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

Texture synthesis: textons revisited

This paper introduces a technique for synthesizing natural textures, with emphasis on quasiperiodic and structural textures. Textures are assumed to be composed of three components, namely illumination, structure, and stochastic. The contribution of this work is that, in contrast to previous techniques, it proposes a joint approach for handling the texture's global illumination, irregular structure, and stochastic component which may be correlated to the other two components. Furthermore, the proposed technique does not produce verbatim copies in the synthesized texture. More specifically, a top-down approach is used for extraction of texture elements (textons) in which, in contrast to previous texton-based approaches, no assumptions regarding perfect periodicity are made. The structure itself can be modeled as a stochastic process. Consequently, textons are allowed to have irregular and nonidentical shapes. In the synthesis stage, a new nonregular textural structure is designed from the original one that defines the place holders for textons. We call such place holders empty textons (e-textons). The e-textons are filled in by a representative texton. Since e-textons do not have identical shapes, a texton shape-matching procedure is required. After adding the illumination to the structural component, a strictly localized version of a block sampling technique is applied to add the stochastic component. The block sampling technique combined with the addition of the illumination component provides a significant improvement in the appearance of synthesized textures. Results show that the proposed method is successful in synthesizing structural textures visually indistinguishable to the original. Moreover, the method is successful in synthesizing a variety of stochastic textures.

Texture decomposition by harmonics extraction from higher order statistics

In this paper, a method of harmonics extraction from Higher Order Statistics (HOS) is developed for texture decomposition. We show that the diagonal slice of the fourth-order cumulants is proportional to the autocorrelation of a related noiseless sinusoidal signal with identical frequencies. We propose to use this fourth-order cumulants slice to estimate a power spectrum from which the harmonic frequencies can be easily extracted. Hence, a texture can be decomposed into deterministic components and indeterministic components as in a unified texture model through a Wold-like decomposition procedure. The simulation and experimental results demonstrated that this method is effective for texture decomposition and it performs better than traditional lower order statistics based decomposition methods.

Reduced complexity modeling and reproduction of colored textures

An unsupervised color texture synthesis-by analysis method is described. The texture is reproduced to appear perceptually similar to a given prototype by copying its statistical properties up to the second order. The synthesized texture is obtained at the output of a single-input three-output nonlinear system driven by a realization of a white Gaussian random field. Significant complexity reduction is gained by exploiting the rank deficiency of the cross power spectral density matrix of the color texture samples.

Texture synthesis-by-analysis with hard-limited Gaussian processes

A twin stage texture synthesis-by-analysis method is presented. It aims to approximate first- and second-order distributions of the texture, accordingly to the Julesz conjecture. In the first stage, the binary textural behavior of a given prototype is represented by means of a hard-limited Gaussian process. In the second stage, the texture is synthesized by passing the binary hard-limited Gaussian process through a linear filter followed by a zero memory histogram equalizer.

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.

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.