This paper deals with parametric techniques for the description of texture on very high resolution (VHR) remote sensing images. These techniques focus on the property of anisotropy as described by the local structure tensor (LST). The novelty of this paper consists in proposing several comprehensive statistical frameworks to handle LST fields for rotation-invariant texture discrimination tasks. These frameworks are all based on probability models defined on the Riemannian manifold of positive definite matrices: a recent Riemannian Gaussian model on the affine-invariant metric space and a multivariate Gaussian distribution on the Log-Euclidean space. A thorough comparison of the proposed methods is performed with respect to some state-of-the-art texture analysis methods. Three experimental protocols are considered based on VHR remote sensing data. The first one consists of a content-based image retrieval (CBIR) protocol for browsing oyster field patches. The second one concerns a supervised classification protocol for grouping maritime pine forest stands in different age classes. The third one is, again, a CBIR protocol performed on the UC Merced land use/land cover patch collection. Tensor-based approaches show similar or even better results than the state-of-the-art texture analysis methods considered for comparison in all the experimental contexts.

This paper presents local structure tensor (LST) based methods for extracting the anisotropy and orientation information characterizing a textured image sample. A Log-Euclidean (LE) multivariate Gaussian model is proposed for representing the marginal distribution of the LST field of a texture. An extended model is considered as well for describing its spatial dependencies. The potential of these approaches are tested in a rotation invariant content based image retrieval (CBIR) context. Experiments are conducted on real data presenting anisotropic textures: very high resolution (VHR) remote sensing maritime pine forest images and material images representing dense carbons at nanometric scale.

This paper proposes a two-stage texture synthesis algorithm. At the first stage, a structure tensor map carrying information about the local orientation is synthesized from the exemplar's data and used at the second stage to constrain the synthesis of the texture. Keeping in mind that the algorithm should be able to reproduce as faithfully as possible the visual aspect, statistics, and morphology of the input sample, the method is tested on various textures and compared objectively with existing methods, highlighting its strength in successfully synthesizing the output texture in many situations where traditional algorithms fail to reproduce the exemplar's patterns. The promising results pave the way towards the synthesis of accurately large and multi-scale patterns as it is the case for carbon material samples showing laminar structures, for example.

Exemplar-based texture synthesis schemes are promising for virtual material design. They provide impressive results in many cases, but fail in difficult situations with large and multi-scale patterns, or with long range directional variations. Since a prior synthesis of a geometric layer may help in the synthesis of the texture layer, a two-stage structure/texture synthesis algorithm is proposed. At the first stage, a structure tensor map carrying information about the local orientation is synthesized from the exemplar's data, and at the second stage, the synthesized tensor field is used to constrain the synthesis of the texture. Results show that the proposed approach not only yields better synthesized textures, but also successfully synthesizes the output texture in many situations where traditional algorithms fail to reproduce the exemplar's patterns, which paves the way towards the synthesis of accurately large and multi-scale patterns as it is the case for pyrolytic carbon samples showing laminar structures observed by Transmission Electronic Microscopy.

Data on forest variables (e.g., biomass, trunk height, density) are necessary for environmental and forest management applications. It has been shown that texture can be used instead of the usual σo/age relationships at P-band to retrieve plantation forest parameters, but the analysis of σo spatial characteristics has not been fully explored. The aim of this letter is to investigate the relationships between stand age (which is correlated to forest variables) and texture descriptors calculated from statistics generated by the gray-level co-occurrence matrix for varying distance d, and orientation α, values used to calculate the matrix. Synthetic aperture radar images are P-band airborne data acquired by the ONERA RAMSES instrument over a controlled homogeneous test site located in the Landes region, France. It is found that texture descriptors contrast, inverse difference moment, homogeneity, and correlation are strongly influenced by the parameters (d, α) related to forest stand structure (forest rows, stand density) and image resolution. In contrast, energy and entropy are observed to be highly correlated to stand age and displayed a stable performance whatever the distance and orientation parameters (d, α), thus rendering them a good contender as an alternative to the usual σo based relationships applied to this type of forest.

We propose a genuine 3D texture synthesis algorithm based on a probabilistic 2D Markov random field conceptualization, capable of capturing the visual characteristics of a texture into a unique statistical texture model. We intend to reproduce, in the volumetric texture, the interactions between pixels learned in an input 2D image. The learning is done by nonparametric Parzen-windowing. Optimization is handled voxel by a relaxation algorithm, aiming at maximizing the likelihood of each voxel in terms of its local conditional probability function. Variants are proposed regarding the relaxation algorithm and the heuristic strategies used for the simultaneous handling of the orthogonal slices containing the voxel. The procedures are materialized on various textures through a comparative study and a sensitivity analysis, highlighting the variants strengths and weaknesses. Finally, the probabilistic model is compared objectively with a nonparametric neighborhood-search-based algorithm.

We propose a genuine 3D texture synthesis algorithm based on a probabilistic 2D Markov Random Field conceptualization. We intend to reproduce, in the volumetric texture, the interactions between pixels learned non-parametrically in an input 2D image. Optimization is handled voxel by voxel by a deterministic algorithm, deciding for each voxel the most probable grey level. Variants are proposed regarding the heuristic strategies used for the simultaneous handling of the orthogonal slices containing the voxel. Voxel relaxation and scale handling policies are al so investigated. The procedures are materialized on various textures to identify their strengths and weaknesses.

Textural analysis can bring valuable information in the classification or the segmentation process of land covers displaying regular patterns in very high resolution remotely sensed images. In this study, we investigate how features extracted by multivariate modeling of the local spatial dependence in the wavelet domain can efficiently capture the textural content of maritime pine forest images in comparison with a commonly used texture analysis approach, the GLCM. To evaluate the performances of the tested methods, we used a content based image retrieval framework and created a database of image patches representing different development stages of the forest stands. Results show that multivariate models display higher retrieval rates than GLCM-based methods with yet a higher sensitivity to the dominant orientation in anisotropic textures. These observations open up new perspectives in the use of multivariate modeling for textural features extraction in very high resolution image classification.

The goal of this paper is to evaluate non-parametric algorithms that achieve 3D texture synthesis from a single 2D sample. The algorithms under study are variants of the algorithm proposed by Wei and Levoy [1]. Several authors have proposed different algorithms that intend to better reproduce, in the output texture, the diversity learned in the input sample. Hence, we turn our attention to the improved algorithm proposed by Kopf et al. [2] and the particular histogram matching approach of Chen and Wang [3]. In addition, we propose to visit the voxels during synthesis according to the 3D extension of space filling curves. We investigate the algorithms capability to reproduce anisotropic textures. In particular we are interested in laminar textures, i.e. textures made of anisotropic sheets stacked along a given direction. Examples of such textures are snapshots of dense carbons observed by high resolution transmission electronic microscopy (HRTEM). Beyond the traditional subjective evaluation of the synthesized textures, we propose a genuine quantitative benchmark for the analysis of the synthesized textures which consists in comparing input and output gray level statistics and patterns morphology.

In this paper, we investigate both linear and circular stochastic models in the context of texture discrimination. These models aim at representing the magnitudes and orientations obtained by a complex wavelet decomposition, such as the steerable pyramid.The novelty consists in considering specific parametric models for circular data such as von Mises and psi- distributions to describe the distributions of orientations. Particular attention is paid to the choice of a metric and to its adequation to the models. Indexing experiments are conducted to quantitatively evaluate the performances of the proposed models and of the chosen matrices, i.e. the L1and Kullback-Leibler distances.

Given textured images considered as realizations of 2-D stochastic processes, a framework is proposed to evaluate the stationarity of their mean and variance. Existing strategies focus on the asymptotic behavior of the empirical mean and variance (respectively EM and EV), known for some types of nondeterministic processes. In this paper, the theoretical asymptotic behaviors of the EM and EV are studied for large classes of second-order stationary ergodic processes, in the sense of the Wold decomposition scheme, including harmonic and evanescent processes. Minimal rates of convergence for the EM and the EV are derived for these processes; they are used as criteria for assessing the stationarity of textures. The experimental estimation of the rate of convergence is achieved using a nonparametric block sub-sampling method. Our framework is evaluated on synthetic processes with stationary or nonstationary mean and variance and on real textures. It is shown that anomalies in the asymptotic behavior of the empirical estimators allow detecting nonstationarities of the mean and variance of the processes in an objective way.

This paper focuses on directional textures. It provides a new framework for the design of convolution masks dedicated to orientation estimation. We propose a new technique based on the combination of two complementary operators: a gradient-based operator which is adapted to sloped regions and a valleyness detector which fits the crests and valleys. On each operator, a double optimization procedure is carried out with respect to bias and noise sensitivity reduction. The procedure is generic and applies to any kind of underlying directional texture. Experiments on a synthetic sine wave texture and on natural textures are provided and show the efficiency and the relevance of our approach.

Topographic approaches are often used in the framework of texture characterization. More particularly, level curves proved to be interesting features to describe textures containing elongated patterns. Here, we provide an algorithm for level curve tracking based on a step by step propagation of a level set from a pixel to its neighbors. Textural feature extraction is then considered; orientation and pattern length measurement techniques are proposed. Pattern length retrieval is then exercised on composite material images taken from transmission electron microscopy.

This paper deals with the characterization of textures. It focuses on textural properties based on the local differences of attributes, such as homogeneity and orientation. We introduce the scaled scattering indicator (SSI) in order to estimate such textural properties. SSI is computed at various observation scales to take into account micro-textures as well as macro-textures involved in pictures. We establish the theoretical behavior of SSI in the case of a pavement filled with a given textural pattern. We devote this indicator to the multiscale characterization of the anisotropy of pictures. Simulation results on synthetic and real pictures confirm the the theoretical approach we have provided: SSI provides an accurate estimation of textural properties like anisotropy, but also gives an estimation of the size of the textural patterns involved in the picture.