Generalized Digital Reassembly using Geometric Registration Anthousis Andreadis, Georgios Papaioannou and Pavlos Mavridis Department of Informatics, Athens University of Economics and Business Email: {anthousis, gepap, pmavridis}@aueb.gr Abstract—We present a novel and generic user-guided ap- proach for the digital reconstruction of cultural heritage finds from fragments, which operates directly on generic 3D objects. Central to our approach is a three-tier geometric registration approach that addresses the reassembly problem using i) the contact surface of the fractured objects, ii) feature curves on the intact surfaces and iii) partial object symmetries. In contrast to most existing methodologies, our approach is more generic and addresses even the most difficult cases, where contact surface is unusable, small or absent. We evaluate our method using digitized fragments from the Nidaros Cathedral. Keywords—Reassembly, registration, alignment, features, sym- metry detection, geometric priors I. I NTRODUCTION The reconstruction of cultural heritage finds is a time- consuming and difficult task, especially for large objects or large collections of fragments. The digital counterpart, virtual object reassembly, has received significant research interest in the past years, mainly with regard to specialized object types, such as frescos and pottery. This virtual, computer-assisted domain provides numerous advantages, including the access to remotely located physical finds and the ability to easily manipulate 3D shapes, whose physical counterparts may be hard to handle. Above all, it benefits from the exploitation of robust and fast (semi-) automatic algorithms for computing and exhaustively testing hypotheses at a large problem scale, even extreme ones. Interestingly, algorithms and methods developed in the scope of computational archaeology can be also applied to the domains of forensics and computer-assisted surgery, which have also expressed interest in such methods and perform related research. In computational archaeology, the problem is described as the automatic process that involves the identification of potentially fractured parts/regions of an object, the search for corresponding pieces within a fragment collection and finally the clustering and pose estimation of multiple parts that result in a virtual representation of (partially) reassembled objects. In the general case, the problem has 2 ...N input part representa- tions (surfaces, volumes, point-clouds etc.), each expressed in its own local coordinate system. The resulting solution consists of 1 ...M clusters. If no cyclic associations are allowed, this translates to at most N -M rigid transformations that describe the pose of the fragments in the output clusters. Typically, the process starts with the digitization (e.g. 3D scanning) of the physical fragments and continues with the pre-processing of the fragment geometry in order to extract the fractured and intact surfaces (segmentation and classification). Subsequently, all pairwise combinations of the fragments are tested for alignment and a matching error is computed. This step usually begins with a global registration process that examines the solution search space for a good but rough alignment, that in turn initiates a local registration process in order to refine the solution. The complete set of the pairwise results drives subsequently the multi-part alignment (reassembly), where complete objects are formed by finding the global position for each fragment. In this work, we focus mainly on the pairwise and multi- part registration steps of the reassembly by introducing a three-tier geometric registration approach that was designed to help expert users during the reassembly process. The main contribution of our approach is the ability to provide plausible solutions for objects with high erosion or even large missing parts, which is usually the case in most cultural heritage scenarios and which almost all existing approaches fail to address. In the rest of the paper we initially present an overview of existing work in the field, we proceed to elaborate on our three-tier geometric registration approach and finally, we present results of our approach, when applied to actual cultural heritage data from the Nidaros Cathedral in Trondheim. II. PREVIOUS WORK Depending on the type of the fragments, the general reassembly problem can be specialized according to the fol- lowing categories: Two-Dimensional (2D) Reassembly. While all real objects have a third dimension, for certain relatively flat objects, such as frescos and stone tablets, it is safe to make a simplification and reduce the problem to two dimensions, without this affecting the quality of the final reassembly. The work of Leitao and Stolfi [1], Kong and Kimia [2] and Papaodysseus et al. [3] are some of the most representative examples in this category that utilize some form of elastic curve matching to address the problem. Different approaches have also been presented, such as the work of Saˇ giroˇ glu and Erc ¸il [4], where texture synthesis and in-painting techniques are used in order to find the solution. Restricted Three-Dimensional (2.5D) Reassembly. Methods in this category solve the reassembly problem using 3D objects for which either the actual dimensionality is less than 3 (e.g. contours or surfaces embedded in 3D space) or the degrees of freedom for the matching reduces the pose estimation trans- formation to a two-dimensional problem. In the literature, the first set of problems usually regards ”thin-walled fragments”,