A Fast Algorithm for Geodesic Active Contours with Applications to Medical Image Segmentation

The geodesic active contour model (GAC) is a commonly used segmentation model for medical image segmentation. The level set method (LSM) is the most popular approach for solving the model, via implicitly representing the contour by a level set function. However, the LSM suffers from high computation burden and numerical instability, requiring additional regularization terms or re-initialization techniques. In this paper, we use characteristic functions to implicitly approximate the contours, propose a new representation to the GAC and derive an efficient algorithm termed as the iterative convolution-thresholding method (ICTM). Compared to the LSM, the ICTM is simpler and much more efficient and stable. In addition, the ICTM enjoys most desired features (e.g., topological changes) of the level set-based methods. Extensive experiments, on 2D synthetic, 2D ultrasound, 3D CT, and 3D MR images for nodule, organ and lesion segmentation, demonstrate that the ICTM not only obtains comparable or even better segmentation results (compared to the LSM) but also achieves dozens or hundreds of times acceleration.