Wavelet Frame Based Multiphase Image Segmentation

Abstract

Wavelet frames have been successfully applied to various image restoration problems, such as denoising, inpainting, and deblurring. However, they are rarely used in geometric applications, except for the recent work of [B. Dong, ]. Motivated by the theoretical connection between wavelet frame based and total variation based image restoration models recently established in [we propose here a convex multiphase segmentation model based on wavelet frame transform. The proposed model allows us to automatically identify complex tubular structures, including blood vessels, leaf vein systems, etc. Numerical results show that our method can extract more details than existing variational methods especially when the image contains different scales of structures. The proposed method is parallelized, and its efficiency is further improved by a graphics processing unit implementation. In addition, we analyze the connection between solutions of the convexified model and the original binary constrained model. Introduction.Multiphase image segmentation, or multiphase labeling, is the process of partitioning an image into multiple regions with respect to specific goals and applications. It is a basic but very important image analysis task that has been extensively investigated for many years. Among all the models, regularization based variational models have proved to be especially successful. Variational models started with the classic work by Mumford and Shah [42] and active contour models [33,39]. Later, the Chan-Vese active contour model [19] and its variants based on level sets and total variation [47] were proposed to improve earlier results in terms of both segmentation accuracy and computation efficiency; see [17,19,34,35]. However, the quality of the Chan-Vese model relies on initializations due to the nonconvexity of the model. The Mumford-Shah model is a special case of the classical Potts model in a discrete setting. The general Potts model consists of solving the image segmentation problem by minimizing a sum of the lengths of the boundaries of the regions and data fidelity, and it is known that solving the Potts model is NP hard for multiphase cases [5]. Many kinds of

Duality for Frames

“…Wavelet frame related algorithms have been developed to solve medical and biological image processing problems, e.g. medical image segmentation [44,113], X-ray computer tomography (CT) image reconstruction [47], and protein molecule 3D reconstruction from electron microscopy images [83]. Frames provide large flexibility in designing filters with improved performance in applications.…”

A Hybrid Segmentation and D-Bar Method for Electrical Impedance Tomography

“…In the following, we present a primal-dual splitting method used in [60,29,17,65]. Denote u = (u 1 , · · · , u K ), f = (f 1 , · · · , f K ) and J(u) = K k=1 Ω g(x)|∇u k |dx and u, f = K k=1 Ω u k (x)f k (x)dx, then the convex minimization problem is rewritten as: (20) u * = arg min…”

A variational model for thin structure segmentation based on a directional regularization

“…In the context of tubular structures, extensions of the Chan-Vese model have been proposed by adding tubular priors, e.g., superellipsoids [10], B-splines framelet [11], adaptive dictionaries [12] and elastical regularization [13]. In [14], we also proposed a variational approach for tubular structure restoration.…”