Joint Segmentation and Nonlinear Registration Using Fast Fourier Transform and Total Variation

Chapter
Part of the Association for Women in Mathematics Series book series (AWMS, volume 12)

Abstract

Image segmentation and registration play active roles in machine vision and medical image analysis of historical data. We explore the joint problem of segmenting and registering a template (current) image given a reference (past) image. We formulate the joint problem as a minimization of a functional that integrates two well-studied approaches in segmentation and registration: geodesic active contours and nonlinear elastic registration. The template image is modeled as a hyperelastic material (St. Venant-Kirchhoff model) which undergoes deformations under applied forces. To segment the deforming template, a two-phase level set-based energy is introduced together with a weighted total variation term that depends on gradient features of the deforming template. This particular choice allows for fast solution using the dual formulation of the total variation. This allows the segmenting front to accurately track spontaneous changes in the shape of objects embedded in the template image as it deforms. To solve the underlying registration problem, we use gradient descent and adopt an implicit-explicit method and use the fast Fourier transform.

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Copyright information

© The Author(s) and the Association for Women in Mathematics 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Applied Mathematics & StatisticsCase Western Reserve UniversityClevelandUSA

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