Fast distance preserving level set evolution for medical image segmentation

Accurate and fast image segmentation algorithms are of paramount importance for a wide range of medical imaging applications. Level set algorithms based on narrow band implementation have been among the most widely used segmentation algorithms. However, the accuracy of standard level set algorithms is compromised by the fact that their evolution schemes deteriorate the signed distance level set functions required for accurate computation of normals and curvatures. The most common remedy is to use an ad-hoc reinitialization step to rebuild the signed distance function frequently. Meanwhile, complex upwind finite difference schemes are required for stable evolution. They together make the overall computation expensive. In this paper, we propose a novel fast narrow band distance preserving level set evolution algorithm that eliminates the need for both reinitialization and complex upwind finite difference schemes. This is achieved by incorporating into a variational level set formulation with a signed distance preserving term that regularizes the evolution. As a result, stable, accurate, fast evolution could be obtained using a simple finite difference scheme within a very narrow band, defined as the union of all 3 x 3 pixel blocks around the zero crossing pixels. Also, our method allows the use of larger time step to speed up the convergence while ensuring accurate result, as well as the use of more general and computational efficient initial level set functions rather than the signed distance functions required by standard level set methods. The proposed algorithm has been applied on both synthetic and real images of different modalities with promising results.