A Riemannian framework for matching point clouds represented by the Schrödinger distance transform.
A Riemannian framework for matching point clouds represented by the Schrödinger distance transform.
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DOI：
10.1109/cvpr.2014.486
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发表时间：
2014-06
期刊：
影响因子：
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通讯作者：
Vemuri BC
中科院分区：
文献类型：
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作者：
Deng Y;Rangarajan A;Eisenschenk S;Vemuri BC
在本文中，我们将点云匹配问题转化为形状匹配问题，将每个给定的点云转换为称为薛定谔距离变换（SDT）表示的形状表示。这是通过求解静态薛定谔方程而不是相应的静态哈密顿-雅可比方程来实现的。SDT表示是一个解析表达式，并且遵循理论物理文献，可以被归一化为具有单位L2范数-使其成为平方根密度，其与单位希尔伯特球面上的点相识别，其内在几何形状是完全已知的。Fisher-Rao度量是密度空间的一种自然度量，它导致了这个球面上点之间的测地线距离的解析表达式。在本文中，我们使用著名的黎曼框架从未用于点云匹配，并提出了一种新的匹配算法。在这个框架中，我们提出了刚性和非刚性变换下的点集匹配，并使用标准的非线性优化技术解决了变换。最后，我们的算法被称为SDTM的性能进行评估，我们提出了几个合成和真实的数据的例子沿着与国家的最先进的技术进行广泛的比较。实验表明，我们的算法优于国家的最先进的点集配准算法在许多定量指标。
In this paper, we cast the problem of point cloud matching as a shape matching problem by transforming each of the given point clouds into a shape representation called the Schrödinger distance transform (SDT) representation. This is achieved by solving a static Schrödinger equation instead of the corresponding static Hamilton-Jacobi equation in this setting. The SDT representation is an analytic expression and following the theoretical physics literature, can be normalized to have unit L2 norm—making it a square-root density, which is identified with a point on a unit Hilbert sphere, whose intrinsic geometry is fully known. The Fisher-Rao metric, a natural metric for the space of densities leads to analytic expressions for the geodesic distance between points on this sphere. In this paper, we use the well known Riemannian framework never before used for point cloud matching, and present a novel matching algorithm. We pose point set matching under rigid and non-rigid transformations in this framework and solve for the transformations using standard nonlinear optimization techniques. Finally, to evaluate the performance of our algorithm—dubbed SDTM—we present several synthetic and real data examples along with extensive comparisons to state-of-the-art techniques. The experiments show that our algorithm outperforms state-of-the-art point set registration algorithms on many quantitative metrics.