Rotation invariant moments and transforms for geometrically invariant image watermarking

We present a way to construct a complete set of scaling rotation and translation invariants extract directly from Zernike moments. Zernike moment can be constructed by Radial moment. In our method in order to construct invariant Zernike moment is to achieve invariant Radial moment which is component of Zernike moment. We use matrix form to denote relationship between Radial and Zernike moment, which makes derivation more comprehensible. The translation invariant Radial moment is first introduced, for it is most complicated part of all the three invariant. Rotation and scaling invariant Radial moment is achieved by normalizing the factor caused by rotation and scaling. The form of invariant radial moment is to combine three parts of invariant. Some experiment has done to test the performance of invariance. In this experiment we take an image library containing 23,329 files which are built by translation rotation and zoom in out of one origin Latin character image. Most of the value of standard deviation ratio by mean of proposed moments is nearly 1%. In addition, retrieval experiment is to test the discrimination ability. MPEG-7 CE shape1 - Part A library is taken in this experiment. The recall rate in part A1 is 96.6% and is 100% in part A2.

This paper introduces an efficient method for face localization and recognition in color images. The proposed method uses the location of eyes for computation and extraction of a face's bounding ellipse. In this way, parameters of a face's ellipse (center, orientation, major and minor axis), is computed by the location of eyes in a face image. In the next step, we apply Pseudo Zernike Moments (PZM), Zernike Moments (ZM) and Principal Component Analysis (PCA) for feature extraction. For classification of these feature vectors a new structure of RBF neural networks with a novel distance function is introduced and a new method for determination of RBF unit parameters is proposed. Finally, we compare the efficiency of the proposed system for three types of feature vectors (PZM, ZM and PCA). Results emphasize the high accuracy and efficiency of the PZM features proportion to other features (ZM and PCA) for use in the proposed recognition system.

Shape descriptors and mapping methods for full-field comparison of experimental to simulation data

The performance of digital watermarking algorithm is mainly manifested in invisibility and robustness. At present, many algorithms improve these two aspects by sacrificing embedding capacity for the reason that if watermark embedding amount is small, the watermark has little influence on the visuality of the cover image, and its robustness is also higher. Therefore, how to improve the anti-attack performance of the algorithm without reducing the amount of embedding has become a major research direction. This paper proposed a new robust watermarking scheme based on feature extraction techniques. Firstly, the SIFT (scale invariant feature transform) algorithm is used to extract the stable feature points from cover image to form embedding region. Then watermark is composed of the cover’s texture features obtained by LBP (local binary pattern) extracting method. Finally, embedding region is transformed by singular value decomposition (SVD) and the watermark is embedded into its singular value vector. The simulation results showed that the watermark embedding capacity of this algorithm is relatively high, and it has good resistance to common image processing and geometric transformation.

Zernike Moments (ZMs) have been widely used in pattern recognition and image analysis due to their merits of near-zero information redundancy and rotation invariance. However, the discrete sampling error introduced by state-of-the-art algorithms degrades their rotation invariance. In this paper, a novel algorithm for computing the accurate ZMs of binary images is presented. The new algorithm is based on Non-Symmetry Anti-Packing Image Representation (NAIR) and it computes the accurate ZMs of the whole image by summing up the ZMs of all rectangular regions without introducing the discrete sampling error. The experimental results in this paper show that the NAIR-based algorithm for accurate ZMs is faster than the state-of-the-art accurate algorithms.

Pseudo-Zernike moments have better feature representation capability, and are more robust to image noise than those of the conventional Zernike moments. However, due to the computation complexity of pseudo-Zernike polynomials, pseudo-Zernike moments are yet to be extensively used as feature descriptors as compared to Zernike moments. In this paper, we propose two new algorithms, namely coefficient method and p-recursive method, to accelerate the computation of pseudo-Zernike moments. Coefficient method calculates polynomial coefficients recursively. It eliminates the need of using factorial functions. Individual order or index of pseudo-Zernike moments can be derived independently, which is useful if selected orders or indices of moments are needed as pattern features. p-recursive method uses a combination of lower order polynomials to derive higher order polynomials with the same index q. Fast computation is achieved because it eliminates the requirements of calculating polynomial coefficients, Bpqk, and power of radius, rk, in each polynomial. The performance of the proposed algorithms on moment computation and image reconstruction, as compared to those of the present methods, are experimentally verified using a set of binary and grayscale images.

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.

Ladar range images have attracted considerable attention in automatic target recognition fields. In this paper, Zernike moments (ZMs) are applied to classify the target of the range image from an arbitrary azimuth angle. However, ZMs suffer from high computational costs. To improve the performance of target recognition based on small samples, even-order ZMs with serial-parallel backpropagation neural networks (BPNNs) are applied to recognize the target of the range image. It is found that the rotation invariance and classified performance of the even-order ZMs are both better than for odd-order moments and for moments compressed by principal component analysis. The experimental results demonstrate that combining the even-order ZMs with serial-parallel BPNNs can significantly improve the recognition rate for small samples.

In this paper, a coarse to fine strategy is presented to achieve the geometrical synchronization incorporating Zernike moments and the template. At the coarse stage, the rotation and scaling parameters are estimated with Zernike moments of the translation-normalized image, while the translation parameters are estimated with the centroid’s increments between the original image and the image that is corrected for rotation and scaling. At the fine stage, the accurate Rotation, Scaling and Translation (RST) parameters are obtained by matching the template around the roughly estimated RST values. A watermarking scheme based on the vector Hidden Markov Model in wavelet domain (DWT-HMM) is also adopted. High robustness is observed against geometric manipulations and other StirMark attacks in our simulations.

We consider the use of Zernike moments (ZMs) for rotation- and scale-invariant classification of images. It is well known that ZMs are rotation-invariant only. We make use of the major benefit of the Fourier-Mellin (FM) transformation, which changes the rotation and the scale into translation. We introduce a new algorithm, which fuses the ZMs with the FM transform and is invariant under both rotation and scaling. Two sets of images were used to test the proposed algorithm. Experimental results reveal that the proposed algorithm has much better recognition rate than using ZMs within a variation of rotation between 0 and 360 deg, and scaling down and up between 25% and 400% of the original size.

Image analysis with logarithmic Zernike moments

Digital video is one of the popular multimedia data exchanged in the internet. Due to their perfectly replicable nature many illegal copies of the original video can be made. Methods are needed to protect copyrights of the owner and prevent illegal copying. A video can also undergo several intentional attacks like frame dropping, averaging, cropping and median filtering and unintentional attacks like addition of noise and compression which can compromise the owner information thereby denying authentication. In this paper, a robust Discrete Wavelet Transform (DWT)-based blind digital video watermarking scheme with scrambled watermarks based on scene changes has been proposed for authentication of digital video, which embeds different parts of a single watermark into different scenes of a video. The video watermarking algorithm is robust against the attacks of frame dropping, averaging and compression, which are considered as some of the common types of attacks applied particularly on the video and due to the use of DWT it can also withstand geometrical attacks making the watermark perceptually invisible. Furthermore, it allows blind retrieval of embedded watermark which does not need the original video. The proposed algorithm has been compared with an existing DWT based watermarking scheme and is found to exhibit better robustness.

This paper presents the use of Hidden Markov Models (HMM) to classifying Arabic words that have been represented by moments into a set of predefined classes. The proposed scheme results in enhanced performance because it deals effectively with errors that commonly originate during the feature extraction stage and it accounts for variations due to the individual handwriting performance of different data sets. To overcome the variations in images, each is represented by rotation and scale invariant feature vector known as Pseudo Zernike Moments (PZM). To demonstrate its effectiveness, the proposed classification scheme has been employed in the context of different sets of handwritten Arabic words. The classification results demonstrate that the proposed approach can classify handwritten Arabic word with a error rate less than 10%.

One of the main contributions of this paper is to show that contrary to the common belief Tchebichef moments are more sensitive to noise added to the image than Zernike moments. We show this by imposing different types and levels of noise on various images and measuring the error due to the added noise alone after image reconstruction. To calculate the error due to added noise alone, the image reconstruction error is subtracted from the total error, which initially includes both reconstruction and added noise errors. Another contribution of this paper is to present some analysis and compare the reconstruction capability of Tchebichef moments to that of Zernike and Legendre moments in noise free environments independent of the image used. We show this by spectrally analyzing the performance of Tchebichef, Legendre, and Zernike moments using single frequency images. Here the total reconstruction error of an arbitrary image is equal to the integration of the spectral errors, whose transfer functions are calculated using single frequency images, for all frequencies.

In this paper, we propose a new identification method based on the retinal images. In this algorithm, we use rotation invariant features extracted from the retinal images. Then, we use them for identification. Experimental results on a database, including 60 retina images obtained from 40 subjects of DRIVE database and 20 subjects from STARE database, show the average true identification accuracy rate equal to 99.78 percent for the proposed algorithm.