Image segmentation algorithm based on the Allen-Cahn energy function

In this paper, we introduce a novel algorithm for image segmentation, which is based on the Allen-Cahn (AC) energy function. Our methodology involves calculating the energy feature at a local level in an image by means of the sliding window technique on the image matrix, which ultimately produces the energy matrix necessary for segmenting the image. Subsequently, constraints are constructed using the extreme values in the energy matrix. By varying the parameters in the constraints and the size of the sliding window, image segmentation results are obtained for different demand purposes. This paper empirically analyzes various simple and complex images, demonstrating the algorithm's effectiveness in segmentation across different complexities and its excellent performance in agronomy and medicine. We also compare our method with other state-of-the-arts and our algorithm exhibits significant advantages in terms of time-saving. In order to further optimise the parameter selection process, we improve the algorithm so that it can autonomously output the parameters that make the segmentation results optimal. Additionally, we conduct experiments on several classical image segmentation datasets, as well as evaluating the segmentation results through the introduction of evaluation metrics, to demonstrate the effectiveness and applicability of our optimised algorithm. Our method demonstrates outstanding performance in image segmentation experiments on the CO-SKEL dataset, with an average segmentation time of 0.2 s. The accuracy exceeds 95%, and precision, recall, and F1 scores all surpass 90%. Even under various noise interferences, the segmentation accuracy of the algorithm remains above 94%, highlighting its efficiency and robustness.