Quaternion Wavelet Research Articles

Forensics feature analysis in quaternion wavelet domain for distinguishing photographic images and computer graphics

In this paper, a novel set of features based on Quaternion Wavelet Transform (QWT) is proposed for digital image forensics. Compared with Discrete Wavelet Transform (DWT) and Contourlet Wavelet Transform (CWT), QWT produces the parameters, i.e., one magnitude and three angles, which provide more valuable information to distinguish photographic (PG) images and computer generated (CG) images. Some theoretical analysis are done and comparative experiments are made. The corresponding results show that the proposed scheme achieves 18 percents’ improvements on the detection accuracy than Farid’s scheme and 12 percents than Ozparlak’s scheme. It may be the first time to introduce QWT to image forensics, but the improvements are encouraging.

New banknote defect detection algorithm using quaternion wavelet transform

In order to improve the accuracy of detection of defects in banknote sorting, a new algorithm is proposed to detect cracks and scratches on banknote images. The quaternion wavelet transform and the least squares method are used for the banknote image registration. The features of the defects that are robust to gray intensity changes are constructed using edge information captured by the Kirsch operator. The banknote image is divided into several subzones of fixed size. The level of defect of the banknote image is estimated based on the defective features of each sub-zone. The experimental results show that the proposed algorithm is robust even with low quality banknote images and can obtain a high recognition rate and high stability. The proposed algorithm has already been used in a practical banknote sorting system.

Boost image denoising via noise level estimation in quaternion wavelet domain

Wavelet thresholding is an important branch of the image denoising field. A key parameter in the algorithms is noise level. As a novel tool of image analysis, quaternion wavelet owns some superior properties compared to discrete wavelets, such as nearly shift-invariant wavelet coefficients and phase based texture presentation. We aim to propose an easy and efficient method to estimate the noise level accurately via quaternion wavelet and further improve the denoising performance. We find that the variance sum of high frequency coefficients of quaternion wavelet is approximately equal to the noise level. However, with the advent of strong edges and/or less smooth regions, this metric would overestimate the noise level. Phases in the quaternion wavelet domain can represent the image texture information. On the premise of detecting smooth regions via phases operation, i.e. without many textures, the proposed noise level estimation method is also suitable to images with complex scenes. The performance of the proposed noise level estimation algorithm is demonstrated superior to classical algorithms. Also, the proposed algorithm can enhance those noise level dependent techniques to improve the denoising performances which are competitive to the state-of-art denoising algorithms.

Quaternionic wavelet coefficients modeling for a Reduced-Reference metric

This paper proposes a new Reduced-Reference metric based on the modeling of the Quaternionic Wavelet Transform coefficients from Information Criteria. To obtain the Reduced-References, we will model the Quaternionic Wavelet Transform coefficients using probability density functions whose parameters are used as Reduced-References. Information Criteria are proposed in order to build optimal histograms of the Quaternionic Wavelet Transform coefficients and to obtain the number of distributions in the mixture model. The Quaternionic Wavelet Transform is an improvement of the Discrete Wavelet Transform providing a richer scale-space analysis for 2-D signals. This recent transform separates the information contained in the image better than a classical Discrete Wavelet Transform, and provides a multiscale image analysis whose coefficients are 2D analytic, with one near-shift invariant magnitude and with phase information. From these models, we propose a measure of degradation by comparing probability density functions of the reference image and the distributions of the degraded image of the Quaternionic Wavelet Transform subbands. We shall demonstrate that one phase of the Quaternionic Wavelet Transform provides relevant information in the Image Quality Assessment. Experimentation confirmed the potential of this new structural information (this Reduced-Reference system produces good coefficients of correlation with the Human Visual System).

Optimal and secure audio watermarking scheme based on self-adaptive particle swarm optimization and quaternion wavelet transform

In this paper, a new audio watermarking scheme based on self-adaptive particle swarm optimization (SAPSO) and quaternion wavelet transform (QWT) is proposed. By obtaining optimal watermark strength using a uniquely designed objective function, SAPSO addresses the conflicting problem of robustness, imperceptibility, and capacity of audio watermarking scheme using self-adjusted parameters. To withstand de-synchronization attack, a synchronization sequence generated by chaotic signals is also adopted in our scheme. Furthermore, the utilization of chaotic signals significantly enhances the security of the proposed scheme. The experimental results validate that our scheme is not only robust against de-synchronization attack, but also typical signal manipulations and StirMark attack. Our comparative analysis also revealed that the proposed scheme outperforms the state-of-the-arts audio watermarking schemes.

The Method of Quaternions Wavelet Image Denoising

Based on traditional wavelet image denoising model, studies the quaternion, the application of wavelet transform in image denoising, quaternions are given three on the wavelet transform domain image denoising model and algorithm: (1) based on quaternion wavelet hidden markov tree model of image denoising; (2) based on quaternion wavelet transform non-gaussian bivariate distribution image denoising algorithm of bayesian statistical model; (3) based on quaternion mixing statistical model of wavelet image denoising. Experiments show that: in this paper, the denoising effect of these methods, in both the peak signal-to-noise ratio and the visual effects are better than many classic denoising algorithms.

Optimal image watermarking scheme based on chaotic map and quaternion wavelet transform

In this paper, an intelligent watermarking scheme optimized by adaptive differential evolution (ADE) is proposed based on chaotic map and quaternion wavelet transform (QWT). Watermark is first scrambled by a piecewise linear chaotic map to increase security and then inserted into the real QWT amplitude coefficients intelligently. ADE algorithm is explored to optimize the watermarking parameter (i.e., scaling factors) automatically. The experimental results demonstrate the high robustness against common signal processing operations, especially geometrical distortions of the proposed algorithm. Comparison results also indicate the superiority of the proposed algorithm over the existing watermarking algorithm.

Magnitude-phase of the dual-tree quaternionic wavelet transform for multispectral satellite image denoising

In this paper, we study the potential of the quaternionic wavelet transform for the analysis and processing of multispectral images with strong structural information. This new representation gives a very good division of the coefficients in terms of magnitude and three-phase angles and generalizes better the concept of analytic signal to image. Furthermore, it retains the property of shift invariant and directivity. We show an application of this transform in satellite image denoising. The proposed approach relies on the adaptation of thresholding procedures based on the dependency between magnitude quaternionic coefficients in local neighborhoods and phase regularization. In addition a non-marginal aspect of multispectral representation is introduced. Thanks to coherent analysis provided by the quaternionic wavelet transformation, the results obtained indicate the potential of this multispectral representation with magnitude thresholding and phase smoothing in noise reduction and edge preservation compared with classical wavelet thresholding methods that do not use phase or multiband information.

Anisotropic analysis of trabecular architecture in human femur bone radiographs using quaternion wavelet transforms.

In this work, anisotropy of compressive and tensile strength regions of femur trabecular bone are analysed using quaternion wavelet transforms. The normal and abnormal femur trabecular bone radiographic images are considered for this study. The sub-anatomic regions, which include compressive and tensile regions, are delineated using pre-processing procedures. These delineated regions are subjected to quaternion wavelet transforms and statistical parameters are derived from the transformed images. These parameters are correlated with apparent porosity, which is derived from the strength regions. Further, anisotropy is also calculated from the transformed images and is analyzed. Results show that the anisotropy values derived from second and third phase components of quaternion wavelet transform are found to be distinct for normal and abnormal samples with high statistical significance for both compressive and tensile regions. These investigations demonstrate that architectural anisotropy derived from QWT analysis is able to differentiate normal and abnormal samples.

English

Recognizing the objects in complex natural scenes is the challenging task as the object may be occluded, may vary in shape, position and in size. In this paper a method to recognize objects from different categories of images using quaternionic wavelet transform (QWT) is presented. This transform separates the information contained in the image better than a traditional Discrete wavelet transform and provides a multiscale image analysis whose coefficients are 2D analytic, with one near-shift invariant magnitude and three phases. The two phases encode local image shifts and the third one contains texture information. In the domain of object recognition, it is often to classify objects from images that make only limited part of the image. Hence to identify local features and certain region of images, patches are extracted over the interest points detected from the original image using Wavelet based interest point detector. Here QWT magnitude and phase features are computed for every patch. Then these features are trained, tested and classified using SVM classifier in order to have supervised learning model. In order to compare the performance of local feature with global feature, the transform is applied to the entire image and the global features are derived. The performance of QWT is compared with discrete wavelet transform (DWT) and dual tree discrete wavelet transform (DTDWT). Observations revealed that QWT outperforms the DWT and shift invariant DTDWT with lesser equal error rate. The experimental evaluation is done using the complex Graz databases. Defence Science Journal, Vol. 64, No. 4, July 2014, pp. 350-357, DOI:http://dx.doi.org/10.14429/dsj.64.4503

Multi-focus Image Fusion Based on Quaternion Wavelet

Multi-focus Image Fusion Based on Quaternion Wavelet

Visual objects tracking and identification based on reduced quaternion wavelet transform

In this paper, a new method for tracking moving objects based on reduced quaternion wavelet transform by using color space information is proposed. The reduced quaternion wavelet transform is a new multi-scale analysis tool for geometric image features. Meanwhile, it is a near-shift-invariant tight frame representation whose coefficients can sport local image shift and geometric information. The main objective of visual tracking is to closely follow objects in each frame of video stream. The new proposed method can calculate the mean value and edge energy of visual objects by using the reduced quaternion wavelet coefficients. The experimental results show that the proposed method is effective and efficient.

Video Segmentation of Multiresolution Dynamic Spatiotemporal Model Based on Quaternion Wavelet Transform

How to achieve a meaningful video representation is an important problem in various research communities. Automatically segmenting non-specific objects is an open problem. To deal with the error segmentation problem of the existing video algorithms under dynamic scenes, we propose a dynamic spatiotemporal saliency model based on the quaternion wavelet transform for video segmentation in this paper, which has the capability of segmenting the salient objects from moving background automatically. The model is a dynamic combination of the temporal attention model and static salient model. In temporal attention model, motion contrast information can be computed from the phase disparity between two consecutive frames. The phase is extracted from quaternionic pyramid. In static salient model, the spatial attention information is computed by an inverse quaternion wavelet transform over the set of scale-weighted center-surround responses. The scale-weighting function has been optimized to better replicate psychophysical data on color appearance. We combine the two kinds of attention information to get the preliminary results and use Grabuct algorithm for the optimization of the result finally. The segmentation and comparison experimental results demonstrate the validity of proposed algorithm.

Dual tree fractional quaternion wavelet transform for disparity estimation

This paper proposes a novel phase based approach for computing disparity as the optical flow from the given pair of consecutive images. A new dual tree fractional quaternion wavelet transform (FrQWT) is proposed by defining the 2D Fourier spectrum upto a single quadrant. In the proposed FrQWT, each quaternion wavelet consists of a real part (a real DWT wavelet) and three imaginary parts that are organized according to the quaternion algebra. First two FrQWT phases encode the shifts of image features in the absolute horizontal and vertical coordinate system, while the third phase has the texture information. The FrQWT allowed a multi-scale framework for calculating and adjusting local disparities and executing phase unwrapping from coarse to fine scales with linear computational efficiency.

Image denoising using normal inverse gaussian model in quaternion wavelet domain

This paper proposes a novel image denoising algorithm that can more effectively remove Gaussian white noise. The proposed algorithm is based on a design of a Maximum Posteriori Estimator (MAP) combined with a Quaternion Wavelet Transform (QWT) that utilizes the Normal Inverse Gaussian (NIG) Probability Density Function (PDF). The QWT is a near shift-invariant whose coefficients include one magnitude and three phase values. An NIG PDF which is specified by four real-value parameters is capable of modeling the heavy-tailed QWT coefficients, and describing the intra-scale dependency between the QWT coefficients. The NIG PDF is applied as a prior probability distribution, to model the coefficients by utilizing the Bayesian estimation technique. Additionally, a simple and fast method is given to estimate the parameters of the NIG PDF from the neighboring QWT coefficients. Experimental results show that the proposed method outperforms other existing denoising methods in terms of the PSNR, the structural similarity, and the edge preservation. It is clear that the proposed method can remove Gaussian white noise more effectively.

Region level based multi-focus image fusion using quaternion wavelet and normalized cut

Region level based methods are popular in recent years for multifocus image fusion as they are the most direct fusion ways. However, the fusion result is not ideal due to the difficulty in focus region segmentation. In this paper, we propose a novel region level based multifocus image fusion method that can locate the boundary of the focus region accurately. As a novel tool of image analysis, phases in the quaternion wavelet transform (QWT) are capable of representing the texture information in the image. We use the local variance of the phases to detect the focus or defocus for every pixel initially. Then, we segment the focus detection result by the normalized cut to remove detection errors, thus initial fusion result is acquired through copying from source images according to the focus detection results. Next, we compare initial fusion result with spatial frequency weighted fusion result to accurately locate the boundary of the focus region by structural similarity. Finally, the fusion result is obtained using spatial frequency as fusion weight along the boundary of the focus region. Furthermore, we conduct several experiments to verify the feasibility of the fusion framework. The proposed algorithm is demonstrated superior to the reference methods.

Magnitude-Phase of Quaternion Wavelet Transform for Texture Representation Using Multilevel Copula

A Copula-based joint statistical model is proposed for texture representation on the domain of quaternion wavelet transform (QWT). Both the magnitude and the three phases of QWT are used as the discriminative information for constructing a 2-level Copula model, which consists of inner and outer Copulas. The inner Copula is applied to the intra-scale dependence while the outer Copula to capture the magnitude-phase dependence. Texture retrieval experiments based on Bayesian framework are carried out to evaluate our model. Experimental results show that, based on the multilevel Copula model, the performance of texture representation is improved by taking into account both the magnitude-phase dependence and the intra-scale dependence.

Novel focus region detection method for multifocus image fusion using quaternion wavelet

For local smooth regions in multifocus images, it is difficult to judge whether they are in focus or not, whether using human eyes or special focus measures. We propose to classify the images into smooth and nonsmooth regions based on structural similarity index. Quaternion wavelet transform (QWT), as a novel tool of image analysis, has some superior properties compared to discrete wavelet transform, such as nearly shift-invariant wavelet coefficients and phase-based texture representation. We use the local variance of the QWT phases to detect the focus position for the pixels belonging to the nonsmooth image regions. Thus, binary images of the left-focus, right-focus, and smooth region, e.g., there are two different focuses, are obtained. Then, the connected components labeling algorithm is exploited to label the two binary images containing the focus position information, and the regions with focus measure errors are transferred between the two binary images. The fusion result is finally acquired through three weighted binary images combined with the original multifocus images. Furthermore, we conduct several experiments to verify the feasibility of the proposed fusion method. The performance is demonstrated to be superior to current methods.

Employing quaternion wavelet transform for banknote classification

In order to improve the performance of the banknote classification, this paper presents a new feature extraction method based on quaternion wavelet transform (QWT). The QWT yields one shift invariant magnitude and three phases based on quaternion algebra. The generalized Gaussian density (GGD) is applied to capture the statistical characteristics of QWT coefficients. The neural network is used as classifier in the framework of banknote classification. Experimental results demonstrate its effectiveness and the proposed method obtains a higher recognition rate in the banknote classification.

Texture classification based on quaternion wavelet transform and multifractal characteristics

The paper incorporated the multifractal analysis method into the idea of Quaternion Wavelet Transform(QWT),which took advantage of the rotation-invariant properties and multifractal properties of texture image,and could make up for the lacks of ability to decompose input image into multiple orientation in texture classification when using wavelet transform.The experiment of texture classification using the images from UIUC shows the method has higher classification accuracy and the average correct classification rate is 96.69%.It proves this texture classification method is reasonable and effective.