Mahalanobis distance

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

Addressing Nonlinear Relative Motion For Spacecraft Collision Probability

Abstract: Linear methods for computing satellite collision probability can be extended to accommodate nonlinear relative motion in the presence of changing position and velocity uncertainties. Collision probability analysis for spherical objects exhibiting linear relative motion is accomplished by combining covariances and physical object dimensions at the point of closest approach. The resulting covariance ellipsoid and hardbody are projected onto the plane perpendicular to relative velocity by assuming linear relative motion and constant positional uncertainty throughout the brief encounter. Collision potential is determined from the object footprint on the projected, two-dimensional, covariance ellipse. For nonlinear motion, the dimension associated with relative velocity must be reintroduced. This can be simply done by breaking the collision tube into sufficiently small cylinders such that the sectional motion is nearly linear, computing the linear probability associated with each section, and then summing. The method begins with object position and velocity data at the time of closest approach. Propagation of position, velocity, and covariance is done forward/backward in time until a user limit is reached. An alternate method is presented that creates a voxel grid in Mahalanobis space, computes the probability of each affected voxel as the combined object passes through the space, and sums. These general methods are not dependent on a specific propagator or linear probability model.

Adaptive Cluster Distance Bounding for High-Dimensional Indexing

Abstract: We consider approaches for similarity search in correlated, high-dimensional data sets, which are derived within a clustering framework. We note that indexing by “vector approximation” (VA-File), which was proposed as a technique to combat the “Curse of Dimensionality,” employs scalar quantization, and hence necessarily ignores dependencies across dimensions, which represents a source of suboptimality. Clustering, on the other hand, exploits interdimensional correlations and is thus a more compact representation of the data set. However, existing methods to prune irrelevant clusters are based on bounding hyperspheres and/or bounding rectangles, whose lack of tightness compromises their efficiency in exact nearest neighbor search. We propose a new cluster-adaptive distance bound based on separating hyperplane boundaries of Voronoi clusters to complement our cluster based index. This bound enables efficient spatial filtering, with a relatively small preprocessing storage overhead and is applicable to euclidean and Mahalanobis similarity measures. Experiments in exact nearest-neighbor set retrieval, conducted on real data sets, show that our indexing method is scalable with data set size and data dimensionality and outperforms several recently proposed indexes. Relative to the VA-File, over a wide range of quantization resolutions, it is able to reduce random IO accesses, given (roughly) the same amount of sequential IO operations, by factors reaching 100X and more.

Outdoor Path Labeling Using Polynomial Mahalanobis Distance

Abstract: Autonomous robot navigation in outdoor environments remains a challenging and unsolved problem A key issue is our ability to identify safe or navigable paths far enough ahead of the robot to allow smooth trajectories at acceptable speeds Colour or texture-based labeling of safe path regions in image sequences is one way to achieve this far field prediction A challenge for classifiers identifying path and nonpath regions is to make meaningful comparisons of feature vectors at pixels or over a window Most simple distance metrics cannot use all the information available and therefore the resulting labeling does not tightly capture the visible path We introduce a new Polynomial Mahalanobis Distance and demonstrate its ability to capture the properties of an initial positive path sample and produce accurate path segmentation with few outliers Experiments show the method’s effectiveness for path segmentation in natural scenes using both colour and texture feature vectors The new metric is compared with classifications based on Euclidean and standard Mahalanobis distance and produces superior results

Combined 2D/3D Face Recognition Using Log-Gabor Templates

Abstract: The addition of Three Dimensional (3D) data has the potential to greatly improve the accuracy of Face Recognition Technologies by providing complementary information. In this paper a new method combining intensity and range images and providing insensitivity to expression variation based on Log-Gabor Templates is presented. By breaking a single image into 75 semi-independent observations the reliance of the algorithm upon any particular part of the face is relaxed allowing robustness in the presence of occulusions, distortions and facial expressions. Also presented is a new distance measure based on the Mahalanobis Cosine metric which has desirable discriminatory characteristics in both the 2D and 3D domains. Using the 3D database collected by University of Notre Dame for the Face Recognition Grand Challenge (FRGC), benchmarking results are presented demonstrating the performance of the proposed methods.