Normal estimation on manifolds by gradient learning. (English) Zbl 1245.62029
Summary: Normal estimation is an important topic for processing point cloud data and surface reconstruction in computer graphics. We consider the problem of estimating normals for a (unknown) submanifold of a Euclidean space of codimension 1 from random points on the manifold. We propose a kernel-based learning algorithm in an unsupervised form of gradient learning. The algorithm can be implemented by solving a linear algebra problem. Error analysis is conducted under conditions on the true normals of the manifold and the sampling distribution.
MSC:
| 62G05 | Nonparametric estimation |
| 68T05 | Learning and adaptive systems in artificial intelligence |
| 46N30 | Applications of functional analysis in probability theory and statistics |
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