8,767 research outputs found
Object identification by using orthonormal circus functions from the trace transform
In this paper we present an efficient way to both compute and extract salient information from trace transform signatures to perform object identification tasks. We also present a feature selection analysis of the classical trace-transform functionals, which reveals that most of them retrieve redundant information causing misleading similarity measurements. In order to overcome this problem, we propose a set of functionals based on Laguerre polynomials that return orthonormal signatures between these functionals. In this way, each signature provides salient and non-correlated information that contributes to the description of an image object. The proposed functionals were tested considering a vehicle identification problem, outperforming the classical trace transform functionals in terms of computational complexity and identification rate
Shape from periodic texture using the eigenvectors of local affine distortion
This paper shows how the local slant and tilt angles of regularly textured curved surfaces can be estimated directly, without the need for iterative numerical optimization, We work in the frequency domain and measure texture distortion using the affine distortion of the pattern of spectral peaks. The key theoretical contribution is to show that the directions of the eigenvectors of the affine distortion matrices can be used to estimate local slant and tilt angles of tangent planes to curved surfaces. In particular, the leading eigenvector points in the tilt direction. Although not as geometrically transparent, the direction of the second eigenvector can be used to estimate the slant direction. The required affine distortion matrices are computed using the correspondences between spectral peaks, established on the basis of their energy ordering. We apply the method to a variety of real-world and synthetic imagery
Estimating the polarization degree of polarimetric images in coherent illumination using maximum likelihood methods
This paper addresses the problem of estimating the polarization degree of polarimetric images in coherent illumination. It has been recently shown that the degree of polarization associated to polarimetric images can be estimated by the method of moments applied to two or four images assuming fully developed speckle. This paper shows that the estimation can also be conducted by using maximum likelihood methods. The maximum likelihood estimators of the
polarization degree are derived from the joint distribution of the image intensities. We show that the joint distribution of polarimetric images is a multivariate gamma distribution whose marginals are univariate, bivariate or trivariate gamma distributions. This property is used to derive maximum likelihood estimators of the polarization degree using two, three or four images. The proposed
estimators provide better performance that the estimators of
moments. These results are illustrated by estimations conducted on synthetic and real images
Algebraic statistical models
Many statistical models are algebraic in that they are defined in terms of
polynomial constraints, or in terms of polynomial or rational parametrizations.
The parameter spaces of such models are typically semi-algebraic subsets of the
parameter space of a reference model with nice properties, such as for example
a regular exponential family. This observation leads to the definition of an
`algebraic exponential family'. This new definition provides a unified
framework for the study of statistical models with algebraic structure. In this
paper we review the ingredients to this definition and illustrate in examples
how computational algebraic geometry can be used to solve problems arising in
statistical inference in algebraic models
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