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Parametric statistics
About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.
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TL;DR: This work proposes a principled optimization strategy where nonparametric representations of these likelihoods are maximized within a hierarchy of smoothed estimates and is shown to outperform some common existing methods on the task of generic face fitting.
Abstract: Deformable model fitting has been actively pursued in the computer vision community for over a decade. As a result, numerous approaches have been proposed with varying degrees of success. A class of approaches that has shown substantial promise is one that makes independent predictions regarding locations of the model's landmarks, which are combined by enforcing a prior over their joint motion. A common theme in innovations to this approach is the replacement of the distribution of probable landmark locations, obtained from each local detector, with simpler parametric forms. In this work, a principled optimization strategy is proposed where nonparametric representations of these likelihoods are maximized within a hierarchy of smoothed estimates. The resulting update equations are reminiscent of mean-shift over the landmarks but with regularization imposed through a global prior over their joint motion. Extensions to handle partial occlusions and reduce computational complexity are also presented. Through numerical experiments, this approach is shown to outperform some common existing methods on the task of generic face fitting.
908 citations
TL;DR: In this paper, the theory of highly directional receivers and transmitters that may be constructed with the nonlinearity of the equations of fluid motion is presented, and the theory is extended to the case of a single antenna.
Abstract: This paper presents the theory of highly directional receivers and transmitters that may be “constructed” with the nonlinearity of the equations of fluid motion.
908 citations
01 Jan 1965
TL;DR: Markov parametric algorithm for effective construction of minimal realizations of linear state-variable finite-dimensional dynamical systems from input-output data is presented in this article, where a Markov-parametric algorithm is used to construct the minimal realization.
Abstract: Markov parametric algorithm for effective construction of minimal realizations of linear state-variable finite-dimensional dynamical systems from input-output data
908 citations
IBM1
TL;DR: A sharper code length is obtained as the stochastic complexity and the associated universal process are derived for a class of parametric processes by taking into account the Fisher information and removing an inherent redundancy in earlier two-part codes.
Abstract: By taking into account the Fisher information and removing an inherent redundancy in earlier two-part codes, a sharper code length as the stochastic complexity and the associated universal process are derived for a class of parametric processes. The main condition required is that the maximum-likelihood estimates satisfy the central limit theorem. The same code length is also obtained from the so-called maximum-likelihood code.
906 citations
TL;DR: The authors apply flexible constraints, in the form of a probabilistic deformable model, to the problem of segmenting natural 2-D objects whose diversity and irregularity of shape make them poorly represented in terms of fixed features or form.
Abstract: Segmentation using boundary finding is enhanced both by considering the boundary as a whole and by using model-based global shape information. The authors apply flexible constraints, in the form of a probabilistic deformable model, to the problem of segmenting natural 2-D objects whose diversity and irregularity of shape make them poorly represented in terms of fixed features or form. The parametric model is based on the elliptic Fourier decomposition of the boundary. Probability distributions on the parameters of the representation bias the model to a particular overall shape while allowing for deformations. Boundary finding is formulated as an optimization problem using a maximum a posteriori objective function. Results of the method applied to real and synthetic images are presented, including an evaluation of the dependence of the method on prior information and image quality. >
888 citations