Details:
Title  Feature controlled adaptive difference operators  Author(s)  Kristof Teelen, Peter Veelaert  Type  Article in Journal  Abstract  Differential operators are essential for many image processing applications which require the computation of typical characteristics of 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 adaptive difference operators, resulting in a more accurate computation of the required derivatives in each pixel neighborhood. Both the set of feature detectors and the set of difference operators have a rigid mathematical structure, which is described by a set of Groebner bases for each class of fitting functions. This representation allows a systematic description of the hierarchical structure with ordering relations for all different function classes. The explicit computation of fitting functions is avoided by our technique and replaced by a function classification process. A set of simple local feature detectors is used to find the class of fitting functions which locally yields the best approximation for the digitized image surface. By a systematic optimization process, we determine for each fitting function class a difference operator which is an optimal approximation for a particular differential operator. As an example, we describe how to compute the best discrete approximation for the Laplacian differential operator in each pixel neighborhood and illustrate how the Laplacian of Gaussian edge detection method can benefit from these results.  Keywords  Difference operators, Groebner basis, Local feature detectors  ISSN  0166218X 
URL 
http://www.sciencedirect.com/science/article/pii/S0166218X08002370 
Language  English  Journal  Discrete Applied Mathematics  Volume  157  Number  3  Pages  571  582  Year  2009  Note  International Conference on Discrete Geometry for Computer ImageryDGCI 2006International Conference on Discrete Geometry for Computer Imagery  Edition  0  Translation 
No  Refereed 
No 
