Paper
26 August 1996 Optimal compressions and retrieval of point patterns through minimal spanning tree representations
Christophe Dussert, Annabelle Chardin
Author Affiliations +
Proceedings Volume 2785, Vision Systems: New Image Processing Techniques; (1996) https://doi.org/10.1117/12.248557
Event: Lasers, Optics, and Vision for Productivity in Manufacturing I, 1996, Besancon, France
Abstract
Spatial point pattern recognition is a frequent step, sometimes the last one, in a general pattern recognition process. Some techniques have been devised to this purpose, generally based on graphs. From statistical geometry considerations we demonstrate the optimal graph representation to be the minimal spanning tree one. The minimal spanning tree (MST) is a graph which provides several ways to analyze the topography (spatial relationships) of objects sets: global degree of order (the so-called m-sigma diagram), hierarchical classification (single linkage cluster analysis), non-hierarchical pattern recognition (by graph theory or anisotropy diagrams). The statistical geometry derivation, based on the maximum entropy principle, leads as well to estimate the allowed compression rate of information by using this graph. Anyway the best test of an information compression quality is to compare the original pattern to the retrieved one. We have thus investigated various ways to reconstruct those patterns from information derived, with various compression levels, from the MST. Among them one of the most promising (figure) is the simulated annealing technique with parameters related to the statistical geometry of the graph. Starting from the hypothesis that the analysis of the spatial patterns of objects may lead to display and determine the interactions and control processes between the objects which have induced those patterns, the MST is well suited to analyze these interactions simultaneously at the local and global levels. The method has been applied to the analysis of physical as well as biological systems.
© (1996) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Christophe Dussert and Annabelle Chardin "Optimal compressions and retrieval of point patterns through minimal spanning tree representations", Proc. SPIE 2785, Vision Systems: New Image Processing Techniques, (26 August 1996); https://doi.org/10.1117/12.248557
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KEYWORDS
Pattern recognition

Statistical analysis

Biological research

Algorithms

Monte Carlo methods

Process control

Chemical species

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