From level set evolution to threshold optimization: A grayscale level set framework for image segmentation

The segmentation of multiple degradations has been a challenging problem in the field of image segmentation. Existing level set approaches commonly adopt a length regularization term to constrain the geometric shape of the segmentation contour. However, the introduction of the length term often results in numerical instability and high computational cost. In this paper, we show that the length term is not essential under certain smoothness constraints, and theoretically prove that the presence of the length term affects the property of $|\nabla φ|=1$. Based on the finding, we define a class of smooth images, construct the grayscale level set, and propose a fast segmentation framework for degraded images, such as heavily noisy images and intensity inhomogeneous images. The framework transforms PDE evolution into one-dimensional threshold search, which has significant advantages in computational speed, especially on large-scale images. Experiments validate the segmentation performance of the proposed framework on various degraded images.