Determining number of clusters and prototype locations via multi-scale clustering
Pattern Recognition Letters
The Topological Structure of Scale-Space Images
Journal of Mathematical Imaging and Vision
Clustering by Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mean Shift: A Robust Approach Toward Feature Space Analysis
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
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
Mode estimation using pessimistic scale space tracking
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
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We present a hierarchical clustering method for a dataset based on the deep structure of the probability density function (PDF) of the data in the scale space. The data clusters correspond to the modes of the PDF, and their hierarchy is determined by regarding the nonparametric estimation of the PDF with the Gaussian kernel as a scale-space representation. It is shown that the number of clusters is statistically deterministic above a certain critical scale, even though the positions of the data points are stochastic. Such a critical scale is estimated by analysing the distribution of cluster lifetime in the scale space, and statistically valid clusters are detected above the critical scale. This cluster validation using the critical scale can be recursively employed according to the hierarchy of the clusters.