Description of 3D digital curves using the theory free groups

Atsushi Imiya; Muneaki Oosawa

doi:10.1117/12.364116

23 September 1999 Description of 3D digital curves using the theory free groups

Atsushi Imiya, Muneaki Oosawa

Proceedings Volume 3811, Vision Geometry VIII; (1999) https://doi.org/10.1117/12.364116
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

In this paper, we propose a new descriptor for two- and three- dimensional digital curves using the theory of free groups. A spatial digital curve is expressed as a word which is an element of the free group which consists from three elements. These three symbols correspond to the directions of the orthogonal coordinates, respectively. Since a digital curve is treated as a word which is a sequence of alphabetical symbols, this expression permits us to describe any geometric operation as rewriting rules for words. Furthermore, the symbolic derivative of words yields geometric invariants of digital curves for digital Euclidean motion. These invariants enable us to design algorithms for the matching and searching procedures of partial structures of digital curves. Moreover, these symbolic descriptors define the global and local distances for digital curves as an editing distance.

Citation Download Citation

Atsushi Imiya and Muneaki Oosawa "Description of 3D digital curves using the theory free groups", Proc. SPIE 3811, Vision Geometry VIII, (23 September 1999); https://doi.org/10.1117/12.364116

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