An O(n log n) algorithm for the all-nearest-neighbors problem
Discrete & Computational Geometry
Generating textures on arbitrary surfaces using reaction-diffusion
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
SIGMOD '95 Proceedings of the 1995 ACM SIGMOD international conference on Management of data
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
An optimal algorithm for approximate nearest neighbor searching
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
The digital Michelangelo project: 3D scanning of large statues
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Multidimensional binary search trees used for associative searching
Communications of the ACM
Database Systems: The Complete Book
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Proceedings of the conference on Visualization '01
Efficient simplification of point-sampled surfaces
Proceedings of the conference on Visualization '02
R-trees: a dynamic index structure for spatial searching
SIGMOD '84 Proceedings of the 1984 ACM SIGMOD international conference on Management of data
SSD '95 Proceedings of the 4th International Symposium on Advances in Spatial Databases
Estimating surface normals in noisy point cloud data
Proceedings of the nineteenth annual symposium on Computational geometry
Level of Detail for 3D Graphics
Level of Detail for 3D Graphics
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
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ACM SIGGRAPH 2003 Papers
ACM SIGGRAPH 2003 Papers
Locality-sensitive hashing scheme based on p-stable distributions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
The k-Nearest Neighbour Join: Turbo Charging the KDD Process
Knowledge and Information Systems
Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling)
Gorder: an efficient method for KNN join processing
VLDB '04 Proceedings of the Thirtieth international conference on Very large data bases - Volume 30
Fast algorithms for the all nearest neighbors problem
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Redundant bit vectors for quickly searching high-dimensional regions
Proceedings of the First international conference on Deterministic and Statistical Methods in Machine Learning
Post-processing of scanned 3D surface data
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Bounds on the k-neighborhood for locally uniformly sampled surfaces
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
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Algorithms that use point-cloud models make heavy use of the neighborhoods of the points. These neighborhoods are used to compute the surface normals for each point, mollification, and noise removal. All of these primitive operations require the seemingly repetitive process of finding the k nearest neighbors of each point. These algorithms are primarily designed to run in main memory. However, rapid advances in scanning technologies have made available point-cloud models that are too large to fit in the main memory of a computer. This calls for more efficient methods of computing the k nearest neighbors of a large collection of points many of which are already in close proximity. A fast k nearest neighbor algorithm is presented that makes use of the locality of successive points whose k nearest neighbors are sought to significantly reduce the time needed to compute the neighborhood needed for the primitive operation as well as enable it to operate in an environment where the data is on disk. Results of experiments demonstrate an order of magnitude improvement in the time to perform the algorithm and several orders of magnitude improvement in work efficiency when compared with several prominent existing method.