Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Wavelet and Multiscale Methods

[no abstract available

Discontinuity-Aware Base-Mesh Modeling of Depth for Scalable Multiview Image Synthesis and Compression

This thesis is concerned with the challenge of deriving disparity from sparsely communicated depth for performing disparity-compensated view synthesis for compression and rendering of multiview images. The modeling of depth is essential for deducing disparity at view locations where depth is not available and is also critical for visibility reasoning and occlusion handling. This thesis first explores disparity derivation methods and disparity-compensated view synthesis approaches. Investigations reveal the merits of adopting a piece-wise continuous mesh description of depth for deriving disparity at target view locations to enable disparity-compensated backward warping of texture. Visibility information can be reasoned due to the correspondence relationship between views that a mesh model provides, while the connectivity of a mesh model assists in resolving depth occlusion. The recent JPEG 2000 Part-17 extension defines tools for scalable coding of discontinuous media using breakpoint-dependent DWT, where breakpoints describe discontinuity boundary geometry. This thesis proposes a method to efficiently reconstruct depth coded using JPEG 2000 Part-17 as a piece-wise continuous mesh, where discontinuities are driven by the encoded breakpoints. Results show that the proposed mesh can accurately represent decoded depth while its complexity scales along with decoded depth quality. The piece-wise continuous mesh model anchored at a single viewpoint or base-view can be augmented to form a multi-layered structure where the underlying layers carry depth information of regions that are occluded at the base-view. Such a consolidated mesh representation is termed a base-mesh model and can be projected to many viewpoints, to deduce complete disparity fields between any pair of views that are inherently consistent. Experimental results demonstrate the superior performance of the base-mesh model in multiview synthesis and compression compared to other state-of-the-art methods, including the JPEG Pleno light field codec. The proposed base-mesh model departs greatly from conventional pixel-wise or block-wise depth models and their forward depth mapping for deriving disparity ingrained in existing multiview processing systems. When performing disparity-compensated view synthesis, there can be regions for which reference texture is unavailable, and inpainting is required. A new depth-guided texture inpainting algorithm is proposed to restore occluded texture in regions where depth information is either available or can be inferred using the base-mesh model

Graph Signal Processing:Sparse Representation and Applications

Over the past few decades we have been experiencing an explosion of information generated by large networks of sensors and other data sources. Much of this data is intrinsically structured, such as traffic evolution in a transportation network, temperature values in different geographical locations, information diffusion in social networks, functional activities in the brain, or 3D meshes in computer graphics. The representation, analysis, and compression of such data is a challenging task and requires the development of new tools that can identify and properly exploit the data structure. In this thesis, we formulate the processing and analysis of structured data using the emerging framework of graph signal processing. Graphs are generic data representation forms, suitable for modeling the geometric structure of signals that live on topologically complicated domains. The vertices of the graph represent the discrete data domain, and the edge weights capture the pairwise relationships between the vertices. A graph signal is then defined as a function that assigns a real value to each vertex. Graph signal processing is a useful framework for handling efficiently such data as it takes into consideration both the signal and the graph structure. In this work, we develop new methods and study several important problems related to the representation and structure-aware processing of graph signals in both centralized and distributed settings. We focus in particular in the theory of sparse graph signal representation and its applications and we bring some insights towards better understanding the interplay between graphs and signals on graphs. First, we study a novel yet natural application of the graph signal processing framework for the representation of 3D point cloud sequences. We exploit graph-based transform signal representations for addressing the challenging problem of compression of data that is characterized by dynamic 3D positions and color attributes. Next, we depart from graph-based transform signal representations to design new overcomplete representations, or dictionaries, which are adapted to specific classes of graph signals. In particular, we address the problem of sparse representation of graph signals residing on weighted graphs by learning graph structured dictionaries that incorporate the intrinsic geometric structure of the irregular data domain and are adapted to the characteristics of the signals. Then, we move to the efficient processing of graph signals in distributed scenarios, such as sensor or camera networks, which brings important constraints in terms of communication and computation in realistic settings. In particular, we study the effect of quantization in the distributed processing of graph signals that are represented by graph spectral dictionaries and we show that the impact of the quantization depends on the graph geometry and on the structure of the spectral dictionaries. Finally, we focus on a widely used graph process, the problem of distributed average consensus in a sensor network where sensors exchange quantized information with their neighbors. We propose a novel quantization scheme that depends on the graph topology and exploits the increasing correlation between the values exchanged by the sensors throughout the iterations of the consensus algorithm

Applied Harmonic Analysis and Sparse Approximation

Efficiently analyzing functions, in particular multivariate functions, is a key problem in applied mathematics. The area of applied harmonic analysis has a significant impact on this problem by providing methodologies both for theoretical questions and for a wide range of applications in technology and science, such as image processing. Approximation theory, in particular the branch of the theory of sparse approximations, is closely intertwined with this area with a lot of recent exciting developments in the intersection of both. Research topics typically also involve related areas such as convex optimization, probability theory, and Banach space geometry. The workshop was the continuation of a first event in 2012 and intended to bring together world leading experts in these areas, to report on recent developments, and to foster new developments and collaborations