Mahalanobis distance

About: Mahalanobis distance is a research topic. Over the lifetime, 4616 publications have been published within this topic receiving 95294 citations.

Registration of 3D shapes under anisotropic scaling: Anisotropic-scaled iterative closest point algorithm.

Abstract: Several medical imaging modalities exhibit inherent scaling among the acquired data: The scale in an ultrasound image varies with the speed of sound and the scale of the range data used to reconstruct organ surfaces is subject to the scanner distance In the context of surface-based registration, these scaling factors are often assumed to be isotropic, or as a known prior Accounting for such anisotropies in scale can potentially dramatically improve registration and calibrations procedures that are essential for robust image-guided interventions We introduce an extension to the ordinary iterative closest point (ICP) algorithm, solving for the similarity transformation between point-sets comprising anisotropic scaling followed by rotation and translation The proposed anisotropic-scaled ICP (ASICP) incorporate a novel use of Mahalanobis distance to establish correspondence and a new solution for the underlying registration problem The derivation and convergence properties of ASICP are presented, and practical implementation details are discussed Because the ASICP algorithm is independent of shape representation and feature extraction, it is generalizable for registrations involving scaling Experimental results involving the ultrasound calibration, registration of partially overlapping range data, whole surfaces, as well as multi-modality surface data (intraoperative ultrasound to preoperative MR) show dramatic improvement in fiducial registration error We present a generalization of the ICP algorithm, solving for a similarity transform between two point-sets by means of anisotropic scales, followed by rotation and translation Our anisotropic-scaled ICP algorithm shares many traits with the ordinary ICP, including guaranteed convergence, independence of shape representation, and general applicability

On the robustness of hotelling's T2-test anb distribution of linear and quadratic forms III sampling from a mixture of two mult11ariate normal populations

Abstract: In this paper, the joint distribution of (a) a linear and-a quadratic form, and (b) two quadratic forms are obtained when the sample is taken from a mixture of two p-co»ponent multivariate normal distributions with mean JJ. and JJ« respectively and common covarlaece matrix Z # Also the distribution of Hotelling's t2-statistic is obtained when irji- + (1-ir)^ - j) t where w f O^i^l f Is the mixing proportion (contamination, 1-w). Actual values of a (level of significance) when nominal level a Is 0»05 are computed for some particolar combination of parameters* These results show that the si2e of the test can differ greatly even for a contan-ination as small as 0,05 if the Mahalanobis (square) distance Is large and/or the sample size Is large

Hierarchical Probabilistic Fusion Framework for Matching and Merging of 3-D Occupancy Maps

Abstract: Fusing 3-D maps generated by multiple robots in real/semi-real time distributed mapping systems are addressed in this paper. A 3-D occupancy grid-based approach for mapping is utilized to satisfy the real/semi-real time and distributed operating constraints. This paper proposes a novel hierarchical probabilistic fusion framework, which consists of uncertainty modeling, map matching, transformation evaluation, and map merging. Before the fusion of maps, the map features and their uncertainties are explicitly modeled and integrated. For map matching, a two-level probabilistic map matching (PMM) algorithm is developed to include high-level structural and low-level voxel features. In the PMM, the structural uncertainty is first used to generate a coarse matching between the maps and its result is then used to improve the voxel level map matching, resulting in a more efficient and accurate matching between maps with a larger convergence basin. The relative transformation output from PMM algorithm is then evaluated based on the Mahalanobis distance, and the relative entropy filter is used subsequently to integrate the map dissimilarities more accurately, completing the map fusion process. The proposed approach is evaluated using map data collected from both simulated and real environments, and the results validate the accuracy, efficiency, and the support for larger convergence basin of the proposed 3-D occupancy map fusion framework.

Applying the Mahalanobis-Taguchi strategy for software defect diagnosis

Abstract: The Mahalanobis-Taguchi (MT) strategy combines mathematical and statistical concepts like Mahalanobis distance, Gram-Schmidt orthogonalization and experimental designs to support diagnosis and decision-making based on multivariate data. The primary purpose is to develop a scale to measure the degree of abnormality of cases, compared to "normal" or "healthy" cases, i.e. a continuous scale from a set of binary classified cases. An optimal subset of variables for measuring abnormality is then selected and rules for future diagnosis are defined based on them and the measurement scale. This maps well to problems in software defect prediction based on a multivariate set of software metrics and attributes. In this paper, the MT strategy combined with a cluster analysis technique for determining the most appropriate training set, is described and applied to well-known datasets in order to evaluate the fault-proneness of software modules. The measurement scale resulting from the MT strategy is evaluated using ROC curves and shows that it is a promising technique for software defect diagnosis. It compares favorably to previously evaluated methods on a number of publically available data sets. The special characteristic of the MT strategy that it quantifies the level of abnormality can also stimulate and inform discussions with engineers and managers in different defect prediction situations.