A Characteristic Function-based Algorithm for Geodesic Active Contours

TL;DR

This paper introduces an efficient characteristic function-based algorithm called ICTM for geodesic active contours, offering comparable or better segmentation results with significantly reduced computational complexity compared to traditional level set methods.

Contribution

The paper proposes a novel characteristic function-based representation and an iterative convolution-thresholding algorithm for geodesic active contours, improving efficiency and stability over existing level set methods.

Findings

ICTM achieves faster segmentation than level set methods.

Segmentation quality is comparable or superior to traditional methods.

Effective on 2D and 3D medical images for various segmentation tasks.

Abstract

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.