Robust image watermarking using local Zernike moments

In this work, we propose a robust image watermarking algorithm using local Zernike moments, which are computed over circular patches around feature points. The proposed algorithm locally computes Zernike moments and modifies them to embed watermarks, achieving robustness against cropping and local geometric attacks. Moreover, to deal with scaling attacks, the proposed algorithm extracts salient region parameters, which consist of an invariant centroid and a salient scale, and transmits them to the decoder. The parameters are used at the decoder to normalize a suspect image and detect watermarks. Extensive simulation results show that the proposed algorithm detects watermarks with low error rates, even if watermarked images are distorted by various geometric attacks as well as signal processing attacks.     

Zernike矩不变性分析及其改进

在分析了Zernike矩不变性后,提出了一种基于图像整个区域形状描述算子的改进Zernike矩。改进的Zernike矩不仅具有旋转不变性,而且还具有改进前不具有的比例不变性。试验结果证明,和改进前的Zernike矩相比,改进后的Zernike矩具有更好的不变特征,可用作基于区域的形状描述算子。     

Accurate computation of bit error probabilities of band-limited asynchronous DS-CDMA systems using higher order moments

An existing method called the simplified improved Gaussian approximation (SIGA) was previously applied to compute the bit error probabilities (BEPs) of band-limited asynchronous direct sequence code division multiple access (DS-CDMA) systems employing general pulse shaping (IEEE Trans. Commun., vol. 50, p. 656, 2002). The SIGA method uses moments up to the second order and is more accurate than the standard Gaussian approximation (SGA) (IEEE Trans. Commun., vol. 50, p. 656, 2002). In this paper, a new method that uses moments up to the fourth order is proposed for computing the BEP. The method is derived from a five-point Chebyshev interpolation formula and is inherently more accurate than the SIGA. Like the SIGA, the new method requires the evaluation of only closed-form expressions and the error function. The new method achieves higher accuracy with a modest increase in computational complexity.     

Analysis of principle deviation of subpixel Zernike moments operator

In original Zernike moments subpixel edge operator, ideal step edge model is chosen for calculating four parameters of a pixel point, and therefore principle deviation is caused by edge model. In order to discuss the effect of principle deviation on edge location, sampled edge model is chosen for calculating edge parameters, principle deviation of edge translation l is derived based on Zernike moments edge detection theory, and modified formula of l is given for Zernike moments operator with masks of 5×5 size. Both theory analysis and testing result demonstrate that principle deviation is zero when edge translation l is limited in central pixel of a sampled window. In another case, the modification of l should be considered, which results in edge location accuracy of non-subpixel level for this subpixel edge operator.     

Zernike moments and LDP-weighted patches for content-based image retrieval

This paper proposes a new algorithm using global and local features for content-based image retrieval. Global features are extracted using the magnitude of Zernike moments (ZMs). Local features are obtained through local directional pattern (LDP). Generally, LDP is used to extract texture-based features from an image. In this paper, LDP is used to encode both texture and shape information of an image to represent more meaningful features. To encode texture-based features, original image is used to compute the LDP features. To extract shape information from an image, dual-tree complex wavelet transform (DT-CWT) is applied on image which generates six directional wavelets. These six directional wavelets are superimposed in order to obtain shape-encoded image. LDP is then applied on this wavelet-based shape-encoded image. Further, to enhance retrieval accuracy, LDP features are extracted from patches of both original and shape-encoded images. These patches are assigned with weights based on average discrimination capability of features in a patch. Experiments are performed using three different standard databases with various variations such as pose, distortion, partial occlusion and complex structure. The proposed technique achieves 96.4 and 98.76 % retrieval accuracy at a recall of 50 %, for Kimia-99 and COIL-100 databases, respectively. For MPEG-7 CE-2 shape database, retrieval accuracy of 61.93 % is achieved in terms of average Bull’s eye performance (BEP). The proposed technique is also tested on Springer medical image database to explore its scope in other areas, wherein it attains average BEP of 69.68 % in comparison with 61.52 % with ZMs. It is observed that the proposed technique outperforms other well-known existing methods of image retrieval.     

Generating rectangular coordinates in polar coordinate order

This paper proposes a means by which 2D data represented using the rectangular coordinate system can be converted to its equivalent in the polar coordinate system. Taking note that the order in which data becomes available with a polar coordinate measuring device is most unnatural from the point of view of a rectangular coordinate system, this paper presents a simple yet elegant algorithm that generates the points of a rectangular coordinate system in the natural order in which they would be obtained in a polar coordinate system. The algorithm uses only integer arithmetic and a few simple tests. It can quickly identify the grid points between any two angles or the polar coordinate measurements needed to compute rectangular coordinate measurements by interpolation.     

Zernike矩结合Sobel算子的边缘检测

提出了一种亚像素级的噪声图像边缘检测算法。首先使用基于各向异性扩散的非线性正则化Perona-Malik模型,实现对图像的平滑滤波;然后用改进的Sobel算子对图像进行初步边缘检测,将检测到的包括真正的和少数伪边缘点的坐标生成链表记录下来,原灰度图像保留;最后利用Zernike矩进行亚像素级的边缘精确定位。实验结果表明,此算法解决了传统算法中伪边缘点过多和边缘检测结果较宽的问题,图像的质量接近于定位准确度为亚像素级的小波算法。     

Slant estimation of handwritten characters by means of Zernike moments

Slant estimation is an indispensable technique for handwriting analysis. A novel method is proposed for slant estimation based on the average inclination of the Zernike reconstructed images for low moments. This method improves the linearity of the characteristic curve in comparison with a generalised chain code method.     

Efficient computation of local geometric moments

Local moments have attracted attention as local features in applications such as edge detection and texture segmentation. The main reason for this is that they are inherently integral-based features, so that their use reduces the effect of uncorrelated noise. The computation of local moments, when viewed as a neighborhood operation, can be interpreted as a convolution of the image with a set of masks. Nevertheless, moments computed inside overlapping windows are not independent and convolution does not take this fact into account. By introducing a matrix formulation and the concept of accumulation moments, this paper presents an algorithm which is computationally much more efficient than convolving and yet as simple.     

基于Zernike矩的三维目标多视点特性视图建模

目标的模型化是三维目标识别的一个重要环节。由于从多视点特征法建立的模型能够避免从二维图像中恢复目标的三维结构．在三维目标识别中应用比较广泛。使用镶嵌式多面体分割视觉空间以得到三维目标的多视点投影图像,采用较小的镶嵌单元尺寸以完备地描述目标各种姿态的信息。Zernike矩具有旋转不变性,并能够方便地由各阶矩重建图像。计算多面体各个单元的投影图像的Zernike矩．所需的矩的最高阶次由重建图像与原图像的差别确定,通过聚类方式合并那些图像的矩变化很小的投影对应的几个小单元．每个新单元可以提取一幅特性视图．实现较小数目的多视点特性视图的建模。实验证明了这种方法的可行性。     

一种Zernike矩的高精度板材尺寸测量方法

目前技术条件下,对于大视场的高精度边缘测量而言,工业级面阵CCD传感器的分辨率难以满足要求.文章针对钢板尺寸测量系统,首先介绍了测量环境和工作原理.继而在Zernike矩以及Zernike矩亚像素精度边缘检测原理的基础上,提出了适用于钢板尺寸测量的亚像素精度边缘检测算法.该算法不仅具较好的抗噪性能和检测精度,而且在传统界定边缘点的阈值处理方法上进行了改进,使边缘受限于单个像素的宽度范围内,能够实现亚像素精度的定位.系统实际运行表明,该方法能够有效提高测量精度,具有良好的效果和实用价值.     

Verification system robust to occlusion using low-order Zernike moments of palmprint sub-images

This paper proposes a palmprint based verification system which uses low-order Zernike moments of palmprint sub-images. Euclidean distance is used to match the Zernike moments of corresponding sub-images of query and enrolled palmprints. These matching scores of sub-images are fused using a weighted fusion strategy. The proposed system can also classify the sub-image of palmprint into non-occluded or occluded region and verify user with the help of non-occluded regions. So it is robust to occlusion. The palmprint is extracted from the acquired hand image using a low cost flat bed scanner. A palmprint extraction procedure which is robust to hand translation and rotation on the scanner has been proposed. The system is tested on IITK, PolyU and CASIA databases of size 549, 5239 and 7752 hand images respectively. It performs with accuracy of more than 98%, and FAR, FRR less than 2% for all the databases.     

基于Zernike矩及支持向量机的猪的姿态识别

为监控猪的行为,提出了基于Zernike矩及支持向量机的猪的行走姿态识别方法。首先对原始图像进行预处理,提取出原始图像中猪的轮廓图像。然后,根据标准矩对上述图像进行归一化,再对归一化后的二值轮廓图提取Zernike矩特征。在此基础上,利用支持向量机理论设计了多种姿态分类器,实现对猪的正常行走、低头行走、抬头行走、躺卧等四种姿态进行识别。实验结果表明,此方法对猪的姿态分类识别的准确度达到了95%以上。该项研究对猪的姿态识别方面具有显著价值。     

Digital reconstruction of images from their projections in polar coordinates

In a wide variety of applications, it is necessary to infer the structure of a three-dimensional object from its projections. Usually, the problem is reduced to the reconstruction of a series of two-dimensional (planar) sections from a set of one-dimensional (linear) projections. In this paper, starting from a polar representation of the density function, we present some closed form formulas, which can be successfully used in the reconstruction of images. The results of some numerical tests are also presented.     

Using Zernike moments for the illumination and geometry invariantclassification of multispectral texture

We develop a method for recognizing color texture independent of rotation, scale, and illumination. Color texture is modeled using spatial correlation functions defined within and between sensor bands. Using a linear model for surface spectral reflectance with the same number of parameters as the number of sensor classes, we show that illumination and geometry changes in the scene correspond to a linear transformation of the correlation functions and a linear transformation of their coordinates. A several step algorithm that includes scale estimation and correlation moment computation is used to achieve the invariance. The key to the method is the new result that illumination, rotation, and scale changes in the scene correspond to a specific transformation of correlation function Zernike moment matrices. These matrices can be estimated from a color image. This relationship is used to derive an efficient algorithm for recognition. The algorithm is substantiated using classification results on over 200 images of color textures obtained under various illumination conditions and geometric configurations.     

A new Zernike moments based technique for camera identification and forgery detection

In multimedia forensics, it is important to identify those images that were captured by a specific camera from a given set of N data images as well as detecting the tampered region in these images if forged. This paper presents a new technique based on Zernike moments feature extraction for blindly classifying correlated PRNU images as well as locating the tampered regions in image under investigation. The proposed clustering algorithm is based on estimating the Zernike moments and applying a hierarchical clustering for classification. The forgery detection algorithm is based on picking up the peak Euclidean distance between the Zernike moments vector of blocks of the scaled-down forged image and its corresponding ones in the capturing camera PRNU. As Zernike moments are scale and rotational invariant, its feature when computed using scaled-down PRNU images lead to considerable computation time saving. Simulation examples are given to verify the effectiveness of the proposed techniques when compared to other state-of-the-art techniques even in case of very weakly correlated PRNU.     

Contouring control of biaxial systems based on polar coordinates

A contouring controller for biaxial systems that integrates the effects of feedback, feedforward, and cross-coupled control is proposed in this study. Conventional approaches to contouring control suffer from the complicated contour-error model and from lack of a systematic way for controller design. The integrated controller is based on polar coordinates under which a relatively simple contour-error model can be obtained. Taking the simple contour error as a state variable, the contouring-control problem is transformed into a stabilization problem. The feedback-linearization technique incorporated with linear feedback or robust control (such as sliding-mode control) can then yield the integrated controller. The proposed method is verified both numerically and experimentally and is compared with the conventional approach. It is found that the proposed controller is better for high speed and/or noncircular contouring. In addition, it can be applied to either linear plants or nonlinear plants (like linear motors).