Efficient Nearest Neighbor Search Using Dynamic Programming
Fuente:
arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866909709606322176 |
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| author | Wang, Pengfei Song, Jiantao Xin, Shiqing Chen, Shuangmin Tu, Changhe Wang, Wenping Wang, Jiaye |
| author_facet | Wang, Pengfei Song, Jiantao Xin, Shiqing Chen, Shuangmin Tu, Changhe Wang, Wenping Wang, Jiaye |
| contents | Given a collection of points in R^3, KD-Tree and R-Tree are well-known nearest neighbor search (NNS) algorithms that rely on space partitioning and spatial indexing techniques. However, when the query point is far from the data points or the data points inherently represent a 2-manifold surface, their query performance may degrade. To address this, we propose a novel dynamic programming technique that precomputes a Directed Acyclic Graph (DAG) to encode the proximity structure between data points. More specifically, the DAG captures how the proximity structure evolves during the incremental construction of the Voronoi diagram of the data points. Experimental results demonstrate that our method achieves a 1x-10x speedup. Additionally, our algorithm demonstrates significant practical value across diverse applications. We validated its effectiveness through extensive testing in four key applications: Point to Mesh Distance Queries, Iterative Closest Point (ICP) Registration, Density Peak Clustering, and Point to Segments Distance Queries. A particularly notable feature of our approach is its unique ability to efficiently identify the nearest neighbor among the first k points in the point cloud a capability that enables substantial acceleration in low-dimensional applications like Density Peak Clustering. As a natural extension of our incremental construction process, our method can also be readily adapted for farthest point sampling tasks. These experimental results across multiple domains underscore the broad applicability and practical importance of our approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_15023 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Efficient Nearest Neighbor Search Using Dynamic Programming Wang, Pengfei Song, Jiantao Xin, Shiqing Chen, Shuangmin Tu, Changhe Wang, Wenping Wang, Jiaye Computational Geometry Graphics Given a collection of points in R^3, KD-Tree and R-Tree are well-known nearest neighbor search (NNS) algorithms that rely on space partitioning and spatial indexing techniques. However, when the query point is far from the data points or the data points inherently represent a 2-manifold surface, their query performance may degrade. To address this, we propose a novel dynamic programming technique that precomputes a Directed Acyclic Graph (DAG) to encode the proximity structure between data points. More specifically, the DAG captures how the proximity structure evolves during the incremental construction of the Voronoi diagram of the data points. Experimental results demonstrate that our method achieves a 1x-10x speedup. Additionally, our algorithm demonstrates significant practical value across diverse applications. We validated its effectiveness through extensive testing in four key applications: Point to Mesh Distance Queries, Iterative Closest Point (ICP) Registration, Density Peak Clustering, and Point to Segments Distance Queries. A particularly notable feature of our approach is its unique ability to efficiently identify the nearest neighbor among the first k points in the point cloud a capability that enables substantial acceleration in low-dimensional applications like Density Peak Clustering. As a natural extension of our incremental construction process, our method can also be readily adapted for farthest point sampling tasks. These experimental results across multiple domains underscore the broad applicability and practical importance of our approach. |
| title | Efficient Nearest Neighbor Search Using Dynamic Programming |
| topic | Computational Geometry Graphics |
| url | https://arxiv.org/abs/2409.15023 |