Mathematical morphology for structure without translation symmetry
Signal Processing
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
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Locally adaptable mathematical morphology using distance transformations
Pattern Recognition
Image filtering using morphological amoebas
Image and Vision Computing
Theoretical Foundations of Spatially-Variant Mathematical Morphology Part I: Binary Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Theoretical Foundations of Spatially-Variant Mathematical Morphology Part II: Gray-Level Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Morphological bilateral filtering and spatially-variant adaptive structuring functions
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
General adaptive neighborhood viscous mathematical morphology
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Adaptive structuring elements based on salience information
ICCVG'12 Proceedings of the 2012 international conference on Computer Vision and Graphics
Adaptive morphology using tensor-based elliptical structuring elements
Pattern Recognition Letters
Conditional Toggle Mappings: Principles and Applications
Journal of Mathematical Imaging and Vision
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The standard morphological operators are (i) defined on Euclidean space, (ii) based on structuring elements, and (iii) invariant with respect to translation. There are several ways to generalise this. One way is to make the operators adaptive by letting the size or shape of structuring elements depend on image location or on image features. Another one is to extend translation invariance to more general invariance groups, where the shape of the structuring element spatially adapts in such a way that global group invariance is maintained. We review group-invariant morphology, discuss the relations with adaptive morphology, point out some pitfalls, and show that there is no inherent incompatibility between a spatially adaptive structuring element and global translation invariance of the corresponding morphological operators.