic property of an algebraic hypersurface or curve, which relies no more on the existence of the surface or curve as its planar version. The new definition also generalizes the cross-ratio by relaxing the collinearity and number of points for the cross-ratio. We employ the characteristic number to construct more informative shape descriptors that improve the performance of shape recognition, especially when severe affine and perspective deformations occur. In addition to the application to shape recognition, we incorporate the geometric constraints on facial feature points derived from the characteristic number into facial feature matching. The experiments show the improvements on accuracy and robustness to pose and view changes over the method with the collinearity and cross-ratio constraints.
... wherex andȳ denote the x and y coordinates transformed by a moving frame. TheP ij are invariant functions under Euclidean transformation acting on R 2 [8], i.e., η ij =P ij . The first and second invariant functions, i + j = 1 or 2, were explicitly derived as shown below ...
... Let us use the affine invariants as an example to illustrate this method. For a curve (x n , y n ), n ∈ {1, 2, · · · , N}, the m th semi-local summation affine invariant is given by [8]: Given N sampled points on a curve, one can compute semi-local summation invariants with non-overlapping or overlapping intervals. Obviously, using overlapping intervals will yield high dimensional features. ...
... In this experiment, the number of sample points on each re-sampled contour is chosen to be N 0 = 512. The relationship between affine-transformed contourx[n] and re-sampled contourx [n] described as [8]: ...
Invariant features play a key role in ob- ject and pattern recognition studies. Features that are invariant to geometrical transformations offer suc- cinct representations of underlying objects so that they can be reliably identified. In this paper, a family of novel invariant features is introduced based on Car- tan's theory of moving frames. These new features is called summation invariants. Compared to existing invariant features, summation invariants are inher- ently numerically stable, and do not require computa- tionally complex numerical integrations or analytical representations of underlying data. A robust methods for extracting summation invariants from sampled 2D contours introduced. Then, these new invariant fea- tures are applied to 2D object recognition and com- pared to other methods, e.g. wavelet and found to be more efficient.
... The face image is usually divided into small regions that contain the extracted invariant features and a statistical model is built. As a result, the feature of each region, together with relationships between these regions suggest different facial expressions, illumination condition, viewpoints, etc. [9] The drawback of this kind of method is that image features could be severely destroyed due to bad illumination condition, noise, and other occlusion, and the boundaries between features could be too weak to detect while the shadows could produce strong fake edges. Image invariants can be designed to fit the needs of specific systems. ...
... Thus, having a descriptive feature that is invariant to geometric transformations, like translation, rotation, scale or shear, or that is invariant to all of them, is highly desirable. Summation invariants are one family of geometrically invariant features that was developed recently1234567. This paper will briefly review some other existing invariant features and will summarize the summation invariants developed thus far. ...
... However, summation invariants are defined with potentials that are summations instead of integrals, so calculating them will not involve numerical approximations. Summation invariants have been applied to fish shapes [1, 6] and face recognition4567. ...
... However, summation invariants are defined with potentials that are summations instead of integrals, so calculating them will not involve numerical approximations. Summation invariants have been applied to fish shapes [1, 6] and face recognition4567. ...
The method of moving frames, a powerful mathematical tool for deriving geometrically invariant functions, is described. A systematic approach is outlined for the derivation of new members of a family of geometrically invariant features using the moving frame method. This family of features is called summation invariant. An example derivation is given to illustrate the procedure. The current members of this family are summarized and several implementation considerations for these features are investigated. A naming convention is given and a standard test is defined for the purpose of comparing the discrimination ability of these features. This test is used to compare the features derived so far using the application of face recognition and the Face Recognition Grand Challenge (FRGC2.0) dataset.
Recently a novel family of geometrically invariant features, called summation invariant, has been developed and applied to object recognition. The range of this family of features is expanded here beyond the Euclidean and affine transformation groups to planar projective transformations. Whereas other methods require small changes in view, or collinear points, this method removes those limitations and allows recognition of general planar objects over wide ranges of viewpoint. The derivation of these new features requires the innovation of deriving the invariants in the homogeneous coordinate space, yet yields results formulated in terms of Cartesian coordinates. Simulations demonstrate the effectiveness of this new approach to object recognition under projective transformations like those encountered in camera networks.
