Image Segmentation using Backward Stochastic Differential Equations
Dariusz Borkowski
⚠ This is a preprint. It may change before it is accepted for publication.

Abstract

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. The segmentation algorithm is based on the BSDEs approximation methodology. 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.

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