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

Adaptive multiresolution analysis based on synchronization

We propose an adaptive multiscale approach to data analysis based on synchronization. The approach is nonlinear, data driven in the sense that it does not rely on a priori chosen basis, and automatically determines the data scale. Numerical results for one- and two-dimensional cases illustrate that the method works effectively for the usual modulated signals such as chirps, etc., as well as for more complicated data with multiple scales. The method extends straightforwardly to functions defined on weighted graphs and grids in high dimensions. Connections with some other recent approaches to multiscale analysis are briefly discussed

Numerics and Fractals

Local iterated function systems are an important generalisation of the standard (global) iterated function systems (IFSs). For a particular class of mappings, their fixed points are the graphs of local fractal functions and these functions themselves are known to be the fixed points of an associated Read-Bajactarevi\'c operator. This paper establishes existence and properties of local fractal functions and discusses how they are computed. In particular, it is shown that piecewise polynomials are a special case of local fractal functions. Finally, we develop a method to compute the components of a local IFS from data or (partial differential) equations.Comment: version 2: minor updates and section 6.1 rewritten, arXiv admin note: substantial text overlap with arXiv:1309.0243. text overlap with arXiv:1309.024

Automatic face recognition using stereo images

Face recognition is an important pattern recognition problem, in the study of both natural and artificial learning problems. Compaxed to other biometrics, it is non-intrusive, non- invasive and requires no paxticipation from the subjects. As a result, it has many applications varying from human-computer-interaction to access control and law-enforcement to crowd surveillance. In typical optical image based face recognition systems, the systematic vaxiability arising from representing the three-dimensional (3D) shape of a face by a two-dimensional (21)) illumination intensity matrix is treated as random vaxiability. Multiple examples of the face displaying vaxying pose and expressions axe captured in different imaging conditions. The imaging environment, pose and expressions are strictly controlled and the images undergo rigorous normalisation and pre-processing. This may be implemented in a paxtially or a fully automated system. Although these systems report high classification accuracies (>90%), they lack versatility and tend to fail when deployed outside laboratory conditions. Recently, more sophisticated 3D face recognition systems haxnessing the depth information have emerged. These systems usually employ specialist equipment such as laser scanners and structured light projectors. Although more accurate than 2D optical image based recognition, these systems are equally difficult to implement in a non-co-operative environment. Existing face recognition systems, both 2D and 3D, detract from the main advantages of face recognition and fail to fully exploit its non-intrusive capacity. This is either because they rely too much on subject co-operation, which is not always available, or because they cannot cope with noisy data. The main objective of this work was to investigate the role of depth information in face recognition in a noisy environment. A stereo-based system, inspired by the human binocular vision, was devised using a pair of manually calibrated digital off-the-shelf cameras in a stereo setup to compute depth information. Depth values extracted from 2D intensity images using stereoscopy are extremely noisy, and as a result this approach for face recognition is rare. This was cofirmed by the results of our experimental work. Noise in the set of correspondences, camera calibration and triangulation led to inaccurate depth reconstruction, which in turn led to poor classifier accuracy for both 3D surface matching and 211) 2 depth maps. Recognition experiments axe performed on the Sheffield Dataset, consisting 692 images of 22 individuals with varying pose, illumination and expressions