基于图像建模理论的多幅图像正则化超分辨率重建算法研究
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摘要
随着信息时代的逐步发展和图像处理的日益普及,科学研究和实际应用对图像分辨率的要求越来越高,因而对感光器制造技术逐渐提出新的挑战。目前,通过减小单位像素尺寸和增大感光器芯片尺寸的硬件方案都存在技术上的瓶颈,同时价格昂贵的高精密感光器不适用于普及应用。超分辨率(Super-Resolution;SR)重建技术利用已有低分辨率成像系统,通过信号处理的方法提高图像分辨率,获得国内外学术界与商业界的极大关注和深入研究,具有重要的理论意义和应用价值。
本文研究以基于图像建模理论的空域SR重建算法为主线,针对SR重建退化模型中的图像去噪、图像放大、图像增强、运动估计等关键子问题,重点研究发展了边缘保持、纹理保持、以及角形保持的图像建模,并且在此基础上相应地提出了一系列基于图像建模理论的多幅图像正则超分辨率重建算法。本文取得的创新理论及主要成果包括:
(1)针对各向同性MRF(Markov Random Field)图像先验模型,定义了一类非负稳健ρ-函数作为边缘保持势函数,同时将双边滤波推广到稳健双边滤波,建立了双边滤波与Bayesian MAP框架之间的理论联系。进一步地,通过同时考虑像素的亮度信息和图像的几何信息,设计了一种结构自适应的各向异性数字滤波器。在此基础上,提出了各向异性的MRF图像先验模型,同时建立了基于各向异性MRF图像模型的联合图像配准和高分辨率图像估计的边缘增强SR重建算法。重建图像的视觉效果和峰值信噪比显示,本文算法不仅能够更好地抑制噪声和保持边缘,而且能够同时抑制平坦区域中的阶梯效应。
(2)针对Rudin和Osher提出的连续全变差模型(Continuous Total Variation;CTV)在数字图像处理中的不足,分别提出了边缘保持的超数字化全变差(Beyond Digital TV;BDTV)模型和纹理保持的自适应超连续型全变差(Adaptive Beyond Continous TV;ABCTV)模型。BDTV模型不仅能够保持边缘结构的清晰度,而且能够抑制平坦区域中的阶梯效应,尤其适用于近似卡通图像的数字图像处理。ABCTV模型利用曲面的主曲率信息实现连续TV模型和高阶连续TV模型的自适应耦合,能够在抑制噪声过程中同时保持图像的边缘和纹理结构。进一步地,分别在参数化全局运动和非参数局部运动两种情形下提出基于BDTV模型的联合超分辨率重建和运动估计算法框架。重建图像的视觉效果和峰值信噪比均验证了本文算法的有效性。
(3)重点研究了如何在图像插值过程中同时实现边缘结构的光滑重建和角形结构的尖锐重建,首次提出可以用于增强角形结构的角形冲击滤波器的概念。角形冲击滤波器的设计主要分为两步:通过角形强度度量确定角形冲击流的速度;基于水平线演化理论确定角形冲击流的方向。通过耦合角形冲击滤波器和Osher等提出的边缘冲击滤波器,能够同时实现增强边缘结构和角形结构的目的。将角形冲击滤波器与方向扩散PDE图像插值算法耦合,不仅能够去除边缘上的锯齿效应,而且能够同时抑制方向扩散PDE在角形区域的扩散,大大提高了插值图像的视觉质量。在此基础上,提出了几何结构增强的PDE超分辨率重建算法框架,理论分析和实验结果均表明,本文算法是对Capel和Kim的PDE-SR重建算法合理有效的发展。
(4)重点对基于结构张量的变分PDE的滤波性能进行了系统的分析研究。Weickert等提出的散度型各向异性PDE对应的是具有角形保持作用的平滑-增强型滤波机制;而Tschumperlé等提出的可计算迹型PDE是散度型各向异性PDE的一种退化情形,对应的是平滑型滤波机制但是不具有角形保持作用。在此基础上,研究分析了基于结构张量的变分泛函满足角形保持性能的条件。最后,建立了一种面向应用的统一正则PDE框架,能够更为直观、有效地刻画PDE在平坦区域、边缘结构、以及角形结构的滤波性能。图像滤波、图像插值、图像修补等多种图像处理结果均验证了本文统一PDE框架的有效性。
(5)在刚性图像变换模型下提出基于几何结构相似度最大化的鲁棒图像配准算法。几何结构相似度定义为参考图像与待配准图像在几何结构方向场之间的一致性,更加符合人类感知的鲁棒性,并且提出利用结构张量增强方向场估计对随机噪声、光学模糊、频谱混叠等退化因素的鲁棒性。实验结果表明,本文算法在精确性、鲁棒性、以及适用性上优于当前SR重建中常用的KPB(Keren-Peleg-Brada)配准算法,对获得高质量的SR重建图像具有重要的应用价值。
Along with the gradual development of the information age and the growing popularity of image processing, image resolution has been increasingly and highly demanded in scientific research and practical applications,which gradually raises new challenges for the manufacturing technology on imaging sensors.At present,hardware programmes are,however,technically bottleneck,such as reducing the pixel size or increasing the chip size.In the meanwhile,prices of expensive high precision photographic are not applicable to wider applications.The technique of super-resolution(SR)reconstruction has become one of the hottest research topics in the world,consisting in that not only a high-resolution image can be reconstructed at a relatively low cost,but also the existing low-resolution imaging systems can be still utilized.Therefore,it is of great significance to research on the problem of super-resolution.
For image denoising,image interpolation,image enhancement,motion estimation and other key issues in SR, this paper manily focuses on image modeling for edge-preservation,texture-preservation,and comer-preservation, and correspondingly proposes several regularized SR reconstruction algorithms.
(1)The edge-preserving potential functions in isotropic MRF modeling are systematically discussed,and a type of non-negative robustρnorms is particularly defined for potential functions.In the meanwhile,the bilateral filtering is closely connected with the Bayesian MAP approaches,and subsequently generalized to the so-called robust bilateral filtering.Furthermore,a kind of structure-adaptive anisotropic filtering is designed based on both the luminance and the geometry of pixels,following which an anisotropic MRF-based edge-enhancing SR algorithm is proposed,capable of simultaneously estimating the high resolution image and the subpixel motion among low-resolution frames.Experimental results demonstrate the effectiveness of the proposed approach,both in the visual effect and the PSNR value.
(2)To overcome the shortcomings of the continuous total variation(CTV)model,this paper respectively proposes the edge-preserving beyond digital TV(BDTV)model and the texture-preserving adaptive beyond continous TV(ABCTV)model.BDTV is particularly applicable to cartoon images,capable of simultaneously prerving edges and removing staircase artifacts on homogeneous regions.ABCTV achieves the adaptive coupling of the CTV with higher-order CTV using the principal curvatures,not only able to preserve edges but also able to preserve textures.Based on BDTV,two simultaneous SR reconstruction and motion estimation algorithms are proposed,respectively using image registration and optical flow techniques to estimate the sub-pixel motion.Both static and dynamic SR experimental results demonstrate the effectiveness of the proposed algorithms.
(3)There have been proposed many magnification algorithms in the past decades,most of which concentrate on the smooth reconstruction of edge structures.Edge reconstruction,however,may usually destroy the corners,thus producing perceptually unpleasant rounded comer structures.A kind of comer shock filtering is particularly designed to enhance the corner structures,based on a new measure of corner strength and the theory of level-sets motion under curvature.Through combining the directional diffusion,the edge shock filtering.and the corner shock filtering,a regularized PDE approach for magnification is proposed to simultaneously reconstruct the edges and enhance the comers.The proposed PDE approach is also robust to random noise.Based on the regularized PDE interpolation approach,a structure enhancing PDE SR algorithm is subsequently proposed,which is actually the effective development of Capel and Kim's TV-based PDE SR algorithm.Both static and dynamic SR experimental results demonstrate the effectiveness of the proposed algorithms.
(4)The paper also analyzes the filtering behavior of the structure tensor based variational PDE approaches, utilizing the edge shock filtering and the proposed corner shock filtering,Weickert's anisotropic PDE corresponds to a kind of smoothing-enhancing and corner-preserving filtering mechanism;while Tschumperle's computable trace-based PDE is the reduced version of Weickert's approach,corresponding to a kind of smoothing filtering mechanism but not capable of corner-preservation.Furthermore,comer-preserving conditions are intuitively proposed for structure tensor based variational functionals.Based on above discussions,a kind of common regularization PDE framework is proposed for different image applications.The filtering behavior on homogeneous regions,edge and corner structures can be described more intuitively and efficiently by the common framework.Experimental results of image filtering,magnification,and inpainting demonstrate the efficiency of the common PDE framework.
(5)A SR-objected robust registration algorithm for the rigid image transform is proposed,through maximizing the designed structure similarity based on the robust estimation of structure orientation by the structure tensor. Experimental results demonstrate that the proposed algorithm is robust to random noise,optical blur,and spectrum aliasing,and behaves better than the commonly utilized KPB algorithm in accuracy,robustness,and applicability.
本文研究以基于图像建模理论的空域SR重建算法为主线,针对SR重建退化模型中的图像去噪、图像放大、图像增强、运动估计等关键子问题,重点研究发展了边缘保持、纹理保持、以及角形保持的图像建模,并且在此基础上相应地提出了一系列基于图像建模理论的多幅图像正则超分辨率重建算法。本文取得的创新理论及主要成果包括:
(1)针对各向同性MRF(Markov Random Field)图像先验模型,定义了一类非负稳健ρ-函数作为边缘保持势函数,同时将双边滤波推广到稳健双边滤波,建立了双边滤波与Bayesian MAP框架之间的理论联系。进一步地,通过同时考虑像素的亮度信息和图像的几何信息,设计了一种结构自适应的各向异性数字滤波器。在此基础上,提出了各向异性的MRF图像先验模型,同时建立了基于各向异性MRF图像模型的联合图像配准和高分辨率图像估计的边缘增强SR重建算法。重建图像的视觉效果和峰值信噪比显示,本文算法不仅能够更好地抑制噪声和保持边缘,而且能够同时抑制平坦区域中的阶梯效应。
(2)针对Rudin和Osher提出的连续全变差模型(Continuous Total Variation;CTV)在数字图像处理中的不足,分别提出了边缘保持的超数字化全变差(Beyond Digital TV;BDTV)模型和纹理保持的自适应超连续型全变差(Adaptive Beyond Continous TV;ABCTV)模型。BDTV模型不仅能够保持边缘结构的清晰度,而且能够抑制平坦区域中的阶梯效应,尤其适用于近似卡通图像的数字图像处理。ABCTV模型利用曲面的主曲率信息实现连续TV模型和高阶连续TV模型的自适应耦合,能够在抑制噪声过程中同时保持图像的边缘和纹理结构。进一步地,分别在参数化全局运动和非参数局部运动两种情形下提出基于BDTV模型的联合超分辨率重建和运动估计算法框架。重建图像的视觉效果和峰值信噪比均验证了本文算法的有效性。
(3)重点研究了如何在图像插值过程中同时实现边缘结构的光滑重建和角形结构的尖锐重建,首次提出可以用于增强角形结构的角形冲击滤波器的概念。角形冲击滤波器的设计主要分为两步:通过角形强度度量确定角形冲击流的速度;基于水平线演化理论确定角形冲击流的方向。通过耦合角形冲击滤波器和Osher等提出的边缘冲击滤波器,能够同时实现增强边缘结构和角形结构的目的。将角形冲击滤波器与方向扩散PDE图像插值算法耦合,不仅能够去除边缘上的锯齿效应,而且能够同时抑制方向扩散PDE在角形区域的扩散,大大提高了插值图像的视觉质量。在此基础上,提出了几何结构增强的PDE超分辨率重建算法框架,理论分析和实验结果均表明,本文算法是对Capel和Kim的PDE-SR重建算法合理有效的发展。
(4)重点对基于结构张量的变分PDE的滤波性能进行了系统的分析研究。Weickert等提出的散度型各向异性PDE对应的是具有角形保持作用的平滑-增强型滤波机制;而Tschumperlé等提出的可计算迹型PDE是散度型各向异性PDE的一种退化情形,对应的是平滑型滤波机制但是不具有角形保持作用。在此基础上,研究分析了基于结构张量的变分泛函满足角形保持性能的条件。最后,建立了一种面向应用的统一正则PDE框架,能够更为直观、有效地刻画PDE在平坦区域、边缘结构、以及角形结构的滤波性能。图像滤波、图像插值、图像修补等多种图像处理结果均验证了本文统一PDE框架的有效性。
(5)在刚性图像变换模型下提出基于几何结构相似度最大化的鲁棒图像配准算法。几何结构相似度定义为参考图像与待配准图像在几何结构方向场之间的一致性,更加符合人类感知的鲁棒性,并且提出利用结构张量增强方向场估计对随机噪声、光学模糊、频谱混叠等退化因素的鲁棒性。实验结果表明,本文算法在精确性、鲁棒性、以及适用性上优于当前SR重建中常用的KPB(Keren-Peleg-Brada)配准算法,对获得高质量的SR重建图像具有重要的应用价值。
Along with the gradual development of the information age and the growing popularity of image processing, image resolution has been increasingly and highly demanded in scientific research and practical applications,which gradually raises new challenges for the manufacturing technology on imaging sensors.At present,hardware programmes are,however,technically bottleneck,such as reducing the pixel size or increasing the chip size.In the meanwhile,prices of expensive high precision photographic are not applicable to wider applications.The technique of super-resolution(SR)reconstruction has become one of the hottest research topics in the world,consisting in that not only a high-resolution image can be reconstructed at a relatively low cost,but also the existing low-resolution imaging systems can be still utilized.Therefore,it is of great significance to research on the problem of super-resolution.
For image denoising,image interpolation,image enhancement,motion estimation and other key issues in SR, this paper manily focuses on image modeling for edge-preservation,texture-preservation,and comer-preservation, and correspondingly proposes several regularized SR reconstruction algorithms.
(1)The edge-preserving potential functions in isotropic MRF modeling are systematically discussed,and a type of non-negative robustρnorms is particularly defined for potential functions.In the meanwhile,the bilateral filtering is closely connected with the Bayesian MAP approaches,and subsequently generalized to the so-called robust bilateral filtering.Furthermore,a kind of structure-adaptive anisotropic filtering is designed based on both the luminance and the geometry of pixels,following which an anisotropic MRF-based edge-enhancing SR algorithm is proposed,capable of simultaneously estimating the high resolution image and the subpixel motion among low-resolution frames.Experimental results demonstrate the effectiveness of the proposed approach,both in the visual effect and the PSNR value.
(2)To overcome the shortcomings of the continuous total variation(CTV)model,this paper respectively proposes the edge-preserving beyond digital TV(BDTV)model and the texture-preserving adaptive beyond continous TV(ABCTV)model.BDTV is particularly applicable to cartoon images,capable of simultaneously prerving edges and removing staircase artifacts on homogeneous regions.ABCTV achieves the adaptive coupling of the CTV with higher-order CTV using the principal curvatures,not only able to preserve edges but also able to preserve textures.Based on BDTV,two simultaneous SR reconstruction and motion estimation algorithms are proposed,respectively using image registration and optical flow techniques to estimate the sub-pixel motion.Both static and dynamic SR experimental results demonstrate the effectiveness of the proposed algorithms.
(3)There have been proposed many magnification algorithms in the past decades,most of which concentrate on the smooth reconstruction of edge structures.Edge reconstruction,however,may usually destroy the corners,thus producing perceptually unpleasant rounded comer structures.A kind of comer shock filtering is particularly designed to enhance the corner structures,based on a new measure of corner strength and the theory of level-sets motion under curvature.Through combining the directional diffusion,the edge shock filtering.and the corner shock filtering,a regularized PDE approach for magnification is proposed to simultaneously reconstruct the edges and enhance the comers.The proposed PDE approach is also robust to random noise.Based on the regularized PDE interpolation approach,a structure enhancing PDE SR algorithm is subsequently proposed,which is actually the effective development of Capel and Kim's TV-based PDE SR algorithm.Both static and dynamic SR experimental results demonstrate the effectiveness of the proposed algorithms.
(4)The paper also analyzes the filtering behavior of the structure tensor based variational PDE approaches, utilizing the edge shock filtering and the proposed corner shock filtering,Weickert's anisotropic PDE corresponds to a kind of smoothing-enhancing and corner-preserving filtering mechanism;while Tschumperle's computable trace-based PDE is the reduced version of Weickert's approach,corresponding to a kind of smoothing filtering mechanism but not capable of corner-preservation.Furthermore,comer-preserving conditions are intuitively proposed for structure tensor based variational functionals.Based on above discussions,a kind of common regularization PDE framework is proposed for different image applications.The filtering behavior on homogeneous regions,edge and corner structures can be described more intuitively and efficiently by the common framework.Experimental results of image filtering,magnification,and inpainting demonstrate the efficiency of the common PDE framework.
(5)A SR-objected robust registration algorithm for the rigid image transform is proposed,through maximizing the designed structure similarity based on the robust estimation of structure orientation by the structure tensor. Experimental results demonstrate that the proposed algorithm is robust to random noise,optical blur,and spectrum aliasing,and behaves better than the commonly utilized KPB algorithm in accuracy,robustness,and applicability.
引文
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