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On the Parameter Estimation Accuracy of Model-Matching Feature Detectors

Baker, Simon

The performance of model-fitting feature detectors is critically dependent upon the function used to measure the degree of fit between the feature model and the image data. In this paper, we consider the class of weighted L² norms as potential fitting functions and study the effect which the choice of fitting function has on one particular aspect of performance, namely parameter estimation accuracy. We first derive an optimality criterion based upon how far an ideal feature instance is perturbed around the feature manifold when noise is added to it. We then show that a first-order(linear) approximation to the feature manifold results in the Euclidean L² norm being optimal. We next show empirically that for non-linear manifolds the Euclidean L² norm is no longer, in general, optimal. Finally, we present the results of several experiments comparing the performance of various weighting functions on a number of ubiquitous features.

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Academic Units
Computer Science
Publisher
Department of Computer Science, Columbia University
Series
Columbia University Computer Science Technical Reports, CUCS-011-97
Published Here
April 25, 2011