Improving Difference Operators by Local Feature Detection
Differential operators are required to compute several characteristics for continuous surfaces, as e.g. tangents, curvature, flatness, shape descriptors. We propose to replace differential operators by the combined action of sets of feature detectors and locally adapted difference operators. A set of simple local feature detectors is used to find the fitting function which locally yields the best approximation for the digitized image surface. For each class of fitting functions, we determine which difference operator locally yields the best result in comparison to the differential operator. Both the set of feature detectors and the difference operator for a function class have a rigid mathematical structure, which can be described by Groebner bases. In this paper we describe how to obtain discrete approximates for the Laplacian differential operator and how these difference operators improve the performance of the Laplacian of Gaussian edge detector.
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