Parametric estimation of the orientation of textured planar surfaces.

This paper presents a parametric solution to the problem of estimating the orientation in space of a planar textured surface, from a single, noisy, observed image of it. The coordinate transformation from surface to image coordinates, due to the perspective projection, transforms each homogeneous sinusoidal component of the surface texture into a sinusoid whose frequency is a function of location. The functional dependence of the sinusoid phase in location is uniquely determined by the tilt and slant angles of the surface. Using the phase differencing algorithm we fit a polynomial phase model to a sinusoidal component of the observed texture. Assuming the estimated polynomial coefficients are the coefficients of a Taylor series expansion of the phase, we establish a linear recursive relation between the model parameters and the unknown slant and tilt. A linear least squares solution of the resulting system provides the slant and tilt estimates. To improve accuracy, an iterative refinement procedure is applied in a small neighborhood of these estimates. The performance of the proposed algorithms is evaluated by applying them to images of different planar surfaces, and by comparing their statistical performance with the Cramer-Rao bound. The combined two-stage algorithm is shown to produce estimates that are close to the bound.

Adaptive restoration of textured images with mixed spectra.

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.

An estimation algorithm for 2-D polynomial phase signals.

We consider nonhomogeneous 2-D signals that can be represented by a constant modulus polynomial-phase model. A novel 2-D phase differencing operator is introduced and used to develop a computationally efficient estimation algorithm for the parameters of this model. The operation of the algorithm is illustrated using an example.

Texture coding using a Wold decomposition model.

A novel approach for coding textured images is presented. The texture field is assumed to be a realization of a regular homogeneous random field, which can have a mixed spectral distribution. On the basis of a two-dimensional (2-D) Wold-like decomposition, the field is represented as a sum of a purely indeterministic, harmonic, and countable number of evanescent fields. We present an algorithm for estimating and coding the texture model parameters, and show that the suggested algorithm yields high-quality reconstructions at low bit rates. The model and the resulting coding algorithm are seen to be applicable to a wide variety of texture types found in natural images.

Maximum likelihood parameter estimation of textures using a Wold-decomposition based model.

We present a solution to the problem of modeling, parameter estimation, and synthesis of natural textures. The texture field is assumed to be a realization of a regular homogeneous random field, which can have a mixed spectral distribution. On the basis of a 2-D Wold-like decomposition, the field is represented as a sum of a purely indeterministic component, a harmonic component, and a countable number of evanescent fields. We present a maximum-likelihood solution to the joint parameter estimation problem of these components from a single observed realization of the texture field. The proposed solution is a two-stage algorithm. In the first stage, we obtain an estimate for the number of harmonic and evanescent components in the field, and a suboptimal initial estimate for the parameters of their spectral supports. In the second stage, we refine these initial estimates by iterative maximization of the likelihood function of the observed data. By introducing appropriate parameter transformations the highly nonlinear least-squares problem that results from the maximization of the likelihood function, is transformed into a separable least-squares problem. The solution for the unknown spectral supports of the harmonic and evanescent components reduces the problem of solving for the transformed parameters of the field to a linear least squares. Solution of the transformation equations then provides a complete solution of the field-model parameter estimation problem. The Wold-based model and the resulting analysis and synthesis algorithms are applicable to a wide variety of texture types found in natural images.