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A. J. Roberts, “Use the Information Dimension, Not the Hausdorff,” Nonlinear Sciences, 2005, pp. 1-9.

has been cited by the following article:

  • TITLE: Robust Pre-Attentive Attention Direction Using Chaos Theory for Video Surveillance

    AUTHORS: Michael E. Farmer

    KEYWORDS: Image Change Detection; Image Sequence Analysis; Chaos; Fractals; Nonlinearities

    JOURNAL NAME: Applied Mathematics, Vol.4 No.9A, September 30, 2013

    ABSTRACT: Attention direction for active vision systems has been of substantial interest in the image processing and computer vision communities for video surveillance. Biological vision systems have been shown to possess a hierarchical structure where a pre-attentive processing function directs the visual attention to regions of interest which are then possibly further processed by higher-level vision functions. Biological neural systems are also highly responsive to signals which appear to be chaotic in nature. In this paper we explore applying measures from chaos theory and fractal analysis to provide a robust pre-attentive processing engine for vision. The approach is applied to two standard data sets related to video surveillance for detecting bags left suspiciously in public places. Results compare quite favorably in terms of probability of detection versus false detection rate shown through Receiver Operating Characteristic (ROC) curves against two traditional methods for low-level change detection, namely Mutual Information, Sum of Absolute Differences, and Gaussian Mixture Models.