A Hitherto Unnoticed Singularity of Scale-Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multiresolution Hierarchical Approach to Image Segmentation Based on Intensity Extrema
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale and the differential structure of images
Image and Vision Computing - Special issue: information processing in medical imaging 1991
Scale and segmentation of grey-level images using maximum gradient paths
Image and Vision Computing - Special issue: information processing in medical imaging 1991
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
The Gaussian scale-space paradigm and the multiscale local jet
International Journal of Computer Vision
Probabilistic Multiscale Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Topological Numbers and Singularities in Scalar Images: Scale-Space Evolution Properties
Journal of Mathematical Imaging and Vision
Determining number of clusters and prototype locations via multi-scale clustering
Pattern Recognition Letters
Medical Image Analysis: Progress over Two Decades and the Challenges Ahead
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Geometry-Driven Diffusion in Computer Vision
Geometry-Driven Diffusion in Computer Vision
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
International Journal of Computer Vision - Joint special issue on image analysis
Gaussian Scale-Space Theory
Pseudo-Linear Scale-Space Theory
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
The Morphological Structure of Images: The Differential Equations of Morphological Scale-Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Multiscale Gradient Magnitude Watershed Segmentation
ICIAP '97 Proceedings of the 9th International Conference on Image Analysis and Processing-Volume I - Volume I
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
CAIP '95 Proceedings of the 6th International Conference on Computer Analysis of Images and Patterns
On manifolds in Gaussian scale space
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Gradient watersheds in morphological scale-space
IEEE Transactions on Image Processing
Image segmentation and analysis via multiscale gradient watershed hierarchies
IEEE Transactions on Image Processing
The hierarchical structure of images
IEEE Transactions on Image Processing
Exploring and exploiting the structure of saddle points in Gaussian scale space
Computer Vision and Image Understanding
Combining invariance, robustness, and stability in computer vision
CGIM '08 Proceedings of the Tenth IASTED International Conference on Computer Graphics and Imaging
Tree edit distances from singularity theory
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
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In order to investigate the deep structure of Gaussian scale space images, one needs to understand the behaviour of critical points under the influence of blurring. We show how the mathematical framework of catastrophe theory can be used to describe the different types of annihilations and the creation of pairs of critical points and how this knowledge can be exploited in a scale space hierarchy tree for the purpose of a topology based segmentation. A key role is played by scale space saddles and iso-intensity manifolds through them. We discuss the role of non-generic catastrophes and their influence on the tree and the segmentation. Furthermore it is discussed, based on the structure of iso-intensity manifolds, why creations of pairs of critical points don't influence the tree. We clarify the theory with an artificial image and a simulated MR image.