I am trying to solve this problem by using of Monte-Carlo Flooding algorithm. As result I receive set of semicircles (the picture below), but the requested solution is for trapezoid like polygons. Please, can you suggest me an algorithm by which I will be able to transform this semicircles in polygons? 
How to convert the result of Monte-Carlo Flooding algorithm to set of polygons?
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First, you extract your pieces as contours, using Suzuki-Abe algorithm (Suzuki, S. and Abe, K., Topological Structural Analysis of Digitized Binary Images by Border Following. CVGIP 30 1, pp 32-46 (1985)). You'll get all contours out of your image as they are produced.
Then, you approximate contours into polygons using Ramer-Douglas-Peucker algorithm.
THere is well-known library which does it all - OpenCV, see link for details https://docs.opencv.org/2.4.13.2/modules/imgproc/doc/structural_analysis_and_shape_descriptors.html