On the Parameter Estimation Accuracy of Model-Matching Feature Detectors

The performance of modeltting feature detectors is critically dependent upon the function used to measure the degree of t between the feature model and the image data. In this paper, we consider the class of weighted L norms as potential tting functions and study the e ect which the choice of tting function has on one particular aspect of performance, namely parameter estimation accuracy. We rst 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 rst-order (linear) approximation to the feature manifold results in the Euclidean L norm being optimal. We next show empirically that for non-linear manifolds the Euclidean L 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.