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1. The Erdös distance problem
by Garbaldi, Julia, 1976 and Iosevich, Alex, 1967 and Senger, Steven, 1982
2011, Student mathematical library, ISBN 9780821852811, Volume 56, xii, 150
Geometry | Harmonic analysis | Combinatorial analysis | Number theory
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2. Full Text Euclidean distance geometry and applications
by Liberti, Leo and Lavor, Carlile and Maculan, Nelson and Mucherino, Antonio
SIAM Review, ISSN 0036-1445, 2014, Volume 56, Issue 1, pp. 3 - 69
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data... 
Sensor network | Protein conformation | Bar-and-joint framework | Graph rigidity | Inverse problem | Matrix completion | inverse problem | MATHEMATICS, APPLIED | BUILDUP ALGORITHM | matrix completion | protein conformation | PROGRAMMING RELAXATION | INVERSE KINEMATICS | bar-and-joint framework | graph rigidity | SYNCHRONIZATION | INDIVIDUAL-DIFFERENCES | sensor network | GLOBAL OPTIMIZATION | GENERIC RIGIDITY | SENSOR NETWORK LOCALIZATION | POSITIVE SEMIDEFINITE | Euclidean geometry | Usage | Analysis | Conformational analysis | Geometry, Plane | Distances | Tests, problems and exercises | Geometry, Solid | Bioinformatics | Computer Science | Operations Research
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3. Full Text Shape Classification Using the Inner-Distance
by Haibin Ling and Jacobs, D.W
IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 02/2007, Volume 29, Issue 2, pp. 286 - 299
Part structure and articulation are of fundamental importance in computer and human vision. We propose using the inner-distance to build shape descriptors that... 
Computer vision | Shape measurement | shape | Humans | texture | MPEG 7 Standard | shape distance | articulation | Object recognition | Jacobian matrices | Databases | Euclidean distance | Robustness | Testing | invariants | Articulation | Shape | Shape distance | Texture | Invariants | object recognition | SHOCK GRAPHS | PARTS | REPRESENTATION | COMPONENTS | CURVES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | computer vision | DEFORMATIONS | Reproducibility of Results | Algorithms | Artificial Intelligence | Image Interpretation, Computer-Assisted - methods | Sensitivity and Specificity | Imaging, Three-Dimensional - methods | Image Enhancement - methods | Pattern Recognition, Automated - methods | Euclidean geometry | Machine vision | Analysis | Geometry, Plane | Pattern recognition | Object recognition (Computers) | Methods | Geometry, Solid | Studies | Construction | Human motion | Articulated | Classification | Shortest-path problems | Surface layer
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4. Full Text 2D Euclidean distance transform algorithms
: A comparative survey
by Fabbri, Ricardo and Costa, Luciano Da and Torelli, Julio and Bruno, Odemir
ACM Computing Surveys (CSUR), ISSN 0360-0300, 02/2008, Volume 40, Issue 1, pp. 1 - 44
The distance transform (DT) is a general operator forming the basis of many methods in computer vision and geometry, with great potential for practical... 
computational geometry | performance evaluation | shape analysis | exact Euclidean distance map | Dijkstra's algorithm | Distance transform | Performance evaluation | Computational geometry | Exact Euclidean distance map | Shape analysis | graph integrity constraints | ARBITRARY DIMENSIONS | languages | VISION | LINEAR-TIME ALGORITHM | DIGITAL IMAGES | CLASSIFICATION | graph database models | MAPS | management | design | graph query languages | database models | BINARY IMAGES | COMPUTER SCIENCE, THEORY & METHODS | COMPUTATION | VORONOI DIAGRAMS | PROPAGATION | database systems | graph databases
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5. Full Text Fast Exact Euclidean Distance (FEED): A New Class of Adaptable Distance Transforms
by Schouten, Theo E and van den Broek, Egon L
IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 11/2014, Volume 36, Issue 11, pp. 2159 - 2172
A new unique class of foldable distance transforms of digital images (DT) is introduced, baptized: Fast exact euclidean distance (FEED) transforms. FEED class... 
Algorithm design and analysis | Image Representation | languages | Segmentation | Region growing | distance transformation | Transforms | Computational Geometry and Object Modeling | Search problems | Computing Methodologies | distance transform | benchmark | Computer Graphics | and systems | Euclidean distance | Image Processing and Computer Vision | Approximation algorithms | partitioning | Geometric algorithms | Feeds | Morphological | COMPUTE | LINEAR-TIME ALGORITHM | Voronoi | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | adaptive | Fast exact euclidean distance (FEED) | VORONOI DIAGRAMS | PROPAGATION | computational complexity | Usage | Approximation theory | Image processing | Mathematical optimization | Methods | Innovations | Algorithms | Approximation | Intelligence | Tiles | Disengaging | Images | Pattern analysis
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6. Full Text The Mahalanobis distance
by De Maesschalck, R and Jouan-Rimbaud, D and Massart, D.L
Chemometrics and Intelligent Laboratory Systems, ISSN 0169-7439, 2000, Volume 50, Issue 1, pp. 1 - 18
The theory of many multivariate chemometrical methods is based on the measurement of distances. The Mahalanobis distance (MD), in the original and principal... 
Mahalanobis distance | Euclidean distance | Principal components | CHEMISTRY, ANALYTICAL | OUTLIER DETECTION | MULTIVARIATE | CLASSIFICATION | STATISTICS & PROBABILITY | CHROMATOGRAPHY | CONTROL CHARTS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | INSTRUMENTS & INSTRUMENTATION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PATTERN-RECOGNITION | REGULARIZED DISCRIMINANT-ANALYSIS | principal components | NEAR-INFRARED SPECTRA | AUTOMATION & CONTROL SYSTEMS | STATISTICAL PROCESS-CONTROL
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7. Full Text Distance Distributions in Regular Polygons
by Khalid, Z and Durrani, S
IEEE Transactions on Vehicular Technology, ISSN 0018-9545, 06/2013, Volume 62, Issue 5, pp. 2363 - 2368
This paper derives the exact cumulative density function (cdf) of the distance between a randomly located node and any arbitrary reference point inside a... 
Geometry | Wireless networks | Distance distributions | regular polygons | Euclidean distance | Probability density function | Density functional theory | random distances | Vectors | Indexes | wireless networks | PROBABILITY | UNIFORMLY RANDOM NETWORKS | AD-HOC NETWORKS | TRANSPORTATION SCIENCE & TECHNOLOGY | TELECOMMUNICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | Wireless sensor networks | Usage | Frequency modulation | Innovations | Distribution (Probability theory) | Research | Mathematical optimization
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8. Full Text PARTIAL DISTANCE CORRELATION WITH METHODS FOR DISSIMILARITIES
by Gábor J. Székely and Maria L. Rizzo
The Annals of Statistics, ISSN 0090-5364, 12/2014, Volume 42, Issue 6, pp. 2382 - 2412
Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties,... 
Covariance | Random sampling | False positive errors | Correlations | Inner products | Mantels | Hilbert spaces | Euclidean space | Mathematical vectors | Covariance matrices | Partial distance correlation | Dissimilarity | Multivariate | Energy statistics | Independence | partial distance correlation | HETEROSIS | TESTS | energy statistics | STATISTICS | multivariate | STATISTICS & PROBABILITY | dissimilarity | COVARIANCE | DEPENDENCE | 62H15 | 62H20 | 62Gxx | 62Hxx
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9. Full Text DISTANCE COVARIANCE IN METRIC SPACES
by Russell Lyons
The Annals of Probability, ISSN 0091-1798, 9/2013, Volume 41, Issue 5, pp. 3284 - 3305
We extend the theory of distance (Brownian) covariance from Euclidean spaces, where it was introduced by Székely, Rizzo and Bakirov, to general metric spaces.... 
Embeddings | Covariance | Center of gravity | Separable spaces | Hilbert spaces | Fourier transformations | Euclidean space | Mathematical moments | Random variables | Hypothesis testing | Distance correlation | Brownian covariance | Negative type | Independence | POSITIVE-DEFINITE FUNCTIONS | hypothesis testing | STATISTICS & PROBABILITY | independence | distance correlation | 62H15 | 30L05 | 62G20 | 62H20 | 51K99
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10. Full Text Inverse Sparse Tracker With a Locally Weighted Distance Metric
by Dong Wang and Huchuan Lu and Ziyang Xiao and Ming-Hsuan Yang
IEEE Transactions on Image Processing, ISSN 1057-7149, 09/2015, Volume 24, Issue 9, pp. 2646 - 2657
Sparse representation has been recently extensively studied for visual tracking and generally facilitates more accurate tracking results than classic methods.... 
Target tracking | Shape | Object tracking | Noise | Image reconstruction | Euclidean distance | Visual tracking | APPEARANCE MODEL | K-SELECTION | RECOGNITION | REPRESENTATION | ROBUST VISUAL TRACKING | inverse sparse tracker | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | sparse representation | robust distance | OBJECT TRACKING | ENGINEERING, ELECTRICAL & ELECTRONIC | Robust statistics | Usage | Mathematical optimization | Analysis
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11. Full Text On the Euclidean distance of images
by Liwei Wang and Yan Zhang and Jufu Feng
IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 08/2005, Volume 27, Issue 8, pp. 1334 - 1339
We present a new Euclidean distance for images, which we call image Euclidean distance (IMED). Unlike the traditional Euclidean distance, IMED takes into... 
Support vector machines | positive definite function | Image recognition | Smoothing methods | Face recognition | Support vector machine classification | Euclidean distance | Robustness | Linear discriminant analysis | Index Terms- Image metric | Image classification | Principal component analysis | Image metric | Positive definite function | image metric | face recognition | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Information Storage and Retrieval - methods | Artificial Intelligence | Humans | Image Interpretation, Computer-Assisted - methods | Models, Statistical | Biometry - methods | Subtraction Technique | Algorithms | Models, Biological | Computer Simulation | Face - anatomy & histology | Image Enhancement - methods | Pattern Recognition, Automated - methods | Cluster Analysis | Geometry, Plane | Image coding | Euclidean geometry | Geometry, Solid | Databases | Perturbation methods | Images | Transforms | Transformations
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12. Full Text Reverse Nearest Neighbors in Unsupervised Distance-Based Outlier Detection
by Radovanovic, Milos and Nanopoulos, Alexandros and Ivanovic, Mirjana
IEEE Transactions on Knowledge and Data Engineering, ISSN 1041-4347, 05/2015, Volume 27, Issue 5, pp. 1369 - 1382
Outlier detection in high-dimensional data presents various challenges resulting from the "curse of dimensionality." A prevailing view is that distance... 
Context | Histograms | Correlation | Euclidean distance | high-dimensional data | Educational institutions | Outlier detection | reverse nearest neighbors | Noise measurement | distance concentration | Standards | COMPUTER SCIENCE, INFORMATION SYSTEMS | ALGORITHMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Object recognition (Computers) | Research | Pattern recognition | Methods | Estimating techniques | Data analysis | Production methods | Outliers (statistics) | Lists | Data sets | Labels | Counting
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13. Full Text Asymmetric Distances for Binary Embeddings
by Gordo, Albert and Perronnin, Florent and Yunchao Gong and Lazebnik, Svetlana
IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 01/2014, Volume 36, Issue 1, pp. 33 - 47
In large-scale query-by-example retrieval, embedding image signatures in a binary space offers two benefits: data compression and search efficiency. While most... 
Algorithm design and analysis | asymmetric distances | Large-scale retrieval | Quantization (signal) | binary codes | Euclidean distance | Vectors | Matrix decomposition | Kernel | Principal component analysis | Asymmetric distances | Binary codes | SCENE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Error-correcting codes | Usage | Image processing | Hashing functions | Iterative methods (Mathematics) | Innovations | Data compression | Algorithms | Asymmetry
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14. Full Text Beyond Distance Measurement: Constructing Neighborhood Similarity for Video Annotation
by Meng Wang and Xian-Sheng Hua and Jinhui Tang and Richang Hong
IEEE Transactions on Multimedia, ISSN 1520-9210, 04/2009, Volume 11, Issue 3, pp. 465 - 476
In the past few years, video annotation has benefited a lot from the progress of machine learning techniques. Recently, graph-based semi-supervised learning... 
Machine learning algorithms | Content based retrieval | Error analysis | Humans | Neighborhood similarity | video annotation | Learning systems | Euclidean distance | Machine learning | Semisupervised learning | Distance measurement | Large-scale systems | semi-supervised learning | Video annotation | Semi-supervised learning | COMPUTER SCIENCE, SOFTWARE ENGINEERING | COMPUTER SCIENCE, INFORMATION SYSTEMS | TELECOMMUNICATIONS | Studies | Learning | Multimedia | Algorithms | Annotations | Similarity | Classification | Labels
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15. Full Text A kernel semi-supervised distance metric learning with relative distance: Integration with a MOO approach
by Sanodiya, Rakesh Kumar and Saha, Sriparna and Mathew, Jimson
Expert Systems With Applications, ISSN 0957-4174, 07/2019, Volume 125, pp. 233 - 248
Metric learning, which aims to determine an appropriate distance function to measure the similarity and dissimilarity between data points accurately, is one of... 
Semi supervised classification | Clustering | Multi objective optimization | Bregman projection | Metric learning | FEATURE-SELECTION | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | GENETIC ALGORITHM | ENGINEERING, ELECTRICAL & ELECTRONIC | Computer science | Usage | Algorithms | Data mining | Machine learning | Cluster analysis | Euclidean geometry | Data points | Human motion | Similarity | Vector quantization | Labelling | Moving object recognition | Smartphones | Kernels | Activity recognition | Multiple objective
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16. Full Text Improved Iris Recognition through Fusion of Hamming Distance and Fragile Bit Distance
by Hollingsworth, K. P and Bowyer, K. W and Flynn, P. J
IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 12/2011, Volume 33, Issue 12, pp. 2465 - 2476
The most common iris biometric algorithm represents the texture of an iris using a binary iris code. Not all bits in an iris code are equally consistent. A bit... 
Biometrics | score fusion | Hamming distance | fragile bits | Iris biometrics | Cameras | Iris recognition | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Measurement | Robust statistics | Euclidean geometry | Usage | Frequency modulation | Innovations | Geometry, Plane | Graph theory | Pattern recognition | Geometry, Solid | Analysis | Gates (Electronics) | Object recognition (Computers) | Codes | Algorithms | Intelligence | Images | Surface layer | Pattern analysis | Texture | Recognition
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17. Full Text Multiscale Distance Matrix for Fast Plant Leaf Recognition
by Rongxiang Hu and Wei Jia and Haibin Ling and Deshuang Huang
IEEE Transactions on Image Processing, ISSN 1057-7149, 11/2012, Volume 21, Issue 11, pp. 4667 - 4672
In this brief, we propose a novel contour-based shape descriptor, called the multiscale distance matrix, to capture the shape geometry while being invariant to... 
Training | Histograms | Shape | multiscale distance matrix (MDM) | plant leaf | Euclidean distance | inner distance | Feature extraction | Cost matrix | shape recognition | Principal component analysis | NONRIGID SHAPES | REPRESENTATION | SINGLE CLOSED CONTOUR | IDENTIFICATION | EFFICIENT | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Reproducibility of Results | Algorithms | Artificial Intelligence | Plant Leaves - anatomy & histology | Image Processing, Computer-Assisted - methods | Pattern Recognition, Automated - methods | Plant Leaves - classification | Databases, Factual | Usage | Image processing | Scalability | Analysis | Innovations | Time-series analysis | Graph theory | Pattern recognition | Object recognition (Computers)
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18. Full Text Distance transform network for shape analysis
by Ribas, Lucas Correia and Neiva, Mariane Barros and Bruno, Odemir Martinez
Information Sciences, ISSN 0020-0255, 01/2019, Volume 470, pp. 28 - 42
Shape is known as an important source of information in object analyzes and has been studied for many years for this context. In the object classification... 
Shape classification | Shape analysis | Complex network | Euclidean distance transform | RECOGNITION | ALGORITHM | FOURIER | COMPUTER SCIENCE, INFORMATION SYSTEMS | TEXTURE ANALYSIS | CLASSIFICATION | DESCRIPTORS
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