亥姆霍兹涡量方程与偏微分方程耦合修复模型

提出一种基于图像几何特征的形态学不变的耦合修复模型。耦合模型使用流体力学中无粘度亥姆霍兹涡量方程平滑的修复图像缺失信息区域。本文证明了亥姆霍兹涡量方程与传输平滑度信息的图像修复模型的等价性。曲率是图像几何特征作用的结果,本文提出沿等照度线方向传输曲率信息的三阶形态学不变偏微分方程,并将抑制涡量的无粘亥姆霍兹方程和正向传输曲率信息的三阶偏微分方程耦合。耦合模型平滑的修复图像并保持图像中的线性特征。理论和实验证明了本文提出的耦合模型在图像修复中的有效性。     

Strong-continuation, contrast-invariant inpainting with a third-order optimal PDE.

PDE-based image inpainting has become a very active area of research after the pioneering works of Masnou and Morel, Bertalmío et al., and Ballester et al. In this paper, we take a different approach, inspired by the excellent work of Caselles et al. We view the inpainting problem as a particular case of image interpolation in which we intend to propagate level lines. Expressing this in terms of local neighborhoods and using a Taylor expansion we derive a third-order PDE that performs inpainting. This PDE is optimal in the sense that it is the most accurate third-order PDE which can ensure continuation of level lines. The continuation is strong, allowing the restoration of thin structures occluded by a wide gap. The result is also contrast invariant. This is a novel PDE, which, in both its accuracy and contrast invariance, outperforms the approaches cited above.     

Orthogonal-directional forward diffusion image inpainting and denoising model

In this paper, an orthogonal-directional forward diffusion Partial Differential Equation （PDE） image inpainting and denoising model which processes image based on variation problem is proposed. The novel model restores the damaged information and smoothes the noise in image simultaneously. The model is morphological invariant which processes image based on the geometrical property. The regularization item of it diffuses along and cross the isophote, and then the known image information is transported into the target region through two orthogonal directions. The cross isophote diffusion part is the TV （Total Variation） equation and the along isophote diffusion part is the inviscid Helmholtz vorticity equation. The equivalence between the Helmholtz equation and the inpainting PDEs is proved. The model with the fidelity item which is used in the whole image domain denoises while preserving edges. So the novel model could inpaint and denoise simultaneously. Both theoretical analysis and experiments have verified the validity of the novel model proposed in this paper.     

数字图像处理中的偏微分方程方法

图像是获取信息的重要媒介,图像处理技术广泛用于人类生活及社会生产中.偏微分方程是一种数学分析方法,并且它的特性由扩散方向和扩散项决定,这一点对图像处理大为有利.本文综述了近年来受到广泛重视的数字图像处理中的偏微分方程方法.给出了偏微分方程在图像去噪、图像放大、图像分割、图像修复中主要算法的优势及不足,同时给出了我们的改进算法,并展示了实验结果.     

改进的TV-Stokes图像修复模型及其算法

该文在研究图像修复的基础上,提出了一种改进的TV-Stokes图像修复模型。通过分析新模型的性质,给出一种高效且快速的数值算法。由于新模型耦合了两个变量,因此新算法首先采用交替迭代策略化原问题为两个去耦的次问题,然后再对两个次问题分别利用对偶方法和分裂Bregman方法进行数值求解。实验结果表明该文所提出的算法不但修复图像的效果较好,而且修复的速度较快。     

基于三通道多小波紧标架的图像曲率修复模型

为解决正交小波域图像修复方法的现存小波 系数不能提供丢 失小波系数的充足信息问题,将曲率修复(CDD)模型扩展到非正交小波域,提出一种新的基 于三通道多小波 紧标架的图像CDD模型。进一步考虑到CDD模型的等照度线是按照直线连接的问 题,提出了一种新的CCD模型。新模型的修复在两个方向上进行,在法向上按照改进的曲率 函数进行修复, 在切向上实现输运机制。新模型结合了多小波紧标架分解技术和改进的CDD模型的 优势,利用标架域中 小波系数之间具有的冗余性对缺损的信息进行弥补,对现有CDD模型进行改进。给出了 有效的split Bregman 仿真算法,并采用不同的图像进行了仿真。实验结果表明,新模型对大面积缺损修复及噪声 抑制都具有良好 的修复效果,即使在大量小波系数丢失的情况下,也能保持图像的边缘结构等几何特征,大 大的改善修复质量。     

2DInpaint: A novel privacy-preserving scheme for image inpainting in an encrypted domain over the cloud

The low cost, agility, and mobility of cloud services for processing and storage data have attracted user’s attention today. Untrusted third parties support these services, and users are always concerned about utilizing them for personal data. Addressing these data-privacy issues for image inpainting over the cloud infrastructure(s), we propose a model, 2DInpaint, to perform image inpainting by protecting image information from an eavesdropping adversary. Inpainting is a technique for modifying an image in an undetectable manner with applications ranging from restoration of damaged photographs to object-removal and replacement of lost blocks in image coding and transmission. It can be accomplished by propagating the information in the isophotes direction of the desired region(s) from the neighborhood. Performing this propagation when the image is in the encrypted domain (ED) is a challenging dilemma. The challenge is addressed by employing a modified version of 2D-bicubic interpolation over the region to be inpainted in ED. The ramp secret sharing scheme is utilized to secure image information and to reduce storage overhead over the cloud server. 2DInpaint is proved to be information-theoretical secure in a probabilistic viewpoint and through various cryptographic attacks. The qualitative and quantitative results of 2DInpaint are analyzed under the scenarios of classical image inpainting, object-removal, and text-removal, and compared with the schemes in the plain domain. Moreover, no limitations related to the topology of the region to be inpainted are required using our approach. To the best of our knowledge, 2DInpaint is the first move towards image inpainting in the ED.     

Image segmentation and inpainting using hierarchical level set and texture mapping

Image inpainting is an artistic procedure to recover a damaged painting or picture. We propose a novel approach for image inpainting by using the Mumford-Shah (MS) model and the level set method to estimate image structure of the damaged regions. This approach has been successfully used in image segmentation problem. Compared to some other inpainting methods, the MS model approach detects and preserves edges in the inpainting areas. We propose a fast and efficient algorithm that achieves both inpainting and segmentation. In previous works on the MS model, only one or two level set functions are used to segment an image. While this approach works well on simple cases, detailed edges cannot be detected in complicated image structures. Although multi-level set functions can be used to segment an image into many regions, the traditional approach causes extensive computations and the solutions depend on the location of initial curves. Our proposed approach utilizes faster hierarchical level set method and guarantees convergence independent of initial conditions. Because we detect both the main structure and the detailed edges, our approach preserves edges in the inpainting area. Also, exemplar-based approach for filling textured regions is employed. Experimental results demonstrate the advantage of our method.     

一种基于TV模型的自适应图像修复方法

图像修复是数字图像处理的重要内容，可用于被损坏的图像和视频修复、视频文字去除以及视频错误隐藏等。基于TV模型的修复方法有较好的恢复效果，但对参数的选取比较敏感，且运算量较大。本文提出了一种基于TV模型的自适应图像修复方法，与原方法相比可以有效提高该算法的稳健性，并能显著的减少运算时间。     

基于Navier-Stokes方程的视频去隔行方法

随着技术的发展,常需将已有的隔行视频转换成高质量的逐行视频。本文提出一种基于Navier-Stokes（N-S）方程的视频去隔行方法。将基于N-S方程的图像修复模型应用到视频空间,由理想三维流体方程,建立视频的局部约束条件;然后,根据其各向异性特征,导出单个像素点的修复方程;最后,通过对隔行视频间隔区域的逐点修复,实现视频去隔行。实验表明,本文方法能够较好的抑制运动虚像和边沿锯齿。      

Non-texture image inpainting using histogram of oriented gradients

This paper presents a novel and efficient algorithm for non-texture inpainting of images based on using the dominant orientation of local gradients. It first introduces the concept of a new matrix called orientation matrix and then uses it for faster and better inpainting. The process of propagating information is carried out by using a new formulation which leads to much more efficient computations than the previous methods. The gain is both in terms of computational complexity and visual quality. The promising results in contexts of text, scratch, and block loss inpainting demonstrate the effectiveness of the proposed method.     

Inpainting of binary images using the Cahn-Hilliard equation.

Image inpainting is the filling in of missing or damaged regions of images using information from surrounding areas. We outline here the use of a model for binary inpainting based on the Cahn-Hilliard equation, which allows for fast, efficient inpainting of degraded text, as well as super-resolution of high contrast images.     

Image inpainting using directional wavelet packets originating from polynomial splines

The paper presents a new algorithm for the image inpainting problem. The algorithm uses a recently designed versatile library of quasi-analytic complex-valued wavelet packets (qWPs) which originate from polynomial splines of arbitrary orders. Tensor products of 1D qWPs provide a diversity of 2D qWPs oriented in multiple directions. For example, a set of the fourth-level qWPs comprises 62 different directions. The properties of these qWPs such as refined frequency resolution, directionality of waveforms with unlimited number of orientations, (anti-)symmetry of waveforms and windowed oscillating structure of waveforms with a variety of frequencies, make them efficient in image processing applications, in particular, in dealing with the inpainting problem addressed in the paper. The obtained results for this problem are quite competitive with the best state-of-the-art algorithms. The inpainting is implemented by an iterative scheme, which expands the Split Bregman Iteration (SBI) procedure by supplying it with an adaptive variable soft thresholding based on the Bivariate Shrinkage algorithm. In the inpainting experiments, performance comparison between the qWP-based methods and the state-of-the-art algorithms is presented.     

基于压缩感知的图像处理与重构方法

针对图像修复和插值等图像处理问题进行研究,通过将图像修复和插值模型在压缩感知(CS)理论的框架下进行转换,建立了新的图像修复和插值模型,该模型与CS理论中的重构模型相对应。对此转化得到的重构问题,基于图像在复数小波变换上的稀疏性,利用迭代硬阈值方法求解重构模型,进而获得重构图像。仿真和实测数据处理结果验证本文方法的有效性。     

分层级联生成对抗网络用于手背静脉图像修复

为解决在识别过程中因手背静脉图像信息缺失而造成识别效率低下的问题,本文提出了分层级联生成对抗网络的手背静脉图像修复框架。该网络框架分别以级联与并行分层的方式进行修复操作,通过并行分层结构创新性的融合了不同静脉图像的特征信息;为有效地利用静脉图像的上下文信息对缺失的静脉图像信息进行预测与补全,在网络中创新性的引入了空洞卷积核与非局部注意力网络;为保证修复静脉图像质量与其真实图像的一致性,创新性的结合对抗损失与感知损失进行优化。实验结果表明,本文算法在视觉效果、峰值信噪比（Peak Signal to Noise Ratio,PSNR）和结构相似性（Structural Similarity Index,SSIM）等方面表现优于已有算法,并在两个公开的掌纹与指纹数据集上进行了有效的泛化验证。此外,修复图像相较于缺失图像在身份识别效率方面有了一定的提高。      

局部特征分类的自适应扩散模型

本文提出了一种既能保持图像特征又能加快扩散速度的自适应扩散模型。首先,该模型利用平均梯度矩阵的特征值区分出图像的平坦区域、线条边缘和角点;其次,该模型根据平均梯度矩阵及其特征向量来控制图像信息的扩散方向;这样,该模型可以在不同的区域自适应地选择不同的扩散方向和扩散速度,从而很好地保持了图像特征并自适应地加快了扩散速度。实验结果表明,该模型可以保持图像结构特征,抑制噪声,应用到数字图像修复中,既能加快图像修复速度,又能使修复后的图像具有更好的视觉效果。      

一种基于Poisson方程的分离型图像修复方法

图像修复是一种恢复图像中损坏部分的技术,具有广泛的应用.基于采样复制的修复方法对纹理图像有较好的效果,但容易产生块效应,而且对结构信息的修复可能产生较大的偏差.本文提出了一种基于Poisson方程的分离型修复算法,首先将原图分解为结构图像和纹理图像两部分,然后根据其特件分别进行修复,叠加后得到最终的修复结果.对结构图像使用Laplacian算子强化结构信息,然后对Laplacian场进行修复并使用Poisson方程重建,可以同时保持锐利的区域边界以及平滑的区域背景.实验表明该方法可以有效改善修复的视觉效果,对大区域修复也有良好的表现.     

A global approach for solving evolutive heat transfer for image denoising and inpainting.

This paper proposes an alternative to partial differential equations (PDEs) for solving problems in computer vision based on evolutive heat transfer. Traditionally, the method for solving such physics-based problems is to discretize and solve a PDE by a purely mathematical process. Instead of using the PDE, we propose to use the global heat principle and to decompose it into basic laws. We show that some of these laws admit an exact global version since they arise from conservative principles.We also show that the assumptions made about the other basic Iaws can be made wisely, taking into account knowledge about the problem and the domain. The numerical scheme is derived in a straightforward way from the modeled problem, thus providing a physical explanation for each step in the solution. The advantage of such an approach is that it minimizes the approximations made during the whole process and it modularizes it, allowing changing the application to a great number of problems. We apply the scheme to two applications: image denoising and inpainting which are modeled with heat transfer. For denoising, we propose a new approximation for the conductivity coefficient and we add thin lines to the features in order to block diffusion.     

A MAP-Based Algorithm for Destriping and Inpainting of Remotely Sensed Images

Remotely sensed images often suffer from the common problems of stripe noise and random dead pixels. The techniques to recover a good image from the contaminated one are called image destriping (for stripes) and image inpainting (for dead pixels). This paper presents a maximum a posteriori (MAP)-based algorithm for both destriping and inpainting problems. The main advantage of this algorithm is that it can constrain the solution space according to a priori knowledge during the destriping and inpainting processes. In the MAP framework, the likelihood probability density function (PDF) is constructed based on a linear image observation model, and a robust Huber-Markov model is used as the prior PDF. The gradient descent optimization method is employed to produce the desired image. The proposed algorithm has been tested using moderate resolution imaging spectrometer images for destriping and China-Brazil Earth Resource Satellite and QuickBird images for simulated inpainting. The experiment results and quantitative analyses verify the efficacy of this algorithm.     

Object removal and loss concealment using neighbor embedding methods

Exemplar-based inpainting methods involve three critical steps: finding the patch processing order, searching for best matching patches, and estimating the unknown pixels from the best matching patches. The paper addresses each step and first introduces a new patch priority term taking into account the presence of edges in the patch to be filled-in. The paper then presents a method using linear regression based local learning of subspace mapping functions to enhance the search for the nearest neighbors (K-NN) to the input patch in the particular case of inpainting. Several neighbor embedding (NE) methods are then considered for estimating the unknown pixels. The performances of the resulting inpainting algorithms are assessed in two application contexts: object removal and loss concealment. In the loss concealment application, the ground truth is known, hence objective measures (e.g., PSNR) can be used to assess the performances of the different methods. The inpainting results are compared against those obtained with various state-of-the-art solutions for both application contexts.