Locally Regularized Smoothing B-Snake
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Research Article Locally Regularized Smoothing B-Snake ´ ome ˆ Jer Velut, Hugues Benoit-Cattin, and Christophe Odet CREATIS, CNRS UMR 5220, Inserm U 630, INSA, Bˆatiment Blaise Pascal, 69621 Villeurbanne, France Received 22 July 2005; Revised 25 July 2006; Accepted 17 December 2006 Recommended by Jiri Jan We propose a locally regularized snake based on smoothing-spline filtering. The proposed algorithm associates a regularization process with a force equilibrium scheme leading the snake’s deformation. In this algorithm, the regularization is implemented with a smoothing of the deformation forces. The regularization level is controlled through a unique parameter that can vary along the contour. It provides a locally regularized smoothing B-snake that offers a powerful framework to introduce prior knowledge. We illustrate the snake behavior on synthetic and real images, with global and local regularization. ˆ Copyright © 2007 J´erome Velut et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Active contour models (or snakes) are well adapted for edge detection and segmentation. Since snakes were introduced by Kass et al. [1], they have been widely used in many domains and improved using different contour representations and deformation algorithms. Menet et al. [2] proposed the B-snakes that take advantages of the Bspline representation. A local control of the curve continuity and a limited number of processed points increase the convergence speed and the segmentation reliability. At the same time, L. Cohen and I. Cohen [3] focused on external forces that drive the snake toward the features of interest in the image and proposed the balloon force that increases considerably the attainability zone. Then, Xu and Prince [4] defined another external force called gradient vector flow (GVF) that brings a better control on the deformation directions: they proposed to diffuse the gradient over the image according to optical flow theory. Beside these works, the multiresolution frameworks were integrated within the active contours. Wang et al. [5] used a B-spline representation that allows a coarseto-fine evolution of the snake. Brigger et al. [6, 7] extended Wang’s technique with a multiscale approach in both the image and the parametric contour domain. Precioso et al. [8] proposed a region-based active contour that achieves real-time computation adapted to video segmentation. They extended their model by applying a smoothing B-spline filter [9, 10] on the contour. It increases considerably the robustness to noise without additional compu-
tation. Recently, new energies have been proposed by Jacob et al. [11] who unify the edge-based scheme with the regionbased one. Existing snakes suffer from several limitations when a local regularization is wanted. With the original snake [1], a local regularization involves a matrix inversion step at each ite
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