A Hitherto Unnoticed Singularity of Scale-Space
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
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
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
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
Combining different types of scale space interest points using canonical sets
SSVM'07 Proceedings of the 1st international conference on Scale space and variational 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
Image processing by minimising Lp norms
Pattern Recognition and Image Analysis
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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 parameter-driven blurring. During this evolution two different types of special points are encountered, the so-called scale space saddles and the catastrophe points, the latter describing the pairwise annihilation and creation of critical points. The mathematical framework of catastrophe theory is used to model nongeneric events that might occur due to e.g. local symmetries in the image. It is shown how this knowledge can be exploited in conjunction with the scale space saddle points, yielding a scale space hierarchy tree that can be used for segmentation. Furthermore the relevance of creations of pairs of critical points with respect to the hierarchy is discussed. We clarify the theory with an artificial image and a simulated MR image.