Biological Cybernetics
A Hitherto Unnoticed Singularity of Scale-Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
Solid shape
A Multiresolution Hierarchical Approach to Image Segmentation Based on Intensity Extrema
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generic evolutions of edges on families of diffused greyvalue surfaces
Journal of Mathematical Imaging and 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
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
Linear Scale-Space has First been Proposed in Japan
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
Multiscale Gradient Magnitude Watershed Segmentation
ICIAP '97 Proceedings of the 9th International Conference on Image Analysis and Processing-Volume I - Volume I
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
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
An Extensible MRI Simulator for Post-Processing Evaluation
VBC '96 Proceedings of the 4th International Conference on Visualization in Biomedical Computing
CAIP '95 Proceedings of the 6th International Conference on Computer Analysis of Images and Patterns
The Relevance of Non-Generic Events in Scale Space Models
International Journal of Computer Vision
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
Gradient Structure of Image in Scale Space
Journal of Mathematical Imaging and Vision
Critical Scale for Unsupervised Cluster Discovery
MLDM '07 Proceedings of the 5th international conference on Machine Learning and Data Mining in Pattern Recognition
Statistically Valid Graph Representations of Scale-Space Geometry
ICISP '08 Proceedings of the 3rd international conference on Image and Signal Processing
Exploring and exploiting the structure of saddle points in Gaussian scale space
Computer Vision and Image Understanding
Unsupervised cluster discovery using statistics in scale space
Engineering Applications of Artificial Intelligence
IEEE Transactions on Image Processing
Mutual information aspects of scale space images
Pattern Recognition
On manifolds in Gaussian scale space
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Scale-space clustering with recursive validation
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Towards a new paradigm for motion extraction
ICIAR'06 Proceedings of the Third international conference on Image Analysis and Recognition - Volume Part I
Tree-Based tracking of temporal image
GbRPR'05 Proceedings of the 5th IAPR international conference on Graph-Based Representations in Pattern Recognition
Deep structure from a geometric point of view
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Scale-Space hierarchy of singularities
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Figure field analysis of linear scale-space image
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Combinatorial properties of scale space singular points
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Bifurcation of segment edge curves in scale space
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Image processing by minimising Lp norms
Pattern Recognition and Image Analysis
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We investigate the deep structure of a scale space image. We concentrate on scale space critical points—points with vanishing gradient with respect to both spatial and scale direction. We show that these points are always saddle points. They turn out to be extremely useful, since the iso-intensity manifolds through these points provide a scale space hierarchy tree and induce a “pre-segmentation”: a segmentation without a priori knowledge. Furthermore, both these scale space saddles and the so-called catastrophe points form the critical points of the parameterised critical curves—the curves along which the spatial critical points move in scale space. This enables one to localise these two types of special points relatively easy and automatically. Experimental results concerning the hierarchical representation and pre-segmentation are given and show results that correspond to a fair degree to both the mathematical and the intuitive forecast.