Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA)

This paper describes a novel inpainting algorithm that is capable of filling in holes in overlapping texture and cartoon image layers. This algorithm is a direct extension of a recently developed sparse-representation-based image decomposition method called MCA (morphological component analysis), designed for the separation of linearly combined texture and cartoon layers in a given image (see [J.-L. Starck, M. Elad, D.L. Donoho, Image decomposition via the combination of sparse representations and a variational approach, IEEE Trans. Image Process. (2004), in press] and [J.-L. Starck, M. Elad, D.L. Donoho, Redundant multiscale transforms and their application for morphological component analysis, Adv. Imag. Electron Phys. (2004) 132]). In this extension, missing pixels fit naturally into the separation framework, producing separate layers as a by-product of the inpainting process. As opposed to the inpainting system proposed by Bertalmio et al., where image decomposition and filling-in stages were separated as two blocks in an overall system, the new approach considers separation, hole-filling, and denoising as one unified task. We demonstrate the performance of the new approach via several examples.     

测地线活动轮廓模型的图像分割快速算法

从最优化理论的角度来看,目前求解图像分割的测地线活动轮廓(geodesic active contour,GAC)模型大多采用固定步长的最速下降算法.而众所周知,该算法收敛速度较慢,这在能量泛函的梯度较小时尤为明显.对求解GAC模型的快速算法进行了研究.首先,回顾了GAC模型的演化方程;随后,将共轭梯度(conjugate gradient,CG)算法引入到GAC模型的求解中,形成一种新的求解图像分割问题的数值方法,即GAC模型的CG算法;最后,通过试验对比传统的数值方法,表明CG算法具有良好的收敛性.     

Nonlocal patches based Gaussian mixture model for image inpainting

We consider the inpainting problem for noisy images. It is very challenge to suppress noise when image inpainting is processed. An image patches based nonlocal variational method is proposed to simultaneously inpainting and denoising in this paper. Our approach is developed on an assumption that the small image patches should be obeyed a distribution which can be described by a high dimension Gaussian Mixture Model. By a maximum a posteriori (MAP) estimation, we formulate a new regularization term according to the log-likelihood function of the mixture model. To optimize this regularization term efficiently, we adopt the idea of the Expectation Maximization (EM) algorithm. In which, the expectation step can give an adaptive weighting function which can be regarded as a nonlocal connections among pixels. Using this fact, we built a framework for non-local image inpainting under noise. Moreover, we mathematically prove the existence of minimizer for the proposed inpainting model. By using a splitting algorithm, the proposed model are able to realize image inpainting and denoising simultaneously. Numerical results show that the proposed method can produce impressive reconstructed results when the inpainting region is rather large.     

A symmetric color image encryption algorithm using the intrinsic features of bit distributions

In recent years, a variety of chaos-based image encryption algorithms have been proposed. Most of them employ the confusion-diffusion architecture and operate at the pixel level. In this paper, we analyze the intrinsic features of the bit distributions, the high correlation among bit planes and other issues related to the bit information of an image. Due to the superior characteristics of bit-level operations and the intrinsic bit features of the image, an expand-and-shrink strategy is employed to shuffle the image with reconstructed permuting plane. Simulations have been carried out and the results demonstrate the superior security and high efficiency of the proposed scheme.     

A modified fixed-point iterative algorithm for image restoration using fourth-order PDE model

In this paper, we propose a modified fixed point iterative algorithm to solve the fourth-order PDE model for image restoration problem. Compared with the standard fixed point algorithm, the proposed algorithm needn?t to compute inverse matrices so that it can speed up the convergence and reduce the roundoff error. Furthermore, we prove the convergence of the proposed algorithm and give some experimental results to illustrate its effectiveness by comparing with the standard fixed point algorithm, the time marching algorithm and the split Bregman algorithm.     

Analysis of a hyperbolic-parabolic type system for image inpainting

In this paper we consider the initial boundary value problem of a hyperbolic-parabolic type system for image inpainting in a 2-D bounded domain, and establish the existence of weak solutions to the system by employing the method of vanishing viscosity.     

A multiscale fourth‐order model for the image inpainting and low‐dimensional sets recovery

We consider a fourth‐order variational model, to solve the image inpainting problem, with the emphasis on the recovery of low‐dimensional sets (edges and corners) and the curvature of the edges. The model permits also to perform simultaneously the restoration (filtering) of the initial image where this one is available. The multiscale character of the model follows from an adaptive selection of the diffusion parameters that allows us to optimize the regularization effects in the neighborhoods of the small features that we aim to preserve. In addition, because the model is based on the high‐order derivatives, it favors naturally the accurate capture of the curvature of the edges, hence to balance the tasks of obtaining long curved edges and the obtention of short edges, tip points, and corners. We analyze the method in the framework of the calculus of variations and the Γ‐convergence to show that it leads to a convergent algorithm. In particular, we obtain a simple discrete numerical method based on a standard mixed‐finite elements with well‐established approximation properties. We compare the method to the Cahn–Hilliard model for the inpainting, and we present several numerical examples to show its performances. Copyright © 2016 John Wiley & Sons, Ltd.     

A fractional partial differential equation based multiscale denoising model for texture image

Traditional integer‐order partial differential equation based image denoising approach can easily lead edge and complex texture detail blur, thus its denoising effect for texture image is always not well. To solve the problem, we propose to implement a fractional partial differential equation (FPDE) based denoising model for texture image by applying a novel mathematical method—fractional calculus to image processing from the view of system evolution. Previous studies show that fractional calculus has some unique properties that it can nonlinearly enhance complex texture detail in digital image processing, which is obvious different with integer‐order differential calculus. The goal of the modeling is to overcome the problems of the existed denoising approaches by utilizing the aforementioned properties of fractional differential calculus. Using classic definition and property of fractional differential calculus, we extend integer‐order steepest descent approach to fractional field to implement fractional steepest descent approach. Then, based on the earlier fractional formulas, a FPDE based multiscale denoising model for texture image is proposed and further analyze optimal parameters value for FPDE based denoising model. The experimental results prove that the ability for preserving high‐frequency edge and complex texture information of the proposed fractional denoising model are obviously superior to traditional integral based algorithms, as for texture detail rich images. Copyright © 2013 John Wiley & Sons, Ltd.     

Fast fractal image compression using spatial correlation

Fractal image compression is time consuming in the encoding process. The time is essentially spent on the search for the best-match block in a large domain pool. In this paper, the spatial correlations in both the domain pool and the range pool are utilized to reduce the searching space. With this technique, the encoding speed is 2.6 times faster than that of the full search method while the quality of the retrieved image is almost the same. Moreover, since the searching space is limited to the matched blocks of the previous range blocks, fewer bits are required to represent the transform. The bit rate is thus improved by about 20%.     

An efficient self-adaptive model for chaotic image encryption algorithm

In this paper, an efficient self-adaptive model for chaotic image encryption algorithm is proposed. With the help of the classical structure of permutation-diffusion and double simple two-dimensional chaotic systems, an efficient and fast encryption algorithm is designed. However, different from most of the existing methods which are found insecure upon chosen-plaintext or known-plaintext attack in the process of permutation or diffusion, the keystream generated in both operations of our method is dependent on the plain-image. Therefore, different plain-images will have different keystreams in both processes even just only a bit is changed in the plain-image. This design can solve the problem of fixed chaotic sequence produced by the same initial conditions but for different images. Moreover, the operation speed is high because complex mathematical methods, such as Runge–Kutta method, of solving the high-dimensional partial differential equations are avoided. Numerical experiments show that the proposed self-adaptive method can well resist against chosen-plaintext and known-plaintext attacks, and has high security and efficiency.     

求解图像分割CV模型的BB算法

给出图像分割的一种新算法——BB算法.该方法的优点在于利用迭代过程中当前点和前一点的信息确定搜索步长,从而更有效地搜索最优解.为此,首先通过变分水平集方法将CV模型转化为最优化问题;其次,将BB算法引入该优化问题进行求解;然后,对BB算法进行收敛性分析,为该算法应用在CV模型中提供了理论依据;最后将该方法与已有的最速下降法、共轭梯度法的分割结果进行比较.结果表明,跟其他两种方法相比,BB算法在保证较好分割效果的前提下,提高了算法的速度和性能.     

A fast algorithm for the total variation model of image denoising

The total variation model of Rudin, Osher, and Fatemi for image denoising is considered to be one of the best denoising models. In the past, its solutions were based on nonlinear partial differential equations and the resulting algorithms were very complicated. In this paper, we propose a fast algorithm for the solution of the total variation model. Our algorithm is very simple and does not involve partial differential equations. We also provide a rigorous proof for the convergence of our algorithm.     

Fast fractal image encoding using one-norm of normalised block

The baseline fractal image encoding with full search typically requires a very long encoding time, which is essentially spent on searching for the best-matched block to an input range block in a large domain pool. In this paper, one-norm of normalised block is first utilized to avoid the excessive search, in which the search process might be early terminated, and thus remaining domain blocks could be safely discarded. Then the encoding schemes proposed recently by the authors are used to further reduce the search space and improve the decoded image quality. Experiments show that, for three popular 512 × 512 test images, the proposed algorithm can averagely reduce the runtime by about 40 times while there is averagely the PSNR gain of 0.91 dB, in comparison with the baseline fractal algorithm. Besides, when combined with the kick-out condition and the zero contrast prediction proposed recently by Lai et al. [Lai CM, Lam KM, Siu WC. A fast fractal image coding based on kick-out and zero contrast conditions. IEEE Trans Image Process 2003:11;1398–403], the combined algorithm further reduced the runtime by about 10% while maintaining the same PSNR exactly as that of the proposed algorithm.     

Fuzzy measures for color image retrieval

In this paper we present a scheme for fuzzy similarity based strategy to retrieve an image from a library of color images. Color features are among the most important features used in image database retrieval. Due to its compact representation and low complexity, direct histogram comparison is the most commonly used technique in measuring color similarity of images. A gamma membership function, derived from the Gamma distribution, has been proposed to find the membership values of the gray levels of the histogram. We present here an image retrieval scheme with some popular vector fuzzy distance measures using a gamma membership function for finding the membership values of the gray levels and evaluate the matching function to select the appropriate retrieval mechanism.     

An automatic regularization parameter selection algorithm in the total variation model for image deblurring

Image restoration is an inverse problem that has been widely studied in recent years. The total variation based model by Rudin-Osher-Fatemi (1992) is one of the most effective and well known due to its ability to preserve sharp features in restoration. This paper addresses an important and yet outstanding issue for this model in selection of an optimal regularization parameter, for the case of image deblurring. We propose to compute the optimal regularization parameter along with the restored image in the same variational setting, by considering a Karush Kuhn Tucker (KKT) system. Through establishing analytically the monotonicity result, we can compute this parameter by an iterative algorithm for the KKT system. Such an approach corresponds to solving an equation using discrepancy principle, rather than using discrepancy principle only as a stopping criterion. Numerical experiments show that the algorithm is efficient and effective for image deblurring problems and yet is competitive.     

Large deviations estimates for some non-local equations: Fast decaying kernels and explicit bounds

We study large deviations for some non-local parabolic type equations. We show that, under some assumptions on the non-local term, problems defined in a bounded domain converge with an exponential rate to the solution of the problem defined in the whole space. We compute this rate in different examples, with different kernels defining the non-local term, and it turns out that the estimate of convergence depends strongly on the decay at infinity of that kernel.     

Fast algorithm for viscous Cahn-Hilliard equation

The main purpose of this paper is to solve the viscous Cahn-Hilliard equation via a fast algorithm based on the two time-mesh (TT-M) finite element (FE) method to ease the problem caused by strong nonlinearities. The TT-M FE algorithm includes the following main computing steps. First, a nonlinear FE method is applied on a coarse time-mesh τ_c. Here, the FE method is used for spatial discretization and the implicit second-order θ scheme (containing both implicit Crank-Nicolson and second-order backward difference) is used for temporal discretization. Second, based on the chosen initial iterative value, a linearized FE system on time fine mesh is solved, where some useful coarse numerical solutions are found by Lagrange’s interpolation formula. The analysis for both stability and a priori error estimates is made in detail. Numerical examples are given to demonstrate the validity of the proposed algorithm. Our algorithm is compared with the traditional Galerkin FE method and it is evident that our fast algorithm can save computational time.