Computational geometry: an introduction
Computational geometry: an introduction
Partial match retrieval of multidimensional data
Journal of the ACM (JACM)
Algorithms
An O(n log n) algorithm for the all-nearest-neighbors problem
Discrete & Computational Geometry
Vector quantization and signal compression
Vector quantization and signal compression
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Nearest neighbor queries in metric spaces
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Alignment by Maximization of Mutual Information
International Journal of Computer Vision
A Simple Algorithm for Nearest Neighbor Search in High Dimensions
IEEE Transactions on Pattern Analysis and Machine Intelligence
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Approximate nearest neighbors: towards removing the curse of dimensionality
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
Data structures and algorithms for nearest neighbor search in general metric spaces
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Computing nearest neighbors for moving points and applications to clustering
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Locally lifting the curse of dimensionality for nearest neighbor search (extended abstract)
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
An Algorithm for Finding Best Matches in Logarithmic Expected Time
ACM Transactions on Mathematical Software (TOMS)
The Quadtree and Related Hierarchical Data Structures
ACM Computing Surveys (CSUR)
Multidimensional binary search trees used for associative searching
Communications of the ACM
Analysis of range search for random k-d trees
Acta Informatica
Efficient Search for Approximate Nearest Neighbor in High Dimensional Spaces
SIAM Journal on Computing
Similarity Indexing with the SS-tree
ICDE '96 Proceedings of the Twelfth International Conference on Data Engineering
Fast Nearest Neighbor Search in Medical Image Databases
VLDB '96 Proceedings of the 22th International Conference on Very Large Data Bases
Using k-d Trees to Improve the Retrieval Step in Case-Based Reasoning
EWCBR '93 Selected papers from the First European Workshop on Topics in Case-Based Reasoning
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Shape Indexing Using Approximate Nearest-Neighbour Search in High-Dimensional Spaces
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Alignment by maximization of mutual information
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Multi-Modality Image Registration Maximization of Mutual Information
MMBIA '96 Proceedings of the 1996 Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA '96)
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
Locality-sensitive hashing scheme based on p-stable distributions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
The skip quadtree: a simple dynamic data structure for multidimensional data
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Entropy based nearest neighbor search in high dimensions
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
IEEE Transactions on Visualization and Computer Graphics
An Algorithm for Finding Nearest Neighbors
IEEE Transactions on Computers
Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions
Communications of the ACM - 50th anniversary issue: 1958 - 2008
Fast algorithms for the all nearest neighbors problem
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Dynamic half-space reporting, geometric optimization, and minimum spanning trees
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
On local intrinsic dimension estimation and its applications
IEEE Transactions on Signal Processing
High-dimensional entropy estimation for finite accuracy data: R-NN entropy estimator
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
Indexing in large scale image collections: Scaling properties and benchmark
WACV '11 Proceedings of the 2011 IEEE Workshop on Applications of Computer Vision (WACV)
IEEE Transactions on Information Theory
Nearest neighbor pattern classification
IEEE Transactions on Information Theory
Quad-tree based entropy estimator for fast and robust brain image registration
WBIR'12 Proceedings of the 5th international conference on Biomedical Image Registration
| Hi-index | 0.08 |
Information theoretic criteria such as mutual information are often used as similarity measures for inter-modality image registration. For better performance, it is useful to consider vector-valued pixel features. However, this leads to the task of estimating entropy in medium to high dimensional spaces, for which standard histogram entropy estimator is not usable. We have therefore previously proposed to use a nearest neighbor-based Kozachenko-Leonenko (KL) entropy estimator. Here we address the issue of determining a suitable all nearest neighbor (NN) search algorithm for this relatively specific task. We evaluate several well-known state-of-the-art standard algorithms based on k-d trees (FLANN), balanced box decomposition (BBD) trees (ANN), and locality sensitive hashing (LSH), using publicly available implementations. In addition, we present our own method, which is based on k-d trees with several enhancements and is tailored for this particular application. We conclude that all tree-based methods perform acceptably well, with our method being the fastest and most suitable for the all-NN search task needed by the KL estimator on image data, while the ANN and especially FLANN methods being most often the fastest on other types of data. On the other hand, LSH is found the least suitable, with the brute force search being the slowest.