Generic evolutions of edges on families of diffused greyvalue surfaces
Journal of Mathematical Imaging and Vision
Properties of Ridges and Cores for Two-Dimensional Images
Journal of Mathematical Imaging and Vision
The Topological Structure of Scale-Space Images
Journal of Mathematical Imaging and Vision
Branch Points in One-Dimensional Gaussian Scale Space
Journal of Mathematical Imaging and Vision
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Transitions of the 3D Medial Axis under a One-Parameter Family of Deformations
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Multiscale Gradient Magnitude Watershed Segmentation
ICIAP '97 Proceedings of the 9th International Conference on Image Analysis and Processing-Volume I - Volume I
Symmetry Sets and Medial Axes in Two and Three Dimensions
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
Generic Events for the Gradient Squared with Application to Multi-Scale Segmentation
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
The Relevance of Non-Generic Events in Scale Space Models
International Journal of Computer Vision
Using Catastrophe Theory to Derive Trees from Images
Journal of Mathematical Imaging and Vision
Transitions of a Multi-scale Image Hierarchy Tree
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
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An representation based on the singularity structure of the gradient magnitude over scale is used as the atoms in a space of images. This representation is summarized as a rooted tree. The generic transitions of the functional of the scale space images are analysed and listed for the scale parameter and one free parameter. A distance measure between images is deduced soly from these generic transistions. The singular transitions are translated into the language of the tree transitions such that one generic transition corresponds to one unit edit operation of the tree structure. The distance between two images is the size of the smallest set of edit operations necessary to transform the corresponding tree representations into each other.