Algorithm for identification in the v-gap metric

This paper suggests a method for identification in the v-gap metric. For a finite number of frequency response samples, a problem for identification in the v-gap metric is formulated and an approximate solution is described. It uses an iterative technique for obtaining an L2-gap approximation. Each stage of the iteration involves solving an LMI optimisation. Given a known stabilising controller and the L2-gap approximation, it is shown how to derive a v-gap approximation.

Riemannian metric and geometric mean for positive semidefinite matrices of fixed rank

This paper introduces a new metric and mean on the set of positive semidefinite matrices of fixed-rank. The proposed metric is derived from a well-chosen Riemannian quotient geometry that generalizes the reductive geometry of the positive cone and the associated natural metric. The resulting Riemannian space has strong geometrical properties: it is geodesically complete, and the metric is invariant with respect to all transformations that preserve angles (orthogonal transformations, scalings, and pseudoinversion). A meaningful approximation of the associated Riemannian distance is proposed, that can be efficiently numerically computed via a simple algorithm based on SVD. The induced mean preserves the rank, possesses the most desirable characteristics of a geometric mean, and is easy to compute. © 2009 Society for Industrial and Applied Mathematics.

the trustworthiness metric model of software process quality based-on life circle

Communication University of China; Wuhan University; James Madison University; Institute of Policy and Management, Chinese Academy of Sciences; IEEE Wuhan Section

A Video Quality Assessment Metric Based on Human Visual System

It is important for practical application to design an effective and efficient metric for video quality. The most reliable way is by subjective evaluation. Thus, to design an objective metric by simulating human visual system (HVS) is quite reasonable and available. In this paper, the video quality assessment metric based on visual perception is proposed. Three-dimensional wavelet is utilized to decompose video and then extract features to mimic the multichannel structure of HVS. Spatio-temporal contrast sensitivity function (S-T CSF) is employed to weight coefficient obtained by three-dimensional wavelet to simulate nonlinearity feature of the human eyes. Perceptual threshold is exploited to obtain visual sensitive coefficients after S-T CSF filtered. Visual sensitive coefficients are normalized representation and then visual sensitive errors are calculated between reference and distorted video. Finally, temporal perceptual mechanism is applied to count values of video quality for reducing computational cost. Experimental results prove the proposed method outperforms the most existing methods and is comparable to LHS and PVQM.

Distance Metric Between 3D Models and 3D Images for Recognition and Classification

Similarity measurements between 3D objects and 2D images are useful for the tasks of object recognition and classification. We distinguish between two types of similarity metrics: metrics computed in image-space (image metrics) and metrics computed in transformation-space (transformation metrics). Existing methods typically use image and the nearest view of the object. Example for such a measure is the Euclidean distance between feature points in the image and corresponding points in the nearest view. (Computing this measure is equivalent to solving the exterior orientation calibration problem.) In this paper we introduce a different type of metrics: transformation metrics. These metrics penalize for the deformatoins applied to the object to produce the observed image. We present a transformation metric that optimally penalizes for "affine deformations" under weak-perspective. A closed-form solution, together with the nearest view according to this metric, are derived. The metric is shown to be equivalent to the Euclidean image metric, in the sense that they bound each other from both above and below. For Euclidean image metric we offier a sub-optimal closed-form solution and an iterative scheme to compute the exact solution.