Global computational algebraic topology approach for diffusion

Marie-Flavie Auclair-Fortier; Djemel Ziou; Madjid Allili

doi:10.1117/12.525975

21 May 2004 Global computational algebraic topology approach for diffusion

Marie-Flavie Auclair-Fortier, Djemel Ziou, Madjid Allili

Proceedings Volume 5299, Computational Imaging II; (2004) https://doi.org/10.1117/12.525975
Event: Electronic Imaging 2004, 2004, San Jose, California, United States

Abstract

One physical process involved in many computer vision problems is the heat diffusion process. Such Partial differential equations are continuous and have to be discretized by some techniques, mostly mathematical processes like finite differences or finite elements. The continuous domain is subdivided into sub-domains in which there is only one value. The diffusion equation comes from the energy conservation then it is valid on a whole domain. We use the global equation instead of discretize the PDE obtained by a limit process on this global equation. To encode these physical global values over pixels of different dimensions, we use a computational algebraic topology (CAT)-based image model. This model has been proposed by Ziou and Allili and used for the deformation of curves and optical flow. It introduces the image support as a decomposition in terms of points, edges, surfaces, volumes, etc. Images of any dimensions can then be handled. After decomposing the physical principles of the heat transfer into basic laws, we recall the CAT-based image model and use it to encode the basic laws. We then present experimental results for nonlinear graylevel diffusion for denoising, ensuring thin features preservation.

Citation Download Citation

Marie-Flavie Auclair-Fortier, Djemel Ziou, and Madjid Allili "Global computational algebraic topology approach for diffusion", Proc. SPIE 5299, Computational Imaging II, (21 May 2004); https://doi.org/10.1117/12.525975

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