The multi-fractal structure of contrast changes in natural images: from sharp edges to textures

We present a formalism that leads very naturally to a hierarchical description of the different contrast structures in images, providing precise definitions of sharp edges and other texture components. Within this formalism, we achieve a decomposition of pixels of the image in sets, the fractal components of the image, such that each set only contains points characterized by a fixed stregth of the singularity of the contrast gradient in its neighborhood. A crucial role in this description of images is played by the behavior of contrast differences under changes in scale. Contrary to naive scaling ideas where the image is thought to have uniform transformation properties \cite{Fie87}, each of these fractal components has its own transformation law and scaling exponents. A conjecture on their biological relevance is also given.Comment: 41 pages, 8 figures, LaTe

Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

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

Information Loss-Guided Multi-Resolution Image Fusion

Spatial downscaling is an ill-posed, inverse problem, and information loss (IL) inevitably exists in the predictions produced by any downscaling technique. The recently popularized area-to-point kriging (ATPK)-based downscaling approach can account for the size of support and the point spread function (PSF) of the sensor, and moreover, it has the appealing advantage of the perfect coherence property. In this article, based on the advantages of ATPK and the conceptualization of IL, an IL-guided image fusion (ILGIF) approach is proposed. ILGIF uses the fine spatial resolution images acquired in other wavelengths to predict the IL in ATPK predictions based on the geographically weighted regression (GWR) model, which accounts for the spatial variation in land cover. ILGIF inherits all the advantages of ATPK, and its prediction has perfect coherence with the original coarse spatial resolution data which can be demonstrated mathematically. ILGIF was validated using two data sets and was shown in each case to predict downscaled images more accurately than the compared benchmark methods

Combining local regularity estimation and total variation optimization for scale-free texture segmentation

Texture segmentation constitutes a standard image processing task, crucial to many applications. The present contribution focuses on the particular subset of scale-free textures and its originality resides in the combination of three key ingredients: First, texture characterization relies on the concept of local regularity ; Second, estimation of local regularity is based on new multiscale quantities referred to as wavelet leaders ; Third, segmentation from local regularity faces a fundamental bias variance trade-off: In nature, local regularity estimation shows high variability that impairs the detection of changes, while a posteriori smoothing of regularity estimates precludes from locating correctly changes. Instead, the present contribution proposes several variational problem formulations based on total variation and proximal resolutions that effectively circumvent this trade-off. Estimation and segmentation performance for the proposed procedures are quantified and compared on synthetic as well as on real-world textures