Showing papers on "Mahalanobis distance published in 1984"

Distance transformations in arbitrary dimensions

Abstract: In many applications of digital picture processing, distances from certain feature elements to the nonfeature elements must be computed. In two dimensions at least four different families of distance transformations have been suggested, the most popular one being the city block/chessboard distance family. The purpose of this paper is twofold: To generalize these transformations to higher dimensions and to compare the computed distances with the Euclidean distance. All of the four distance transformation families are presented in three dimensions, and the two fastest ones are presented in four and arbitrary dimensions. The comparison with Euclidean distance is given as upper limits for the difference between the Euclidean distance and the computed distances.

Text/continuous tone image decision processor

Abstract: Grayscale image data obtained by scanning a document to be duplicated is partitioned into contiguous image data blocks which are processed to determine whether the portions of the image represented by the data blocks correspond to text or continuous tone portions of the document. An average grayscale value is determined for each data block and used as an indexing variable for at least one additional characteristic determined for the block. Disclosed additional characteristics include a block variance, a block edge count, a block agreement count and a block text average. A one dimensional Gaussian distribution is generated to distribute the data values of any additional characteristics for each possible grayscale value of a block. The mean and standard deviation are determined for each data distribution and the Mahalanobis distance for each characteristic data value is determined. The Mahalanobis distance is a representative probability for whether the image data block corresponds to a text portion of the image or a continuous tone portion of the image.

Some Aspects of Allocation and Discrimination

Abstract: The application of multivariate statistical methods to problems in physical anthropology involves both the allocation of new individuals and the description of group differences. It is not uncommon to find techniques which are appropriate for the description of group differences, such as canonical variate analysis, being used to allocate new individuals (see, e.g., Rightmire, 1979)

On the Determination of Hominid Affinities

Abstract: When comparing populations or classifying unknown specimens on the basis of their morphology, one can either rely on visual comparison or follow an approach which involves the use of the mathematical techniques of discriminant analysis.

Multivariate analysis applied to tomato hybrid production

Abstract: Twenty characters were measured on 60 tomato varieties cultivated in the open-air and in polyethylene plastic-house. Data were analyzed by means of principal components, factorial discriminant methods, Mahalanobis D2 distances and principal coordinate techniques. Factorial discriminant and Mahalanobis D2 distances methods, both of which require collecting data plant by plant, lead to similar conclusions as the principal components method that only requires taking data by plots. Characters that make up the principal components in both environments studied are the same, although the relative importance of each one of them varies within the principal components. By combining information supplied by multivariate analysis with the inheritance mode of characters, crossings among cultivars can be experimented with that will produce heterotic hybrids showing characters within previously established limits.

EStimating mahalanobis's distance using bayesian analysis

Abstract: In this paper we are concerned with the problem of estimating Mahalanobis's distance between two or more populations using Bayesian approach. We first consider the case of two independent univariate normal populations having a common variance. We derive the posterior distribution of the

Evaluation of the "Mahalanobis' generalized distance" method of quality control: monitoring system of multivariate data.

Abstract: The purpose of this article is to evaluate the effectiveness of a monitoring system that utilizes the multivariate data. The system monitors the data of an individual patient by comparing them with his previous data. The Mahalanobis' generalized distance is introduced to measure the difference between the present and previous data. The authors applied this method to several sets of laboratory data, and it was shown to be useful for the monitoring system of laboratory errors. As a practical application, they developed a batch program and introduced it in the daily routine of the computer system. They expect that this method will be employed as a useful monitoring system in clinical laboratories, like the limit and delta checks.

Semi-invariants of the interclass Mahalanobis distance

Abstract: A new closed-form expression for the semi-invariants of the interclass Mahalanobis distance is derived. Typically, in the analysis of two multivariate Gaussian populations with different covariance matrices, simultaneous diagonalization of these matrices is required. The semi-invariants are given directly in terms of the mean vectors and inverse covariance matrices by the results established. In addition, a new iterative algorithm is derived for computing the moments of the interclass Mahalanobis distance from the semi-invariants.

Genetic diversity in horses inferred from distribution of hemotypes—I. Analysis of similarity among 14 populations of 10 breeds using generalized Mahalanobis distance (D2)

Abstract: 1. 1. Ninety-one pairwise comparisons of 14 populations yielded highly significant T2 values for inter-breed differences while four subpopulations of Thoroughbred horses were nearly identical. 2. 2. Generalized Mahalanobis distance was carried out by comparing simultaneously all 14 populations with respect to 26 variables (phenotypes) contributing most to the discriminant function. 3. 3. The number of variables could be reduced to 12 phenotypes in final comparisons. 4. 4. In general the calculated distances agreed with known relationships between horse breeds. 5. 5. However the obtained distances are thought to be biased due to the nature of selected phenotypes which do not always correspond to “breed-markers”.

Complexity, Testability, and Fault Analysis of Digital, Analog, and Hybrid Systems.

Abstract: : The research described in this report is divided into two major areas: (1) discrete mathematical descriptions of digital, analog, and hybrid systems, and (2) techniques for measuring parameters for characterizing certain aspects of such systems. New results are presented in decision trees, fault trees, testing complexity, optimal solution of linear inequalities, and the computation of moments and semi-invariants of the interclass Mahalanobis distance. (Author)