中文摘要：

针对传统的物理质心在形状弯曲的情况下有可能落在物体外部的问题,提出基于惯性矩的几何质心定义及计算方法.根据惯性矩把传统的质心定义拓展到三维流形上,首先基于热传导方程计算物体内部距离得到物体关于某点的惯性矩;然后采用梯度下降法寻找惯性矩的极小值得到几何质心.该几何质心一定落于物体的内部,并且当输入模型为凸时退化为物理质心.实验结果表明,该方法对噪声和姿势变化不敏感,可用于形状分析等目的..

英文摘要：

In physics,mass center is defined to be the average position with regard to mass distribution,which may be located outside the object when the shape is non-convex.To overcome the disadvantage,we extend masscenter to3-manifold objects based on moments of inertia.We first replace Euclidean distance with interior distanceby exploiting the discrete heat equation,and then minimize the moments by the gradient descent method.Mass center of this new type has two distinguished properties.First,it must be located inside the given object.Second,it degenerates into conventional mass center when the input shape is convex.Therefore,we call it geometric centroid in this paper.Numerous experimental results show that geometric centroid is insensitive to noise and shape deformation,and hopefully helpful for shape analysis.