Estimation of Vector Fields in Unconstrained and Inequality Constrained Variational Problems for Segmentation and Registration

  • Gozde Unal
  • Greg Slabaugh


Vector fields arise in many problems of computer vision, particularly in non-rigid registration. In this paper, we develop coupled partial differential equations (PDEs) to estimate vector fields that define the deformation between objects, and the contour or surface that defines the segmentation of the objects as well. We also explore the utility of inequality constraints applied to variational problems in vision such as estimation of deformation fields in non-rigid registration and tracking. To solve inequality constrained vector field estimation problems, we apply tools from the Kuhn-Tucker theorem in optimization theory. Our technique differs from recently popular joint segmentation and registration algorithms, particularly in its coupled set of PDEs derived from the same set of energy terms for registration and segmentation. We present both the theory and results that demonstrate our approach.


Variational problems Equality constraints Inequality constraints Kuhn-Tucker theorem Vector fields Nonrigid registration Joint registration and segmentation Tracking 


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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Faculty of Engineering and Natural SciencesSabanci UniversityTuzlaTurkey
  2. 2.Intelligent Vision and ReasoningSiemens Corporate ResearchPrincetonUSA

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