Study Of A Number Of Issues In The Recovery Of The Computer-aided Cultural Relics

Historical relics are artifacts and sites which have historical, artistic and scientific value in the development of human history. However, most of the excavated archaeological finds are damaged due to human and nature. So recovery of historical relics is a necessary, technical and onerous work in archaeology and relic research. Computer-aided relic recovery, especially virtual assembly of historical relic fragments using computer graphics, image processing and virtual reality techniques, is an important and urgent research. It can reduce the difficulty in relic restoration and avoid further damage to relics due to improper treatment. The digital models of restored relics can also be used in exhibition and retrieval system of digital museum. In all, computer-aided restoration of relics is an import research issue in both theory and practical application.Due to the complexity of relic digitization and large computing requirement, the research progress was very slow before 1990s. Recently the performance of computers has improved remarkably and capacities of storage devices have increased rapidly. Equipments such as scanners, photo cameras, videos and three-dimensional scanners are used widely. Moreover grid computing has developed. So lots of scholars are interested in computer-aided restoration of relics, which becomes one of the popular issues in the fields of computer graphics and computer vision.The problem of computer-aided restoration of relics consists of techniques such as relic digital information acquirement, assembly of fragments, hole-filling of missing parts. Among these techniques, archaeological experts are most interested in assembly of relic fragments, which is the most difficult part in recovery of relics. The objects of computer-aided relic restoration can be classified into two categories, which are planar fragments and surface objects. Fragments of pottery are one of the most important surface objects. Potteries were made on potter's wheels and are radially symmetric, whose fragments of these potteries are called revolving surface fragments. Planar fragments are digitalizedas images. Using three-dimensional scanners, we can easily sample surface fragments and obtain dense point clouds. Compared with traditional mesh process, point clouds have many advantages, such as data fidelity, simple geometrical structure, etc. Digital geometry process has evolved rapidly. So we take point clouds as the digitalization of surface fragments in our research.There are three distinct stages in the process of computer-aided reassembly of relic fragments:(l preprocessing of fragments and extraction of features,(2)local matching of fragments for pairwise affinity, and (3)searching for a globally optimal arrangement of fragments for shape recovery. The first stage is the basis and the second stage is the most difficult one. The big hurdles in the present methods that have to be overcome are unreliable features in stage one and a large mount of mismatching in stage two, which result in a very big searching space in the final stage. So the robust methods of feature extraction and effective pairwise matching of relic fragments are focused here. In the thesis the assembly process of planar fragments and revolving surface fragments are described in detail. The main contributions of the thesis are as follows:1. A method for assembling planar relic fragments based on the longest common subsequences is proposed. Boundary is the fundamental geometrical feature of a planar fragment. The longest common subsequences can be used to obtain the most possible pairwise matching of fragments because their matching is usually not perfect. First, the boundary of each fragment is obtained and split at breakpoints into sub-curves;then boundary curve is represented by local curvature, which is calculated based on a moving vector. After the longest common subsequences between all sub-curves taken from two fragments are found with which absolute orientation and fine alignments between the two fragments are obtained, the pairs that violate the overlapping constraint are rule out and the other matches are rank-ordered according to some given measures. Experimental results show that this method is robust and the most possible correct matching of fragments can be found.2. We have proposed a boundary extraction algorithm for surface fragments using maximum cycles. The boundaries are vital to the assembly of surface fragments. Unorganized point sets are by nature unstructured. So defining and extracting their boundaries is a difficult problem, which can also be used in many other applications, such as surface reconstruction, detection of undersamplingregion and hole-filling in point clouds. The algorithm is based the maximum cycle and can extract the globally optimum boundary curve. It consists of three steps. For each point its boundary probability is first computed based on its k nearest neighbours using three criteria. In order to distinguish the real boundary points from the false ones, in the second step a weighted graph is constructed using the boundary probability and local neighborhoods of points. Finally the boundary curve is extracted as the maximum cycle in the graph. The maximum cycle can be reduced to the maximum-cost perfect matching in another constructed graph, which can be found using Edmonds' polynomial-time algorithm.3. A method for axis and profile estimation of revolving surface fragments is brought up. The shape of a pot can be characterized by its profile and axis of rotation, which can be used in the assembly, hole-filling, classification and retreival of fragments. But fragments are only parts of a pot and usually have some additional decorations and carvings on their surface which affect the estimation of axis and profile. So a robust estimation is needed. First, the normals of the surface are represented in Plucker coordinates. Based on the basic geometrical relationship between the normals of surface and the axis of rotation of the object, the axis of rotation is estimated under the RANSAC paradigm. Then all points on the surface and their corresponding normals are transformed by a rotation around its axis of rotation into a plane which contains the axis of rotation. Finally an algebraic curve is fitted to the transformed profile points.4. A method of assembling two revolving surface fragments is devised. Two revolving surface fragments can be assembled by their boundaries, axes of rotation and profiles through optimization. First the revolving axes of two surface fragments are aligned through a three-dimensional transformation. Then the boundaries are broken into sub-contours using curvature and feature points. The optimal matching between two fragments can be reduced to a geometric optimization problem, which has two free parameters, the translation along common axis and rotation about the axis. Through traditional Nelder-Mead method, the optimization problem can be solved with a corresponding measure of affinity.The assembly of fragments is most focused in the computer-aided restoration of relics, of which feature extaction and pairwise matching are the most difficult parts. In the thesis, pairwise matching of planar fragments and revolving surfacefragments are solved based on the boundary extraction algorithm using maximum cycles, longest common subsequences, and robust estimation of axes of rotation and profiles, which lays a solid foundation to the global assembly of whole relics.