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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


Increased IMPACT FACTOR 2013: 0.593
Rank 143 out of 299 in category Mathematics in the 2013 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR): 0.466
Source Normalized Impact per Paper (SNIP): 1.251

Mathematical Citation Quotient 2013: 0.51

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Motion estimation by hybrid diffusion: theory and implementation

L. X. Yang / D. N. Hào / H. Sahli

ETRO/IRIS, Vrije Universiteit Brussel, Pleinlaan 2, B-1050 Brussel, Belgium. E-mails: , ,

Citation Information: Journal of Inverse and Ill-posed Problems jiip. Volume 14, Issue 3, Pages 307–330, ISSN (Online) 1569-3953, ISSN (Print) 0928-0219, DOI: 10.1515/156939406777340900,

Publication History

Published Online:

2D motion field is the velocity field which presents the apparent motion from one image to another one in an image sequence. It provides important motion information and is widely used in image processing and computer vision. In this paper, with the objective of accurate estimation of a 2D dense motion field, a hybrid diffusion model is proposed. The present approach differs from those in the literature in the sense that the diffusion model and its associated objective functional are driven by both the flow field and image, through a nonlinear isotropic diffusion term and a linear anisotropic diffusion term, respectively. The diffusion function in the model is required to be non increasing, non negative, differentiable and bounded. Using Schauder's fixed point theorem, we prove the existence, stability and uniqueness of the solution to the proposed hybrid diffusion model. A semi-implicit finite difference scheme is proposed to implement the hybrid diffusion model. We demonstrate its efficiency and accuracy by experiments on both synthetic and real image sequences.

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