J. Francos - Academia.edu (original) (raw)

Papers by J. Francos

Research paper thumbnail of 7 Orthogonal decompositions of 2D random fields and their applications for 2D spectral estimation

Handbook of Statistics, 1993

Research paper thumbnail of A 2-D autoregressive, finite support, causal model for texture analysis and synthesis

International Conference on Acoustics, Speech, and Signal Processing

A 2-D AR (autoregressive), finite-support, half-plane, causal model for homogeneous random fields... more A 2-D AR (autoregressive), finite-support, half-plane, causal model for homogeneous random fields is developed and applied to the analysis and synthesis of homogeneous random textures. The conditions under which the finite, discontinuous-support, 2-D Levinson type algorithm can be applied to solve the 2-D normal equations are presented. In the texture analysis case, these conditions are met by first removing all

Research paper thumbnail of A study of Gaussian mixture models of color and texture features for image classification and segmentation

Pattern Recognition, 2006

Research paper thumbnail of Bounds for estimation of complex exponentials in unknown colored noise

IEEE Transactions on Signal Processing, 1995

Research paper thumbnail of Texture coding using a Wold decomposition model

IEEE Transactions on Image Processing, 1996

Research paper thumbnail of An estimation algorithm for 2-D polynomial phase signals

IEEE Transactions on Image Processing, 1996

Research paper thumbnail of Parameter estimation of two-dimensional moving average random fields

IEEE Transactions on Signal Processing, 1998

Research paper thumbnail of An order fitting rule for optimal subspace averaging

2016 IEEE Statistical Signal Processing Workshop (SSP), 2016

Research paper thumbnail of Parametric Estimation of Multi-Dimensional Affine Transformations: An Exact Linear Solution

Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005., 2000

Research paper thumbnail of Registration of Joint Geometric and Radiometric Image Deformations in the Presence of Noise

2007 IEEE/SP 14th Workshop on Statistical Signal Processing, 2007

ABSTRACT We consider the problem of object registration where the observed template simultaneousl... more ABSTRACT We consider the problem of object registration where the observed template simultaneously undergoes an affine transformation of coordinates and a non-linear mapping of the intensities. More generally, the problem is that of jointly estimating the geometric and radiometric deformations relating two observations on the same object. We show that, in the absence of noise, the original high dimensional non-convex search problem that needs to be solved in order to register the observation to the template is replaced by an equivalent problem, expressed in terms of a sequence of two linear systems of equations. A solution to this sequence provides an exact solution to the registration problem. It is further shown that in the presence of noise, the original stochastic registration problem can be mapped, almost surely, to a new deterministic problem in the form of a classic deconvolution problem. Solution of the deconvolution problem reduces the solution of the original estimation problem to the form derived for the noise-free case.

Research paper thumbnail of On a wold-like decomposition of 2-D discrete random fields

International Conference on Acoustics, Speech, and Signal Processing, 1990

Imposing a total-order on a two-dimensional discrete homogeneous random field induces an orthogon... more Imposing a total-order on a two-dimensional discrete homogeneous random field induces an orthogonal decomposition of the random field into two components: a purely indeterministic field and a deterministic one. The purely indeterministic component is shown to have a two-dimensional white-innovations driven MA representation. The two-dimensional deterministic random field can be perfectly predicted from the field's past samples. This field is further orthogonally decomposed into a purely deterministic field that represents the remote past of the field and can thus be perfectly predicted given enough arbitrarily located data samples, and an evanescent component. The evanescent component can be further decomposed into a remote columnwise past component and a column-to-column renewal field

Research paper thumbnail of Estimation of amplitude and phase of non-stationary signals

Proceedings of 27th Asilomar Conference on Signals, Systems and Computers, 1993

We consider the problem of estimating signals consisting of one or more components of the form a(... more We consider the problem of estimating signals consisting of one or more components of the form a(t)ejφ(t), where the amplitude and phase functions are represented by a linear parametric model. A maximum likelihood algorithm for estimating the phase and amplitude parameters is presented, and the corresponding Cramer Rao bound (CRB) is derived. By analyzing the CRB for the single-component case it is shown that the estimation of the amplitude and the phase are decoupled. The performance of the maximum likelihood algorithm is illustrated by Monte-Carlo simulations, and its statistical efficiency is verified

Research paper thumbnail of Asymptotic normality of the sample convariances of evanescent fields in noise

IEEE/SP 13th Workshop on Statistical Signal Processing, 2005, 2005

We consider the asymptotic properties of the sample covariance sequence of a field composed of th... more We consider the asymptotic properties of the sample covariance sequence of a field composed of the sum of evanescent components and a purely-indeterministic component. In this framework a Bartlett-type formula for the covariance function of the sample covariances of a horizontal evanescent field observed in the presence of a purely-indeterministic field, is derived. The asymptotic normality of the sample covariances

Research paper thumbnail of Icassp 2891: Gaussian Mixture Models of Texture and Colour for Image Database Retrieval

We introduce Gaussian mixture models of 'structure' and colour features in order to cla... more We introduce Gaussian mixture models of 'structure' and colour features in order to classify coloured textures in im- ages, with a view to the retrieval of textured colour im- ages from databases. Classifications are performed sepa- rately using structure and colour and then combined using a confidence criterion. We apply the models to the VisTex database and to the classification of man-made and natural areas in aerial images. We compare these models with oth- ers in the literature, and show an overall improvement in performance.

Research paper thumbnail of The rank of the covariance matrix of an evanescent field

Journal of Multivariate Analysis, 2010

Research paper thumbnail of The evanescent field transform for estimating the parameters of homogeneous random fields with mixed spectral distributions

IEEE Transactions on Signal Processing, 1999

Research paper thumbnail of On the accuracy of estimating the parameters of a regular stationary process

IEEE Transactions on Information Theory, 1996

Research paper thumbnail of Maximum-likelihood parameter estimation of the harmonic, evanescent, and purely indeterministic components of discrete homogeneous random fields

IEEE Transactions on Information Theory, 1996

Research paper thumbnail of Maximum likelihood parameter estimation of textures using a Wold-decomposition based model

IEEE Transactions on Image Processing, 1995

Research paper thumbnail of Adaptive restoration of textured images with mixed spectra

IEEE Transactions on Image Processing, 1996

We consider the adaptive restoration of inhomogeneous textured images, where the individual regio... more We consider the adaptive restoration of inhomogeneous textured images, where the individual regions are modeled using a Wold-like decomposition. A generalized Wiener filter is developed to accommodate mixed spectra, and unsupervised restoration is achieved by using the expectation-maximization (EM) algorithm to estimate the degradation parameters. This algorithm yields superior results when compared with supervised Wiener filtering using autoregressive (AR) image models.

Research paper thumbnail of 7 Orthogonal decompositions of 2D random fields and their applications for 2D spectral estimation

Handbook of Statistics, 1993

Research paper thumbnail of A 2-D autoregressive, finite support, causal model for texture analysis and synthesis

International Conference on Acoustics, Speech, and Signal Processing

A 2-D AR (autoregressive), finite-support, half-plane, causal model for homogeneous random fields... more A 2-D AR (autoregressive), finite-support, half-plane, causal model for homogeneous random fields is developed and applied to the analysis and synthesis of homogeneous random textures. The conditions under which the finite, discontinuous-support, 2-D Levinson type algorithm can be applied to solve the 2-D normal equations are presented. In the texture analysis case, these conditions are met by first removing all

Research paper thumbnail of A study of Gaussian mixture models of color and texture features for image classification and segmentation

Pattern Recognition, 2006

Research paper thumbnail of Bounds for estimation of complex exponentials in unknown colored noise

IEEE Transactions on Signal Processing, 1995

Research paper thumbnail of Texture coding using a Wold decomposition model

IEEE Transactions on Image Processing, 1996

Research paper thumbnail of An estimation algorithm for 2-D polynomial phase signals

IEEE Transactions on Image Processing, 1996

Research paper thumbnail of Parameter estimation of two-dimensional moving average random fields

IEEE Transactions on Signal Processing, 1998

Research paper thumbnail of An order fitting rule for optimal subspace averaging

2016 IEEE Statistical Signal Processing Workshop (SSP), 2016

Research paper thumbnail of Parametric Estimation of Multi-Dimensional Affine Transformations: An Exact Linear Solution

Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005., 2000

Research paper thumbnail of Registration of Joint Geometric and Radiometric Image Deformations in the Presence of Noise

2007 IEEE/SP 14th Workshop on Statistical Signal Processing, 2007

ABSTRACT We consider the problem of object registration where the observed template simultaneousl... more ABSTRACT We consider the problem of object registration where the observed template simultaneously undergoes an affine transformation of coordinates and a non-linear mapping of the intensities. More generally, the problem is that of jointly estimating the geometric and radiometric deformations relating two observations on the same object. We show that, in the absence of noise, the original high dimensional non-convex search problem that needs to be solved in order to register the observation to the template is replaced by an equivalent problem, expressed in terms of a sequence of two linear systems of equations. A solution to this sequence provides an exact solution to the registration problem. It is further shown that in the presence of noise, the original stochastic registration problem can be mapped, almost surely, to a new deterministic problem in the form of a classic deconvolution problem. Solution of the deconvolution problem reduces the solution of the original estimation problem to the form derived for the noise-free case.

Research paper thumbnail of On a wold-like decomposition of 2-D discrete random fields

International Conference on Acoustics, Speech, and Signal Processing, 1990

Imposing a total-order on a two-dimensional discrete homogeneous random field induces an orthogon... more Imposing a total-order on a two-dimensional discrete homogeneous random field induces an orthogonal decomposition of the random field into two components: a purely indeterministic field and a deterministic one. The purely indeterministic component is shown to have a two-dimensional white-innovations driven MA representation. The two-dimensional deterministic random field can be perfectly predicted from the field's past samples. This field is further orthogonally decomposed into a purely deterministic field that represents the remote past of the field and can thus be perfectly predicted given enough arbitrarily located data samples, and an evanescent component. The evanescent component can be further decomposed into a remote columnwise past component and a column-to-column renewal field

Research paper thumbnail of Estimation of amplitude and phase of non-stationary signals

Proceedings of 27th Asilomar Conference on Signals, Systems and Computers, 1993

We consider the problem of estimating signals consisting of one or more components of the form a(... more We consider the problem of estimating signals consisting of one or more components of the form a(t)ejφ(t), where the amplitude and phase functions are represented by a linear parametric model. A maximum likelihood algorithm for estimating the phase and amplitude parameters is presented, and the corresponding Cramer Rao bound (CRB) is derived. By analyzing the CRB for the single-component case it is shown that the estimation of the amplitude and the phase are decoupled. The performance of the maximum likelihood algorithm is illustrated by Monte-Carlo simulations, and its statistical efficiency is verified

Research paper thumbnail of Asymptotic normality of the sample convariances of evanescent fields in noise

IEEE/SP 13th Workshop on Statistical Signal Processing, 2005, 2005

We consider the asymptotic properties of the sample covariance sequence of a field composed of th... more We consider the asymptotic properties of the sample covariance sequence of a field composed of the sum of evanescent components and a purely-indeterministic component. In this framework a Bartlett-type formula for the covariance function of the sample covariances of a horizontal evanescent field observed in the presence of a purely-indeterministic field, is derived. The asymptotic normality of the sample covariances

Research paper thumbnail of Icassp 2891: Gaussian Mixture Models of Texture and Colour for Image Database Retrieval

We introduce Gaussian mixture models of 'structure' and colour features in order to cla... more We introduce Gaussian mixture models of 'structure' and colour features in order to classify coloured textures in im- ages, with a view to the retrieval of textured colour im- ages from databases. Classifications are performed sepa- rately using structure and colour and then combined using a confidence criterion. We apply the models to the VisTex database and to the classification of man-made and natural areas in aerial images. We compare these models with oth- ers in the literature, and show an overall improvement in performance.

Research paper thumbnail of The rank of the covariance matrix of an evanescent field

Journal of Multivariate Analysis, 2010

Research paper thumbnail of The evanescent field transform for estimating the parameters of homogeneous random fields with mixed spectral distributions

IEEE Transactions on Signal Processing, 1999

Research paper thumbnail of On the accuracy of estimating the parameters of a regular stationary process

IEEE Transactions on Information Theory, 1996

Research paper thumbnail of Maximum-likelihood parameter estimation of the harmonic, evanescent, and purely indeterministic components of discrete homogeneous random fields

IEEE Transactions on Information Theory, 1996

Research paper thumbnail of Maximum likelihood parameter estimation of textures using a Wold-decomposition based model

IEEE Transactions on Image Processing, 1995

Research paper thumbnail of Adaptive restoration of textured images with mixed spectra

IEEE Transactions on Image Processing, 1996

We consider the adaptive restoration of inhomogeneous textured images, where the individual regio... more We consider the adaptive restoration of inhomogeneous textured images, where the individual regions are modeled using a Wold-like decomposition. A generalized Wiener filter is developed to accommodate mixed spectra, and unsupervised restoration is achieved by using the expectation-maximization (EM) algorithm to estimate the degradation parameters. This algorithm yields superior results when compared with supervised Wiener filtering using autoregressive (AR) image models.