Optimal compressions and retrieval of point patterns through minimal spanning tree representations

Christophe Dussert; Annabelle Chardin

doi:10.1117/12.248557

26 August 1996 Optimal compressions and retrieval of point patterns through minimal spanning tree representations

Christophe Dussert, Annabelle Chardin

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.

Citation Download Citation

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

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available