Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/44400
Title: Analysis of adaptive forward-backward diffusion flows with applications in image processing
Authors: Prasath, V B Surya
Urbano, José Miguel
Vorotnikov, Dmitry
Issue Date: 2015
Publisher: IOP Publishing
Abstract: The nonlinear diffusion model introduced by Perona and Malik (1990 IEEE Trans. Pattern Anal. Mach. Intell. 12 629–39) is well suited to preserve salient edges while restoring noisy images. This model overcomes well-known edge smearing effects of the heat equation by using a gradient dependent diffusion function. Despite providing better denoizing results, the analysis of the PM scheme is difficult due to the forward-backward nature of the diffusion flow. We study a related adaptive forward-backward diffusion equation which uses a mollified inverse gradient term engrafted in the diffusion term of a general nonlinear parabolic equation. We prove a series of existence, uniqueness and regularity results for viscosity, weak and dissipative solutions for such forward-backward diffusion flows. In particular, we introduce a novel functional framework for wellposedness of flows of total variation type. A set of synthetic and real image processing examples are used to illustrate the properties and advantages of the proposed adaptive forward-backward diffusion flows.
Peer review: yes
URI: http://hdl.handle.net/10316/44400
DOI: 10.1088/0266-5611/31/10/105008
Publisher Version: https://doi.org/10.1088/0266-5611/31/10/105008
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

Files in This Item:
File Description SizeFormat 
Urbano_paper6.pdf469.89 kBAdobe PDFView/Open    Request a copy


FacebookTwitterDeliciousLinkedInDiggGoogle BookmarksMySpace
Formato BibTex MendeleyEndnote Degois 

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.