Abstract
The Perona---Malik equation (PM), in the continuum limit, is interpreted as the gradient flow for a functional, corresponding to the reconstruction of an image with edges with non-zero thickness. This result is based on an image model (u,Γ) where Γ is an edge set, and u is a slowly-varying function. PM simplifies the image by reducing the jump across each component of Γ, resulting in an automatic edge pruning procedure. The initial-value problem thus defined is well-posed, but practically stable only for small times: it leads to a semi-group with exponential growth. The rigorous analysis gives a mathematical basis for empirical observations, including edge localization and the need to use a small number of iterations. The variational formulation enables an easy comparison with earlier methods.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
