IEEE TRANSACTIONS ON IMAGE PROCESSING 1 Divergence of Gradient Convolution: Deformable Segmentation with Arbitrary Initializations

Abstract—In this paper, we propose a unified approach to de-formable model based segmentation. The fundamental force field of the proposed method is based on computing the divergence of a gradient convolution field (GCF), which makes full use of directional information of the image gradient vectors and their interactions across image domain. However, instead of directly using such a vector field for deformable segmentation as in conventional approaches, we derive a more salient representation for contour evolution, and very importantly we demonstrate that this representation of image force field not only leads to global minimum through convex relaxation but also can achieve the same result using conventional gradient descent with an intrinsic regularization. Thus, the proposed method can handle arbitrary initializations. The proposed external force field for deformable segmentation has both edge-based properties in that GCF is computed from image gradients, and region-based attributes since its divergence can be treated as a region indication function. Moreover, nonlinear diffusion can be conveniently applied to GCF to improve its performance in dealing with noise inter-ference. We also show the extension of GCF from 2-D to 3-D. In comparison to state-of-the-art deformable segmentation techniques, the proposed method shows greater flexibility in model initialization and optimization realization, as well as better performance toward noise interference and appearance variation. Index Terms—Deformable models, gradient convolution diver-gence, initialization invariance, global minimization, nonlinear diffusion, level set method. I