Piecewise uniform switched vector quantization of the memoryless two-dimensional Laplace source

A simple and complete asymptotical analysis of an optimal piecewise uniform quantization of two-dimensional memoryless Laplacian source with the respect to distortion (D) i.e. the mean-square error (MSE) is presented. Piecewise uniform quantization consists of L different uniform vector quan-tizers. Uniform quantizer optimality conditions and all main equations for optimal number of output points and levels for each partition are presented (using rectangular cells). The optimal granular distortion (i) for each partition in a closed form is derived. Switched quantization is used in order to give higher quality by increasing signal-to-quantization noise ratio (SQNR) in a wide range of signal volumes (variances) or to decrease necessary sample rate

Geometry-based scene representation with distributed vision sensors.

This paper addresses the problem of efficient representation and compression of scenes captured by distributed vision sensors. We propose a novel geometrical model to describe the correlation between different views of a three-dimensional scene. We first approximate the camera images by sparse expansion over a dictionary of geometric atoms, as the most important visual features are likely to be equivalently dominant in images from multiple cameras. The correlation model is then built on local geometrical transformations between corresponding features taken in different views, where correspondences are defined based on shape and epipolar geometry constraints. Based on this geometrical framework, we design a distributed coding scheme with side information, which builds an efficient representation of the scene without communication between cameras. The Wyner-Ziv encoder partitions the dictionary into cosets of dissimilar atoms with respect to shape and position in the image. The joint decoder then determines pairwise correspondences between atoms in the reference image and atoms in the cosets of the Wyner-Ziv image. It selects the most likely correspondence among pairs of atoms that satisfy epipolar geometry constraints. Atom pairing permits to estimate the local transformations between correlated images, which are later used to refine the side information provided by the reference image. Experiments demonstrate that the proposed method leads to reliable estimation of the geometric transformations between views. The distributed coding scheme offers similar rate-distortion performance as joint encoding at low bit rate and outperforms methods based on independent decoding of the different images

Dictionary learning in stereo imaging

This paper presents a new method for learning overcomplete dictionaries adapted to efficient joint representation of stereo images. We first formulate a sparse stereo image model where the multi-view correlation is described by local geometric transforms of dictionary atoms in two stereo views. A maximum-likelihood method for learning stereo dictionaries is then proposed, which includes a multi-view geometry constraint in the probabilistic modeling in order to obtain dictionaries optimized for the joint representation of stereo images. The dictionaries are learned by optimizing the maximum-likelihood objective function using the expectation- maximization algorithm. We illustrate the learning algorithm in the case of omnidirectional images, where we learn scales of atoms in a parametric dictionary. The resulting dictionaries provide both better performance in the joint representation of stereo omnidirectional images and improved multi- view feature matching. We finally discuss and demonstrate the benefits of dictionary learning for distributed scene representation and camera pose estimation

3D Face Recognition with Sparse Spherical Representations

This paper addresses the problem of 3D face recognition using simultaneous sparse approximations on the sphere. The 3D face point clouds are first aligned with a novel and fully automated registration process. They are then represented as signals on the 2D sphere in order to preserve depth and geometry information. Next, we implement a dimensionality reduction process with simultaneous sparse approximations and subspace projection. It permits to represent each 3D face by only a few spherical functions that are able to capture the salient facial characteristics, and hence to preserve the discriminant facial information. We eventually perform recognition by effective matching in the reduced space, where Linear Discriminant Analysis can be further activated for improved recognition performance. The 3D face recognition algorithm is evaluated on the FRGC v.1.0 data set, where it is shown to outperform classical state-of-the-art solutions that work with depth images

FST-based Reconstruction of 3D-models from Non-Uniformly Sampled Datasets on the Sphere

This paper proposes a new method for reconstruction of star-shaped 3D surfaces from scattered datasets, where such surfaces are considered as signals living in the space of square integrable functions on the unit sphere. We first propose a generalization of the Fourier transform on the sphere. A practical reconstruction method is then presented, which interpolates a spherical signal on an equiangular grid, from non-uniformly sampled dataset representing a 3D point cloud. The experiments show that the proposed interpolation method results in smoother surfaces, and higher reconstruction PSNRs than the nearest neighbor interpolation method

Dictionary learning in stereo imaging

This paper presents a new method for learning overcomplete dictionaries adapted to efficient joint representation of stereo images. We first formulate a sparse stereo image model where the multi-view correlation is described by local geometric transforms of dictionary atoms in two stereo views. A maximum-likelihood method for learning stereo dictionaries is then proposed, which includes a multi-view geometry constraint in the probabilistic modeling in order to obtain dictionaries optimized for the joint representation of stereo images. The dictionaries are learned by optimizing the maximum-likelihood objective function using the expectation- maximization algorithm. We illustrate the learning algorithm in the case of omnidirectional images, where we learn scales of atoms in a parametric dictionary. The resulting dictionaries provide both better performance in the joint representation of stereo omnidirectional images and improved multi- view feature matching. We finally discuss and demonstrate the benefits of dictionary learning for distributed scene representation and camera pose estimation

Omnidirectional views selection for scene representation

This paper proposes a new method for the selection of sets of omnidirectional views, which contribute together to the efficient representation of a 3d scene. When the 3d surface is modelled as a function on a unit sphere, the view selection problem is mostly governed by the accuracy of the 3d surface reconstruction from non-uniformly sampled datasets. A novel method is proposed for the reconstruction of signals on the sphere from scattered data, using a generalization of the Spherical Fourier Transform. With that reconstruction strategy, an algorithm is then proposed to select the best subset of $n$ views, from a predefined set of viewpoints, in order to minimize the overall reconstruction error. Starting from initial viewpoints determined by the frequency distribution of the 3d scene, the algorithm iteratively refines the selection of each of the viewpoints, in order to maximize the quality of the representation. Experiments show that the algorithm converges towards a minimal distortion, and demonstrate that the selection of omnidirectional views is consistent with the frequency characteristics of the 3d scene

Conditions for recovery of sparse signals correlated by local transforms

This paper addresses the problem of correct recovery of multiple sparse correlated signals using distributed thresholding. We consider the scenario where multiple sensors capture the same event, but observe different signals that are correlated by local transforms of their sparse components. In this context, the signals do not necessarily have the same sparse support, but instead the support of one signal is built on local transformations of the atoms in the sparse support of another signal. We establish the sufficient condition for the correct recovery of such correlated signals using independent thresholding of the multiple signals. The validity of the derived recovery condition is confirmed by experimental results in noiseless and noisy scenarios

Coarse scene geometry estimation from sparse approximations of multi-view omnidirectional images

This paper presents a framework for coarse scene geometry estimation, based on sparse representations of omnidirectional images with geometrical basis functions. We introduce a correlation model that relates sparse components in different views with local geometrical transforms, under epipolar constraints. By combining selected pairs of features represented by sparse components, we estimate the disparity map between images, evaluate coarse depth information, and recover the relative camera pose. The proposed framework allows to estimate the geometry of the scene, hence disparity between images, using only coarse approximations of multi-view images. The experimental results demonstrate that only a few components are sufficient to estimate the disparity map and the camera pose. This is certainly beneficial for predictive multi-view compression schemes, where the scene reconstruction relies on the disparity mapping from low-resolution images in order to progressively decode the higher image resolutions

Wyner-Ziv coding of multi-view omnidirectional images with overcomplete decompositions

This paper addresses the problem of distributed coding of light fields in camera networks. A novel distributed coding scheme with side information is presented, based on spherical image expansion over an overcomplete dictionary of geometric atoms. We propose to model the correlation between views with local geometrical transformations of corresponding features in the sparse representations of different views. We design a Wyner-Ziv encoder by partitioning the dictionary into cosets of dissimilar atoms, with respect to their shape and position on the image. The joint decoder finds pairwise correspondences between atoms in the reference image and atoms in cosets of the Wyner-Ziv image. It selects the most likely correspondence among pairs of atoms that satisfy epipolar geometry constraints. This permits to estimate local transformations between correlated images that eventually help to refine the side information provided by the reference image. Experiments demonstrate that the proposed method is capable of estimating the geometric transformations between views, and hence to reconstruct the Wyner-Ziv image