A contour processing method for fast binary neighbourhood operations
Pattern Recognition Letters
A Multiscanning Approach Based on Morphological Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Toward a computational theory of shape: an overview
ECCV 90 Proceedings of the first european conference on Computer vision
Morphological signal processing and the slope transform
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Scale-Space Properties of the Multiscale Morphological Dilation-Erosion
IEEE Transactions on Pattern Analysis and Machine Intelligence
A General Framework for Geometry-Driven Evolution Equations
International Journal of Computer Vision
On the Scale-Space Theorem of Chen and Yan
IEEE Transactions on Pattern Analysis and Machine Intelligence
Hierarchical volume analysis and visualization based on morphological operators
Proceedings of the conference on Visualization '98
Journal of Mathematical Imaging and Vision
International Journal of Computer Vision - Joint special issue on image analysis
International Journal of Computer Vision
A Dynamic Scale–Space Paradigm
Journal of Mathematical Imaging and Vision
Decomposition of Separable Concave Structuring Functions
Journal of Mathematical Imaging and Vision
A Hamiltonian Approach to the Eikonal Equation
EMMCVPR '99 Proceedings of the Second International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Nonlinear PDEs and Numerical Algorithms for Modeling Levelings and Reconstruction Filters
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
Numerical Solution Schemes for Continuous-Scale Morphology
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
Scale-Space Theories for Scalar and Vector Images
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Scale-Spaces, PDE's, and Scale-Invariance
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Fractal Analysis of Bone Images
MMBIA '96 Proceedings of the 1996 Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA '96)
Comparison of Multiscale Representations for a Linking-Based Image Segmentation Model
MMBIA '96 Proceedings of the 1996 Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA '96)
Object-Based Image Analysis Using Multiscale Connectivity
IEEE Transactions on Pattern Analysis and Machine Intelligence
Using Catastrophe Theory to Derive Trees from Images
Journal of Mathematical Imaging and Vision
A Lattice Approach to Image Segmentation
Journal of Mathematical Imaging and Vision
Detecting cartoons: a case study in automatic video-genre classification
ICME '03 Proceedings of the 2003 International Conference on Multimedia and Expo - Volume 2
Improving the accuracy of isotropic granulometries
Pattern Recognition Letters
Morphological multiscale decomposition of connected regions with emphasis on cell clusters
Computer Vision and Image Understanding
Basic morphological operations, band-limited images and sampling
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Families of generalised morphological scale spaces
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Review article: Edge and line oriented contour detection: State of the art
Image and Vision Computing
A numerical-experimental method for damage location based on rotation fields spatial differentiation
Computers and Structures
Segmentation of biological volume datasets using a level-set framework
VG'01 Proceedings of the 2001 Eurographics conference on Volume Graphics
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We introduce a class of nonlinear differential equations that are solved using morphological operations. The erosion and dilation act as morphological propagators propagating the initial condition into the "scale-space", much like the Gaussian convolution is the propagator for the linear diffusion equation. The analysis starts in the set domain, resulting in the description of erosions and dilations in terms of contour propagation. We show that the structuring elements to be used must have the property that at each point of the contour there is a well-defined and unique normal vector. Then given the normal at a point of the dilated contour we can find the corresponding point (point-of-contact) on the original contour. In some situations we can even link the normal of the dilated contour with the normal in the point-of-contact of the original contour. The results of the set domain are then generalized to grey value images. The role of the normal is replaced with the function gradient. The same analysis also holds for the erosion. Using a family of increasingly larger structuring functions we are then able to link infinitesimal changes in grey value with the gradient in the image.