A combined segmentation and registration framework with a nonlinear elasticity smoother

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• 作者：Carole Le Guyader^a ;   ; ^{carole.le-guyader@insa-rouen.fr} ; Luminita A. Vese^b ;   ; ^{lvese@math.ucla.edu}
• 关键词：Image segmentation ; Image registration ; Nonlinear elasticity ; Ogden materials ; Saint Venant&ndash ; Kirchhoff materials ; Calculus of variations ; Augmented Lagrangian
• 刊名：Computer Vision and Image Understanding
• 出版年：2011
• 出版时间：December 2011
• 年：2011
• 卷：115
• 期：12
• 页码：1689-1709
• 全文大小：8476 K

文摘

In this paper, we present a new non-parametric combined segmentation and registration method. The shapes to be registered are implicitly modeled with level set functions and the problem is cast as an optimization one, combining a matching criterion based on the active contours without edges for segmentation (Chan and Vese, 2001) and a nonlinear-elasticity-based smoother on the displacement vector field. This modeling is twofold: first, registration is jointly performed with segmentation since guided by the segmentation process; it means that the algorithm produces both a smooth mapping between the two shapes and the segmentation of the object contained in the reference image. Secondly, the use of a nonlinear-elasticity-type regularizer allows large deformations to occur, which makes the model comparable in this point with the viscous fluid registration method. In the theoretical minimization problem we introduce, the shapes to be matched are viewed as Ciarlet¨CGeymonat materials. We prove the existence of minimizers of the introduced functional and derive an approximated problem based on the Saint Venant¨CKirchhoff stored energy for the numerical implementation and solved by an augmented Lagrangian technique. Several applications are proposed to demonstrate the potential of this method to both segmentation of one single image and to registration between two images.