Multiple Widths Yield Reliable Finite Differences (Computer Vision)
IEEE Transactions on Pattern Analysis and Machine Intelligence
An analysis of image interpolation, differentiation, and reduction using local polynomial fits
Graphical Models and Image Processing
A Discrete Expression of Canny's Criteria for Step Edge Detector Performances Evaluation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Digital Step Edges from Zero Crossing of Second Directional Derivatives
IEEE Transactions on Pattern Analysis and Machine Intelligence
Improving difference operators by local feature detection
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Fast polynomial segmentation of digitized curves
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Analysis and comparative evaluation of discrete tangent estimators
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Adaptive and optimal difference operators in image processing
Pattern Recognition
Optimal difference operator selection
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
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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.