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Euclidean Distance Mapping
, 1980
"... Based on a twocomponent descriptor, a distance label for each point, it is shown that Euclidean distance maps can be generated by effective sequential algorithms. The map indicates, for each pixel in the objects (or the background) of the originally binary picture, the shortest distance to the near ..."
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Cited by 229 (0 self)
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Based on a twocomponent descriptor, a distance label for each point, it is shown that Euclidean distance maps can be generated by effective sequential algorithms. The map indicates, for each pixel in the objects (or the background) of the originally binary picture, the shortest distance
Euclidean distance.
"... assumed to be between 0 and 1. The initial values of all the weight vectors are given between 0 and 1 at random. (SOM1) Input an input vector xj to all the neurons simultaneously in parallel. (SOM2) Find a winner c by calculating a distance between the input vector xj and the weight vector wi of ea ..."
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assumed to be between 0 and 1. The initial values of all the weight vectors are given between 0 and 1 at random. (SOM1) Input an input vector xj to all the neurons simultaneously in parallel. (SOM2) Find a winner c by calculating a distance between the input vector xj and the weight vector wi
On the Euclidean Distance of Images
 IEEE Trans. Pattern Anal. Mach. Intell
"... Abstract We present a new Euclidean distance for images, which we call IMage Euclidean Distance (IMED). Unlike the traditional Euclidean distance, IMED takes into account the spatial relationships of pixels. Therefore it is robust to small perturbation of images. We argue that IMED is the only intui ..."
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Cited by 33 (1 self)
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Abstract We present a new Euclidean distance for images, which we call IMage Euclidean Distance (IMED). Unlike the traditional Euclidean distance, IMED takes into account the spatial relationships of pixels. Therefore it is robust to small perturbation of images. We argue that IMED is the only
An efficient euclidean distance transform
 In Combinatorial Image Analysis, IWCIA 2004
, 2004
"... Abstract. Within image analysis the distance transform has many applications. The distance transform measures the distance of each object point from the nearest boundary. For ease of computation, a commonly used approximate algorithm is the chamfer distance transform. This paper presents an efficien ..."
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Cited by 17 (0 self)
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an efficient lineartime algorithm for calculating the true Euclidean distancesquared of each point from the nearest boundary. It works by performing a 1D distance transform on each row of the image, and then combines the results in each column. It is shown that the Euclidean distance squared transform
EUCLIDEAN DISTANCE GEOMETRY AND APPLICATIONS
"... Abstract. Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the inputdataconsistsofanincompleteset of distances, and the output is a set of points in Euclidean space that realizes the given distances. We surv ..."
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Cited by 6 (1 self)
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Abstract. Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the inputdataconsistsofanincompleteset of distances, and the output is a set of points in Euclidean space that realizes the given distances. We
Euclidean Distance Matrices and Applications
"... Over the past decade, Euclidean distance matrices, or EDMs, have been receiving increased attention for two main reasons. The first reason is that the many applications of EDMs, such as molecular conformation in bioinformatics, dimensionality reduction in machine learning and statistics, and especia ..."
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Cited by 14 (0 self)
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Over the past decade, Euclidean distance matrices, or EDMs, have been receiving increased attention for two main reasons. The first reason is that the many applications of EDMs, such as molecular conformation in bioinformatics, dimensionality reduction in machine learning and statistics
Convergent Bounds on the Euclidean Distance
"... Given a set V of n vectors in ddimensional space, we provide an efficient method for computing quality upper and lower bounds of the Euclidean distances between a pair of vectors in V. For this purpose, we define a distance measure, called the MSdistance, by using the mean and the standard deviati ..."
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Cited by 2 (0 self)
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Given a set V of n vectors in ddimensional space, we provide an efficient method for computing quality upper and lower bounds of the Euclidean distances between a pair of vectors in V. For this purpose, we define a distance measure, called the MSdistance, by using the mean and the standard
On the eigenvalues of Euclidean distance matrices
, 2008
"... In this paper, the notion of equitable partitions (EP) is used to study the eigenvalues of Euclidean distance matrices (EDMs). In particular, EP is used to obtain the characteristic polynomials of regular EDMs and nonspherical centrally symmetric EDMs. The paper also presents methods for constructi ..."
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Cited by 3 (0 self)
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In this paper, the notion of equitable partitions (EP) is used to study the eigenvalues of Euclidean distance matrices (EDMs). In particular, EP is used to obtain the characteristic polynomials of regular EDMs and nonspherical centrally symmetric EDMs. The paper also presents methods
ON EUCLIDEAN DISTANCE MATRICES OF GRAPHS ∗
"... Abstract. In this paper, a relation between graph distance matrices and Euclidean distance matrices (EDM) is considered. It is proven that distance matrices of paths and cycles are EDMs. The proofs are constructive and the generating points of studied EDMs are given in a closed form. A generalizatio ..."
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Abstract. In this paper, a relation between graph distance matrices and Euclidean distance matrices (EDM) is considered. It is proven that distance matrices of paths and cycles are EDMs. The proofs are constructive and the generating points of studied EDMs are given in a closed form. A
PENALIZED EUCLIDEAN DISTANCE REGRESSION
"... ABSTRACT. A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized Euclidean distance, where the penalty is the geomet ..."
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ABSTRACT. A new method is proposed for variable screening, variable selection and prediction in linear regression problems where the number of predictors can be much larger than the number of observations. The method involves minimizing a penalized Euclidean distance, where the penalty
Results 1  10
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