On a finite type Multivalued Shape
Diego Mond\'ejar
TL;DR
This paper reviews the development of Borsuk's Shape Theory and introduces a finite type version of Multivalued Shape using hyperspaces over metric compacta.
Contribution
It presents a new finite type version of Multivalued Shape theory based on hyperspaces, extending previous concepts in shape analysis.
Findings
Introduces a finite type shape construction for metric compacta
Connects Borsuk's Shape Theory with Sanjurjo's Multivalued Shape
Provides a framework for analyzing shapes via hyperspaces
Abstract
We briefly review the origins and development of Borsuk's Theory of Shapes and the Multivalued Shape of Sanjurjo. We use a construction over metric compacta using hyperspaces to define a finite type version.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Digital Image Processing Techniques · Advanced Vision and Imaging