一种新的基于伪Zernike矩的图像盲水印算法

抵抗几何攻击的鲁棒性是目前数字水印技术中的热点也是难点。提出一种新的基于伪Zernike矩的图像盲水印算法,首先计算图像归一化后的伪Zernike矩,然后选取部分合适的矩通过量化调制嵌入水印信息。水印提取时,利用伪Zernike矩的相位信息估计旋转角度进行几何校正,以提高矩的几何不变性。实验结果表明,本算法对于抗几何攻击尤其是旋转攻击具有很好的鲁棒性,同时也能抵抗常规的信号处理攻击。     

Robust rotation angle estimator

The conventional method of estimating the rotation angle of a pattern using the principal axes is not suitable for circular symmetric patterns since their eigenvalues are similar in both directions. In the paper, a robust method of estimating a rotation angle using the phase information of Zernike moments is presented. The experimental results show that the proposed method estimates the rotation angle of the circular symmetric patterns more accurately than the principal axes method, even in the presence of noise     

A moment-based nonlocal-means algorithm for image denoising

Image denoising is a crucial step to increase image quality and to improve the performance of all the tasks needed for quantitative imaging analysis. The nonlocal (NL) means filter is a very successful technique for denoising textured images. However, this algorithm is only defined up to translation without considering the orientation and scale for each image patch. In this paper, we introduce the Zernike moments into NL-means filter, which are the magnitudes of a set of orthogonal complex moments of the image. The Zernike moments in small local windows of each pixel in the image are computed to obtain the local structure information for each patch, and then the similarities according to this information are computed instead of pixel intensity. For the rotation invariant of the Zernike moments, we can get much more pixels or patches with higher similarity measure and make the similarity of patches translation-invariant and rotation-invariant. The proposed algorithm is demonstrated on real images corrupted by white Gaussian noise (WGN). The comparative experimental results show that the improved NL-means filter achieves better denoising performance.     

结合Zernike矩和模板具有RST不变性的DWT-HMM鲁棒水印算法

抵抗几何攻击是鲁棒水印研究的关键问题之一。为实现水印同步,提出了一种结合Zernike矩和小波域模板实现由粗到精几何同步的算法,即首先利用平移归一化图像的Zernike矩估计旋转和缩放参数,并用校正旋转和缩放后的图像和原图像之间的质心增量估计平移参数;然后基于粗略估计的参数,通过匹配小波域模板实现旋转、缩放和平移(RST)参数的精确识别和校正,该同步方法可以较大程度地降低搜索空间。水印嵌入和检测采用了小波域向量隐马尔可夫模型(DWT-HMM)。仿真结果表明,利用由粗到精的几何同步方法和基于HMM的水印算法能有效抵抗StirMark平台的多种单项攻击和联合攻击,算法具有较好的鲁棒性能。     

Rotation,scaling and translation invariant texture recognition by Bessel-Fourier moments

The ideal of Bessel-Fourier moments (BFMs) for image analysis and only rotation invariant image cognition has been proposed recently. In this paper, we extend the previous work and propose a new method for rotation, scaling and translation (RST) invariant texture recognition using Bessel-Fourier moments. Compared with the others moments based methods, the radial polynomials of Bessel-Fourier moments have more zeros and these zeros are more evenly distributed. It makes Bessel-Fourier moments more suitable for invariant texture recognition as a generalization of orthogonal complex moments. In the experiment part, we got three testing sets of 16, 24 and 54 texture images by way of translating, rotating and scaling them separately. The correct classification percentages (CCPs) are compared with that of orthogonal Fourier-Mellin moments and Zernike moments based methods in both noise-free and noisy condition. Experimental results validate the conclusion of theoretical derivation: BFM performs better in recognition capability and noise robustness in terms of RST texture recognition under both noise-free and noisy condition when compared with orthogonal Fourier-Mellin moments and Zernike moments based methods.     

一种起始点无关的小波系数形状匹配

小波变换的多分辨率特征使其在计算机视觉中得到广泛的应用,在形状匹配中,小波变换对起始点的依赖制约了小波变换的应用。为了克服小波变换对起始点的依赖,引入Zernike矩,提出一种起始点无关的小波系数形状匹配算法。对输入图像进行预处理后提取目标轮廓,生成具有平移、尺度不变的形状链状表达,并通过小波变换进行多尺度分析。最后计算各个尺度下的各阶Zernike矩,来解决小波变换的起始点问题,实现形状表达的旋转不变性。实验结果表明该算法适用于轮廓较明显的目标,同时具有速度快、精度高、鲁棒性强的优点。     

基于DWT-DCT和Zernike矩的灰度级鲁棒性水印算法

鲁棒性是数字水印极为重要的指标.目前大多数文献中的鲁棒性水印方案对常规信号处理攻击均具有良好的鲁棒性,但抗几何攻击的鲁棒性相对较弱.提出了一种新的灰度级鲁棒性水印算法,对常规信号处理攻击和几何攻击均具有良好的鲁棒性.水印算法的鲁棒性由以下3方面获得:1)选择载体图像的内切圆盘作为Zernike矩的计算域,选择内切圆盘的内接正方形作为水印的嵌入区域.2)在载体图像嵌入区域的层叠DWT-DCT域嵌入水印,获得对常规信号处理攻击的强鲁棒性.3)保存原始含水印图像的2个Zernike矩作为校正几何攻击的参数,获得抗几何攻击能力.实验结果表明,该水印算法嵌入容量大,不仅对大角度旋转和大尺度缩放等几何攻击具有很好的鲁棒性,而且可以有效地抵抗有损压缩和常规信号处理攻击.     

一种快速的具有旋转不变性的模板匹配方法

传统的基于相关的匹配方法计算量相当大,而且当模板相对于搜索图有角度旋转时,匹配的计算量更大。用圆警影和zemike矩的方法对快速的且具有旋转不变性的模板匹配方法进行了研究,圆投影将图像由二维变换成一维,这样就降低了计算复杂度,通过相似性度量可进行快速地粗匹配,然后在可能的匹配点中,再用Zemike矩实现精匹配。     

视觉图像相似性在三维模型相似性比较中的应用

提出一种基于视觉的三维模型相似性比较算法.首先计算三维模型的带深度信息的正交平面投影图像,然后采用Zernike描述子和Reeb图比较这些正交投影图像的形状相似性,最后通过正交投影图像的形状相似性来获得三维模型的相似性.实验结果表明：该算法具有较好的三维模型检索准确性,并且对坐标系旋转变换、模型噪声、网格简化和细分具有较好的鲁棒性.     

Circularly orthogonal moments for geometrically robust image watermarking

Circularly orthogonal moments, such as Zernike moments (ZMs) and pseudo-Zernike moments (PZMs), have attracted attention due to their invariance properties. However, we find that for digital images, the invariance properties of some ZMs/PZMs are not perfectly valid. This is significant for applications of ZMs/PZMs. By distinguishing between the ‘good’ and ‘bad’ ZMs/PZMs in terms of their invariance properties, we design image watermarks with ‘good’ ZMs/PZMs to achieve watermark's robustness to geometric distortions, which has been considered a crucial and difficult issue in the research of digital watermarking. Simulation results show that the embedded information can be decoded at low error rates, robust against image rotation, scaling, flipping, as well as a variety of other common manipulations such as lossy compression, additive noise and lowpass filtering.     

Image analysis by Bessel-Fourier moments

In this paper, we proposed a new set of moments based on the Bessel function of the first kind, named Bessel-Fourier moments (BFMs), which are more suitable than orthogonal Fourier-Mellin and Zernike moments for image analysis and rotation invariant pattern recognition. Compared with orthogonal Fourier-Mellin and Zernike polynomials of the same degree, the new orthogonal radial polynomials have more zeros, and these zeros are more evenly distributed. The Bessel-Fourier moments can be thought of as generalized orthogonalized complex moments. Theoretical and experimental results show that the Bessel-Fourier moments perform better than the orthogonal Fourier-Mellin and Zernike moments (OFMMs and ZMs) in terms of image reconstruction capability and invariant recognition accuracy in noise-free, noisy and smooth distortion conditions.     

Zernike亚像素图像矩边缘检测算子方向角模型研究

基于Zernike图像矩的理想边缘模型,深入研究了方向角模型与亚像素判据间的关系。利用Zernike矩定义及其旋转不变特性,提出一种新的基于4阶方向角的Zernike矩亚像素边缘检测算子。为了提高边缘算子定位速度,首先基于9×9尺寸模板对Zernike图像矩0～4阶正交复数多项式进行了计算,推导出基于4阶方向角的边缘检测算子参数模型。最后将边缘算子应用在理想图像与实际图像上,检测结果表明:相比于传统的Zernike矩算子,基于4阶方向角的边缘检测算子具有更高的检测精度。     

A novel algorithm for fast computation of Zernike moments

Zernike moments (ZMs) have been successfully used in pattern recognition and image analysis due to their good properties of orthogonality and rotation invariance. However, their computation by a direct method is too expensive, which limits the application of ZMs. In this paper, we present a novel algorithm for fast computation of Zernike moments. By using the recursive property of Zernike polynomials, the inter-relationship of the Zernike moments can be established. As a result, the Zernike moment of order n with repetition m, Z_nm, can be expressed as a combination of Z_n−2,m and Z_n−4,m. Based on this relationship, the Zernike moment Z_nm, for n>m, can be deduced from Z_mm. To reduce the computational complexity, we adopt an algorithm known as systolic array for computing these latter moments. Using such a strategy, the multiplication number required in the moment calculation of Z_mm can be decreased significantly. Comparison with known methods shows that our algorithm is as accurate as the existing methods, but is more efficient.     

Robust image watermarking technique using triangular regions and Zernike moments for quantization based embedding

Watermarking is a tool to embed information in the image to provide authentication, copyrights protection, copy control, etc. Some watermarking techniques are robust to intentional /unintentional attacks on the watermarked image. In this study, we propose a robust watermarking approach that can resist geometrical attacks. The proposed technique exploits both the robust image feature points and local Zernike moments for embedding the information. Delaunay tessellation is employed to divide image into distinct triangular segments based on robust features. These features are identified using Harris detector. Zernike moments are calculated for each selected triangular segment, and then the watermark is embedded in the magnitude of Zernike moments using dither modulation. It can be observed from the experimental results that by using proposed approach, the watermark can be detected even in the presence of geometrical distortion, i.e. rotation, cropping, and scaling, and JPEG compression attack.