Optimal Weighting Functions for Feature Detection

One approach to feature detection is to match a parametric model of the feature to the image data. Naturally, the performance of such detectors is highly dependent upon the function used to measure the degree of fit between the feature model and the image data. In this paper, we first show how an existing detector can be extended to use a weighted norm as the matching function with minimal extra computation. Next, we propose optimality criteria for the two fundamental aspects of feature detection performance: feature detection robustness and parameter estimation accuracy. We also show how to combine these criteria in various ways. We analyze the optimality criterion for parameter estimation under the approximating assumption that the feature manifold is locally linear. We also present a numerical algorithm that can be used to estimate the optimal weighting functions for the other optimality criteria. We include the results of applying this algorithm for step edge, line, and corner features.

[1]  Manfred H. Hueckel.  An Operator Which Locates Edges in Digitized Pictures , 1971, J. ACM.

[2]  Manfred H. Hueckel.  A Local Visual Operator Which Recognizes Edges and Lines , 1973, JACM.

[3]  C. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[4]  R. Plackett,et al.  Principles of regression analysis , 1961 .

[5]  Steven W. Zucker,et al.  A Three-Dimensional Edge Operator , 1981, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  A. C. Aitken.  IV.—On Least Squares and Linear Combination of Observations , 1936 .

[7]  Frank O'Gorman,et al.  Edge Detection Using Walsh Functions , 1976, Artif. Intell..

[8]  K. Paton.  Picture Description Using Legendre Polynomials , 1975 .

[9]  Thomas O. Binford,et al.  On Detecting Edges , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Ralph Hartley,et al.  A Gaussian-weighted multiresolution edge detector , 1985, Comput. Vis. Graph. Image Process..

[11]  Robert A. Hummel,et al.  Feature detection using basis functions , 1979 .

[12]  I.E. Abdou,et al.  Quantitative design and evaluation of enhancement/thresholding edge detectors , 1979, Proceedings of the IEEE.

[13]  Charles L. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[14]  Karl Rohr,et al.  Recognizing corners by fitting parametric models , 1992, International Journal of Computer Vision.

[15]  Hiroshi Murase,et al.  Parametric Feature Detection , 1996, International Journal of Computer Vision.

[16]  Reiner Lenz,et al.  Optimal filters for the detection of linear patterns in 2-D and higher dimensional images , 1987, Pattern Recognit..

[17]  Keinosuke Fukunaga,et al.  Introduction to Statistical Pattern Recognition , 1972 .

[18]  David G. Morgenthaler.  A new hybrid edge detector , 1981 .

[19]  John F. Canny,et al.  A Computational Approach to Edge Detection , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.