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

Optimising Spatial and Tonal Data for PDE-based Inpainting

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimising this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work. In the 1D case, we prove results that provide insights into the difficulty of this problem, and we give evidence that a splitting into spatial and tonal (i.e. function value) optimisation does hardly deteriorate the results. In the 2D setting, we present generic algorithms that achieve a high reconstruction quality even if the specified data is very sparse. To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima. After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error. For homogeneous diffusion inpainting, this comes down to a least squares problem for which we prove that it has a unique solution. We demonstrate that it can be found efficiently with a gradient descent approach that is accelerated with fast explicit diffusion (FED) cycles. Our framework allows to specify the desired density of the inpainting mask a priori. Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED. This is exploited to achieve reconstructions with state-of-the-art quality. We also give an extensive literature survey on PDE-based image compression methods

DISC: Deep Image Saliency Computing via Progressive Representation Learning

Salient object detection increasingly receives attention as an important component or step in several pattern recognition and image processing tasks. Although a variety of powerful saliency models have been intensively proposed, they usually involve heavy feature (or model) engineering based on priors (or assumptions) about the properties of objects and backgrounds. Inspired by the effectiveness of recently developed feature learning, we provide a novel Deep Image Saliency Computing (DISC) framework for fine-grained image saliency computing. In particular, we model the image saliency from both the coarse- and fine-level observations, and utilize the deep convolutional neural network (CNN) to learn the saliency representation in a progressive manner. Specifically, our saliency model is built upon two stacked CNNs. The first CNN generates a coarse-level saliency map by taking the overall image as the input, roughly identifying saliency regions in the global context. Furthermore, we integrate superpixel-based local context information in the first CNN to refine the coarse-level saliency map. Guided by the coarse saliency map, the second CNN focuses on the local context to produce fine-grained and accurate saliency map while preserving object details. For a testing image, the two CNNs collaboratively conduct the saliency computing in one shot. Our DISC framework is capable of uniformly highlighting the objects-of-interest from complex background while preserving well object details. Extensive experiments on several standard benchmarks suggest that DISC outperforms other state-of-the-art methods and it also generalizes well across datasets without additional training. The executable version of DISC is available online: http://vision.sysu.edu.cn/projects/DISC.Comment: This manuscript is the accepted version for IEEE Transactions on Neural Networks and Learning Systems (T-NNLS), 201

Recent Progress in Image Deblurring

This paper comprehensively reviews the recent development of image deblurring, including non-blind/blind, spatially invariant/variant deblurring techniques. Indeed, these techniques share the same objective of inferring a latent sharp image from one or several corresponding blurry images, while the blind deblurring techniques are also required to derive an accurate blur kernel. Considering the critical role of image restoration in modern imaging systems to provide high-quality images under complex environments such as motion, undesirable lighting conditions, and imperfect system components, image deblurring has attracted growing attention in recent years. From the viewpoint of how to handle the ill-posedness which is a crucial issue in deblurring tasks, existing methods can be grouped into five categories: Bayesian inference framework, variational methods, sparse representation-based methods, homography-based modeling, and region-based methods. In spite of achieving a certain level of development, image deblurring, especially the blind case, is limited in its success by complex application conditions which make the blur kernel hard to obtain and be spatially variant. We provide a holistic understanding and deep insight into image deblurring in this review. An analysis of the empirical evidence for representative methods, practical issues, as well as a discussion of promising future directions are also presented.Comment: 53 pages, 17 figure