Document Detail


On convergence of the Horn and Schunck optical-flow estimation method.
MedLine Citation:
PMID:  15648874     Owner:  NLM     Status:  MEDLINE    
Abstract/OtherAbstract:
The purpose of this study is to prove convergence results for the Horn and Schunck optical-flow estimation method. Horn and Schunck stated optical-flow estimation as the minimization of a functional. When discretized, the corresponding Euler-Lagrange equations form a linear system of equations We write explicitly this system and order the equations in such a way that its matrix is symmetric positive definite. This property implies the convergence Gauss-Seidel iterative resolution method, but does not afford a conclusion on the convergence of the Jacobi method. However, we prove directly that this method also converges. We also show that the matrix of the linear system is block tridiagonal. The blockwise iterations corresponding to this block tridiagonal structure converge for both the Jacobi and the Gauss-Seidel methods, and the Gauss-Seidel method is faster than the (sequential) Jacobi method.
Authors:
Amar Mitiche; Abdol-Reza Mansouri
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Publication Detail:
Type:  Comparative Study; Journal Article; Research Support, Non-U.S. Gov't    
Journal Detail:
Title:  IEEE transactions on image processing : a publication of the IEEE Signal Processing Society     Volume:  13     ISSN:  1057-7149     ISO Abbreviation:  IEEE Trans Image Process     Publication Date:  2004 Jun 
Date Detail:
Created Date:  2005-01-14     Completed Date:  2005-02-10     Revised Date:  2006-11-15    
Medline Journal Info:
Nlm Unique ID:  9886191     Medline TA:  IEEE Trans Image Process     Country:  United States    
Other Details:
Languages:  eng     Pagination:  848-52     Citation Subset:  IM    
Affiliation:
Institut National de la Recherche Scientifique, INRS-EMT, Montreal QC H5A 1K6, Canada. mitiche@inrs-emt.uquebec.ca
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MeSH Terms
Descriptor/Qualifier:
Algorithms*
Artificial Intelligence
Cluster Analysis
Image Enhancement / methods*
Image Interpretation, Computer-Assisted / methods*
Information Storage and Retrieval / methods
Movement*
Numerical Analysis, Computer-Assisted
Pattern Recognition, Automated / methods*
Reproducibility of Results
Sensitivity and Specificity
Signal Processing, Computer-Assisted
Subtraction Technique*
Video Recording / methods*

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine


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