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Equivalence of cost generators for minimum cost flow phase unwrapping

Hubig, Michael and Suchandt, Steffen and Adam, Nico (2002) Equivalence of cost generators for minimum cost flow phase unwrapping. Journal of the Optical Society of America A, 19 (1), pp. 64-70.

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Abstract

Phase unwrapping represents a crucial Step in processing phase data obtained with techniques such as synthetic aperture radar interferometry, speckle interferomtry, and magnetic resonance imaging. The so-called branch-cut approaches form an important class of phase unwrapping algorithms. In 1996, Costantini proposed to transform the problem of correctly placing branch cuts into a minimum cost flow problem [Proceedings of the Fringe ’96 Workshop (European Space Agency, Munich, 1996), pp. 261-272]. The critical point of this new approach is to generate cost functions that have to represent all the a priori knowledge necessary for phase unwrapping. Any function transforming a priori knowledge into a cost function is called a cost generator. Several types of algorithms ranging from heuristic approaches to generators based on probability-theory interpretations were suggested. A problem arising from the growing diversity of algorithms is to find a criterion for the equivalence of different cost generators. Two cost generators are equivalent if they produce cost functions with the same minimal flow for every residue configuration on every image with all possible a priori knowledge. Comparing the results of different cost generators on test scenes can show only their non-equivalence. We solve this problem by proving the following mathematical classification theorem: Two cost generators are equivalent if and only if one can be transformed into the other by multiplication by a fixed constant.

Document Type:Article
Additional Information: LIDO-Berichtsjahr=2002,
Title:Equivalence of cost generators for minimum cost flow phase unwrapping
Authors:
AuthorsInstitution or Email of Authors
Hubig, MichaelUNSPECIFIED
Suchandt, SteffenUNSPECIFIED
Adam, NicoUNSPECIFIED
Date:2002
Journal or Publication Title:Journal of the Optical Society of America A
Refereed publication:Yes
In ISI Web of Science:Yes
Volume:19
Page Range:pp. 64-70
Status:Published
Keywords:Minimum Cost Flow, MCF, Phase Unwrapping, Cost Generator, SAR Interferometry
HGF - Research field:Aeronautics, Space and Transport (old)
HGF - Program:Space (old)
HGF - Program Themes:W EO - Erdbeobachtung
DLR - Research area:Space
DLR - Program:W EO - Erdbeobachtung
DLR - Research theme (Project):UNSPECIFIED
Location: Oberpfaffenhofen
Institutes and Institutions:Remote Sensing Technology Institute
Deposited By: elib DLR-Beauftragter
Deposited On:26 Jan 2006
Last Modified:06 Jan 2010 22:09

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