Analysis of the map-seeking circuit

Jan Jelinek

doi:10.1117/12.719722

30 April 2007 Analysis of the map-seeking circuit

Jan Jelinek

Proceedings Volume 6560, Intelligent Computing: Theory and Applications V; 656008 (2007) https://doi.org/10.1117/12.719722
Event: Defense and Security Symposium, 2007, Orlando, Florida, United States

Abstract

Arathorn developed a new theory to address the translation, rotation, scale and perspective invariance problem in vision. According to it, both natural and machine vision systems may be built using a basic block which he calls the map-seeking circuit. In his recent book¹, he informally describes the circuit and a number of simulation studies to illustrate his ideas and support his claims. In this paper, we complement his work by providing mathematical analysis of the circuit. We first construct difference equations describing its dynamics and study when they converge to a steady state which represents the circuit's interpretation of the input scene image. We then show that the state corresponds to the minimum of an upper bound on the difference between the input image and its reconstruction done by the circuit using its built-in banks of object memories and construction operators. The fact that the upper bound can be constructed and minimized directly in a computationally efficient and numerically robust manner, without having to recourse to the map-seeking circuit simulation, makes our alternative approach attractive for applications. We explain why the upper bound is not always tight, which leads to the collusion and other matching errors noticed by Arathorn.

Citation Download Citation

Jan Jelinek "Analysis of the map-seeking circuit", Proc. SPIE 6560, Intelligent Computing: Theory and Applications V, 656008 (30 April 2007); https://doi.org/10.1117/12.719722

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