Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.

Alternative Test Criteria in Covariance Structure Analysis: A Unified Approach.

Abstract: In the context of covariance structure analysis, a unified approach to the asymptotic theory of alternative test criteria for testing parametric restrictions is provided. The discussion develops within a general framework that distinguishes whether or not the fitting function is asymptotically optimal, and allows the null and alternative hypothesis to be only approximations of the true model. Also, the equivalent of the information matrix, and the asymptotic covariance matrix of the vector of summary statistics, are allowed to be singular. When the fitting function is not asymptotically optimal, test statistics which have asymptotically a chi-square distribution are developed as a natural generalization of more classical ones. Issues relevant for power analysis, and the asymptotic theory of a testing related statistic, are also investigated.

Simultaneous motion estimation and segmentation

Abstract: We present a Bayesian framework that combines motion (optical flow) estimation and segmentation based on a representation of the motion field as the sum of a parametric field and a residual field The parameters describing the parametric component are found by a least squares procedure given the best estimates of the motion and segmentation fields The motion field is updated by estimating the minimum-norm residual field given the best estimate of the parametric field, under the constraint that motion field be smooth within each segment The segmentation field is updated to yield the minimum-norm residual field given the best estimate of the motion field, using Gibbsian priors The solution to successive optimization problems are obtained using the highest confidence first (HCF) or iterated conditional mode, (ICM) optimization methods Experimental results on real video are shown

Efficient energies and algorithms for parametric snakes

Abstract: Parametric active contour models are one of the preferred approaches for image segmentation because of their computational efficiency and simplicity. However, they have a few drawbacks which limit their performance. In this paper, we identify some of these problems and propose efficient solutions to get around them. The widely-used gradient magnitude-based energy is parameter dependent; its use will negatively affect the parametrization of the curve and, consequently, its stiffness. Hence, we introduce a new edge-based energy that is independent of the parameterization. It is also more robust since it takes into account the gradient direction as well. We express this energy term as a surface integral, thus unifying it naturally with the region-based schemes. The unified framework enables the user to tune the image energy to the application at hand. We show that parametric snakes can guarantee low curvature curves, but only if they are described in the curvilinear abscissa. Since normal curve evolution do not ensure constant arc-length, we propose a new internal energy term that will force this configuration. The curve evolution can sometimes give rise to closed loops in the contour, which will adversely interfere with the optimization algorithm. We propose a curve evolution scheme that prevents this condition.