Wavelet-based texture analysis and synthesis using hidden Markov models

Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint probability density of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training to fit an HMT model to a given data set (e.g., using the expectation-maximization algorithm). We greatly simplify the HMT model by exploiting the inherent self-similarity of real-world images. The simplified model specifies the HMT parameters with just nine meta-parameters (independent of the size of the image and the number of wavelet scales). We also introduce a Bayesian universal HMT (uHMT) that fixes these nine parameters. The uHMT requires no training of any kind, while extremely simple, we show using a series of image estimation/denoising experiments that these new models retain nearly all of the key image structure modeled by the full HMT. Finally, we propose a fast shift-invariant HMT estimation algorithm that outperforms other wavelet-based estimators in the current literature, both visually and in mean square error.

Robustness is the key issue in the development of multi-bit watermarking algorithm. A new algorithm for robust multi-bit image watermarking based on Hidden Markov Model (HMM) in wavelet domain is proposed in this paper. The algorithm is characterized as follows: (1) the proposed blind detector based on vector HMM, which describes the statistics of wavelet coefficients, achieves significant improvement in performance compared to the conventional correlation detector; (2) adaptive watermark embedding scheme is applied to achieve the low distortion according to the Human Visual System (HVS); (3) optimal multi-bit watermark embedding strategy and maximum-likelihood detection for tree structure of vector HMM is proposed through system robustness analysis. Simulation results show that relatively high capacity for watermark embedding in low frequency subbands of wavelet domain is achieved with the proposed algorithm, and high robust results are observed against StirMark attacks, such as JPEG compression, additive noise, median cut and filter.

The granular appearance of speckle noise in synthetic aperture radar (SAR) imagery makes it very difficult to visually and automatically interpret SAR data. Therefore, speckle reduction is a prerequisite for many SAR image processing tasks. In this paper, we propose a contourlet-based despeckling method for the SAR image using the hidden Markov tree (HMT) and Gaussian Markov models. The contourlet transform is a recently developed two-dimensional transform technique. It is reported to be more effective than wavelets in representing smooth curvature details typical of natural images. The HMT and Gaussian Markov models will reflect the correlations of the contourlet coefficients not only across scales and directions but also between neighbors. The experimental results show that the proposed method in contrary to other methods can obtain a better trade-off between smoothing the homogeneous areas and keeping the edges and can get better visual effect.

We introduce a new image texture segmentation algorithm, HMTseg, based on wavelet-domain hidden Markov tree (HMT) models. The HMT model is a tree-structured probabilistic graph that captures the statistical properties of wavelet coefficients. Since the HMT is particularly well suited to images containing singularities (edges and ridges), it provides provides a good classifier for textures. Utilizing the inherent tree structure of the wavelet HMT and its fast training and likelihood computation algorithms, we perform multiscale texture classification at various scales. We then fuse these multiscale classifications using a Bayesian probabilistic graph to obtain a reliable final segmentation. Since HMTseg works on the wavelet transform of the image, it can directly segment wavelet-compressed images, without the need for decompression. We demonstrate the performance of HMTseg with synthetic, aerial photo, and document image segmentations.

This paper presents a technique that used to enhance the image resolution. The input low resolution (LR) image is decomposed into low frequency (LF) and high frequency (HF) sub-bands by using lifting wavelet transform (LWT) and discrete wavelet transform (DWT). The resolution enhancement is done by interpolating HF sub-bands that are generated using LWT from the LR image. The HF sub-bands of DWT are used to preserve the edges of the images. The operation is done on HF sub-bands of LWT and DWT. The HF sub-bands that are generated from the DWT are interpolated and perform addition to the respective interpolated HF sub-bands of LWT. The HF sub-bands that are modified and the LR image will again interpolate and undergoes the inverse lifting wavelet transform (ILWT) to reconstruct the high resolution (HR) image. This implemented method results efficient over conventional methods.

Color image encryption using MSVD, DWT and Arnold transform in fractional Fourier domain

A semi-supervised hidden Markov tree (HMT) model is developed for texture analysis, incorporating both labeled and unlabeled data for training; the optimal balance between labeled and unlabeled data is estimated via the homotopy method. In traditional EM-based semi-supervised modeling, this balance is dictated by the relative size of labeled and unlabeled data, often leading to poor performance. Semi-supervised modeling may be viewed as a source allocation problem between labeled and unlabeled data, controlled by a parameter lambda isin [0,1], where lambda = 0 and 1 correspond to the purely supervised HMT model and purely unsupervised HMT-based clustering, respectively. We consider the homotopy method to track a path of fixed points starting from lambda = 0, with the optimal source allocation identified as a critical transition point where the solution is unsupported by the initial labeled data. Experimental results on real textures demonstrate the superiority of this method compared to the EM-based semi-supervised HMT training

The authors propose a multiscale Bayesian texture segmentation algorithm that is based on a complex wavelet domain hidden Markov tree (HMT) model and a hybrid label tree (HLT) model. The HMT model is used to characterise the statistics of the magnitudes of complex wavelet coefficients. The HLT model is used to fuse the interscale and intrascale context information. In the HLT, the interscale information is fused according to the label transition probability directly resolved by an EM algorithm. The intrascale context information is also fused so as to smooth out the variations in the homogeneous regions. In addition, the statistical model at pixel-level resolution is formulated by a Gaussian mixture model (GMM) in the complex wavelet domain at scale 1, which can improve the accuracy of the pixel-level model. The experimental results on several texture images are used to evaluate the algorithm.

In this paper, a new multiscale texture segmentation method using contextual hidden Markov tree (CHMT) in wavelet domain is proposed. The hidden Markov tree models (HMT) describe persistence property of wavelet coefficients in multiscale images, but loses clustering property. The method is put forward to overcome the shortcoming of standard HMT by using extended coefficients without changing the wavelet tree structure and makes it possible to get a more accurate segmentation result. Experimental results demonstrate that the proposed method is effective for multiscale texture image segmentation.

Progressive texture synthesis can provide an added functional advantage to existing texture synthesis algorithms, which are time consuming and fail to deliver in some application areas. To provide practical solutions to this challenge we have previously proposed a discrete wavelet transform (DWT) based texture synthesis algorithm for 2D surfaces. In this paper we propose the extension of this approach to 3D progressive-texture synthesis. The proposed 3D progressive- texture synthesis algorithm makes use of the EZW (embedded zero-tree wavelet) idea proposed by Shapiro, which is capable of prioritising the coefficients of a DWT decomposed image according to their visual significance. We demonstrate the use of the proposed algorithm on progressive texturing geometric surfaces such as ring dupin cyclides, toruses, spheres, parametrised by rational Bezier patches. We provide experimental results to prove the effectiveness of the proposed approach, when synthesising textures of regular, irregular and stochastic nature. Further experimental results are provided to illustrate the practical use of the proposed progressive texture synthesis algorithm in resource constrained application domains. (10 pages)

Digital multimedia content protection has increasingly become an important issue. Because image watermarking is identified as a major technology used in copyright protection, a key requirement for image watermarking is the development of its imperceptibility and robustness. To meet this requirement, a novel robust image watermarking scheme based on discrete wavelet transform (DWT), singular value decomposition (SVD), and chaotic mixtures is proposed in this paper, In this method, the singular values of the encrypt watermark are embedded on the singular values of the important inscribed circle domain of normalized cover image's DWT sub-bands. Experimental results illustrate that this approach is robust to a wide range of attacks, especially geometrical attacks.

: Signal processing algorithms are pursued for the processing of measured forward-looking infrared (FLIR) imagery. Particular algorithms explored include hidden Markov models and independent component analysis.

This work presents a fast algorithm, namely 2-D Symmetric Mask-based Discrete Wavelet Transform (SMDWT), to address some critical issues of the 2-D Discrete Wavelet Transform (DWT). Unlike the traditional DWT involving dependent decompositions, the SMDWT itself is subband processing independent, which can significantly reduce complexity. Moreover, DWT cannot directly obtain target subbands, which leads to an extra wasting in transpose memory, critical path, and operation time. These problems can be fully improved with the proposed SMDWT. Nowadays, many applications employ DWT as the core transformation approach, the problems indicated above have motivated researchers to develop fast algorithms for DWT. The proposed SMDWT has been proved as a highly efficient independent processing to yield target subbands which can be applied to real-time visual applications, such as moving object detection and tracking, texture segmentation, image/video compression, and any DWT-based applications.

Wavelet-domain hidden Markov models (HMMs) have been recently proposed and applied to image processing, e.g., image denoising. In this paper, we develop a new HMM, called hierarchical hidden Markov tree model (HHMT), by adopting a feasible and fast two stage algorithm which avoids the time-consuming training process to estimate the HMT model parameters. The HHMT can exploit both the local statistics and the interscale dependencies of wavelet coefficients at a low computational complexity. We show that the HHMT model can achieve state-of-the-art medical image denoising performance.

In this paper, a flame detection system based on a pyroelectric (or passive) infrared (PIR) sensor is described. The flame detection system can be used for fire detection in large rooms. The flame flicker process of an uncontrolled fire and ordinary activity of human beings are modeled using a set of hidden Markov models (HMM), which are trained using the wavelet transform of the PIR sensor signal. Whenever there is an activity within the viewing range of the PIR sensor system, the sensor signal is analyzed in the wavelet domain and the wavelet signals are fed to a set of HMMs. A fire or no fire decision is reached according to the HMM producing the highest probability.