A Fast and Robust Method for Image Segmentation Using Fuzzy Solutions of Partial Differential Equations

In this paper, an efficient method for image segmentation with the help of the fuzzy solutions of partial differential equations is presented. We first designed a Poisson equation model for image segmentation using fuzzy solution technology, which aims to find a fuzzy solution to satisfy precisely the PDEs. Then, an appropriate segmentation model was obtained to extract the boundary of objects, according to the numerical characteristic in fuzzy solving process. Comparison with the previous approaches is provides to validate the validity of the proposed method. Experimental results on synthetic and real-world images demonstrate that the proposed method has good performances in terms of speed, accuracy, robustness against Gaussian noise, and effectiveness in shadow.