Hongqing Zhu

Affine Legendre Moment Invariants for Image Watermarking Robust to Geometric Distortions

Geometric distortions are generally simple and effective attacks for many watermarking methods. They can make detection and extraction of the embedded watermark difficult or even impossible by destroying the synchronization between the watermark reader and the embedded watermark. In this paper, we propose a new watermarking approach which allows watermark detection and extraction under affine transformation attacks. The novelty of our approach stands on a set of affine invariants we derived from Legendre moments. Watermark embedding and detection are directly performed on this set of invariants. We also show how these moments can be exploited for estimating the geometric distortion parameters in order to permit watermark extraction. Experimental results show that the proposed watermarking scheme is robust to a wide range of attacks: geometric distortion, filtering, compression, and additive noise.

Symmetric image recognition by Tchebichef moment invariants

In this paper, we proposed a set of translation and rotation invariants extracted from Tchebichef moments. A set of Tchebichef moment invariants is derived from the relationship between Tchebichef moments of the original image and those of the transformed image. These invariants are then used for symmetric image recognition. Contrarily to the methods based on the complex moments in symmetric image analysis, our method does not need the pre-selection of moment values. Experimental results show that the proposed method achieves better performance compared to the existing methods.

Image analysis by generalized Chebyshev-Fourier and generalized pseudo-Jacobi-Fourier moments

In this paper, we present two new sets, named the generalized Chebyshev-Fourier radial polynomials and the generalized pseudo Jacobi-Fourier radial polynomials, which are orthogonal over the unit circle. These generalized radial polynomials are then scaled to define two new types of continuous orthogonal moments, which are invariant to rotation. The classical Chebyshev-Fourier and pseudo Jacobi-Fourier moments are the particular cases of the proposed moments with parameter α = 0 . The relationships among the proposed two generalized radial polynomials and Jacobi polynomials, shift Jacobi polynomials, and the hypergeometric functions are derived in detail, and some interesting properties are discussed. Two recursive methods are developed for computing radial polynomials so that it is possible to improve computation speed and to avoid numerical instability. Simulation results are provided to validate the proposed moment functions and to compare their performance with previous works. HighlightsPaper presents two generalized radial polynomials that are orthogonal over the unit circle.Paper constructs two new generalized descriptors using the scaled radial polynomials.Two recursive strategies for the computation of proposed radial polynomials are presented.The proposed polynomials are related to Jacobi, shift Jacobi polynomials and hypergeometric functions.The distribution of zeroes of the proposed polynomials can be controlled by free parameter α.

General Form for Obtaining Unit Disc-Based Generalized Orthogonal Moments

The rotation invariance of the classical disc-based moments, such as Zernike moments (ZMs), pseudo-ZMs (PZMs), and orthogonal Fourier-Mellin moments (OFMMs), makes them attractive as descriptors for the purpose of recognition tasks. However, less work has been performed for the generalization of these moment functions. In this paper, four general forms are developed to obtain a class of disc-based generalized radial polynomials that are orthogonal over the unit circle. These radial polynomials are scaled to ensure numerical stability, and some useful properties are discussed for potential applications they could be used in. Then, these scaled radial polynomials are used as kernel functions to construct a series of unit discbased generalized orthogonal moments (DGMs). The variation of parameters in DGMs can form various types of orthogonal moments: 1) generalized ZMs; 2) generalized PZMs; and 3) generalized OFMMs. The classical ZMs, PZMs, and OFMMs correspond to a special case of these three generalized moments for which the free parameter α = 0. Each member of this family will share some excellent properties for image representation and recognition tasks, such as orthogonality and rotation invariance. In addition, we have also developed two algorithms, the so-called m-recursive and n-recursive methods for the computation of these proposed radial polynomials to improve the numerical stability. Experimental results show that the proposed methods are superior to the classical disc-based moments in terms of image representation capability and classification accuracy.

Merging Student’s-t and Rayleigh distributions regression mixture model for clustering time-series

Abstract This paper addresses an efficient scheme for clustering time-series through a novel regression mixture strategy (RMM) that simultaneously utilizes the benefits of the Markov random field (MRF) and mean template. Each component of the proposed RMM is a mixture of Student’s-t and non-symmetric Rayleigh distributions. The Student’s-t distribution has been validated to be effective in reducing the influence of outliers. Another advantage is it considers the property of time-series in which spatially adjacent voxels have higher probabilities when belonging to the same cluster; thus, this study seeks to impose the spatially interdependent constraints in the form of a prior through a Bayesian theorem. By introducing the non-symmetric Rayleigh distribution, the proposed method has flexibility to fit various types of observed time-series. To optimize the model parameters, the proposed algorithm is formulated as a maximum a posteriori (MAP) estimation problem. An expectation maximization (EM)-type approach is eventually executed to obtain the update equations. Additionally, an efficient energy function is applied in the proposed approach such that the EM-MAP algorithm can be directly applied to calculate the objective function, which makes the proposed approach easier to implement. To illustrate the suitability of the proposed approach, we have extensively compared clustering accuracy, curve square error, and intraclass index with those of existing similarity methods on synthetic spatiotemporal datasets, synthetic fMRI time-series, and real life fMRI time-series.

A multiphase level set clustering approach using MRF-based Student's-t mixture model

Students-t distribution has attracted widely attention on model-based clustering analysis. In this paper, we propose a new level set energy function framework where the Markov random field-based Students-t mixture model is incorporated for clustering both static images and time-series data. This algorithm provides a general strategy by taking the best of Bayesian technique and level set formulation. A remarkable advantage of the proposed method is that it can overcome the weakness of the classical level set method by filtering out the outliers and stopping at the boundary points. It is mainly because the proposed technique models the probability density function of the data via Students-t mixture model. Another attractive feature is that the local relationship among neighboring pixels is considered into mixture model so that the proposed framework is more robust against noise compared to the other level set based models. Expectation maximization algorithm is applied to obtain model parameters by maximizing the log-likelihood function. Additionally, the proposed model has simplified structure which sharply reduces the computational complexity. Finally, numerical experiments on various synthetic, real-world images, and time-series data are conducted. The performances are compared to other related approaches in terms of effectiveness and accuracy.

fMRI time-series clustering using a mixture of mixtures of Student's-t and Rayleigh distributions

In this paper, a new Markov random field-based mixture model, where each of its components is a mixture of Students-t and Rayleigh distributions, is proposed for clustering fMRI time-series. By introducing the non-symmetric Rayleigh distribution, the proposed algorithm has flexibility to fit various types of observed time-series. Moreover, our method incorporates Markov random field so that the spatial relationships between neighboring voxels are considered, which makes the presented model more robust to noise, and that preserves more details of the clustering results compared with other symmetric distribution-based algorithms. Additionally, the expectation maximization algorithm is directly implemented to estimate the parameter set by maximizing the data log-likelihood function. The proposed framework is evaluated on real fMRI time-series, and the quantitatively compared results are demonstrated in terms of effectiveness and accuracy.

A robust nonsymmetric student's-t finite mixture model for MR image segmentation.

In this paper, a nonsymmetric Students-t distribution model is proposed for magnetic resonance (MR) image segmentation based on Markov random field (MRF) and weighted mean template. The presented nonsymmetric Students-t distribution with longer tails and one more parameter compared to Gaussian distribution is implemented because in real applications, the distribution of data set does not totally follow symmetric distribution. Thus, our method fits much closer to different shapes of observed data. With the help of MRF and weighted mean template, the spatial information is also taken into consideration in MR image segmentation. Then, the expectation-maximization (EM) algorithm is introduced to solve the problem of parameter learning. The accuracy and effectiveness of the proposed method is quantitatively assessed in both simulated and clinical MR images.

Image analysis using separable two-dimensional discrete orthogonal moments

This paper presents three new separable 2-D discrete orthogonal moments. The kernel functions of the proposed Meixner-Krawtchouk moments (MKM), Tchebichef-Charlier moments (TCM), and Meixner-Hahn moments (MHM) are mutually orthogonal and separable. Unlike the traditional 2-D discrete orthogonal moments, in the proposed separable 2-D discrete orthogonal moments, the kernel functions can be expressed as two separable terms by producing two different classical orthogonal polynomials of a variable. Specifically, the tense product of Meixner and Krawtchouk polynomials can be used to generate kernel functions for 2-D discrete orthogonal MKM. The global extraction capabilities of proposed moments are described by analyzing the reconstructed images accuracy. The experimental results show that these proposed moments have better image description capabilities.