Introduction to mathematical morphology
Computer Vision, Graphics, and Image Processing
Computer Vision, Graphics, and Image Processing
Morphological structuring element decomposition
Computer Vision, Graphics, and Image Processing
Image Analysis Using Mathematical Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
A contour processing method for fast binary neighbourhood operations
Pattern Recognition Letters
Decomposition of gray-scale morphological structuring elements
Pattern Recognition
Separable decompositions and approximations of greyscale morphological templates
CVGIP: Image Understanding
Methods for fast morphological image transforms using bitmapped binary images
CVGIP: Graphical Models and Image Processing
A new set of fast algorithms for mathematical morphology I: idempotent geodesic transforms
CVGIP: Image Understanding
Chamfer metrics, the medial axis and mathematical morphology
Journal of Mathematical Imaging and Vision - Special issue on topology and geometry in computer vision
Journal of Mathematical Imaging and Vision
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Recursive erosion, dilation, opening, and closing transforms
IEEE Transactions on Image Processing
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Mathematical Morphology (MM) is a general method forimage processing based on set theory. The two basic morphologicaloperators are dilation and erosion. From these, several non linearfilters have been developed, usually with polynomial complexity andthis because the two basic operators depend strongly on thedefinition of the structural element. Most efforts to improve thealgorithm's speed for each operator are based on structural elementdecomposition and/or efficient codification.In this second part, the concepts developed in part I(see Díaz de León and Sossa Azuela,“Mathematical morphology based on linear combined metric spaces onZ^1 (part I): Fast distance transforms,”Journal of Mathematical Imaging and Vision, Vol. 12, No. 2,pp. 137–154, 2000)are used to prove that it is possible to reduce the complexity of themorphological operators to zero complexity (constant time algorithms) forany regular discrete metric space and to eliminate the use of the structuralelement. In particular, this is done for an infinite family of metric spacesfurther defined. The use of the distance transformation is proposed for itcomprises the information concerning all the discs included in a region toobtain fast morphological operators: erosions, dilations, openings andclosings (of zero complexity) for an infinite (countable) family of regularmetric spaces. New constant time, in contrast with the polynomial timealgorithms, for the computation of these basics operators for any structuralelement are next derived by using this background. Practical examplesshowing the efficiency of the proposed algorithms, final comments andpresent research are also given here.