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

Tight-frame, a generalization of orthogonal wavelets, has been used successfully in various problems in image processing, including inpainting, impulse noise removal, and superresolution image restoration. Segmentation is the process of identifying object outlines within images. There are quite a few efficient algorithms for segmentation such as model-based approaches, pattern recognition techniques, tracking-based approaches, and artificial intelligence--based approaches. In this paper, we propose applying the tight-frame approach to automatically identify tube-like structures in medical imaging, with the primary application of segmenting blood vessels in magnetic resonance angiography images. Our method iteratively refines a region that encloses the potential boundary of the vessels. At each iteration, we apply the tight-frame algorithm to denoise and smooth the potential boundary and sharpen the region. The cost per iteration is proportional to the number of pixels in the image. We prove that the iteration converges in a finite number of steps to a binary image whereby the segmentation of the vessels can be done straightforwardly. Numerical experiments on synthetic and real two-dimensional (2D) and three-dimensional (3D) images demonstrate that our method is more accurate when compared with some representative segmentation methods, and it usually converges within a few iterations.