Computational geometry: an introduction
Computational geometry: an introduction
A Multiresolution Hierarchical Approach to Image Segmentation Based on Intensity Extrema
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Shock Graphs and Shape Matching
International Journal of Computer Vision
The Topological Structure of Scale-Space Images
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
What Do Features Tell about Images?
Scale-Space '01 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
Many-to-many matching of scale-space feature hierarchies using metric embedding
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in 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
Image reconstruction from multiscale critical points
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Many-to-many graph matching via metric embedding
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Exploring and exploiting the structure of saddle points in Gaussian scale space
Computer Vision and Image Understanding
Top-points as interest points for image matching
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Using top-points as interest points for image matching
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
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In previous work, singular points (or top points) in the scale space representation of generic images have proven valuable for image matching. In this paper, we propose a construction that encodes the scale space description of top points in the form of a directed acyclic graph. This representation allows us to utilize graph matching algorithms for comparing images represented in terms of top point configurations instead of using solely the top points and their features in a point matching algorithm, as was done previously. The nodes of the graph represent the critical paths together with their top points. The edge set will capture the neighborhood distribution of vertices in scale space, and is constructed through a Delaunay triangulation scheme. We also will present a many-to-many matching algorithm for comparing such graph-based representations. This algorithm is based on a metric-tree representation of labelled graphs and their low-distortion embeddings into normed vector spaces via spherical encoding. This is a two-step transformation that reduces the matching problem to that of computing a distribution-based distance measure between two such embeddings. To evaluate the quality of our representation, two sets of experiments are considered. First, the stability of this representation under Gaussian noise of increasing magnitude is examined. In the second set of experiments, a series of recognition experiments is run on a small face database.