使用拉普拉斯 - 贝尔特拉米特征函数的热核平滑处理。
Heat kernel smoothing using Laplace-Beltrami eigenfunctions.
作者信息
Seo Seongho, Chung Moo K, Vorperian Houri K
机构信息
Department of Brain and Cognitive Sciences Seoul National University, Korea.
出版信息
Med Image Comput Comput Assist Interv. 2010;13(Pt 3):505-12. doi: 10.1007/978-3-642-15711-0_63.
Abstract
We present a novel surface smoothing framework using the Laplace-Beltrami eigenfunctions. The Green's function of an isotropic diffusion equation on a manifold is constructed as a linear combination of the Laplace-Beltraimi operator. The Green's function is then used in constructing heat kernel smoothing. Unlike many previous approaches, diffusion is analytically represented as a series expansion avoiding numerical instability and inaccuracy issues. This proposed framework is illustrated with mandible surfaces, and is compared to a widely used iterative kernel smoothing technique in computational anatomy. The MATLAB source code is freely available at http://brainimaging.waisman.wisc.edu/ chung/lb.
摘要
我们提出了一种使用拉普拉斯 - 贝尔特拉米特征函数的新型表面平滑框架。流形上各向同性扩散方程的格林函数被构造为拉普拉斯 - 贝尔特拉米算子的线性组合。然后，格林函数被用于构建热核平滑。与许多先前的方法不同，扩散以级数展开的形式进行解析表示，避免了数值不稳定性和不准确性问题。该框架在颌骨表面进行了说明，并与计算解剖学中广泛使用的迭代核平滑技术进行了比较。MATLAB源代码可在http://brainimaging.waisman.wisc.edu/ chung/lb免费获取。
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