Wavelet Frame Based Multiphase Image Segmentation
Cheng Tai, Xiaoqun Zhang, Zuowei Shen · SIAM Journal on Imaging Sciences · 2013
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, A. Chien, and Z. Shen, Commun. Math. Sci., 9 (2011), pp. 551--559; B. Dong and Z. Shen, in Proceedings of the SPIE, Vol. 8401, 2012, 840102]. Motivated by the theoretical connection between wavelet frame based and total variation based image restoration models recently established in [J.-F. Cai, B. Dong, S. Osher, and Z. Shen, J. Amer. Math. Soc., 25 (2012), pp. 1033--1089], 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.