A variational model for thin structure segmentation based on a directional regularization

Tubular structure segmentation is an important task, with many applications in medical image analysis such as vessel segmentation both in 2D and 3D. However, this task is challenging due to the spatial sparsity of these objects, implying a high sensitivity to noise. An important cue in this context is the local orientation of the tubular structures. Using this information, it is possible to regularize the structures without destroying its integrity. In this article, we take advantage of recent advances in orientation estimation to propose a directional regularization prior for tubular structures, suitable for use in a variational framework. We illustrate on both synthetic and 2D real data.