Solid shape
A Multiresolution Hierarchical Approach to Image Segmentation Based on Intensity Extrema
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale and segmentation of grey-level images using maximum gradient paths
Image and Vision Computing - Special issue: information processing in medical imaging 1991
The Topological Structure of Scale-Space Images
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
Journal of Mathematical Imaging and 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
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology 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
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
Statistically Valid Graph Representations of Scale-Space Geometry
ICISP '08 Proceedings of the 3rd international conference on Image and Signal Processing
Unsupervised cluster discovery using statistics in scale space
Engineering Applications of Artificial Intelligence
Validation of Watershed Regions by Scale-Space Statistics
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
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We investigate the topological structure of an image and the hierarchical relationship between local and global structures provided by spatial gradients at different levels of scale. The gradient field curves link stationary points of the image including a local minimum at infinity, and construct the topological structure of the image. The evolution of the topological structure with respect to scale is analysed using pseudograph representation. The hierarchical relationships among the structures at different scales are expressed as trajectories of the stationary points in the scale space, which we call stationary curves. Each toppoint of the local extremum curve generically has a specific gradient field curve, which we call the antidirectional figure-flow curve. The antidirectional figure-flow curve connects between the toppoint and another local extremum to which the toppoint is subordinate. A point at infinity can also be connected to the toppoints of local minimum curves. These hierarchical relationships among the stationary points are expressed as a tree. As an application, we present the temporal segmentation of an image sequence based on the transition of the hierarchical structure.