2011/08/13 by Xiaohao Cai, Raymond Chan, Cai, Xiaohao +5
Computer Science · Engineering · #Advanced Image Fusion Techniques #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Medical Image Segmentation Techniques #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1109.0217
openalex publication_date 2011/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Tight-frame, a generalization of orthogonal wavelets, has been used successfully in various problems in image processing, including inpainting, impulse noise removal, super-resolution image restoration, etc. Segmentation is the process of identifying object outlines within images. There are quite a few efficient algorithms for segmentation that depend on the variational approach and the partial differential equation (PDE) modeling. In this paper, we propose to apply the tight-frame approach to automatically identify tube-like structures such as blood vessels in Magnetic Resonance Angiography (MRA) images. Our method iteratively refines a region that encloses the possible boundary or surface of the vessels. In each iteration, we apply the tight-frame algorithm to denoise and smooth the possible boundary and sharpen the region. We prove the convergence of our algorithm. Numerical experiments on real 2D/3D MRA images demonstrate that our method is very efficient with convergence usually within a few iterations, and it outperforms existing PDE and variational methods as it can extract more tubular objects and fine details in the images.