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
Generic properties of edges and “corners” on smooth greyvalue surfaces
Biological Cybernetics
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Generic evolutions of edges on families of diffused greyvalue surfaces
Journal of Mathematical Imaging and Vision
The Gaussian scale-space paradigm and the multiscale local jet
International Journal of Computer Vision
Topographical Properties of Generic Images
International Journal of Computer Vision
Topological Numbers and Singularities in Scalar Images: Scale-Space Evolution Properties
Journal of Mathematical Imaging and Vision
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
A Computational Method for Segmenting Topological Point-Sets and Application to Image Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Gaussian Scale-Space Theory
Linear Scale-Space has First been Proposed in Japan
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and 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
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
CAIP '95 Proceedings of the 6th International Conference on Computer Analysis of Images and Patterns
Generic transitions of relative critical sets in parametrized families with applications to image analysis
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
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
On the convergence of planar curves under smoothing
IEEE Transactions on Image Processing
Towards a new paradigm for motion extraction
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part I
Deep structure from a geometric point of view
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Tree edit distances from singularity theory
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Add isotropic Gaussian kernels at own risk: more and more resilient modes in higher dimensions
Proceedings of the twenty-eighth annual symposium on Computational geometry
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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 and model 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 non-generic in mathematical sense, they are not unlikely to be encountered in practice due to numerical limitations. Furthermore, the behaviour of these trajectories leads to the observation that fine-to-coarse tracking of critical points doesn't suffice, since they can form closed loops in scale space. The modelling of the trajectories include these loops. We apply the theory to an artificial image and a simulated MR image and show the occurrence of the described behaviour.