146 research outputs found

    Normal variation for adaptive feature size

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    The change in the normal between any two nearby points on a closed, smooth surface is bounded with respect to the local feature size (distance to the medial axis). An incorrect proof of this lemma appeared as part of the analysis of the "crust" algorithm of Amenta and Bern

    Regression Depth and Center Points

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    We show that, for any set of n points in d dimensions, there exists a hyperplane with regression depth at least ceiling(n/(d+1)). as had been conjectured by Rousseeuw and Hubert. Dually, for any arrangement of n hyperplanes in d dimensions there exists a point that cannot escape to infinity without crossing at least ceiling(n/(d+1)) hyperplanes. We also apply our approach to related questions on the existence of partitions of the data into subsets such that a common plane has nonzero regression depth in each subset, and to the computational complexity of regression depth problems.Comment: 14 pages, 3 figure

    GPU LSM: A Dynamic Dictionary Data Structure for the GPU

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    We develop a dynamic dictionary data structure for the GPU, supporting fast insertions and deletions, based on the Log Structured Merge tree (LSM). Our implementation on an NVIDIA K40c GPU has an average update (insertion or deletion) rate of 225 M elements/s, 13.5x faster than merging items into a sorted array. The GPU LSM supports the retrieval operations of lookup, count, and range query operations with an average rate of 75 M, 32 M and 23 M queries/s respectively. The trade-off for the dynamic updates is that the sorted array is almost twice as fast on retrievals. We believe that our GPU LSM is the first dynamic general-purpose dictionary data structure for the GPU.Comment: 11 pages, accepted to appear on the Proceedings of IEEE International Parallel and Distributed Processing Symposium (IPDPS'18

    Largest Placement of One Convex Polygon Inside Another

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    Our aim was to detect tau tangles and beta amyloid plaques in retina for the early diagnosis of Alzheimers Disease (AD)

    Surface Reconstruction from Noisy Point Clouds

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    We show that a simple modification of the power crust algorithm for surface reconstruction produces correct outputs in presence of noise. This is proved using a fairly realistic noise model. Our theoretical results are related to the problem of computing a stable subset of the medial axis. We demostrate the effectiveness of our algorithm with a number of experimental results
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