Image Segmentation Using Backward Stochastic Differential Equations

We introduce a novel image segmentation algorithm based on the methodology of approximating solutions to backward stochastic differential equations (BSDEs). The segmentation method repeats the BSDE reconstruction process, with the parameters of these equations changing in subsequent steps. We are interested in a sequence of images driven by BSDE solutions. As the segmentation result, we define the limit of these images. By their nature, stochastic tools, particularly the Monte Carlo method, have high computational complexity. There are concerns about the running time of the proposed method, especially if we are considering a sequence of stochastic solutions. Experimental segmentation results show that it is possible to obtain results quickly and that the algorithm yields excellent results for images with intense noise.