Vessel Segmentation in Medical Imaging Using a Tight-Frame Based Algorithm

• Main Authors: Cai, Xiaohao, Chan, Raymond, Morigi, Serena, Sgallari, Fiorella
• Format: Journal Article
• Language: English
• Published: 13.08.2011
• Subjects: Computer Science - Computer Vision and Pattern Recognition; Mathematics - Numerical Analysis
• DOI: 10.48550/arxiv.1109.0217

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.