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

Unal, G.B. & Slabaugh, G.G. (2008). Estimation of Vector Fields in Unconstrained and Inequality Constrained Variational Problems for Segmentation and Registration. Journal of Mathematical Imaging and Vision, 31(1), pp. 57-72. doi: 10.1007/s10851-008-0064-7

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Abstract

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.

Item Type: Article
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s10851-008-0064-7
Uncontrolled Keywords: Variational problems, Equality constraints, Inequality constraints, Kuhn-Tucker theorem, Vector fields, Nonrigid registration, Joint registration and segmentation, Tracking
Subjects: H Social Sciences > HF Commerce
Q Science > QA Mathematics
Divisions: School of Informatics > Department of Computing
URI: http://openaccess.city.ac.uk/id/eprint/4391

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