Abstract We consider the structure of divergence-free vector measures on plane. show that such can be decomposed into induced by closed simple curves. More generally, we if divergence a planar vector-valued measure is signed measure, then curves (not necessarily closed). As an application generalize certain rigidity properties fields to measures. Namely, locally finite has zero divergence, vani...

We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. Several statistical examples and motivations are given. These procedures extend the empirical likelihood (EL) method and share common features with generalized empirical likelihood (GEL). We treat the problems of existence and characterization of the diver...

Disagreement between two classifiers regarding the class membership of an observation in pattern recognition can be indicative of an anomaly and its nuance. As in general classifiers base their decision on class aposteriori probabilities, the most natural approach to detecting classifier incongruence is to use divergence. However, existing divergences are not particularly suitable to gauge clas...

An approach to develop new measures of fuzzy directed divergence is proposed here. A new measure of fuzzy directed divergence is proposed, and some mathematical properties of this measure are proved. The application of fuzzy directed divergence in image segmentation is explained. The proposed technique minimizes the fuzzy divergence or the separation between the actual and ideal thresholded image.

Vajda (1972) studied a generalized divergence measure of Csiszar's class, so called "Chi-m divergence measure." Variational distance and Chi-square divergence are the special cases of this generalized divergence measure at m = 1 and m = 2, respectively. In this work, nonparametric nonsymmetric measure of divergence, a particular part of Vajda generalized divergence at m = 4, is taken and charac...

Symmetric positive definite (SPD) matrices are useful for capturing second-order statistics of visual data. To compare two SPD matrices, several measures are available, such as the affine-invariant Riemannian metric, Jeffreys divergence, Jensen-Bregman logdet divergence, etc.; however, their behaviors may be application dependent, raising the need of manual selection to achieve the best possibl...

Symmetric positive definite (SPD) matrices are useful for capturing second-order statistics of visual data. To compare two SPD matrices, several measures are available, such as the affine-invariant Riemannian metric, Jeffreys divergence, Jensen-Bregman logdet divergence, etc.; however, their behaviors may be application dependent, raising the need of manual selection to achieve the best possibl...

We study inverse potential problems with source term the divergence of some unknown (ℝ 3 -valued) measure supported in a plane; e.g. , magnetization for thin plates. investigate methods recovering μ by penalizing measure-theoretic total variation norm ∥ TV and appealing to decomposition divergence-free measures plane as superpositions unit tangent vector fields on rectifiable Jordan curves. In ...