Showing papers on "Mahalanobis distance published in 1994"

Multivariate control charts : control charts for calibration curves

Abstract: The proposed multivariate control charts for p-dimensional vectors are an extension of the conventional control charts for one variable. The controlling quantity is the Mahalanobis distance of vector x from the central value vector x..: D=(x-x..)TĈ-1.(x-x..), where Ĉ is the covariance matrix estimate. The quantity D has Hotelling's T2 distribution. A PC program was set up for the automatic graphical construction of such charts. The program draws the sequential chart of the quantity D as well as the position of the vectors x in the p dimensional control ellipsoid in the axes of the principal components. In this way a control chart was developed for the calibration curve in the photometric determination of Fe3+ with sulfosalicylic acid. Vector x was formed by absorbance values for the calibration curve points (p=5). The chart can assist in detection of even small disturbances of the calibration curve.

Modified mahalanobis filters for grouping pottery by chemical composition

Abstract: A statistical procedure for grouping pottery in provenance studies by chemical data is presented, which now is routinely in use in our laboratory. It is based on the Mahalanobis filter method and X2 -statistics, and can be used for both establishing groups and assigning single sherds to already known groups, thus replacing principal components analysis or cluster analysis and avoiding their problems in grouping pottery. The new method is able to consider correlations, uncertainties of measurement and constant shifts of the data in case of dilution. In particular, considering dilution effects results in both a better assignment to and separation of reference groups and is also equivalent to the compositional data approach, if log-transformed data are used. Other distortions of data (e.g., mixing of clays) can also be considered.

A self-organizing network for hyperellipsoidal clustering (HEC)

Abstract: We propose a self-organizing network (HEC) for hyper-ellipsoidal clustering. The HEC network performs a partitional clustering using the regularized Mahalanobis distance. This regularized Mahalanobis distance measure is proposed to deal with the problems in estimating the Mahalanobis distance when the number of patterns in a cluster is less than (ill-posed problem) or not considerably larger than (poorly-posed problem) the dimensionality of the feature space in clustering multidimensional data. This regularized distance also achieves a tradeoff between hyperspherical and hyperellipsoidal cluster shapes so as to prevent the HEC network from producing unusually large or unusually small clusters. The significance level of the Kolmogrov-Smirnov test on the distribution of the Mahalanobis distances of patterns in a cluster to the cluster center under the multivariate Gaussian assumption is used as a measure of cluster compactness. The HEC network has been tested on a number of artificial data sets and real data sets. Experiments show that the HEC network gives better clustering results compared to the well-known K-means algorithm with the Euclidean distance metric. >

A neural network approach to classification of sidescan sonar imagery from a midocean ridge area

Abstract: A neural-network approach to classification of sidescan-sonar imagery is tested on data from three distinct geoacoustic provinces of a midocean-ridge spreading center: axial valley, ridge flank, and sediment pond. The extraction of representative features from the sidescan imagery is analyzed, and the performance of several commonly used texture measures are compared in terms of classification accuracy using a backpropagation neural network. A suite of experiments compares the effectiveness of different feature vectors, the selection of training patterns, the configuration of the neural network, and two widely used statistical methods: Fisher-pairwise classifier and nearest-mean algorithm with Mahalanobis distance measure. The feature vectors compared here comprise spectral estimates, gray-level run length, spatial gray-level dependence matrix, and gray-level differences. The overall accurate classification rates using the best feature set for the three seafloor types are: sediment ponds, 85.9%; ridge flanks, 91.2%; and valleys, 80.1%. While most current approaches are statistical, the significant finding in this study is that high performance for seafloor classification in terms of accuracy and computation can be achieved using a neural network with the proper combination of texture features. These are preliminary results of our program toward the automated segmentation and classification of undersea terrain. >

Principal component outlier detection and SIMCA: a synthesis

Abstract: Principal component outlier detection methods are discussed and their application in the soft independent modelling of class analogy (SIMCA) method of pattern recognition is clarified. SIMCA is compared to allocation procedures based on the Mahalanobis distance. Finally, the differences between the SIMCA method and quadratic discriminant analysis are discussed. The discussion is illustrated with an example from spectroscopy.

The efficient computation of unbiased mahalanobis distances and their interpretation in archaeometry

Abstract: This paper argues for cross-validation to reduce bias in estimating Mahalanobis distances of individuals to groups, a particular problem with small sample sizes. Formulae for the efficient computation of cross-validated distances, which avoid excessive matrix inversion, are given. The use of Mahalanobis distances as measures of consistency, or as indications of outlying values, is described. The little-known technique of gamma plotting is outlined and discussed as an aid to interpreting distances in these terms. Both cross-validation and gamma plotting are illustrated in an example on marble composition.

Distance classifier correlation filters

Abstract: The performance of shift-invariant distance classifiers based on correlation filters is evaluated. First, the effect of noise on a classifier designed to recognize synthetic aperture radar (SAR) is observed. Then, a 2-class ATR designed to recognize infrared images of actual targets is evaluated. The results attest to the ability of the distance classifier to tolerate distortions, and recognize targets in the presence of noise and clutter.

Image staining and differential diagnosis of ultrasound scans based on the Mahalanobis distance

Abstract: The covariance matrices associated with each state of health or disease from a previous study are used as the basis of an image staining display technique for aid in quantitative differential diagnosis. A state of health or disease is chosen by the clinician: this selects the covariance matrix from the data base. A region of interest (ROI) is then scrolled through an abdominal B-scan. For each position of the ROI a point in the four-dimensional feature space is calculated. A natural measure of the distance of this point from the center of mass (multivariate mean) of the disease class is calculated in terms of the covariance matrix of this class; this measure is the Mahalanobis distance. The confidence level for acceptance or rejection of the hypothesized disease class is obtained from the probability distribution of this distance, the T/sup 2/ probability law. This confidence level is color coded and used as a color stain that overlays the original scan at that position. The variability of the calculated features is studied as a function of ROI size, or the spatial resolution of the color coded image, and it is found that for an ROI in the neighborhood of 4 cm/sup 2/ most of the variability due to the finite number of independent samples (speckles) is averaged out, leaving the "noise floor" associated with inter- and intra-patient variability. ROIs on the order of 1 cm/sup 2/ may result with technical advances in B-scan resolution. A small number of points on organ boundaries are entered by the user, to fit with arcs of ellipses to be used to switch between organ (liver and kidney) data bases as the ROI encounters the boundary. By selecting in turn various state-of-health or state-of-disease databases, such images of confidence levels may be used for quantitative differential diagnosis. The method is not limited to ultrasound, being applicable in principle to features obtained from any modality or multimodality combination. >

Method for the classification of a pattern, for example on a banknote or a coin

Abstract: For the classification of a pattern in particular on a banknote or a coin, a receiving system detects, by a measurement procedure, vectors of a test item, a pre-processing system transforms the measured vectors into local feature vectors ALCi(l) and a learning classification system carries out a plurality of testing operations. A first activity compares in a first testing operation each of the local feature vectors ALCi(l) to a vectorial reference value. It is only if the first testing operation takes place successfully that the first activity, by means of first estimates which are stored in a data base, links the local feature vectors ALC(l) to provide global line feature vectors AGIi. In a second testing operation a third activity compares the global line feature vectors AGIi to corresponding reference values and, if the second testing operation is successful, computes a single global surface vector AGF of which a fourth activity. in a third testing operation, compares its distance in accordance with Mahalanobis relative to an estimated surface vector to a reference value. The test item is reliably classified if all three testing operations take place successfully.

Improved chromosome classification using monotonic functions of mahalanobis distance and the transportation method

Abstract: It is shown that the accuracy of chromosome classification constrained by class size can be improved over previously reported results by a combination of straightforward modifications to previously used methods. These are (i) the use of the logarithm of the Mahalanobis distance of an unknown chromosome's feature vector to estimated class mean vectors as the basis of the transportation method objective function, rather than the estimated likelihood; (ii) the use of all available features and full estimated covariance to compute the Mahalanobis distance, rather than a subset of features and the diagonal (variance) terms only; (iii) a modification to the way the transportation model deals with the constraint on the number of sex chromosomes in a metaphase cell; and (iv) the use of a newly discovered heuristic to weight off-diagonal elements of the covariance; this proved to be particularly valuable in cases where relatively few training examples were available to estimate covariance. The methods have been verified using 5 different sets of chromosome data.

Segmentation of polar scenes using multi-spectral texture measures and morphological filtering

Abstract: Two segmentation and two unsupervised classification schemes are applied to four Landsat TM Antarctic scenes. The methods include the region-growing and the region-oriented segmentation approaches and the Divide-and-Conquer and the Mahalanobis classifiers. Combinations of spectral signatures and Grey Level Difference Vector (GLDV) textural measures are computed for each of the seven TM bands. Correlation matrices then are constructed to reduce the feature vector. Means, standard deviations, and angular second moments are selected, usually for TM channels 4, 5, and 6. In general it is found that the segmentation schemes produce results which are judged to be more reliable and useful than those obtained from the classification schemes. The region-oriented segmentation approach is found to produce the best results. The morphological three-dimensional opening and closing operators are used as a preprocessing step in both the segmentation and classification approaches. It is found that a 7 by 7 pixel ...

Correlation filters for texture recognition and applications to terrain-delimitation in wide-area surveillance

Abstract: Terrain-delimitation is an important component of wide-area-surveillance with applications to battlefield terrain and agricultural terrain. Recently a statistical method was proposed by Mahalanobis and Singh [1] to design spatial filters to recognize and discriminate between various textures. We extend the technique for delimitation-through-texture-discrimination in SAR images. Spatial correlation filters are used for texture distinction. The filters are implementable as optical (or digital) correlators for fast real-time texture recognition without segmentation. The filter coefficients are determined via eigenvector analysis. Examples will be given to illustrate the proposed scheme for terrain-discrimination in SAR images. >

Sensor data fusion using Mahalanobis distance and single linkage algorithm

Abstract: Multi-sensor data fusion fuses the output from two or more devices that contain sensor or sensor groups and retrieve one or more particular properties of the environment. Commonly used sensors for robotic control include video cameras, range finders, sonar sensors, infrared sensors, tactile sensors, torque sensors, and proximity sensors. Since the measurements obtained by the sensors are uncertain due to noise and accuracy, the sensor data is not always reliable. So, directly using this data may cause inaccurate, even wrong actions, for systems. This paper discusses sensor fusion using Mahalanobis distance single linkage algorithm. The data fusion here involves testing sensor data closeness, merging close sensor data and optimizing the close sensor data. Mahalanobis distance technique is used to test sensor data closeness, the single linkage algorithm is used for merging close sensors, and the maximum likelihood estimation method is applied for optimizing close sensor data. In this paper we show how to apply these well known mathematical techniques for general sensor data fusion. >

Line and circle finding by the weighted Mahalanobis distance transform and extended Kalman filtering

Abstract: The paper presents a new parameter space approach, called the Weighted Mahalanobis Distance Hough Transform (WMDHT) whose main merit is to incorporate formal stochastic image and feature noise models. It is aimed at improving the efficiency, accuracy and reducing the size of the accumulator arrays by combining it with extended Kalman filter refinement. It works by detecting image feature points in the neighbourhood of a contour instead of exactly on the contour through a Mahalanobis distance measure modified by a weight function inversely proportional to the distance between the point and an ideal contour. The method is applicable to geometric features of any dimensionality and the paper illustrates it by considering detection of straight and circular segments. >

The Mahalanobis distance Hough transform with extended Kalman filter refinement

Abstract: This paper presents a new Hough function based on a Mahalanobis distance measure that incorporates a formal stochastic model for measurement and model noise. Thus, the effects of image and parameter space quantisation can be incorporated directly. An extended Kalman filtering process is proposed combined with this flexible model for feature refinement, which is particularly applicable when using coarse parameter resolutions. For a given resolution, the method provides better performance than the SHT. >

A comparison between the standard Hough transform and the Mahalanobis distance Hough transform

Abstract: The Hough Transform is a class of medium-level vision techniques generally recognised as a robust way to detect geometric features from a 2D image. This paper presents two related techniques. First, a new Hough function is proposed based on a Mahalanobis distance measure that incorporates a formal stochastic model for measurement and model noise. Thus, the effects of image and parameter space quantisation can be incorporated directly. Given a resolution of the parameter space, the method provides better results than the Standard Hough Transform (SHT), including under high geometric feature densities. Secondly, Extended Kalman Filtering is used as a further refinement process which achieves not only higher accuracy but also better performance than the SHT. The algorithms are compared with the SHT theoretically and experimentally.

Contiguity in discriminant factorial analysis for image clustering

Abstract: In this paper, we present a method using contiguity in Discriminant Factorial Analysis at the assignment step, where the neighbourhood of a point is defined by a contiguity graph. Two criteria, both based on Mahalanobis distance are proposed. They use a new notion called the “possible” classes of the neighbourhood of a point, according to the smallest distances recorded for the latter. A new “distance” taking into account the neighbourhood of a point is also introduced. These methods have been applied to image clustering.

3D Distance Metric for Pose Estimation and Object Recognition for 2D Projections

Abstract: Model based object recognition and model based pose estimation require some distance metric to find the optimal pose and to measure the distance between the measurements and possible models during the recognition process When the measurements are given in 2D (such as in orthographic and perspective projections) the commonly used distance between the 3D model features and the 2D image features is the 2D Euclidean distance measured in the image plane However, this 2D distance does not, usually, increase monotonically with the real 3D distance and thus does not really represent the distance being measured In this paper we propose a new scheme in which both, the optimal positioning and the evaluation of similarity between the 2D image and the model is performed relative to the 3D distance This distance is calculated between the model features and a 3D predicted object which is a permissible reconstruction of the measured object and is the ``closest'''' to the model features

Comparison of texture-based and fuzzy classification approaches for regenerating tropical forest mapping using LANDSAT TM

Abstract: The two classification approaches based on texture and fuzzy sets were investigated for tropical forest regrowth mapping on Landsat TM (Manaus area, Brazil). Texture-based classifiers (based on Markov random field model consistently provided a higher classification accuracies (for testing set), indicating that they are more able to accurately characterize different tropical forest regeneration classes and two species of trees (cecropia and vismia). Memberships derived from the three classification algorithms: based on the probability density function, a posteriori probability, and the Mahalanobis distance were used for post- classification of fuzzy image. Post-classification (summation of memberships in the neighborhood or application of homogeneity approach for post-classification) of the fuzzy image can increase the classification accuracies (for training and testing data) by 10% in comparison with maximum likelihood classification for 11 classes of tropical forest region. Texture-based classification and post-classification of fuzzy image give the comparable classification accuracies for the same 11 classes of tropical forest region.

Statistical approaches to the analysis of multivariate heterogeneous biological systems

Abstract: To describe multivariate heterogeneous biosystems and their reactions to various impacts and to compare the objects with different complexity the integral characteristics are proposed. The characteristics can be obtained by means of non-standard statistical approaches: variants of correlation analysis with the use of Fisher's Z-transformations followed by convolution and Mahalanobis multidimensional intervals. Applicability of these approaches to medical and biological problems is shown.

Machine Lip-Reading of Japanese Vowels Utilizing A Stereoscopic Vision System.

Abstract: The lip-shape recognition of Japanese vowels utilizing a stereoscopic vision system has been performed to enhance the discrimination of five vowels by machine lip-reading. The opening angle P4 between the upper lip and the lower lip is selected as the typical three-dimensional feature parameter of lip shape, in addition to the usual feature parameters such as the width P1 and the height P2 of the lip shape and distance P3 between the tips of the upper lip and the chin. Compared with the 3 two-dimensional parameters P1, P2 and P3 used in a single-vision system, the 3 and 4 three-dimensional parameters led to the significant increase of discrimination rate, and in particular, the discrimination rate by the 4 three-dimensional parameters was more than 90% for every tested subject. Recognition for an unspecified subject was also examined, based on the selections of the variance-covariance matrix and the mean vector of feature variables, by which the Mahalanobis' generalized square distance and the maximum likelihood discrimination function were determined.

A simple cleaning procedure for improvement of training site statistics

Abstract: For improving the effectiveness of supervised training, a simple cleaning procedure which operates by selectively dropping training site pixels based on the Mahalanobis distance and class probability has been proposed. The method is iterative and takes into account the spectral overlap in all image bands with all the user specified classes. The procedure results in greater classification accuracy with narrower confidence interval. On the test data, Bhattacharrya distance measure of class separability unproved front an average value of 1.9373 to 1.9797 with a maximum change for a class pair from 1.2671 to 1.9052. The overall classification accuracy increased from 94.74 ±0.64 to 99.63 ± 0.19.