Shape as an Information-Thermodynamical Concept and the Pattern Recognition Problem

✍ Scribed by Roman S. Ingarden; Lech Górniewicz

• Publisher: John Wiley and Sons
• Year: 1990
• Tongue: English
• Weight: 727 KB
• Volume: 145
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19901450108

✦ Synopsis

A hierarchical classification of different concepts of shape of compact connected sets in Rn (topological, LIPSHITZ, homotopic, BORSTJE and homological shapes) is given. The most general among them is the homological shape. There is only a countable number of homological shapes for connected compact sets in Rn. In the case n = 2 even the number of different BORSUE shapes for connected compact gets is countable. Giving a probability distribution of shapes we can define a shape entropy, a mean shape and shape fluctuations. This enables a formulation of information thermodynamics of shape and its applications to different field6 (physicssmall systems, chemistry, biophysics, pattern recognition). The paper does not develop yet these applications, its aim is to clear the basic notions.