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Mahalanobis distance

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


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Journal ArticleDOI
TL;DR: A new technique for radiometric normalization is proposed, which uses three sequential methods for an accurate PIFs selection: spectral measures of temporal data, density scatter plot analysis (ridge method), and robust regression.
Abstract: Radiometric precision is difficult to maintain in orbital images due to several factors (atmospheric conditions, Earth-sun distance, detector calibration, illumination, and viewing angles). These unwanted effects must be removed for radiometric consistency among temporal images, leaving only land-leaving radiances, for optimum change detection. A variety of relative radiometric correction techniques were developed for the correction or rectification of images, of the same area, through use of reference targets whose reflectance do not change significantly with time, i.e., pseudo-invariant features (PIFs). This paper proposes a new technique for radiometric normalization, which uses three sequential methods for an accurate PIFs selection: spectral measures of temporal data (spectral distance and similarity), density scatter plot analysis (ridge method), and robust regression. The spectral measures used are the spectral angle (Spectral Angle Mapper, SAM), spectral correlation (Spectral Correlation Mapper, SCM), and Euclidean distance. The spectral measures between the spectra at times t1 and t2 and are calculated for each pixel. After classification using threshold values, it is possible to define points with the same spectral behavior, including PIFs. The distance and similarity measures are complementary and can be calculated together. The ridge method uses a density plot generated from images acquired on different dates for the selection of PIFs. In a density plot, the invariant pixels, together, form a high-density ridge, while variant pixels (clouds and land cover changes) are spread, having low density, facilitating its exclusion. Finally, the selected PIFs are subjected to a robust regression (M-estimate) between pairs of temporal bands for the detection and elimination of outliers, and to obtain the optimal linear equation for a given set of target points. The robust regression is insensitive to outliers, i.e., observation that appears to deviate strongly from the rest of the data in which it occurs, and as in our case, change areas. New sequential methods enable one to select by different attributes, a number of invariant targets over the brightness range of the images.

65 citations

Journal ArticleDOI
09 Apr 2015-Sensors
TL;DR: This paper assesses different pixel-based segmentation methods in order to detect reddish grapes: threshold based, Mahalanobis distance, Bayesian classifier, linear color model segmentation and histogram segmentation, to obtain the best estimation of the area of the clusters of grapes in this illumination conditions.
Abstract: This paper presents a method for vineyard yield estimation based on the analysis of high-resolution images obtained with artificial illumination at night. First, this paper assesses different pixel-based segmentation methods in order to detect reddish grapes: threshold based, Mahalanobis distance, Bayesian classifier, linear color model segmentation and histogram segmentation, in order to obtain the best estimation of the area of the clusters of grapes in this illumination conditions. The color spaces tested were the original RGB and the Hue-Saturation-Value (HSV). The best segmentation method in the case of a non-occluded reddish table-grape variety was the threshold segmentation applied to the H layer, with an estimation error in the area of 13.55%, improved up to 10.01% by morphological filtering. Secondly, after segmentation, two procedures for yield estimation based on a previous calibration procedure have been proposed: (1) the number of pixels corresponding to a cluster of grapes is computed and converted directly into a yield estimate; and (2) the area of a cluster of grapes is converted into a volume by means of a solid of revolution, and this volume is converted into a yield estimate; the yield errors obtained were 16% and −17%, respectively.

65 citations

Journal ArticleDOI
TL;DR: In this article, the authors proposed a fast and scalable algorithm to learn a Mahalanobis distance metric, which can be viewed as the Euclidean distance metric on the input data that have been linearly transformed.
Abstract: For many machine learning algorithms such as k-nearest neighbor ( k-NN) classifiers and k-means clustering, often their success heavily depends on the metric used to calculate distances between different data points. An effective solution for defining such a metric is to learn it from a set of labeled training samples. In this work, we propose a fast and scalable algorithm to learn a Mahalanobis distance metric. The Mahalanobis metric can be viewed as the Euclidean distance metric on the input data that have been linearly transformed. By employing the principle of margin maximization to achieve better generalization performances, this algorithm formulates the metric learning as a convex optimization problem and a positive semidefinite (p.s.d.) matrix is the unknown variable. Based on an important theorem that a p.s.d. trace-one matrix can always be represented as a convex combination of multiple rank-one matrices, our algorithm accommodates any differentiable loss function and solves the resulting optimization problem using a specialized gradient descent procedure. During the course of optimization, the proposed algorithm maintains the positive semidefiniteness of the matrix variable that is essential for a Mahalanobis metric. Compared with conventional methods like standard interior-point algorithms or the special solver used in large margin nearest neighbor , our algorithm is much more efficient and has a better performance in scalability. Experiments on benchmark data sets suggest that, compared with state-of-the-art metric learning algorithms, our algorithm can achieve a comparable classification accuracy with reduced computational complexity.

65 citations

Journal ArticleDOI
TL;DR: In this article, a novel approach for initializing covariance matrices is proposed, based on the K-means algorithm with Mahalanobis distances, which is commonly used with the Euclidean metric.

64 citations

Journal ArticleDOI
TL;DR: The Zernike moment descriptor (ZMD) is applied to the problem of mode shape recognition for a circular plate and results show that the ZMD has considerable advantages over the traditional MAC index when identifying the cyclically symmetric mode shapes that occur in axisymmetric structures at identical frequencies.

64 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
2023208
2022452
2021232
2020239
2019249