Ahmed Drissi El Maliani

Color texture classification method based on a statistical multi-model and geodesic distance

A statistical multi-model for color texture classification is proposed.We use perceptual color spaces HSV and Lab as an alternative of RGB.We use the copula theory to build our models for luminance and chrominance.We derive a closed-form of geodesic distance between two copulas.We use the Bayesian classifier to assess the performance of our multi-model. In this paper, we propose a novel color texture classification method based on statistical characterization. The approach consists in modeling complex wavelet coefficients of both luminance and chrominance components separately leading to a multi-modeling approach. The copula theory allows to take into account the spatial dependencies which exist within the intra-luminance sub-bands via the luminance model M L , and also between the inter-chrominance subband coefficients via the chrominance model M C r . The multi-model, i.e. M L and M C r , is used to develop a Bayesian classifier based on the softmax principal. To derive the classifier, we propose a closed-form expression for the Rao geodesic distance between two copulas. Experiments on two sub-families of luminance-chrominance color spaces namely Lab and HSV have been carried out for a wide range of color texture databases. The combination of different statistical sub-models show that the multi-modeling performs better than some existing methods in term of classification rates.

Texture retrieval using mixtures of generalized Gaussian distribution and Cauchy-Schwarz divergence in wavelet domain

This paper presents a novel similarity measure in a texture retrieval framework based on statistical modeling in wavelet domain. In this context, we use the recently proposed finite mixture of generalized Gaussian distribution (MoGG) thanks to its ability to model accurately a wide range of wavelet sub-bands histograms. This model has already been relied on the approximation of Kullback-Leibler divergence (KLD) which hinders significantly the retrieval process. To overcome this drawback, we introduce the Cauchy-Schwarz divergence (CSD) between two MoGG distributions as a similarity measure. Hence, an analytic closed-form expression of this measure is developed in the case of fixed shape parameter. Otherwise, when the shape parameter is variable, two approximations are derived using the well-known stochastic integration with Monte-Carlo simulations and numerical integration with Simpsons rule. Experiments conducted on a well known dataset show good performance of the CSD in terms of retrieval rates and the computational time improvement compared to the KLD. HighlightsWe propose Cauchy Schwarz divergence CSD for texture retrieval.Wavelet coefficients are modeled by mixture of generalized Gaussians MoGG.We derive a closed-form of CSD between MoGG for fixed parameter shape.We use the Monte-Carlo approximation for CSD in the general case.We evaluate the performance in terms of the average retrieval rates and the computational time.

Texture classification based on the Generalized Gamma distribution and the Dual Tree Complex Wavelet Transform

This paper deals with stochastic texture modeling for classification issue. A generic stochastic model based on three-parameter Generalized Gamma (GG) distribution function is proposed. The GG modeling offers more flexibility parameterization than other kinds of heavy-tailed density devoted to wavelet empirical histograms characterization. Moreover, Kullback-leibler divergence is chosen as similarity measure between textures. Experiments carried out on Vistex texture database show that the proposed approach achieves good classification rates.

Multi-model approach for multicomponent texture classification

This paper concerns multicomponent texture classification. The aim is to provide a flexible model when wavelet subband coefficients of components do not have the same distributions. Example of such case is when color textures are represented in a perceptual color space. In this kind of representation, the separability between luminance and chrominance components have to be considered in the modeling process. The contribution of this work consists in proposing a multi-model based characterization for this type of multicomponent images. For this, two models ML and MCr are used in order to extract features from luminance and chrominance components, respectively. We discuss in detail and define the multi-model when textures are represented in the HSV color space as a special case of multicomponent analysis. Experimental results show that the proposed approach improves performances of the classification system when compared with existing methods.

Texture Retrieval Using Cauchy-Schwarz Divergence and Generalized Gaussian Mixtures

In this paper, we introduce the Cauchy-Schwarz divergence (CSD) in the context of texture retrieval. First, we model wavelet coefficients histograms using the already existing mixture of generalized Gaussians (MoGG) distribution. Then, we propose the CSD as a similarity measure between two MoGGs. As there is no closed-form of CSD, we compute this measure by a Monte-Carlo sampling method. Thanks to its tractable mathematical expression, CSD becomes computationally less expensive in contrast with Kullback-Leibler divergence (KLD). This later often needs other approximations with good sampling strategies or using bounding methods to avoid the heavy sampling process. Through the conducted experiments on two popular databases VisTeX and Brodatz, a retrieval rate of 98% is achieved.

Rotation-Invariant texture retrieval using a steerable Gaussian copula model

In this paper, we address the problem of rotation invariance in the context of texture retrieval. For this, we propose a framework based on the well-known copula theory which is considered one of the most powerful statistical tools. Prior to apply a such model, we first use the steerable pyramid SP as one of the most relevant transforms. Then, we build a steerable Gaussian copula model which offers a good fitting of the SP coefficients distribution while taking into consideration their rotation invariance property. Finally, we derive a closed-form of the Jefferey divergence as a similarity measure. The latter consists on an angular alignment between the query and the target texture features. Experiments have been conducted on USC database, good performances in term of retrieval rates are achieved compared to previously proposed copula models.

A novel statistical model for content-based stereo image retrieval in the complex wavelet domain

Abstract This paper presents a new stereo image (SI) retrieval method based on a statistical model of complex wavelet coefficients subbands. In this context, a Gaussian copula-based multivariate model is used to capture the dependence between complex wavelet coefficients of both left and right images, and a non-Gaussian univariate model is used to characterize the statistical behavior of the disparity map. Thanks to its flexibility, the copula tool allows us to choose several marginal densities while keeping the multivariate properties. Features are extracted by estimating parameters for both multivariate and univariate models. Finally, a weighted Jeffrey divergence (JD) is used as a similarity measurement between the underlying models. Experimental results on a stereo image database demonstrate the performance of the proposed method in terms of the retrieval rates as well as the computational time.

Rao-Geodesic distance on the generalized gamma manifold: Study of three sub-manifolds and application in the Texture Retrieval domain

KLD is not a distance since it does not satisfy symmetry and triangular inequality properties. In this paper we propose Geodesic distance (GD) as a similarity measure on the Generalized Gamma (GG) manifold, in order to illustrate the importance of geometric reasoning in the image retrieval field. The principle idea is the use of the distances between the probability distributions in precise manner through the GD, as an application in the SM between the texture images which are represented by the parameters of the probability distributions. And that can be a good illustration of the value of the Riemannian geometry through statistical manifold in an applied field such as the texture retrieval. Generalized Gamma is a three parameters distribution that covers Gamma, Weibull and Exponential models as special cases, which allowed the modeling of a wide range of texture families. We take advantage of this property in order to make a prior study of the GD for the Gamma, Weibull and Exponential sub-manifolds due to the cumbersomeness of deriving GD for the generalized gamma directly. Experiments are carried out considering texture retrieval in the domains of dual tree complex wavelet transform and steerable pyramid transform, using the Vistex texture database. Results show that GD achieves performances that are close or higher to KLD for the three sub-manifolds, which is of a great interest since GD is a Riemannian metric contrary to KLD.

Study of magnitude and extended relative phase information for color texture retrieval in L*a*b* color space

This paper presents a univariate multi-model for color texture characterization in luminance-chrominance (LC) color spaces. Such color spaces are known to separate between luminance and chrominance, contrary to RGB representation. The magnitude of the luminance component is then represented via the Gamma distribution. For chrominance, a new proposed information is investigated, namely the extended relative phase (ERP). This latter allows to capture the phase information inter-chrominance components. This information is characterized using the circular Wrapped cauchy (WC) distribution. The resulting {Gamma, WC} model has the advantage to be a linear-circular model. It, thus, represents color components considering their nature. Secondly, it permits to catch an information of dependence between chrominance components while being univariate. This means a modeling with simple feature extraction and straightforward implementation of similarity measurement, compared to the multivariate characterization widely used for color textures. Results on the Vistex database show that the study of {magnitude, ERP} information in LC color spaces, improves the retrieval performances compared to the RGB based characterization.