In a previous work, the equivariant Three-polar representation was introduced, and its effectiveness for face recognition was demonstrated. This approach involves representing 3D objects through a set of closed space curves derived from three reference points extracted from the surface of a 3D model. However, the reconstruction of models from the equivariant representation has not yet been addressed. In this article, we present an almost complete extension of the Threepolar representation for 3D model reconstruction. We propose an optimal reparameterization of the level curves based on the nearest neighbor notion. Finally, we perform the reconstruction of 3D models from the BU-3DFE dataset.

Diabetic retinopathy (DR) is a vision-impairing disease affecting millions of people worldwide. Early diagnosis is crucial for the treatment and prevention of this pathology. In this study, we propose a new model called BERTImages, based on BERT (Bidirectional Encoder Representations from Transformers), for the detection and classification of diabetic retinopathy. Our model incorporates processing of spatial relationships and contextual features of retinal images. Experiments conducted on the APTOS Kaggle dataset show promising results for the detection and classification of diabetic retinopathy. Compared with other deep learning models, our method achieves the best rates in terms of recall, precision and F1 score.

3D video is leading to the emergence of new technologies, such as virtual, augmented, and mixed realities, which find applications in several fields mainly healthcare, education, and industry. Even for the Internet of Things (IoT), the future lies in 3D vision and depth for machines such as autonomous cars, robots, and drones to have a deep perception like humans. Texture-dedicated compression methods are not efficient for depth maps due to features distinctions between depth and texture images. To tackle this issue, we propose a learning variable-rate depth map compression model with conditional quality-controllable autoencoder. Specifically, the encoder extracts deep features from depth maps through an advanced Convolutional Neural Network (CNN) model, trained using a combination of grayscale texture and depth images. This latter incorporates an initial layer of predefined wedgelet filters, succeeded by a VGG 19 pretrained model. To effectively differentiate between depth maps and grayscale textures within the training dataset, an image style classification technique using the learnt deep correlation Features is employed. Our end-to-end compression network ensures better performances over main candidate methods and depth-oriented 3D-HEVC compression standard.

The lack of interpretability, explainability and transparency makes deep learning models untrusted to perform reliably for making critical decisions. Despite their evaluation against disturbances including geometric transformations, occlusion and convolutional noises in the case of DNN-based image classifiers, the evaluation of contour classifiers has only been studied against rigid displacements (rotation and translation). In this paper, we introduce ContourCertif: a new system to certify deep contour classifiers against convolutional attacks. We use the abstract interpretation theory in order to formulate the Lower and Upper Bounds with abstract intervals to support other classes of advanced attacks including filtering.

With the emergence of depth sensors, extraction of depth maps features is becoming more and more solicited and prominent for several computer vision applications, such as gesture recognition, face recognition and segmentation. These applications can be more accurate thanks to the depth information that provides more precise separate foreground objects from background. In this paper, we propose an automatic depth maps features extraction model based on an optimized Convolutional Neural Network (CNN), trained on a mixture of depth maps and grayscale texture images. The CNN includes a first convolutional layer of pre-defined wedgelet filters, followed by a pre-trained VGG-19 neural network. Then, we opt for an image style classification based on Learnt Deep Correlation Features to capture features distinguishing depth maps from grayscale texture images of the training set. Experimental results demonstrate the potential effectiveness of the proposed wedgelet (We) and Learnt Deep Correlation Features (LDCF) based Network (WeLDCFNet) with a mean accuracy gain up to 32.77%, when compared to existing features extraction approaches. As our aim in this paper is depth maps features extraction and not the texture/depth classification itself, we propose, as a use case, to leverage the proposed WeLDCFNet for depth maps learned compression. If our model succeeds to extract depth features that make them distinguishable from texture, it would be useful to save the main compact depth information. Our WeLDCFNet based autoencoder, tailored to compression needs, shows competitive Rate/Distortion tradeoffs when compared to the latest depth maps compression standard.

In a previous work, we have proposed a morphing method based on invertible and stable descriptors that are invariant to Euclidean transformations and to the starting point. The stability guarantees the closeness in the shape sense of the reconstructed intermediate contours. However, this set of descriptors is not defined by a general expression. Here, we propose several sets of stable and invertible finite descriptors expressed by the same formula. Its stability is proven for a subset of this family thanks to the finite-dimension of the invariant space. Such finite dimension results from the Discrete Fourier Transform model that is used instead of Fourier coefficients. Moreover, an analytical general inverse formula is established. The use of the inverse analytical formula and the double utilization of the Fast Fourier Transform ensure an effective blending while being computationally efficient. Finally, we propose a new quantitative criterion for shape morphing. The latter is based on the Euclidean distances between successive curves in a morphing sequence after applying a given registration. Therefore, it allows us to compare the blending results of each set of descriptors. Several experiments are conducted on KIMIA'99 and MPEG-7 datasets. The results highlight the concordance of this criterion with the morphing visual quality and indicate which set of descriptors generates the most appropriate blending.

Here we propose a novel affine registration method for planar curves. It is based on a pseudo-inverse algorithm applied to the source and target curves in their multi-scale version. The proposed registration system selects the relevant scales in the optimized L2distances. The retrieved smoothing parameters are realized with the Gaussian Expectation-Maximization (EM) algorithm. We resolve the global system, formed by equations corresponding to EM selected scales.

The conventional 2D metrics can be used for measuring the quality of depth maps, but none of them is considered to be efficient and is not accurate when used for evaluating 3D quality. In this paper, we propose a new full reference objective metric, called Sparse Representations-Mean Squared Error (SR-MSE), which efficiently evaluates the depth maps compression distortions. It adaptively models the reference and compressed depth maps in a mixed redundant transform domain dedicated to depth features. Then, it computes the mean squared error between the sparse coefficients issued from this modeling. As a benchmark of quality assessment, we perform a subjective evaluation test for depth maps compressed using the latest 3D High Efficiency Video Coding standard at various bitrates. We compare the subjective results with the proposed and conventional objective metrics. Experimental results demonstrate that the proposed SR-MSE, compared to the conventional image quality assessment metrics, yields the highest correlated scores to the subjective ones.

SHVC, the Scalable extension of the High Efficiency Video Coding standard (HEVC), combines large compression efficiency and high visual quality of different versions of a same video in a single bitstream. However, this comes at the cost of a high computational complexity. Many efforts aim to reduce this latter for texture images. In this paper, we aim at the same objective, but for depth maps that are characterized by areas of smoothly varying grey levels separated by sharp discontinuities at object boundaries. Typically, we propose a fast scalable coding scheme while exploiting depth maps specificities, depth information of SHVC Coding Units (CUs) as well as correlation between base and enhancement layers. Experimental results show that the proposed method significantly reduces the execution time of the SHVC encoder; while maintaining the quality of intermediate views synthesized from encoded depth maps.

In this paper, a novel method for blending planar shapes is introduced. This approach is based on the Fined-Fourier-based Invariant Descriptor (Fined-FID) that is invertible, invariant under Euclidean transformations and stable. Our approach extracts the Fined-FID from the two shapes of interest (the source and the target ones). Then, the extracted descriptors are averaged enabling the calculation of intermediate descriptors. Finally, thanks to the inversion criterion, the intermediate shapes are easily recovered by applying the inverse analytical expression to these intermediate descriptors. Compared to previous works, the Fined-FID-based morphing avoid the usual registration step, generates naturally closed intermediate contours and ensure invariance under Euclidean transformations and invariance to the starting point, while being computationally efficient (almost-linear complexity). The performed experiments show the performance of the proposed blending approach with respect to curvature-based methods.

In this paper, we propose a descriptor for Brachiopods classification by using a combination between curvature and Fourier descriptors. The curvature properties provide an apparently powerful cue to the underlying structure of the curve and captures completely the structure of planar curve. In addition, it is stable and complete. Fourier descriptors are powerful features for the recognition of two-dimensional connected shapes. We used the Fourier descriptors proposed by Ghorbel, this set of invariants is also stable and complete. Based on this observation, important features can be extracted. Experiments show that the proposed descriptor is fast to compute and it achieves high recognition rates compared to Curvature Scale Space descriptor.

Completely embedded in the 3D era, depth maps coding becomes a must in order to favour 3D admission to different fields of application, ranging from video games to medical imaging. This study presents a novel depth coding approach that, after a decimation step favouring the foreground, decomposes depth maps onto a set of sparse coefficients and redundant mixed discrete cosine and B‐splines atoms highly correlated to depth maps piece‐wise linear nature. Depth decomposition searches the best rate/distortion tradeoff through minimisation of an adaptive cost function, where its weight parameter is manipulated according to depth homogeneity. The bigger the parameter is, the more the sparsity is favoured at the expense of synthesis quality. Furthermore, handled distortion measure of the cost function quantifies the effect of depth maps coding on rendered views quality. The experiments show the relevance of the proposed method, able to obtain considerable tradeoffs between bitrate and synthesised views distortion.

Referring to the statistical point of view, we present in this work, a new criterion for evaluating neural networks stability compared to the Bayesian classifier. The stability comparison is performed by the error rate probability densities function estimated by the kernel-diffeomorphism semi-bounded Plug-in algorithm. The Bayesian and combination approaches for neural networks improve the performance and stability degree of the classical neural classifiers.

In this paper, we intend to introduce a fast surface registration process which is independent from the original parameterization of the surface and invariant under 3D rigid transformations. It is based on a feature descriptors correspondence. Such feature descriptors are extracted from the superposition of two surfacic curves: geodesic levels and radial ones from local neighborhoods defined around reference points already picked on the surface. A study of the optimal number of those curves thanks to a generalized version of Shannon theorem is developed. Thus, the obtained discretized parametrisation (ordered descriptors) is the basis of the matching phase that becomes obvious and more robust comparing to the classic ICP algorithm. Experimentations are conducted on facial surfaces from the Bosphorus database to test the registration of both rigid and non-rigid shapes (neutral faces vs. faces with expressions). The Hausdorff distance in shape space is used as an evaluation metric to test the robustness to tessellation. The discriminative power in face description is also estimated.

Completely embedded in the 3D era, depth maps coding becomes a must in order to favor 3D admission to different fields of application, ranging from video games to medical imaging. This paper presents a novel depth coding approach that decomposes a decimated version of the original depth image on a sparse set of coefficients and mixed discrete cosine and B-splines atoms. The upstream decimation step reduces encoding bitrate without significant loss of virtual views quality. Depth decomposition is performed through minimization of an adaptive Rate/Distortion cost function, where we manipulate its weight parameter according to depth discontinuities. We then refine the choice of distortion metric in order to quantify the effect of depth maps coding on rendered views quality. Experiments show the relevance of the proposed method, able to obtain considerable tradeoffs between bitrate and synthesized views distortion.

Multiview video plus depth is the most popular 3D video representation that would support novel applications including free viewpoint television. These applications highly depend on high quality rendering of interpolated views which, as well, highly depends on the quality of decoded depth images. Therefore, a depth map coding that preserves perceptual quality, particularly on high frequency regions, is primary. In this paper, we propose a coding depth maps method that deals with emerging sparse signal decomposition technique. Depth images are approximated by a linear combination of few nonzero coefficients and dictionary atoms. Selected atoms are elementary signals based on a mixture of discrete cosine and B-splines of first degree. Sparse depth maps coding is tuned using a couple quality criterion such that depth discontinuities are preserved. The results investigated by objective evaluations over several depth maps imply that the proposed depth maps coding achieves better Rate-Distortion than JPEG and JPEG 2000. Subjective evaluation is also presented to stress the visual quality of interpolated views.

This paper introduces a novel scalable 3D mesh compression technique based on a shape approximation prediction strategy. The proposed approach, so-called Shape Approximation Compression (SAC), directly compresses the levels of detail (LoDs) defined by the content creators, while exploiting their inter-correlations. Here, the geometry of each LoD is used in order to compute a smooth approximation of the next layer. A progressive mesh hierarchy is then built on the top of the approximated version making it possible to efficiently predict and progressively transmit the geometry approximation errors. The SAC codec was evaluated within the framework of the MPEG core experiments on Multi-Resolution 3D Mesh Coding (MR3DMC) and was preliminarily accepted for future standardization.

This paper introduces an original multi-resolution 3D mesh compression technique, called Shape Approximation-based Progressive Mesh (SAPM). The proposed approach losslessly compresses the mesh connectivity and exploits it in order to build a smooth approximation of the original mesh. The obtained mesh approximation is then decimated yielding a progressive mesh hierarchy. This hierarchy is used to efficiently predict and progressively transmit the geometry approximation errors. The proposed codec supports both spatial and quality scalabilities and offers high rate-distortion performances. Experimental evaluation shows that the SAPM codec is on average 38-57% more efficient than the state-of-the-art connectivity preserving 3D mesh compression techniques.

In this paper, we present a new algorithm of snakes with geometric prior. A method of shape alignment using Fourier coefficients is introduced to estimate the Euclidean transformation between the evolving snake and a template of the searched object. This allows the definition of a new field of forces making the evolving snake to have a shape similar to the template one. Furthermore, this strategy can be used to manage several possible templates by computing a shape distance to select the best one at each iteration. The new method also solves some well-known limitations of snakes such as evolution in concave boundaries, and enhances the robustness to noise and partially occluded objects. A series of experimental results is presented to illustrate performances.

This paper presents an original approach for 3D mesh approximate convex decomposition. The proposed algorithm computes a hierarchical segmentation of the mesh triangles by applying a set of topological decimation operations to its dual graph. The decimation strategy is guided by a cost function describing the concavity and the shape of the detected clusters. The generated segmentation is finally exploited to construct a faithful approximation of the original mesh by a set of convex surfaces. This new representation is particularly adapted for collision detection. The experimental evaluation we conducted shows that the proposed technique efficiently decomposes a concave 3D mesh into a small set (with respect to the number of its facets) of nearly convex surfaces. Furthermore, it automatically detects the anatomical structure of the analyzed 3D models, which makes it an ideal candidate for skeleton extraction and patterns recognition applications.

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 functional that includes an additional information on a shape reference called "template" or "prototype". Prior shape knowledge is introduced throw a complete family of Euclidean invariants, computed from the Fourier descriptors of the evolving contour and the prototype. It enhances the model robustness to noise and occlusion, and allows it to evolve in highly concave boundaries. The variational formulation of the proposed approach is described in details. Experimental results on both synthetic and real images are presented and discussed

In this paper, we propose here an affine invariant matching algorithm applied to stereo contour images. A new affme-invariant Fourier descriptors introduced in F. Ghorbel (1998) is tested and implemented. These invariants are produced from the Fourier coefficients of the reparametrized IR/sup 2/-curve. They satisfy the completeness and stability properties, which will be proved experimentally. We note that this set of invariants are computed and used for the first time. Application in stereo matching will be presented in this paper.

This paper presents a new multiscale and zero-crossing, curvature-based shape representation technique for planar curves with general affine transformation. The method consists of the concept of describing a curve at varying levels of detail using features that are invariant with respect to transformations that do not change the shape of the curve. The process of describing a curve at increasing levels of abstraction is referred to as the affine evolution of that curve. This affine evolution does not change the physical interpretation of planar curves and characterize the behaviors of inflexion points of the curves during its evolution.

The aim of this paper is to present two kinds of shape distances in a dynamic images context. The first distance is obtained by the complete and stable set of invariants under rigid motion for closed curves. The second distance is obtained by using a Hausdorff distance for parameter estimation. An original application serves as a useful test for evaluating these proposed distances in coding applications.

We consider the problem of comparing geometric objects in order to determine the extent to which one object resembles another. Invariant feature families are presented. A complete and stable set of invariant features has been applied to define all invariant distance in the shapes space. This distance allows us to detect and follow moving objects in a dynamic scene. In order to evaluate the performance of such a metric, experimental results are given.

The recognition of three-dimensional objects of various size, position and orientation, is an important and difficult problem in scene analysis. The description by moment invariants is recognized as the usual method in this case. Here, we intend to introduce another solution based on the harmonic analysis on a given group. Gray level three-dimensional objects are considered in this paper. Such a description is invariant with respect to general three-dimensional Euclidean motions. Stability under small shape distortions is proven experimentally in the case of superquadric volumes.

We present the bootstrap sampling techniques applied to some pattern recognition algorithms. Two important procedures in image analysis are tested: a statistical segmentation based on expectation-maximisation (EM) family algorithms and two methods of invariant features extraction for gray level images. In the first case, the results we obtain show that the bootstrap sample selection method gives better results than the classical one both in the quality of the segmented image and the computing time. In the second case, the computation of the moment invariants (MI) and the analytical Fourier Mellin transform (AFMT) by the bootstrap approach using the Monte Carlo approximations are implemented. We note that this approach gives a stable approximation and reduces considerably the computing time, since we select only a small representative sample from the image. These algorithms are applied to natural image (medical image).>

Presents the study of a shape representation space by means of its identification to the invariants space. This approach has an algebraic meaning translated by the completion criterion for the set of invariants introduced by Crimmins (1982). The author introduces a new property for Fourier descriptors, the stability which expresses the fact that a low level divergence in the invariants does not induce a noticeable distortion of the shape. This stability gives a topologic meaning to the identification of the space shape with the space of invariants. A complete and stable set of Fourier descriptors with regard to the starting point and the direct group of similarities in the case of the planar closed contours is constructed.>