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

Encoder-Driven Inpainting Strategy in Multiview Video Compression

In free viewpoint video systems, where a user has the freedom to select a virtual view from which an observation image of the 3D scene is rendered, the scene is commonly represented by texture and depth images from multiple nearby viewpoints. In such representation, there exists data redundancy across multiple dimensions: a single visible 3D voxel may be represented by pixels in multiple viewpoint images (inter-view redundancy), a pixel patch may recur in a distant spatial region of the same image due to self-similarity (inter-patch redundancy), and pixels in a local spatial region tend to be similar (inter-pixel redundancy). It isimportant to exploit these redundancies for effective multiview video compression. Existing schemes attempt to eliminate them via the traditional video coding paradigm of hybrid signal prediction/residual coding; typically, the encoder codes explicit information to guide the decoder to the location of the most similar block along with the signal differential. In this paper, we argue that, given the inherent redundancy in the representation, the decoder can often independently recover missing data via inpainting without explicit directions from encoder, resulting in lower coding overhead. Specifically, after pixels in a reference view are projected to a target view via depth image-based rendering (DIBR) at the decoder, the remaining holes in the target view are filled via an inpainting process in a block-by-block manner. First, blocks are ordered in terms of difficulty-to-inpaint by the decoder. Then, explicit instructions are only sent for the reconstruction of the most difficult blocks. In particular, the missing pixels are explicitly coded via a graph Fourier transform (GFT) or a sparsification procedure using DCT, which leads to low coding cost. For the blocks that are easy to inpaint, the decoder independently completes missing pixels via template-based inpainting. We implemented our encoder-driven inpainting strategy as an extension of High Efficiency Video Coding (HEVC). Experimental results show that our coding strategy can outperform comparable implementation of HEVC by up to 0.8dB in reconstructed image qualit

Design and Optimization of Graph Transform for Image and Video Compression

The main contribution of this thesis is the introduction of new methods for designing adaptive transforms for image and video compression. Exploiting graph signal processing techniques, we develop new graph construction methods targeted for image and video compression applications. In this way, we obtain a graph that is, at the same time, a good representation of the image and easy to transmit to the decoder. To do so, we investigate different research directions. First, we propose a new method for graph construction that employs innovative edge metrics, quantization and edge prediction techniques. Then, we propose to use a graph learning approach and we introduce a new graph learning algorithm targeted for image compression that defines the connectivities between pixels by taking into consideration the coding of the image signal and the graph topology in rate-distortion term. Moreover, we also present a new superpixel-driven graph transform that uses clusters of superpixel as coding blocks and then computes the graph transform inside each region. In the second part of this work, we exploit graphs to design directional transforms. In fact, an efficient representation of the image directional information is extremely important in order to obtain high performance image and video coding. In this thesis, we present a new directional transform, called Steerable Discrete Cosine Transform (SDCT). This new transform can be obtained by steering the 2D-DCT basis in any chosen direction. Moreover, we can also use more complex steering patterns than a single pure rotation. In order to show the advantages of the SDCT, we present a few image and video compression methods based on this new directional transform. The obtained results show that the SDCT can be efficiently applied to image and video compression and it outperforms the classical DCT and other directional transforms. Along the same lines, we present also a new generalization of the DFT, called Steerable DFT (SDFT). Differently from the SDCT, the SDFT can be defined in one or two dimensions. The 1D-SDFT represents a rotation in the complex plane, instead the 2D-SDFT performs a rotation in the 2D Euclidean space