Low-rank tensor completion with fractional-Jacobian-extended tensor regularization for multi-component visual data inpainting

Several low-rank tensor completion methods have been integrated with total variation (TV) regularization to retain edge information and promote piecewise smoothness. In this paper, we first construct a fractional Jacobian matrix to nonlocally couple the structural correlations across components and propose a fractional-Jacobian-extended tensor regularization model, whose energy functional was designed proportional to the mixed norm of the fractional Jacobian matrix. Consistent regularization could thereby be performed on each component, avoiding band-by-band TV regularization and enabling effective handling of the contaminated fine-grained and complex details due to the introduction of a fractional differential. Since the proposed spatial regularization is linear convex, we further produced a novel fractional generalization of the classical primal-dual resolvent to develop its solver efficiently. We then combined the proposed tensor regularization model with low-rank constraints for tensor completion and addressed the problem by employing the augmented Lagrange multiplier method, which provides a splitting scheme. Several experiments were conducted to illustrate the performance of the proposed method for RGB and multispectral image restoration, especially its abilities to recover complex structures and the details of multi-component visual data effectively.     

纹理分布分析的快速图像修复算法

目前基于样本块的图像修复算法均是运用平方差和(SSD)准则遍历固定的样本集以选取最优匹配块,算法普遍具有运算效率低的缺点。针对现有算法进行改进,提出一种基于图像纹理分布分析的快速图像修复算法,该算法根据局部纹理变化动态确定样本集大小,解决样本集过大时引起的计算时间浪费以及样本集过小时样本多样性不足的问题。实验结果证明,该算法保证修复结果连续且符合人眼视觉要求,大大提高了图像修复的效率,具有实际意义。     

结合纹理结构的分数阶TV模型的图像修复

目的 TV（total variation）模型在图像修复时易导致图像中具有弱导数性质的纹理和边缘细节等信息变得模糊,为了克服该缺陷,分数阶微分被引入到TV模型中,但传统的分数阶TV模型对弱边缘和弱纹理等细节信息的保持仍不够理想,并且没有充分利用图像已知区域的先验信息,修复精度仍有待提高。方法 针对该问题,提出结合纹理结构信息和分数阶TV模型的图像修复算法。改进的模型在分数阶TV模型求解时,在梯度计算过程中增加了一个极小值,克服了正则项和数据项在零点处的不可微,从而增加了模型的稳定性。再则改进的模型根据图像已知区域的先验信息确定待修复区域的纹理方向,从而更好地保持了图像中的纹理细节和弱边缘信息。结果 将本文算法与3种修复效果较好的算法进行对比,采用客观评价指标：均方差（MSE）、峰值信噪比（PSNR）和差值图像进行评价,实验结果表明本文算法在不同的纹理图像修复中均取得较好的效果,如对标准图像库中的Barbara和Lena图像以及岩石图像进行修复后,与原始TV模型相比,它们的峰值信噪比分别提高5.94%、8.07%和3.85%,灰度均方差分别降低48.66%、65.89%和35%;与分数阶TV模型相比,它们的峰值信噪比分别提高4.17%、8.59%和1.81%,灰度均方差分别降低37.90%、68.00%和18.68%。结论 提出的模型相对于原始的TV模型和分数阶TV模型,均能有效地提高图像修复的精度,适合于包含较多弱纹理和弱边缘信息的图像修复,该模型是TV模型的重要延伸和推广。     

基于块缺失图像修复技术的研究与应用

图像修复是数字图像处理的重要内容，在图像润色、视频图像复原等诸多领域都有着非常广泛的应用。该文以对图像块粗糙度的分析为依据，优化纹理合成算法，并结合JPEG算法，应用于图像压缩，使图像压缩率得到显著提高。     

小波变换与纹理合成相结合的图像修复

目的 为了克服传统的图像修复算法在结构和纹理边界的错误修复,利用小波变换域的系数特征,探讨了一种基于小波变换与纹理合成相结合的修复算法。方法 算法先利用小波变换将待修复图像分解成具有不同分辨率的低频子图和高频子图,然后根据不同子图各自的特征分别进行修复。对代表图像结构信息的低频子图,采用FMM(fast marching method)算法进行修复;对代表图像纹理信息的高频子图,根据各子图中小波系数的特征,利用纹理合成方法进行修复。结果 分层、分类修复方法对边缘破损具有良好的修复效果,其峰值信噪比相比于传统算法提高了1~2 dB。结论 与相关算法相比,本文算法的综合修复能力较好,可以有效修复具有较强边缘和丰富纹理的破损图像,尤其对破损自然图像的修复,修复后图像质量得到较大提升,修复效果更符合人眼视觉效应。     

A model validation approach to texture recognition and inpainting

A new approach to texture recognition and inpainting problems is proposed. The approach is based on the robust model validation and state estimation techniques. The proposed solutions require the modeling of textures by using uncertain dynamical systems. We propose a new modeling method which is efficient in terms of computational and memory requirements. The main aspects of the modeling method include system identification and order reduction of marginally stable uncertain discrete-time systems. To demonstrate the results, both static-image textures and video textures (also known as dynamic textures) are considered.     

基于局部平均灰度熵的快速图像修复算法

使用块拼贴的基于样本的图像修复算法运行时间主要取决于最佳样本块匹配步骤的执行效率。目前算法普遍采用全局搜索获取样本块,逐一与待修复块进行相似性比对,修复质量和修复效率依赖于采样区域的范围大小。为提高计算效率,提出一种基于局部平均灰度熵的图像修复算法,在每次迭代中根据待修复块邻域窗的平均灰度熵自适应确定采样区域范围。实验结果证明,所提算法相较经典Criminisi修复算法提高了修复质量,且大大提高了修复效率。     

A unified method for appearance and geometry completion of point set surfaces

This paper presents a novel approach for appearance and geometry completion over point-sampled geometry. Based on the result of surface clustering and a given texture sample, we define a global texture energy function on the point set surface for direct texture synthesis. The color texture completion is performed by minimizing a constrained global energy using the existing surface texture on the surface as the input texture sample. We convert the problem of context-based geometry completion into a task of texture completion on the surface. The geometric detail is then peeled and converted into a piece of signed gray-scale texture on the base surface of the point set surface. We fill the holes on the base surface by smoothed extrapolation and the geometric details over these patches are reconstructed by a process of gray-scale texture completion. Experiments show that our method is flexible, efficient and easy to implement. It provides a practical texture synthesis and geometry completion tool for 3D point set surfaces.     

基于纹理方向的图像修复算法

在使用基于样本的纹理合成技术的图像修复算法中,搜索纹理的匹配块时,利用纹理的方向特性,可以将搜索过程约束到沿着纹理的方向进行。在Criminisi A的算法基础上,加入了确定纹理方向过程,优化了纹理块的优先权和大小的计算方法。实验结果表明,该方法在处理强方向性的纹理图像的修复时有很好的效果,明显地提高了计算效率。     

基于离散小波变换的图像修补方法*

根据多尺度分析原理,提出了基于离散小波变换的图像修复方法.首先用离散小波变换把图像分解为高频成分与低频成分,对图像不同频率的成分分别进行修补.图像的低频部分采用笔者以前所提出的结合中值滤波和基于曲率扩散方法[1]进行修复.由于高频部分地表示图像的边缘轮廓信息,并且有很强的方向性,对高频图像数据先进行分块,用线性拟合求出每一块的方向,再根据方向信息进行修复.实验表明,该算法能较好地修补破损区域.     

Combined frequency and spatial domain-based patch propagation for image completion

Film and photography archives now have an accelerated rate of degradation. Because the preservation of cultural heritage plays an important role in our society, photograph and film restoration has recently drawn a substantial amount of attention. In this paper, an approach that involves exemplar-based inpainting, aimed at determining patch priority and patch matching, is proposed. Different image regions have different levels of importance for vision perception; hence, a priority score must be assigned. Patch priority is calculated by the energy of its distributed cosine transform coefficients (DCT term) and the edge term. The edge term prioritizes the edge patches and the energy of the DCT coefficients of the patch is used as a discriminator for patches with similar edge terms. Patch inpainting is performed by assessing the similarity between the patches in such a manner that the similarity measure is consistent with human visual judgment. Therefore, a structure-based similarity measure is developed. Further, the interpolated missing pixels at the patch are also considered for applying the structure-based patch matching criteria in finding the candidate patch. Experimental results on damaged digitized photographs and natural images are presented, which demonstrate the effectiveness of the image completion framework for tasks such as scratch/text, object removal and image inpainting.     

一种基于纹理合成的高效图像填充方法

为了更好地解决图像填充与修复问题,提出了一种基于图像样本纹理合成的新方法。该方法提出了一种新的定义像素点优先级的思路,来确定待填充区域的填充顺序,以此来保证处理结果的质量。相较于其他图像填充算法,该算法无需复杂的数学模型和大量的计算过程,从而提高了运算速度。实验证明,该方法不仅在处理效率上取得了很大进步,而且输出图像的质量也取得了理想效果。     

基于统计特征的图像修复

在基于样图图像修复思想的基础上,从填充顺序和匹配准则两个方面进行改进,提出了一种图像修复方法。优先级函数加入了面片梯度信息和方差信息,使得填充顺序能够正确地修复结构和纹理信息。匹配准则采用自定义的颜色特征函数和统计特征函数对相似片进行两重匹配,取最优匹配块填充。一系列的修复实例证明该方法的有效性和鲁棒性。     

基于结构张量的图像修复方法

针对传统各向异性扩散方程在修复图像时仅考虑梯度模的大小,且在修复彩色图像时易产生虚假边缘等缺陷,提出基于结构张量的图像修复方法。将结构张量作为各向异性扩散方程的扩散系数,实现在不同区域有不同的扩散方式。实验结果显示:该方法与整体变分(TV)和BSCB方法相比,提高了图像修复效果,有效地完成对于彩色图像的修复。     

采用TV及纹理合成技术的分层图像修复

整体变分（TV）模型在图像修复中能够保持图像的边缘且数值实现方便,但在图像修复中对于人类视觉连通性的处理还有所不足。根据图像遗失或者损坏的不同类型,针对TV、CDD模型在图像修复中存在的问题,提出了一种结合TV、CDD模型及基于块的纹理合成算法的分层图像修复算法。实验结果表明,这种分层修复的方法在图像的结构修复和纹理修复两方面实现了较好的统一,而且在较大区域图像修复上表现出良好的效果。     

一种具有边界保持特性的图像修补方法

将边界优先级的图像修补方法引入GMRF修补模型中,通过对待修补区域边界像素点优先级的计算,确定像素的修补顺序,并和传统GMRF修补算法的修补结果做出比较。实验结果表明,基于边界优先级的图像修补算法对待修补区域包含边缘的图像有较好的修补效果,能够保持图像缺损区域的结构信息。     

自适应样本块大小的图像修复方法

传统基于样本块的图像修复算法中样本块大小是固定不变的,在修复过程中无法根据图像的具体情况进行调节,这在很大程度上影响了图像的整体修复效果。为了解决这一问题,提出一种自适应确定样本块大小的方法。该算法通过分析图像的梯度域变化,获得各像素点处的结构信息,进而自适应确定待修复样本块的大小。仿真实验结果表明,该算法能够有效克服传统方法中经常出现的诸如结构误传播、图像整体结构丢失等缺点,对具有明显结构变化的图像取得了比较理想的修复效果。     

纹理合成技术在旧照片修补中的应用

图像修复是图像复原研究的一个重要内容,它的目的是根据图像现有的信息自动恢复丢失的信息。在对目前图像修复技术两大类方法分析的基础上,提出了利用改进的纹理合成技术进行旧照片修补的方法,通过实验证明与变分方法图像修补比较有更好的效果,具有很强的实用性。     

A hybrid-based texture synthesis approach

Texture synthesis has been an active research area in computer graphics, vision, and image processing. A hybrid texture synthesis approach that combines the strength of Ashikhmins [1] and Liangs [11] algorithms is presented in this paper. Using patches from the input sample texture to extend the input itself, more suitable valid candidate pixels in the input sample can be more precisely determined. An extra original position array is used to record the valid pixel position in the extended region of input sample texture such that the candidate pixel can be retrieved efficiently. Pasting patches with more global information of texture features to initialize the output texture, the texture synthesis process tends to grow larger pieces in the output texture so that the perceptual similarity is reserved as much as possible. Many classes of textures have been used to test our approach. As the experimental results showed, the proposed hybrid approach effectively and efficiently synthesizes high-quality textures from a wide variety of textures.