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<p><b>Abstract</b>—This paper proposes a statistical framework for computing medial axes of 2D shapes. In this paper, the computation of medial axes is posed as a statistical inference problem not as a mathematical transform. This paper contributes to three aspects in computing medial axes. 1) Prior knowledge is adopted for axes and junctions so that axes around junctions are regularized. 2) Multiple interpretations of axes are possible, each being assigned a probability. 3) A novel stochastic jump-diffusion process is proposed for estimating both axes and junctions in Markov random fields. We argue that the stochastic algorithm for computing medial axes is compatible with existing algorithms for image segmentation, such as region growing [<ref type="bib" rid="bibI115831">31</ref>], snake [<ref type="bib" rid="bibI11587">7</ref>], and region competition [<ref type="bib" rid="bibI115826">26</ref>]. Thus, our method provides a new direction for computing medial axes from texture images. Experiments are demonstrated on both synthetic and real 2D shapes. This algorithm has been successfully applied to shape learning and sampling in a companion paper [<ref type="bib" rid="bibI115830">30</ref>].</p>
Medial axis transform, jump-diffusion process, energy minimization, Markov random field.

S. Zhu, "Stochastic Jump-Diffusion Process for Computing Medial Axes in Markov Random Fields," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 21, no. , pp. 1158-1169, 1999.
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