Wavelet Frames Based Multi-phase Image Segmentation

Wavelet frames have been successfully applied to various image restoration problems, such as denoising, inpainting, deblurring, etc. However, they are rarely used in geometric applications, except for recent work of [22, 23]. Motivated by the theoretical connection between wavelet frames based and total variation based image restoration models recently established in [8], we propose here a convex multi-phase segmentation model based on wavelet frames transform. The proposed model allows us to automatically identify complex tubular structures, including blood vessels, leaf vein system, 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 GPU implementation. In addition, we analyze the connection between solutions of the convexified model and the original binary constrained one.