arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2005.11864math.NAcs.CVcs.NA
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一种由点云数据重建曲面的高效迭代法

An efficient iterative method for reconstructing surface from point clouds

University of Utah(犹他大学)

Dong Wang

摘要:

从点云数据重建曲面是计算机视觉中许多应用的基础步骤。在本文中,我们开发了一个有效的迭代法的变分模型的表面重建从点云。该表面隐式地由指示函数表示,然后基于这种表示使用热核卷积来近似能量泛函。然后,我们开发了一种新的迭代法,以尽量减少近似能量,并证明了在每次迭代过程中的能量衰减性质。然后,我们使用渐近展开,给出了所提出的算法和活动轮廓模型之间的连接。在二维和三维欧几里得空间中进行了大量的数值实验,结果表明,所提出的方法是简单、有效和准确的。

英文摘要:

Surface reconstruction from point clouds is a fundamental step in many applications in computer vision. In this paper, we develop an efficient iterative method on a variational model for the surface reconstruction from point clouds. The surface is implicitly represented by indicator functions and the energy functional is then approximated based on such representations using heat kernel convolutions. We then develop a novel iterative method to minimize the approximate energy and prove the energy decaying property during each iteration. We then use asymptotic expansion to give a connection between the proposed algorithm and active contour models. Extensive numerical experiments are performed in both 2- and 3- dimensional Euclidean spaces to show that the proposed method is simple, efficient, and accurate.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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