The algebraic basis of mathematical morphology. I. dilations and erosions
Computer Vision, Graphics, and Image Processing
The algebraic basis of mathematical morphology
CVGIP: Image Understanding
Recursive Implementation of Erosions and Dilations Along Discrete Lines at Arbitrary Angles
IEEE Transactions on Pattern Analysis and Machine Intelligence
On digital distance transforms in three dimensions
Computer Vision and Image Understanding
Directional Morphological Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Lines and Digital Convexity
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Set Connections and Discrete Filtering (Invited Paper)
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Digital Straight Line Segments
IEEE Transactions on Computers
Convex functions on discrete sets
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
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There are various ways to define digital convexity in Z^n. The proposed approach focuses on structuring elements (and not the sets under study), whose digital versions should allow to construct hierarchies of operators satisfying Matheron semi-groups law @c"@l@c"@m=@c"m"a"x"("@l","@m"), where @l is a size factor. In R^n the convenient class is the Steiner one. Its elements are Minkowski sums of segments. We prove that it admits a digital equivalent when the segments of Z^n are Bezout. The conditions under which the Steiner sets are convex in Z^n, and are connected, are established. The approach is then extended to structuring elements that vary according to the law of perspective, and also to anamorphoses, so that the digital Steiner class and its properties can extend to digital spaces as a sphere or a torus.