A Hitherto Unnoticed Singularity of Scale-Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
Introduction to algorithms
A Multiresolution Hierarchical Approach to Image Segmentation Based on Intensity Extrema
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Journal of Mathematical Imaging and Vision
Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Following Feature Lines Across Scale
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
The Relevance of Non-Generic Events in Scale Space Models
International Journal of Computer Vision
On the Axioms of Scale Space Theory
Journal of Mathematical Imaging and Vision
Using Catastrophe Theory to Derive Trees from Images
Journal of Mathematical Imaging and Vision
A Linear Image Reconstruction Framework Based on Sobolev Type Inner Products
International Journal of Computer Vision
International Journal of Computer Vision
Content based image retrieval using multiscale top points a feasibility study
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Temporal structure tree in digital linear scale space
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Deep structure from a geometric point of view
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Discrete representation of top points via scale space tessellation
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Multi-scale singularity trees: soft-linked scale-space hierarchies
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
On image reconstruction from multiscale top points
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
The hierarchical structure of images
IEEE Transactions on Image Processing
Geometrical PDEs based on second-order derivatives of gauge coordinates in image processing
Image and Vision Computing
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
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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When an image is filtered with a Gaussian of width @s and @s is considered as an extra dimension, the image is extended to a Gaussian scale-space (GSS) image. In earlier work it was shown that the GSS-image contains an intensity-based hierarchical structure that can be represented as a binary ordered rooted tree. Key elements in the construction of the tree are iso-intensity manifolds and scale-space saddles. A scale-space saddle is a critical point in scale space. When it connects two different parts of an iso-intensity manifold, it is called ''dividing'', otherwise it is called ''void''. Each dividing scale-space saddle is connected to an extremum in the original image via a curve in scale space containing critical points. Using the nesting of the iso-intensity manifolds in the GSS-image and the dividing scale-space saddles, each extremum is connected to another extremum. In the tree structure, the dividing scale-space saddles form the connecting elements in the hierarchy: they are the nodes of the tree. The extrema of the image form the leaves, while the critical curves are represented as the edges. To identify the dividing scale-space saddles, a global investigation of the scale-space saddles and the iso-intensity manifolds through them is needed. In this paper an overview of the situations that can occur is given. In each case it is shown how to distinguish between void and dividing scale-space saddles. Furthermore, examples are given, and the difference between selecting the dividing and the void scale-space saddles is shown. Also relevant geometric properties of GSS images are discussed, as well as their implications for algorithms used for the tree extraction. As main result, it is not necessary to search through the whole GSS image to find regions related to each relevant scale-space saddle. This yields a considerable reduction in complexity and computation time, as shown in two examples.