Decomposition based on Object of Convex Shapes Using Poisson Equation

This paper proposes a novel procedure that uses a combination of overlapped basic convex shapes to decompose 2D silhouette image. A basic convex shape is used here as a structuring element to give a meaningful interpretation to 2D images. Poisson equation is utilized to obtain the basic shapes for either the whole image or a partial region or segment of an image. The reconstruction procedure is used to combine the basic convex shapes to generate the original shape. The decomposition process involves a merging stage, filtering stage and finalized by compromising stage. The merging procedure is based on solving Poisson’s equation for two regions satisfying the same symmetrical conditions which leads to finding equivalencies between basic shapes that need to be merged. We implemented and tested our novel algorithm using 2D silhouette images. The test results showed that the proposed algorithm lead to an efficient shape decomposition procedure that transforms any shape into a simpler basic convex shapes.