Light Field Super-Resolution Via Graph-Based Regularization

Light field cameras capture the 3D information in a scene with a single exposure. This special feature makes light field cameras very appealing for a variety of applications: from post-capture refocus, to depth estimation and image-based rendering. However, light field cameras suffer by design from strong limitations in their spatial resolution, which should therefore be augmented by computational methods. On the one hand, off-the-shelf single-frame and multi-frame super-resolution algorithms are not ideal for light field data, as they do not consider its particular structure. On the other hand, the few super-resolution algorithms explicitly tailored for light field data exhibit significant limitations, such as the need to estimate an explicit disparity map at each view. In this work we propose a new light field super-resolution algorithm meant to address these limitations. We adopt a multi-frame alike super-resolution approach, where the complementary information in the different light field views is used to augment the spatial resolution of the whole light field. We show that coupling the multi-frame approach with a graph regularizer, that enforces the light field structure via nonlocal self similarities, permits to avoid the costly and challenging disparity estimation step for all the views. Extensive experiments show that the new algorithm compares favorably to the other state-of-the-art methods for light field super-resolution, both in terms of PSNR and visual quality.Comment: This new version includes more material. In particular, we added: a new section on the computational complexity of the proposed algorithm, experimental comparisons with a CNN-based super-resolution algorithm, and new experiments on a third datase

Image registration with sparse approximations in parametric dictionaries

We examine in this paper the problem of image registration from the new perspective where images are given by sparse approximations in parametric dictionaries of geometric functions. We propose a registration algorithm that looks for an estimate of the global transformation between sparse images by examining the set of relative geometrical transformations between the respective features. We propose a theoretical analysis of our registration algorithm and we derive performance guarantees based on two novel important properties of redundant dictionaries, namely the robust linear independence and the transformation inconsistency. We propose several illustrations and insights about the importance of these dictionary properties and show that common properties such as coherence or restricted isometry property fail to provide sufficient information in registration problems. We finally show with illustrative experiments on simple visual objects and handwritten digits images that our algorithm outperforms baseline competitor methods in terms of transformation-invariant distance computation and classification

Online Resource Inference in Network Utility Maximization Problems

The amount of transmitted data in computer networks is expected to grow considerably in the future, putting more and more pressure on the network infrastructures. In order to guarantee a good service, it then becomes fundamental to use the network resources efficiently. Network Utility Maximization (NUM) provides a framework to optimize the rate allocation when network resources are limited. Unfortunately, in the scenario where the amount of available resources is not known a priori, classical NUM solving methods do not offer a viable solution. To overcome this limitation we design an overlay rate allocation scheme that attempts to infer the actual amount of available network resources while coordinating the users rate allocation. Due to the general and complex model assumed for the congestion measurements, a passive learning of the available resources would not lead to satisfying performance. The coordination scheme must then perform active learning in order to speed up the resources estimation and quickly increase the system performance. By adopting an optimal learning formulation we are able to balance the tradeoff between an accurate estimation, and an effective resources exploitation in order to maximize the long term quality of the service delivered to the users

Distributed Representation of Geometrically Correlated Images with Compressed Linear Measurements

This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear measurements. We propose a geometry-based correlation model in order to describe the common information in pairs of images. We assume that the constitutive components of natural images can be captured by visual features that undergo local transformations (e.g., translation) in different images. We first identify prominent visual features by computing a sparse approximation of a reference image with a dictionary of geometric basis functions. We then pose a regularized optimization problem to estimate the corresponding features in correlated images given by quantized linear measurements. The estimated features have to comply with the compressed information and to represent consistent transformation between images. The correlation model is given by the relative geometric transformations between corresponding features. We then propose an efficient joint decoding algorithm that estimates the compressed images such that they stay consistent with both the quantized measurements and the correlation model. Experimental results show that the proposed algorithm effectively estimates the correlation between images in multi-view datasets. In addition, the proposed algorithm provides effective decoding performance that compares advantageously to independent coding solutions as well as state-of-the-art distributed coding schemes based on disparity learning

Graph-based classification of multiple observation sets

We consider the problem of classification of an object given multiple observations that possibly include different transformations. The possible transformations of the object generally span a low-dimensional manifold in the original signal space. We propose to take advantage of this manifold structure for the effective classification of the object represented by the observation set. In particular, we design a low complexity solution that is able to exploit the properties of the data manifolds with a graph-based algorithm. Hence, we formulate the computation of the unknown label matrix as a smoothing process on the manifold under the constraint that all observations represent an object of one single class. It results into a discrete optimization problem, which can be solved by an efficient and low complexity algorithm. We demonstrate the performance of the proposed graph-based algorithm in the classification of sets of multiple images. Moreover, we show its high potential in video-based face recognition, where it outperforms state-of-the-art solutions that fall short of exploiting the manifold structure of the face image data sets.Comment: New content adde

Graph Signal Representation with Wasserstein Barycenters

In many applications signals reside on the vertices of weighted graphs. Thus, there is the need to learn low dimensional representations for graph signals that will allow for data analysis and interpretation. Existing unsupervised dimensionality reduction methods for graph signals have focused on dictionary learning. In these works the graph is taken into consideration by imposing a structure or a parametrization on the dictionary and the signals are represented as linear combinations of the atoms in the dictionary. However, the assumption that graph signals can be represented using linear combinations of atoms is not always appropriate. In this paper we propose a novel representation framework based on non-linear and geometry-aware combinations of graph signals by leveraging the mathematical theory of Optimal Transport. We represent graph signals as Wasserstein barycenters and demonstrate through our experiments the potential of our proposed framework for low-dimensional graph signal representation

Joint Reconstruction of Multi-view Compressed Images

The distributed representation of correlated multi-view images is an important problem that arise in vision sensor networks. This paper concentrates on the joint reconstruction problem where the distributively compressed correlated images are jointly decoded in order to improve the reconstruction quality of all the compressed images. We consider a scenario where the images captured at different viewpoints are encoded independently using common coding solutions (e.g., JPEG, H.264 intra) with a balanced rate distribution among different cameras. A central decoder first estimates the underlying correlation model from the independently compressed images which will be used for the joint signal recovery. The joint reconstruction is then cast as a constrained convex optimization problem that reconstructs total-variation (TV) smooth images that comply with the estimated correlation model. At the same time, we add constraints that force the reconstructed images to be consistent with their compressed versions. We show by experiments that the proposed joint reconstruction scheme outperforms independent reconstruction in terms of image quality, for a given target bit rate. In addition, the decoding performance of our proposed algorithm compares advantageously to state-of-the-art distributed coding schemes based on disparity learning and on the DISCOVER

Graph-Based Classification of Omnidirectional Images

Omnidirectional cameras are widely used in such areas as robotics and virtual reality as they provide a wide field of view. Their images are often processed with classical methods, which might unfortunately lead to non-optimal solutions as these methods are designed for planar images that have different geometrical properties than omnidirectional ones. In this paper we study image classification task by taking into account the specific geometry of omnidirectional cameras with graph-based representations. In particular, we extend deep learning architectures to data on graphs; we propose a principled way of graph construction such that convolutional filters respond similarly for the same pattern on different positions of the image regardless of lens distortions. Our experiments show that the proposed method outperforms current techniques for the omnidirectional image classification problem