The M–relative distance, denoted by ρM is a generalization of the p–relative distance, which was introduced in [10]. We establish necessary and sufficient conditions under which ρM is a metric. In two special cases we derive complete characterizations of the metric. We also present a way of extending the results to metrics sensitive to the domain in which they are defined, thus finding some con...

This paper proposes a simple color image retrieval method based on multi resolution enhanced orthogonal polynomials model. In the proposed method, a set of orthogonal polynomials has been chosen and the model coefficients are reordered into multiresolution subband like structure. The subband coefficients are quantized into three levels. Then the weighted autocorrelogram is computed from the qua...

This paper introduces a parameterization-based approach for anisotropic surface meshing. Given an input surface equipped with an arbitrary Riemannian metric, this method generates a metric-adapted mesh with user-specified number of vertices. In the proposed method, the edge length of the input surface is directly adjusted according to the given Riemannian metric at first. Then the adjusted surf...

This paper represents another step in overcoming a drawback of K-Means, its lack of defense against noisy features, using feature weights in the criterion. The Weighted K-Means method by Huang et al. (2008, 2004, 2005) [5–7] is extended to the corresponding Minkowski metric for measuring distances. Under Minkowski metric the feature weights become intuitively appealing feature rescaling factors...

The finite-sample risk of the k nearest neighbor classifier that uses a weighted Lpmetric as a measure of class similarity is examined. For a family of classification problems with smooth distributions in Rn, an asymptotic expansion for the risk is obtained in decreasing fractional powers of the reference sample size. An analysis of the leading expansion coefficients reveals that the optimal we...

According to the Uniformization Theorem, any surface can be conformally mapped into a domain of a constant Gaussian curvature. The conformal factor indicates the local scaling introduced by such a mapping. This process could be used to compute geometric quantities in a simplified flat domain with zero Gaussian curvature. For example, the computation of geodesic distances on a curved surface can...

Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted average of the surrounding training examples. The weights are typically computed by a distancebased kernel function and they strongly depend on the distances b...

a simple, sensitive, accurate and precise simultaneous uv spectrophotometric method has been developed for the estimation of carisoprodol, paracetamol and caffeine in tablet dosage form. the absorption maxima of the drugs were found to be 221, 248 and 273 nm for carisoprodol, paracetamol and caffeine respectively, in methanol, using a double beam uv/visible spectrophotometer. carisoprodol, para...

Many metrics used in coding theory are instances of a combinatorial metric introduced by Gabidulin. We define a weighted combinatorial quasimetric. Some relations between these two metrics are established. Given an error and erasure decoder for the combinatorial metric, we propose the Forney-Kovalev soft-input-decoder for the weighted combinatorial metric. The error correcting radius of the alg...