A Geometric Flow Approach for Region-based Image Segmentation-theoretical Analys

本文刊于:《Acta Mathematicae Applicatae Sinica》 2018年第1期

关键词:
L~2-gradient flow;Bi-cubic B-spline;dire

Keywords
L~2-gradient flow;Bi-cubic B-spline;direct method;image segmentation
摘要
     In this paper, we analyze the well-posedness of an image segmentation model. The main idea of that segmentation model is to minimize one energy functional by evolving a given piecewise constant image towards the image to be segmented. The evolution is controlled by a serial of mappings, which can be represented by B-spline basis functions. The evolution terminates when the energy is below a given threshold. We prove that the correspondence between two images in the segmentation model is an injective and surjective mapping under appropriate conditions. We further prove that the solution of the segmentation model exists using the direct method in the calculus of variations. These results provide the theoretical support for that segmentation model.


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