Grey-Scale Morphology with Spatially-Variant Rectangles in Linear Time
ACIVS '08 Proceedings of the 10th International Conference on Advanced Concepts for Intelligent Vision Systems
Spatially-Variant Morpho-Hessian Filter: Efficient Implementation and Application
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Binary morphology with spatially variant structuring elements: algorithm and architecture
IEEE Transactions on Image Processing
Continuous glass patterns for painterly rendering
IEEE Transactions on Image Processing
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Edge detection using morphological amoebas in noisy images
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Overview of adaptive morphology: trends and perspectives
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Adaptivity and group invariance in mathematical morphology
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Adaptive mathematical morphology: a unified representation theory
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Study on nonlocal morphological operators
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Multi-layer filtering approach for map images
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Spatially-variant structuring elements inspired by the neurogeometry of the visual cortex
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Mathematical morphology on bipolar fuzzy sets: general algebraic framework
International Journal of Approximate Reasoning
An attribute weighted distance transform
Pattern Recognition Letters
Efficient non-linear filter for impulse noise removal in document images
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part III
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
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We develop a general theory of spatially-variant (SV) mathematical morphology for binary images in the Euclidean space. The basic SV morphological operators (i.e., SV erosion, SV dilation, SV opening and SV closing) are defined. We demonstrate the ubiquity of SV morphological operators by providing a SV kernel representation of increasing operators. The latter representation is a generalization of Matheron's representation theorem of increasing and translation-invariant operators. The SV kernel representation is redundant, in the sense that a smaller subset of the SV kernel is sufficient for the representation of increasing operators. We provide sufficient conditions for the existence of the minimal basis representation in terms of upper-semi-continuity in the hit-or-miss topology. The latter minimal basis representation is a generalization of Maragos' minimal basis representation for increasing and translation-invariant operators. Moreover, we investigate the upper-semi-continuity property of the basic SV morphological operators. Several examples are used to demonstrate that the theory of spatially-variant mathematical morphology provides a general framework for the unification of various morphological schemes based on spatiallyvariant geometrical structuring elements (e.g., circular, affine and motion morphology). Simulation results illustrate the theory of the proposed spatially-variant morphological framework and show its potential power in various image processing applications.