Rigid-motion-invariant classification of 3-D textures

This paper studies the problem of 3-D rigid-motion-invariant texture discrimination for discrete 3-D textures that are spatially homogeneous by modeling them as stationary Gaussian random fields. The latter property and our formulation of a 3-D rigid motion of a texture reduce the problem to the study of 3-D rotations of discrete textures. We formally develop the concept of 3-D texture rotations in the 3-D digital domain. We use this novel concept to define a "distance" between 3-D textures that remains invariant under all 3-D rigid motions of the texture. This concept of "distance" can be used for a monoscale or a multiscale 3-D rigid-motion-invariant testing of the statistical similarity of the 3-D textures. To compute the "distance" between any two rotations R(1) and R(2) of two given 3-D textures, we use the Kullback-Leibler divergence between 3-D Gaussian Markov random fields fitted to the rotated texture data. Then, the 3-D rigid-motion-invariant texture distance is the integral average, with respect to the Haar measure of the group SO(3), of all of these divergences when rotations R(1) and R(2) vary throughout SO(3). We also present an algorithm enabling the computation of the proposed 3-D rigid-motion-invariant texture distance as well as rules for 3-D rigid-motion-invariant texture discrimination/classification and experimental results demonstrating the capabilities of the proposed 3-D rigid-motion texture discrimination rules when applied in a multiscale setting, even on very general 3-D texture models.     

基于结构张量方向引导的改进的W-L纹理合成算法应用研究

文章设计的算法在Wei和Levoy的思想基础上首先采用结构张量计算出引导图像的方向场,其次在方向场的引导下对样本纹理进行旋转,最后采用邻域相似性查找方法进行纹理合成,为了提升合成效率,文章通过采用向量化树结构的量化方法进行加速,取得了良好的实验效果。文章设计的算法不仅可以应用于方向纹理合成领域,同时通过拓展相关技术也可运用到非真实感绘制与渲染方面。     

The analysis of natural textures using run length features

A family of texture features is presented that have the ability to discriminate different textures in a 3-D scene as well as the ability to recover the range and orientation of the surfaces of the scene. These texture features are derived from the gray-level run-length matrices (GLRLMs) of an image. The GLRLMs are first normalized so that they all have equal average gray-level run length. Features extracted from the normalized GLRLMs are independent of the surface geometry. These features can be used in three-dimensional scene analysis where textures need to be identified according to their differences. Based on the average-run-length information and the classification results, surface range as well as surface orientation of a textured surface can be recovered     

Effective conductivity of a polycrystalline medium with weak macroscopic anisotropy

In the effective medium approximation, an analytical solution is obtained for calculating the tensor of the effective conductivity of a polycrystalline medium with weak uniaxial texture. The medium is assumed to consist of a single type of biaxial spherical crystallites. The orientation of the crystallites is taken into account by means of the theory of rotation group representations. A solution generalized to triaxial textures is obtained.     

A unified texture model based on a 2-D Wold-like decomposition

A unified texture model that is applicable to a wide variety of texture types found in natural images is presented. This model leads to the derivation of texture analysis and synthesis algorithms designed to estimate the texture parameters and to reconstruct the original texture field from these parameters. The texture field is assumed to be a realization of a regular homogeneous random field, which is characterized in general by a mixed spectral distribution. The texture field is orthogonally decomposed into a purely indeterministic component and a deterministic component. The deterministic component is further orthogonally decomposed into a harmonic component, and a generalized-evanescent component. Both analytical and experimental results show that the deterministic components should be parameterized separately from the purely indeterministic component. The model is very efficient in terms of the number of parameters required to faithfully represent textures. Reconstructed textures are practically indistinguishable from the originals     

Texture synthesis via a noncausal nonparametric multiscale Markovrandom field

Our noncausal, nonparametric, multiscale, Markov random field (MRF) model is capable of synthesizing and capturing the characteristics of a wide variety of textures, from the highly structured to the stochastic. We use a multiscale synthesis algorithm incorporating local annealing to obtain larger realizations of texture visually indistinguishable from the training texture.     

Maximum likelihood parameter estimation of textures using aWold-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.     

Long-correlation image models for textures with circular and elliptical correlation structures

A class of random field model having long-correlation characteristics is introduced. Unlike earlier approaches in long-correlation models, the correlation structure is isotropic or elliptical in this new class of random field model. The new model has an advantage of modeling diverse real textures with less than five model parameters. Further, the model parameters match with intuitive attributes of textures, such as smoothness, pattern size, elongation or orientation of patterns. The new long-correlation models are based on the fractional differencing of a two-dimensional (2-D) autoregressive polynomial defined by eight symmetric neighbors, and they are either persistent or periodic models depending whether the roots of the polynomial are real or imaginary. A comprehensive three-step algorithm for parameter estimation is developed, and the statistical properties of the estimators are also discussed. The validity of the new model in modeling textures is tested by synthesizing images from manually selected parameters as well as parameters estimated from real textures. It is shown that an image with desired attributes can be synthesized by selecting proper values of the parameters. Further, it is shown that the models introduced can be used in modeling wide range of textures by synthesizing images resembling real textures from estimated parameters.     

Analysis of optical flow constraints

Different constraint equations have been proposed in the literature for the derivation of optical flow. Despite of the large number of papers dealing with computational techniques to estimate optical flow, only a few authors have investigated conditions under which these constraints exactly model the velocity field, that is, the perspective projection on the image plane of the true 3-D velocity. These conditions are analyzed under different hypotheses, and the departures of the constraint equations in modeling the velocity field are derived for different motion conditions. Experiments are also presented giving measures of these departures and of the induced errors in the estimation of the velocity field.     

A new texture generation method based on pseudo-DCT coefficients.

In this paper, a new method for generating different texture images is presented. This method involves a simple transform from a certain one-dimensional (1-D) signal to an expected two-dimensional (2-D) image. Unlike traditional methods, the input signal is generated by a simple 1-D function in our work instead of a sample texture. We first transform the 1-D input signal into frequency domain using fast Fourier transform. Based on the sufficient analysis in 2-D discrete cosine transform (DCT) domain, where each of the coefficients expresses a texture feature in a certain direction, the 2-D pseudo-DCT coefficients are then constructed by appropriately rearranging the Fourier coefficients in terms of their frequency components. Finally, the corresponding texture image can be produced by 2-D inverse DCT algorithm. We applied the proposed method to generate several stochastic textures (i.e., cloud, illumination, and sand), and several structural texture images. Experimental results indicate the good performance of the proposed method.     

Bispectral analysis and model validation of texture images

Statistical approaches to texture analysis and synthesis have largely relied upon random models that characterize the 2-D process in terms of its first- and second-order statistics, and therefore cannot completely capture phase properties of random fields that are non-Gaussian and/or asymmetric. In this paper, higher than second-order statistics are used to derive and implement 2-D Gaussianity, linearity, and spatial reversibility tests that validate the respective modeling assumptions. The nonredundant region of the 2-D bispectrum is correctly defined and proven. A consistent parameter estimator for nonminimum phase, asymmetric noncausal, 2-D ARMA models is derived by minimizing a quadratic error polyspectrum matching criterion. Simulations on synthetic data are performed and the results of the bispectral analysis on real textures are reported.     

Texture Recognition and Image Retrieval Using Gradient Indexing

Our starting point is gradient indexing, the characterization of texture by a feature vector that comprises a histogram derived from the image gradient field. We investigate the use of gradient indexing for texture recognition and image retrieval. We find that gradient indexing is a robust measure with respect to the number of bins and to the choice of the gradient operator. We also find that the gradient direction and magnitude are equally effective in recognizing different textures. Furthermore, a variant of gradient indexing called local activity spectrum is proposed and shown to have improved performance. Local activity spectrum is employed in an image retrieval system as the texture statistic. The retrieval system is based on a segmentation technique employing a distance measure called Sum of Minimum Distance. This system enables content-based retrieval of database images from templates of arbitrary size.     

A Constrained Factor Decomposition With Application to MIMO Antenna Systems

In this paper, we formulate a new tensor decomposition herein called constrained factor (CONFAC) decomposition. It consists in decomposing a third-order tensor into a triple sum of rank-one tensor factors, where interactions involving the components of different tensor factors are allowed. The interaction pattern is controlled by three constraint matrices the columns of which are canonical vectors. Each constraint matrix is associated with a given dimension, or mode, of the tensor. The explicit use of these constraint matrices provides degrees of freedom to the CONFAC decomposition for modeling tensor signals with constrained structures which cannot be handled with the standard parallel factor (PARAFAC) decomposition. The uniqueness of this decomposition is discussed and an application to multiple-input multiple-output (MIMO) antenna systems is presented. A new transmission structure is proposed, the core of which consists of a precoder tensor decomposed as a function of the CONFAC constraint matrices. By adjusting the precoder constraint matrices, we can control the allocation of data streams and spreading codes to transmit antennas. Based on a CONFAC model of the received signal, blind symbol/code/channel recovery is possible using the alternating least squares algorithm. For illustrating this application, we evaluate the bit-error-rate (BER) performance for some configurations of the precoder constraint matrices.     

Region filling and object removal by exemplar-based image inpainting

A new algorithm is proposed for removing large objects from digital images. The challenge is to fill in the hole that is left behind in a visually plausible way. In the past, this problem has been addressed by two classes of algorithms: 1) "texture synthesis" algorithms for generating large image regions from sample textures and 2) "inpainting" techniques for filling in small image gaps. The former has been demonstrated for "textures"--repeating two-dimensional patterns with some stochasticity; the latter focus on linear "structures" which can be thought of as one-dimensional patterns, such as lines and object contours. This paper presents a novel and efficient algorithm that combines the advantages of these two approaches. We first note that exemplar-based texture synthesis contains the essential process required to replicate both texture and structure; the success of structure propagation, however, is highly dependent on the order in which the filling proceeds. We propose a best-first algorithm in which the confidence in the synthesized pixel values is propagated in a manner similar to the propagation of information in inpainting. The actual color values are computed using exemplar-based synthesis. In this paper, the simultaneous propagation of texture and structure information is achieved by a single, efficient algorithm. Computational efficiency is achieved by a block-based sampling process. A number of examples on real and synthetic images demonstrate the effectiveness of our algorithm in removing large occluding objects, as well as thin scratches. Robustness with respect to the shape of the manually selected target region is also demonstrated. Our results compare favorably to those obtained by existing techniques.     

Magnetite Crystal Orientation in Magnetosome Chains

One‐dimensional magnetic nanostructures have magnetic properties superior to non‐organized materials due to strong uniaxial shape anisotropy. Magnetosome chains in magnetotactic bacteria represent a biological paradigm of such magnet, where magnetite crystals synthesized in organelles called magnetosomes are arranged into linear chains. Two‐dimensional synchrotron X‐ray diffraction (XRD) is applied to cells of magnetotactic bacteria that are pre‐aligned with a magnetic field to determine the crystallographic orientation of magnetosomes relative to the chain axis. The obtained pole figure patterns reveal a [111] fiber texture along the chain direction for magnetospirilla strains MSR‐1 and AMB‐1, whereas a [100] fiber texture is measured for Desulfovibrio magneticus strain RS‐1. The [100] axis appears energetically unfavorable because it represents a magnetic hard axis in magnetite, but can be turned into an effective easy axis by particle elongation along [100] for aspect ratios higher than 1.25, consistent with aspect ratios in RS‐1 magnetosomes determined earlier. The pronounced fiber textures can be explained either by a strain‐specific biological control on crystal orientation at the chain level or by physical alignment effects due to intra‐chain magnetic interactions. In this case, biological control of the axis of elongation would be sufficient to influence the crystallographic texture of the magnetosome chain.     

Shape from texture: estimation of planar surface orientationthrough the ridge surfaces of continuous wavelet transform

In this correspondence, a method is proposed for estimating the surface orientation of a planar texture under perspective projection based on the ridge of a two-dimensional (2-D) continuous wavelet transform (CWT). We show that an analytical solution of the surface orientation can be derived from the scales of the ridge surface. A comparative study with an existing method is given.     

Higher Order SVD Analysis for Dynamic Texture Synthesis

Videos representing flames, water, smoke, etc., are often defined as dynamic textures: "textures" because they are characterized by the redundant repetition of a pattern and "dynamic" because this repetition is also in time and not only in space. Dynamic textures have been modeled as linear dynamic systems by unfolding the video frames into column vectors and describing their trajectory as time evolves. After the projection of the vectors onto a lower dimensional space by a singular value decomposition (SVD), the trajectory is modeled using system identification techniques. Synthesis is obtained by driving the system with random noise. In this paper, we show that the standard SVD can be replaced by a higher order SVD (HOSVD), originally known as Tucker decomposition. HOSVD decomposes the dynamic texture as a multidimensional signal (tensor) without unfolding the video frames on column vectors. This is a more natural and flexible decomposition, since it permits us to perform dimension reduction in the spatial, temporal, and chromatic domain, while standard SVD allows for temporal reduction only. We show that for a comparable synthesis quality, the HOSVD approach requires, on average, five times less parameters than the standard SVD approach. The analysis part is more expensive, but the synthesis has the same cost as existing algorithms. Our technique is, thus, well suited to dynamic texture synthesis on devices limited by memory and computational power, such as PDAs or mobile phones.     

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.