A Mathematical Comparison of Point Detectors

Marco Zuliani (zuliani@ece.ucsb.edu), Vision Research Lab, Electrical 
and Computer Engineering Department, University of California Santa Barbara

Charles Kenney (kenney@ece.ucsb.edu), Vision Research Lab, Electrical 
and Computer Engineering Department, University of California Santa Barbara

Prof. Bangalore S. Manjuanth (manj@ece.ucsb.edu), Electrical and 
Computer Engineering Department, University of California Santa Barbara

Abstract:
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Selecting salient points from two or more images for computing 
correspondences is a fundamental problem in image
analysis. Three methods originally proposed by Harris et al., by Noble 
et al. and by Shi et al. proved to be quite effective and robust and 
have been widely used by the computer vision community. The goal of this 
paper is to analyze these point detectors starting from the algebraic 
and numerical properties of the image auto-correlation matrix. To 
accomplish this task we will first introduce a "natural" constraint that 
needs to be satisfied by any point detector based on the uto-correlation 
matrix. Then, by casting the point detection problem in a mathematical 
framework based on condition theory, we will show that under certain 
hypothesis the point detectors proposed by Noble et al., Shi et al., and 
Kenney et al. are equivalent modulo the choice of a specific matrix 
norm. The results presented in this paper will provide a novel unifying 
description for the most commonly used point detection algorithms.

Paper link:
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http://vision.ece.ucsb.edu/publications/04IVRMarco.pdf