Anisotropic Mesh Adaptation for Image Segmentation Based on Mumford-Shah Functional
This work addresses efficiency and accuracy challenges in image segmentation for high-resolution digital images, representing an incremental improvement over existing methods.
The paper tackles image segmentation for high-resolution images by developing a new algorithm that combines anisotropic mesh adaptation with the finite element method to solve a PDE model based on the Mumford-Shah functional, resulting in faster and better results compared to traditional finite difference methods without resizing images.
As the resolution of digital images increase significantly, the processing of images becomes more challenging in terms of accuracy and efficiency. In this paper, we consider image segmentation by solving a partial differentiation equation (PDE) model based on the Mumford-Shah functional. We develop a new algorithm by combining anisotropic mesh adaptation for image representation and finite element method for solving the PDE model. Comparing to traditional algorithms solved by finite difference method, our algorithm provides faster and better results without the need to resizing the images to lower quality. We also extend the algorithm to segment images with multiple regions.