A Discrete Expression of Canny's Criteria for Step Edge Detector Performances Evaluation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multidimensional Systems and Signal Processing
Concrete Math
Distinctive Image Features from Scale-Invariant Keypoints
International Journal of Computer Vision
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
Feature controlled adaptive difference operators
Discrete Applied Mathematics
Optimal difference operator selection
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
SURF: speeded up robust features
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Improving difference operators by local feature detection
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
FPGA-based architecture for the real-time computation of 2-D convolution with large kernel size
Journal of Systems Architecture: the EUROMICRO Journal
Journal of Real-Time Image Processing
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Differential operators are essential in many image processing applications. Previous work has shown how to compute derivatives more accurately by examining the image locally, and by applying a difference operator which is optimal for each pixel neighborhood. The proposed technique avoids the explicit computation of fitting functions, and replaces the function fitting process by a function classification process using a filter bank of feature detection templates. Both the feature detectors and the optimal difference operators have a specific shape and an associated cost, defined by a rigid mathematical structure, which can be described by Grobner bases. This paper introduces a cost criterion to select the operator of the best approximating function class and the most appropriate template size so that the difference operator can be locally adapted to the digitized function. We describe how to obtain discrete approximates for commonly used differential operators, and illustrate how image processing applications can benefit from the adaptive selection procedure for the operators by means of two example applications: tangent computation for digitized object boundaries and the Laplacian of Gaussian edge detector.