Provable Self-Representation Based Outlier Detection in a Union of Subspaces

Many computer vision tasks involve processing large amounts of data contaminated by outliers, which need to be detected and rejected. While outlier detection methods based on robust statistics have existed for decades, only recently have methods based on sparse and low-rank representation been developed along with guarantees of correct outlier detection when the inliers lie in one or more low-dimensional subspaces. This paper proposes a new outlier detection method that combines tools from sparse representation with random walks on a graph. By exploiting the property that data points can be expressed as sparse linear combinations of each other, we obtain an asymmetric affinity matrix among data points, which we use to construct a weighted directed graph. By defining a suitable Markov Chain from this graph, we establish a connection between inliers/outliers and essential/inessential states of the Markov chain, which allows us to detect outliers by using random walks. We provide a theoretical analysis that justifies the correctness of our method under geometric and connectivity assumptions. Experimental results on image databases demonstrate its superiority with respect to state-of-the-art sparse and low-rank outlier detection methods.Comment: 16 pages. CVPR 2017 spotlight oral presentatio

Graph-Based Decoding in the Presence of ISI

We propose an approximation of maximum-likelihood detection in ISI channels based on linear programming or message passing. We convert the detection problem into a binary decoding problem, which can be easily combined with LDPC decoding. We show that, for a certain class of channels and in the absence of coding, the proposed technique provides the exact ML solution without an exponential complexity in the size of channel memory, while for some other channels, this method has a non-diminishing probability of failure as SNR increases. Some analysis is provided for the error events of the proposed technique under linear programming.Comment: 25 pages, 8 figures, Submitted to IEEE Transactions on Information Theor

Surface networks

© Copyright CASA, UCL. The desire to understand and exploit the structure of continuous surfaces is common to researchers in a range of disciplines. Few examples of the varied surfaces forming an integral part of modern subjects include terrain, population density, surface atmospheric pressure, physico-chemical surfaces, computer graphics, and metrological surfaces. The focus of the work here is a group of data structures called Surface Networks, which abstract 2-dimensional surfaces by storing only the most important (also called fundamental, critical or surface-specific) points and lines in the surfaces. Surface networks are intelligent and “natural ” data structures because they store a surface as a framework of “surface ” elements unlike the DEM or TIN data structures. This report presents an overview of the previous works and the ideas being developed by the authors of this report. The research on surface networks has fou

NEFI: Network Extraction From Images

Networks and network-like structures are amongst the central building blocks of many technological and biological systems. Given a mathematical graph representation of a network, methods from graph theory enable a precise investigation of its properties. Software for the analysis of graphs is widely available and has been applied to graphs describing large scale networks such as social networks, protein-interaction networks, etc. In these applications, graph acquisition, i.e., the extraction of a mathematical graph from a network, is relatively simple. However, for many network-like structures, e.g. leaf venations, slime molds and mud cracks, data collection relies on images where graph extraction requires domain-specific solutions or even manual. Here we introduce Network Extraction From Images, NEFI, a software tool that automatically extracts accurate graphs from images of a wide range of networks originating in various domains. While there is previous work on graph extraction from images, theoretical results are fully accessible only to an expert audience and ready-to-use implementations for non-experts are rarely available or insufficiently documented. NEFI provides a novel platform allowing practitioners from many disciplines to easily extract graph representations from images by supplying flexible tools from image processing, computer vision and graph theory bundled in a convenient package. Thus, NEFI constitutes a scalable alternative to tedious and error-prone manual graph extraction and special purpose tools. We anticipate NEFI to enable the collection of larger datasets by reducing the time spent on graph extraction. The analysis of these new datasets may open up the possibility to gain new insights into the structure and function of various types of networks. NEFI is open source and available http://nefi.mpi-inf.mpg.de