تقرير
Efficient Weingarten Map and Curvature Estimation on Manifolds
| العنوان: | Efficient Weingarten Map and Curvature Estimation on Manifolds |
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| المؤلفون: | Cao, Yueqi, Li, Didong, Sun, Huafei, Assadi, Amir H, Zhang, Shiqiang |
| المصدر: | Machine Learning (2021) |
| سنة النشر: | 2019 |
| المجموعة: | Computer Science Mathematics Statistics |
| مصطلحات موضوعية: | Statistics - Machine Learning, Computer Science - Computer Vision and Pattern Recognition, Computer Science - Machine Learning, Mathematics - Differential Geometry |
| الوصف: | In this paper, we propose an efficient method to estimate the Weingarten map for point cloud data sampled from manifold embedded in Euclidean space. A statistical model is established to analyze the asymptotic property of the estimator. In particular, we show the convergence rate as the sample size tends to infinity. We verify the convergence rate through simulated data and apply the estimated Weingarten map to curvature estimation and point cloud simplification to multiple real data sets. Comment: 23 pages, 8 figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s10994-021-05953-4 |
| URL الوصول: | http://arxiv.org/abs/1905.10725 |
| رقم الأكسشن: | edsarx.1905.10725 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s10994-021-05953-4 |
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