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

Trainable COSFIRE filters for vessel delineation with application to retinal images

Retinal imaging provides a non-invasive opportunity for the diagnosis of several medical pathologies. The automatic segmentation of the vessel tree is an important pre-processing step which facilitates subsequent automatic processes that contribute to such diagnosis. We introduce a novel method for the automatic segmentation of vessel trees in retinal fundus images. We propose a filter that selectively responds to vessels and that we call B-COSFIRE with B standing for bar which is an abstraction for a vessel. It is based on the existing COSFIRE (Combination Of Shifted Filter Responses) approach. A B-COSFIRE filter achieves orientation selectivity by computing the weighted geometric mean of the output of a pool of Difference-of-Gaussians filters, whose supports are aligned in a collinear manner. It achieves rotation invariance efficiently by simple shifting operations. The proposed filter is versatile as its selectivity is determined from any given vessel-like prototype pattern in an automatic configuration process. We configure two B-COSFIRE filters, namely symmetric and asymmetric, that are selective for bars and bar-endings, respectively. We achieve vessel segmentation by summing up the responses of the two rotation-invariant B-COSFIRE filters followed by thresholding. The results that we achieve on three publicly available data sets (DRIVE: Se = 0.7655, Sp = 0.9704; STARE: Se = 0.7716, Sp = 0.9701; CHASE_DB1: Se = 0.7585, Sp = 0.9587) are higher than many of the state-of-the-art methods. The proposed segmentation approach is also very efficient with a time complexity that is significantly lower than existing methods.peer-reviewe

Static/Dynamic Filtering for Mesh Geometry

The joint bilateral filter, which enables feature-preserving signal smoothing according to the structural information from a guidance, has been applied for various tasks in geometry processing. Existing methods either rely on a static guidance that may be inconsistent with the input and lead to unsatisfactory results, or a dynamic guidance that is automatically updated but sensitive to noises and outliers. Inspired by recent advances in image filtering, we propose a new geometry filtering technique called static/dynamic filter, which utilizes both static and dynamic guidances to achieve state-of-the-art results. The proposed filter is based on a nonlinear optimization that enforces smoothness of the signal while preserving variations that correspond to features of certain scales. We develop an efficient iterative solver for the problem, which unifies existing filters that are based on static or dynamic guidances. The filter can be applied to mesh face normals followed by vertex position update, to achieve scale-aware and feature-preserving filtering of mesh geometry. It also works well for other types of signals defined on mesh surfaces, such as texture colors. Extensive experimental results demonstrate the effectiveness of the proposed filter for various geometry processing applications such as mesh denoising, geometry feature enhancement, and texture color filtering

BLADE: Filter Learning for General Purpose Computational Photography

The Rapid and Accurate Image Super Resolution (RAISR) method of Romano, Isidoro, and Milanfar is a computationally efficient image upscaling method using a trained set of filters. We describe a generalization of RAISR, which we name Best Linear Adaptive Enhancement (BLADE). This approach is a trainable edge-adaptive filtering framework that is general, simple, computationally efficient, and useful for a wide range of problems in computational photography. We show applications to operations which may appear in a camera pipeline including denoising, demosaicing, and stylization