Journal of Mathematical Imaging and Vision
The Topological Structure of Scale-Space Images
Journal of Mathematical Imaging and Vision
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Gaussian Scale-Space Theory
Journal of Mathematical Imaging and Vision
Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
The Relevance of Non-generic Events in Scale Space Models
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Understanding and Modeling the Evolution of Critical Points under Gaussian Blurring
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Following Feature Lines Across Scale
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Iso-surface extraction in 4D with applications related to scale space
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
The hierarchical structure of images
IEEE Transactions on Image Processing
Using Catastrophe Theory to Derive Trees from Images
Journal of Mathematical Imaging and Vision
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In an ordinary 2D image the critical points and the isophotes through the saddle points provide sufficient information for classifying the image into distinct regions belonging to the extrema (i.e. a collection of bright and dark blobs), together with their nesting due to the saddle isophotes. For scale space images, obtained by convolution of the image with a Gaussian filter at a continuous range of widths for the Gaussian, things are more complicated. Here only scale space saddle points occur. They are related to spatial saddle points and spatial extrema and can thus provide a scale space based segmentation and hierarchy. However, a spatial extremum can be related to multiple scale space saddles. The key to solve this ambiguity is the investigation of both the scale space saddles and the iso-intensity manifolds (the extension of isophotes in scale space) through them. I will describe the different situations that one can encounter in this investigation, which scale space saddles are relevant, give examples and show the difference between selecting the relevant and the non-relevant ("void") scale space saddles.