摘 要：重庆大足石刻作为“唐宋石刻艺术的文化宝库”与“世界石窟艺术最后的丰碑”，并没有如国内外其他世界文化遗产一样充分利用计算机图形图像处理、移动终端等现代科技手段进行文物的数字化保护、修复与传播，无法契合“互联网+”时代艺术传播接受者的视觉经验与心理期待，传播范围与传播力度受到制约。国内外数字化、虚拟化的文物保护工程的典型案例表明，数字图像修复技术对文物的数字化保护、展示与传播具有奠基性意义。有必要将数字图像修复技术引入大足石刻的保护与修复，推进大足石刻数字图像信息库、数字博物馆及虚拟漫游等工程，实现大足石刻在传播内容与传播方式上的多维化，以及传播影响力上的时空延伸。关键词：数字图像修复；大足石刻；数字化；文物保护与传播Abstract: The Dazu Rock Carvings in Chongqing, as “a cultural treasure-house of the rock carving art of the Tan g and Song Dynasties” and the “last monument of the grotto art in the world”, are restricted in the scope and intensity of their dissemination, because unlike other world cultural heritages in China and abroad, their digital conservation, restoration and dissemination has not been implemented by making full use of computer graphics and image processing, the mobile terminal and other modern technologies, making them fail to conform to the visual experience and psychological expectation of the recipients of art dissemination in the “Internet Plus” era. The typical cases of digital and virtual cultural relics conservation project at home and abroad have indicated that the digital image inpainting technology is of foundational significance to
the digital conversation, display and dissemination of cultural relics. Therefore, it is necessary to introduce the digital image inpainting technology into the conservation and inpainting of Dazu Rock Carvings, and promote such projects as the digital
image database, digital museum and virtual roaming of Dazu Rock Carvings, in an effort to realize the multi-dimensional
content and ways of dissemination of the Dazu Rock Carvings, as well as the extension of influence of dissemination in time and space.
Key words: digital image inpainting; Dazu Rock Carvings; digitization; conservation and dissemination of cultural relics
图1 基于扩散的图像修复过程Fig. 1 Diffusion-based inpainting 图2 基于样本的图像修复过程
Fig. 2 The process of exemplar-based inpainting 6408 2016 北方美术
理论研究. All Rights Reserved.
随着计算机图形图像处理技术与互联网的长足发展，文物的数字化越来越受到文博部门的重视。将数字扫描、3D 成像、虚拟现实（Virtual reality，VR）等科学技术应用于文物的数字保存、辅助修复、虚拟展览等领域的现象已经非常普遍。尤其是利用数字图像修复技术对文物进行辅助修复、重建，更成为建立数字化网上虚拟博物馆的关键。
tf2o大足石刻作为重庆市唯一一项世界文化遗产，是“唐宋石刻艺术的文化宝库”，也是古印度石窟艺术在中国由北至南空间传播过程中所形成的最后一座丰碑。就其本身所具有的艺术价值与艺术地位而言，相比敦煌、云冈等石窟艺术对数字化技术应用的如火如荼，大足石刻的数字化成果则明显不足。大足石刻目前在传播的方式上主要还是以传统的景区展览、博物馆、高校及科研机构的学术研讨会等为主体，其传播影响的力度与广度显得薄弱。本文即在计算机图形图像处理技术的基础上，讨论大足石刻的数字化保护及传播。
一、大足石刻的数字化保护与传播现状
1.数字化保护现状
大足石刻数字博物馆建设工程已经开启，2012年7月国家文物局正式批准《大足石刻宝顶山大佛湾石刻三维数据采集与数据库建设项目》，大足石刻研究院于2013年5月开始启动三维激光扫描测绘，完成基础数据库的采集与建设。大足石刻研究院院长黎方银介绍，此次的三维测绘信息将通过后期数据处理，构建三维模型及制作相关应用图件，为大足石刻4D展示、数字博物馆展示、保护修复等提供科学支撑。［1］同时，历时8年之久的宝顶山千手观音实体修复工程过程中，采用了事先进行虚拟修复、模拟修复的手段。
但相比云冈石窟、敦煌莫高窟等，大足石刻的图像数字化研究正处于起步阶段，而数字图像修复研究
则更少。目前数字图像修复技术在我国主要应用于敦煌壁画、西藏唐卡、中国古画等图像的修复研究，应用于石刻艺术的案例相对较少。
2.大足石刻传播现状
目前，大足石刻的传播方式主要有以下几种：一是以传统的旅游景区、博物馆方式向游客传播，这种实地传播方式由于受到景区和博物馆的容纳量及时空的限制，影响范围有限；二是通过电视、广播、报刊等传统媒介，这种传播方式受到版面、播放时段等限制，传播的时效性有限；三是通过大足石刻研究院举办的历届研讨会及高校与研究院合作的学术活动所进行的传播，这种传播渠道主要属于专业人士之间的学术性交流与传播，传播人及范围受到限制；四是通过互联网和自媒体进行数字化传播，但是目前仅限于常规的网站传播方式，且内容单薄。
2015年6月13日才正式对外开放的大足石刻博物馆，采用数字化、虚拟成像、环幕电影、多媒体等现代科技手段呈现大量文物、资料、图片、影像，［2］不仅吸引了观众的注意力，而且能够充分展示与传播大足石刻的内在艺术价值，
With the considerable development of computer graphics and image processing technology and the Internet, more and more attention has been paid to the digitization of cultural relics by relevant departments of cultural relics. The application of digital scanning, 3D imaging, virtual reality (VR) and
other science and technology to digital preservation, computer-aided restoration, virtual exhibition of cultural relics and other fields is already very common. The use of digital image inpainting technology to assist in the restoration and reconstruction of cultural relics, in particular, has become the key to the establishment of online digital virtual museum.
As the only world cultural heritage in Chongqing, Dazu Rock Carvings are “a cultural treasure-house of the art of rock carving in the Tang and Song Dynasties”, as well as the last monument that was formed in the process of dissemination of ancient Indian grotto art from the north to the south in China. In view of their artistic value and artistic position, digitization of Dazu Rock Carvings is obviously insufficient compared with the energetic application of digital technologies to the grotto art in Dunhuang and Yungang. The main ways of dissemination of Dazu Rock Carvings presently remain traditional exhibitions at scenic spots, museums, academic seminars sponsored by institutions of higher learning and research institutions, and the intensity and breadth of their dissemination seem insufficient. This article aims to discuss the digital conservation and dissemination of Dazu Rock Carvings on the basis of computer graphics and image processing technology.
I. The Status Quo of Digital Conservation and Dissemination of Dazu Rock Carvings
1. The Status Quo of Digital Conservation
The construction project of Dazu Rock Carvings Digital Museum has already started. The Construction Project of Three Dimensional Data Acquisition and Database for the Dafowan Dazu Rock Carvings in Baoding Mountain was officially approved by the State Cultural Relics Bureau in July 2012, and Dazu Rock Carvings Research Institute started its 3D laser scanning and mapping in May 2013 to complete the collection and construction of the basic database. According to Mr. Li Fangyin, director of the Research Institute, the three-dimensional mapping information will be used, after post-processing of data, to construct three-dimensional model and produce related application figures, providing scientific support for 4D display, digital museum display, conservation and restoration of Dazu Rock Carvings.[1] During the process of the restoration project of the Avalokitesvara entity in Baoding Mountain which lasted for eight years, the means of virtual restoration and simulated restoration in advance was adopted.
However, compared with Yungang Grottoes and Mogao Grottoes in Dunhuang, the image digitization research of Dazu Rock Carvings is only in its initial stage, and digital image inpainting research is even more rarely conducted. At present in China, the digital image inpainting technology is mainly applied to the study of restoring Dunhuang murals, Tibetan Thangkas, ancient Chinese pai
ntings and other images, and there are relatively few cases of its application to the art of rock carving.
2. The Status Quo of Dissemination of Dazu Rock Carvings
At present, the major ways of dissemination of Dazu Rock Carvings are as follows: The first, dissemination to tourists through conventional scenic spots and museums, which, due to the limit of the capacity of scenic spots and museums and time and space, only has limited range of influence. The second, dissemination through such traditional media as TV, radio, newspapers, and magazines, which, due to the limit of space of pages and broadcast hours, is limited in timeliness. The third, dissemination through seminars hosted by Dazu Rock Carvings Research Institute and academic activities jointly organized by universities and the Research Institute, which, as academic exchanges and dissemination mainly among professionals, is limited in its breadth. The fourth, digital dissemination through the internet and we-media, which, at present, is only restricted to the conventional website dissemination mode and thin in content.
The Dazu Rock Carvings Museum, which was officially opened to the public as late as on June 13, 2015, by adopting modern means of science and technology, such as digital imaging, VR, circular-sc
reen movie and multimedia etc., to present a large number of cultural relics, materials, pictures and videos, [2] has not only attracted the attention of the audience, but also fully displayed and disseminated the intrinsic artistic value of Dazu Rock Carvings, and thus has pushed forward the digitization of Dazu Rock Carvings to a considerable extent. However, more front-end dissemination modes similar to those used by other
65
西南联合大学NORTHERN ART 2016 08THEORETICAL RESEARCH . All Rights Reserved.
在很大程度上推进了大足石刻的数字化进程。然而，类似于
其他文化遗产所采用的更前端的科技传播方式，如敦煌的
球幕电影院、模拟石窟和云冈的虚拟漫游等则有待进一步
地研发。
二、数字图像修复技术及其在文物保护与传播中的应用现状1.数字图像修复技术艺术图像修复技术由来已久，西方源于欧洲中世纪，中国则在“宋时已露头角，而清乾隆发扬光大至前无古人之境地”。［3
］人工修复技术历来依靠的是纯手工作业，相当费时费力，并且面临着二次损毁的风险。因为人工修复非常依赖于修复师个人的修复经验与艺术修养，并且修复结果大多是不可逆的，所以如何通过多次“试修复”以取得最佳修复效果，是修复师们梦寐以求的。在纯手工修复历史上，这是不可想象的，而计算机技术的发展则提供了这一可能。美国的M. Bertalmio 等人在艺术学校参观学习人工修复的操作步骤之后，根据艺术修复这一灵感，借用其专业术语“修复”（inpainting ），于2000年第一次在计算机领域提出“图像修复”（image inpainting ）这一概念及其算法。［4］如图1所示，一幅破损图像被分成两部分，一部分为图像未缺损区域，界定为图像的已知部分（known part ），另一部分为图像受损或缺失区域，界定为图像的未知部分（unknown part ），记为Ω，∂Ω为图像已知部分与未知部分的交界线，亦称为未
知部分的前沿线。图像的修复过程则是将图像已知部分的图cultural heritages, such as the dome-screen cinema and the simulated Grottos in Dunhuang, and the virtual roaming in Yungang, need further research and development.II. Digital Image Inpainting Technology and the Status Quo of Its Application to Conservation and Dissemination of Cultural Relics
1. Digital Image Inpainting Technology Art image inpainting techniques have existed for a long time. I
n the West, it originated in Europe in the middle ages; while in China, “it already appeared in the Song Dynasty and reached unprecedented prosperity during Emperor Qianlong’s reign in the Qing Dynasty.”[3] Always relying on purely manual work, manual restoration technology is time-consuming and laborious, and faces the risk of a second damage. As manual restoration is very dependent on the restorers’ personal experience and artistic accomplishment, and its results are mostly irreversible, it is a long cherished goal of restorers to be able to achieve the best effect of restoration through numerous “trial restorations”. While this was unimaginable in the history of purely manual restoration, the development of computer technology has made it possible.According to the inspiration gained in art restoration and borrowing the professional term “inpainting”, M. Bertalmio et al. of the United States, after they visited the art school and learned the steps of manual restoration, put forward for the first time in the computer field the concept of “image inpainting” and its algorithm in 2000. [4] As shown in Fig. 1, a damaged image is divided into two parts, one part being the undamaged area of the image, defined as the known part of the image, the other part being the damaged or incomplete area, defined as the unknown part of
the image and marked with Ω.∂Ωstands for the boundary between the known and the unknown parts of the image, also known as the cope line of the unknown part.The process of image inpainting is to gradually spread and disseminate the image information of the known part outwards layer by
process, mathematical modeling of image information of the known part of the image will be followed by automatic generation of the image information of the unknown part, making the restored part visually 图3 修复结果对比图：（a ）黑部分为物体移除后的待修复区域；（b ）基于扩散的修复结果；（c ）基于样本的修复结果。［5］
2011年高考数学
Fig 3 Contrast of results of inpainting: (a) the black part is the area to be restored after the removal of an object; (b) the result of diffusion-based inpainting; (c) the result of exemplar-based inpainting [5]
. All Rights Reserved.
像信息由未知前沿线逐层向外扩散传播，从而推测出受损部分所缺失的图像信息，
这一猜想过程将图像已知部分的图像信息进行数学建模，然后自动生成未知部分的图像信息，使恢复部分在视觉层面上看起来可信。
众多学者随后提出了各种各样的修复算法，我们可以把修复方法粗略地分为两大类［5］：基于扩散的图像修复（diffusion-based inpainting）与基于样本的图像修复（exemplar-based inpainting）。前者专注于图像结构信息的修复，依赖于图像信息的平滑约束（smooth-constraints），通过偏微分方程（partial differential equations，PDEs）或参数模型（parametric models）将图像已知部分的结构信息由内至外扩散传播至图像缺损部分。后者则依据图像信息的相似性约束（similarity-constraints），在纹理合成技术的基础上，试图从图像已知信息部分复制或合成相似图像（块）重建缺失部分，这一
方法的前提依据是图像的已知部分与未知部分具有同样的统计学分布。其修复过程如图2所示，a为待修复图像，其中Ω为待修复的目标区域，其前沿线为∂Ω，Φ为已知信息的源区域，黄与蓝代表两种不同纹理；b
中绿框内区域为以点p∈∂Ω为中心的待修复图像块
p Ψ；
c中图像块与分别为位于两种不同纹理交接线上的待选图像块；d为最佳匹配块被复制到待修复图像块p
Ψ所在位置。［6］
实验证明，基于扩散的修复方法在恢复结构线的连通性上表现优良，但在大面积的纹理重建方面则不尽如人意。而基于样本的修复方法虽在大面积的纹理修复方面性能优越，但在结构线的重建上则稍稍逊。由于自然图像通常既包含有结构又包含有纹理，因此，在图像的修复过程中，自然而然地就形成一种结合上述两类方法优点的混合修复方法：或者先把图像分解为结构部分与纹理部分，然后针对
图像信息的不同，分别采用基于扩散的与基于样本的方法进行修复，最后把两幅修复图像重建成最终的修复图像；或者先重建图像中物体的强边缘线或结构线，得到的修复轮廓图（inpainted
sketch
）用于辅助限定基于样本的方法进一步填充修复缺失credible.
A large number of scholars have subsequently proposed a variety of inpainting algorithms. We can r
一氧化锰oughly divide the inpainting methods into two categories[5]: diffusion-based image inpainting and examplar-based image inpainting. The former, focusing on the restoration of image structural information, relies on the smooth-constraints of the image information, and spreads the structural information of known part of the image from the inside to the damaged part of the image through partial differential equations (PDEs) or parametric models. The latter bases itself on the similarity-constraints of image information, and attempts to duplicate or compose a similar image (block) from the known information of the image and then reconstruct the missing part of the image. The premise of this method is that the known part of the image has the same statistical distribution as the unknown part. The inpainting process is shown in Fig. 2. Part a is the image to be inpainted, in whichΩstands for the target region to be inpainted, with∂Ωdenoting cope line, Φ denoting the source region of the known information, and yellow and blue colors representing two different textures; in b the area in the green frame stands for image block to be inpaintedΨwith p ∈∂Ωas the center; in c the image blocks and stand for the image blocks to be selected on the boundary between two different textures; and in d, the optimal matching block is copied in the position of the image block to be restored, pΨ.
The experimental results prove that the diffusion-based inpainting has good performance in restoring
the connectivity of structural lines, but it is not satisfactory in reconstructing the texture in a large area. The exemplar-based inpainting, though having excellent performance in restoring texture in a large area, is less satisfactory in reconstructing structural lines. As natural images usually contain both structure and texture, a mixed inpainting method with the advantages of the two methods combined has been naturally developed in the process of image inpainting: you first decompose the image into structure part and texture part, then you adopt the diffusion-based and exemplar-based methods respectively according to the differences of the image information, and finally you complete the final inpainted image on the basis of the two inpainted images; or you first reconstruct the strong outline or structural line of the object in the image, and then use the resulting inpainted sketch to assist the limited exemplar-based method and further restore the lookup areas where some pixels are missing. This composite method seems attractive, but it is very difficult in practical operation, for image separation or segmentation technology cannot deal with complex natural images perfectly.
The pioneering work done by Criminisi et al. in 2003—fast exemplar-based inpainting algorithm[6] which adjusted the order of inpainting reached the win-win effect in texture and structure inpainting, and thus attracted the attention of quite a number of researchers, who then put forward a variety of improved algorithms on the basis of their work. At the same time, due to its excellent performance in
texture restoration (Fig. 3), the exemplar-based inpainting algorithm is more suitable for applying to art image inpainting.
2. The Status Quo of the Application of Digital Image Inpainting to the Conservation and Dissemination of Cultural Relics Although digital image inpainting technology is inspired by art
图4 大足石刻部分病害情况 Fig. 4 Some cases of damaged Dazu Rock Carvings . All Rights Reserved.
像素的查区域（lookup areas）。这种复合方法看起来很有吸引力，但在实际操作时却是非常困难的，因为图像分离或分割技术不能很好地处理复杂的自然图像。钱莹微博
Criminisi等人在2003年的开拓性工作——基于样本的快速修复算法［6］，对修复的顺序进行了调整，在纹理与结构的修复上取得双赢，由此而得到了大量科研人员的重视，并在他们的工作基础上提出了各种改进算法。同时，由于在对纹理修复方面的优良表现（图3），基于样本的修复算法更适合应用于艺术图像的修复研究。
2.数字图像修复技术在文物保护与传播中的应用现状
尽管数字图像修复技术的灵感来源于艺术修复，但目前数字图像修复技术仍主要聚焦于对老照片的修
复及图片中文字或物体移除后的修复研究，将此技术反过来应用于实际的艺术图像修复的实践工作虽然不乏但明显不够。而事实上，在对文化遗产的保护中，非常必要也非常迫切地需要这一技术的参与，因为传统的人工修复不仅费时费力，而且个体差异的灵活性与随意性共存，在修复过程中容易将艺术文化遗产置于一种二次损毁的风险之中，而这一损失是难以弥补的。因此，借助数字图像修复技术为修复实践提供可供参考的修复方案，并从中筛选出最优修复措施，从而在对原图像造成最低损伤的基础上作适当的修复就显得非常必要。其次，由于某些文化遗产的损毁是逐年严重，如壁画、石刻等发生霉变、风化的易损性作品，将其进行抢救性数字化采集、虚拟修复与展示（其现有状态与可能原貌）则显得非常必要。
计算机图形图像技术、信息技术等已经在国内外文化遗产的保存、保护、修复、复原、展示、虚拟漫游、辅助考古与研究等领域具备一定的应用基础，并取得了令人瞩目的成果。美国斯坦福大学、华盛顿大学与Cyberware公司合作完成的数字化米开朗基罗计划，用三维扫描仪记录了米开朗基罗所塑造的10座大型雕塑；日本歧阜大学完成的基于测量的白川乡地区的古村落数字化工作；意大利罗马大学的Plinius工程，建立了庞贝城的虚拟现实模型，并实现三维漫游；法国卢浮宫虚拟漫游等均是数字化与虚拟化的文物保护工程的典型案例。播种希望的种子
我国最早意识到计算机图像技术对文物保护所带来机遇的是敦煌研究院。从1993年起，他们便实施了“敦煌壁画计算机存贮与管理系统研究”“濒危珍贵文物的计算机存贮与再现系统研究”等多项科研项目；
后与德国合作创建敦煌信息网站；1997年，又与浙江大学合作立项国家自然科学基金“多媒体及智能技术集成与艺术复原”，完成了莫高窟壁画与彩塑的数字化摄影与保存、壁画图像彩的数字化复原与历史演变过程模拟，开发了石窟虚拟展示与漫游系统、计算机辅助石窟保护修复辅助系统、能临摹创作敦煌风格图案的智能图案辅助设计系统；1998年与美国西北大学、梅隆基金会共同开展“敦煌壁画数字化和国际数字敦煌档案项目的合作研究”，建立起一套平面壁画数字化的技术实现方法。“2004年开始，敦煌研究院与中科院计算所开展技术合作，restoration, presently this technology still focuses on the study of the inpainting of the old photos and the restoration of the image after removal of texts or objects. The application of this technology in turn to practical art image inpainting, though not rare, is obviously insufficient. As a matter of fact, this technology is very necessary and urgently needed in conservation of cultural heritage, for the traditional manual inpainting is not only time-consuming and laborious, but, due to the flexibility and arbitrariness of restoration by individual restorers, also liable to put the artistic and cultural heritage in the risk of a second irretrievable damage. Therefore, it seems very necessary to select the best measure of restoration from the programmes of restoration for reference in practical restoration provided with the aid of digital image inpainting technology and then conduct proper inpainting with minimum possible damage to the original image. Secondly, as the damage of some cultural heritages is getting worse each year, for instance, murals or rock carvings, which are easily damaged due to being moldy or weathered, their
salvage digital data acquisition, virtual restoration and display (the existing state and the possible original appearance) seem necessary.
Computer graphics and image technology and information technology have a certain application foundation in the fields of domestic and foreign cultural heritage conservation, protection, inpainting, restoration, display, virtual roaming, and computer-aided archaeological research, and has made remarkable achievements. The digital Michelangelo project, jointly completed by Stanford University, University of Washington and Cyberware, recorded ten large sculptures by Michelangelo with a three-dimensional scanner; the measurement-based digitization of ancient villages in the Sirakawagou area was completed by Gifu University, Japan; the Plinius project was completed by University of Rome, Italy, with a virtual reality model of Pompeii set up and three-dimensional roaming realized; the virtual roaming of the Louvre Museum in France was realized: they are all typical cases of digital and virtual heritage conservation projects.
Dunhuang Research Academy is the first institution that came to realize in China the opportunity computer image technology brought about for conservation of cultural heritages. Beginning from 1993, they carried out a number of scientific research projects, such as “The Study of the Computer Storage and Management System of Dunhuang Murals” and “The Study of Computer Storage and R
epresentation System of Endangered Precious Cultural Relics”; later they founded the Dunhuang information website in cooperation with Germany; in 1997, they cooperated with University of Zhejiang in carrying out the registered and authorized national natural science fund project “Multimedia and Intelligent Technology Integration and Art Restoration”, completed the digital photography and conversation of murals and painted sculptures in Mogao Grottoes, digital restoration of the color of the murals and simulation of the process of historical evolution of the murals, and developed the grotto virtual display and roaming system, computer-aided grotto protection and restoration system, and the computer-aided intelligent pattern design system which can copy and create Dunhuang-style patterns; in 1998 they worked together with the Northwestern University and Mellon Foundation of the United States to carry out the project of the “Digitization of Dunhuang Murals and the Cooperative Study of International Digital Dunhuang Archives”, and established a set of technological realization methods of digitization of plane murals.
“Beginning from 2004, Dunhuang Research Academy cooperated with the Institute of Computing Technology of the Chinese Academy of Sciences, and chose cave 45 and cave 196 successively to carry out the project of the three dimensional digitization of Dunhuang Grottoes. So far, the Dunhuang Research Academy has completed the three-dimensional animation realistic view roamin
g of 40 caves”.[7] The fulfillment of other projects, such as the digital Imperial Palace, the digital display of “Riverside Scene at Qingming Festival” and panoramic roaming of Yungang Grottoes, has further demonstrated the achievements in conservation, inpainting and display of China’s cultural relics.
In a word, the gradual maturity of such artificial intelligence technologies as computer graphics and image processing has provided new means and methods for the conservation, restoration and research of cultural relics. The emergence of digital and virtual museums has provided new ways for the dissemination of cultural heritages.
III. The Significance of Digital Image Inpainting Technology to Digital Conservation and Dissemination of Dazu Rock Carvings
In its “13th Five-Year Plan”, China proposes to achieve the goal of
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