A Metric for Covariance Matrices

By Wolfgang Förstner, Boudewijn Moonen. 2003

565 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/4f2c48620a7d8cdb12d4546676bb2e6ab18b0ce7

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In Mechanical Engineering

Citations in the corpus

Human Detection via Classification on Riemannian Manifolds (2007, background): “Notice that both operators are point dependent where the dependence is made explicit with the subscript.”
Covariance Tracking using Model Update Based on Lie Algebra (2006, methodology): “Supposing no features in the feature vector would be exactly identical, which states the covariance matrices are positive definite, it is possible apply the distance measure proposed by Förstner [7].”
Gabor-Based Region Covariance Matrices for Face Recognition (2008, background): “Forstner and Moonen [3] and Tuzel et al.”
Online action recognition using covariance of shape and motion (2014, methodology): “(5), proposed by [25], is actually equivalent to the one from Eq.”
Covariance discriminative learning: A natural and efficient approach to image set classification (2012, background): “The first metric, affine-invariant distance (AID) [6], [17], is defined in terms of generalized eigenvalues of two covariance matrices 1 C and 2 C : where the eigenvalues .”
Person Re-identification by Descriptive and Discriminative Classification (2011, background): “Similarity computation between two human appearances is performed by estimating the distance between two covariance matrices [5] in pairwise manner by”
Pedestrian Detection via Classification on Riemannian Manifolds (2008, background): “We note that an equivalent form of the affine-invariant distance metric was first given in [15] in terms of joint eigenvalues of X and Y.”
Region Covariance: A Fast Descriptor for Detection and Classification (2006, background): “We use the distance measure proposed in [13] to measure the dissimilarity of two covariance matrices ρ(C1,C2) = √√√√ n ∑”
Quadratic Shrinkage for Large Covariance Matrices (2020, background): “It is thus a convenient alternative to the affine-equivariant geodesic norm on the manifold of positive-definite matrices (Förstner and Moonen, 1999), and to the Log-Euclidian norm of Arsigny et al.”
A Riemannian Framework for Tensor Computing (2005, methodology): “During the writing of this paper, we discovered that the invariant metric has been independently proposed by [F¨orstner and Moonen, 1999] to deal with covariance matrices, and very recently by [Fletcher and Joshi, 2004] for the analysis of principal modes of sets of diﬀusion tensors.”
Color Invariants for Person Reidentification (2013, methodology): “Covariance descriptors are compared using a metric for covariance matrices [33]:”
Multiclass Brain–Computer Interface Classification by Riemannian Geometry (2012, background): “The space of SPD matrices P (n) is a differentiable Riemannian manifold M [12].”