  Active contour models have been widely used in image segmentation, and the
level set method (LSM) is the most popular approach for solving the models, via
implicitly representing the contour by a level set function. However, the LSM
suffers from high computational burden and numerical instability, requiring
additional regularization terms or re-initialization techniques. In this paper,
we use characteristic functions to implicitly represent the contours, propose a
new representation to the geodesic active contours 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. In addition,
the ICTM enjoys most desired features 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 proposed method not
only obtains comparable or even better segmentation results (compared to the
LSM) but also achieves significant acceleration.
