A Multiresolution Hierarchical Approach to Image Segmentation Based on Intensity Extrema
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
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer 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
Calculations on Critical Points under Gaussian Blurring
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
On detecting all saddle points in 2D images
Pattern Recognition Letters
Using Catastrophe Theory to Derive Trees from Images
Journal of Mathematical Imaging and Vision
On manifolds in Gaussian scale space
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
On the number of modes of a Gaussian mixture
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Laplacian eigenimages in discrete scale space
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
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In order to investigate the deep structure of Gaussian scale space images, one needs to understand the behaviour of spatial critical points under the influence of blurring. We show how the mathematical framework of catastrophe theory can be used to describe the behaviour of critical point trajectories when various different types of generic events, viz. annihilations and creations of pairs of spatial critical points, (almost) coincide. Although such events are nongeneric in mathematical sense, they are not unlikely to be encountered in practice. Furthermore the behaviour leads to the observation that fine-to-coarse tracking of critical points doesn't suffice. We apply the theory to an artificial image and a simulated MR image and show the occurrence of the described behaviour.