Heat Equation to 3D Image Segmentation

Nikolay Sirakov

This paper presents a new approach, capable of 3D image segmentation and objects’ surface reconstruction. The main advantages of the method are: large capture range; quick segmentation of a 3D scene/image to regions; multiple 3D objects reconstruction. The method uses centripetal force and penalty function to segment the entire 3D scene/image to regions containing a single 3D object. Each region is inscribed in a convex, smooth closed surface, which defines a centripetal force. Then the surface is evolved by the geometric heat differential equation toward the force’s direction. The penalty function is defined to stop evolvement of those surface patches, whose normal vectors encountered object’s surface. On the base of the theoretical model Forward Difference Algorithm was developed and coded by Mathematica. Stability convergence condition, truncation error and calculation complexity of the algorithm are determined. The obtained results, advantages and disadvantages of the method are discussed at the end of this paper.

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