This paper addresses the problem of reassembling images from disjointed fragments. More specifically, given an unordered set of fragments, we aim at reassembling one or several possibly incomplete images. The main contributions of this work are: 1) several deep neural architectures to predict the relative position of image fragments that outperform the previous state of the art; 2) casting the reassembly problem into the shortest path in a graph problem for which we provide several construction algorithms depending on available information; 3) a new dataset of images taken from the Metropolitan Museum of Art (MET) dedicated to image reassembly for which we provide a clear setup and a strong baseline.
The reconstruction of archaeological pieces of art leads to better understanding of our history and thus attracts numerous researchers, as Rasheed and Nordin described in their surveys @cite_24 @cite_23 . Most publications of this field rely on the border irregularities and aim for precise alignment. They focus on automated reconstruction, such as @cite_6 @cite_20 @cite_10 and consider jigsaw puzzle solving with missing fragments or with differently sized tiles @cite_14 @cite_26 @cite_5 . These methods perform well on a small dataset with only one source of fragments. On the downside, they stall when fragments come from various sources and they require costly human made annotations. Moreover,they are fragile towards erosion and fragment loss.
@cite_14 @cite_26 @cite_6 @cite_24 @cite_23 @cite_5 @cite_10 @cite_20
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The reconstruction of broken artifacts is a common task in archeology domain; it can be supported now by 3D data acquisition device and computer processing. Many works have been dedicated in the past to reconstructing 2D puzzles but very few propose a true 3D approach. We present here a complete solution including a dedicated transportable 3D acquisition set-up and a virtual tool with a graphic interface allowing the archeologists to manipulate the fragments and to, interactively, reconstruct the puzzle. The whole lateral part is acquired by rotating the fragment around an axis chosen within a light sheet thanks to a step-motor synchronized with the camera frame clock. Another camera provides a top view of the fragment under scanning. A scanning accuracy of 100μm is attained. The iterative automatic processing algorithm is based on segmentation into facets of the lateral part of the fragments followed by a 3D matching providing the user with a ranked short list of possible assemblies. The device has been applied to the reconstruction of a set of 1200 fragments from broken tablets supporting a Latin inscription dating from the first century AD. Manuscript History: An automatic reconstruction of ancient artifact fragments is of great interest in archaeology, and is considered important because it helps archaeologists make inferences about past cultures and civilizations. Therefore, numerous researches proposed various methods to put together and restore the fragments of a piece of pottery to its original form. The aim of this paper is to present an in-depth review of the most important available publications in computer applications related to the area of the classifying and reconstruction of three-dimensional model for archaeological pottery objects over the epoch in the early eighties until the end of 2013. This task classified according to the feature extraction, the classification process and the matching techniques implemented for the purpose of restoration of the fragments of pottery object to its original form. Moreover, this paper focused on review and analyze the results that they have achieved. The algebraic reconstruction technique (ART), based on the well known algorithm proposed by Kaczmarz in 1937, is one of the most important class of solution methods for image reconstruction problems. But unfortunately, almost all the methods from the ART class give satisfactory results only in the case of consistent problems. In the inconsistent case (and unfortunately this is what happens in real applications, because of measurement errors) they give only more or less "controllable" versions of the exact solutions. This is exactly the case that we analyze in the present paper. We start with a theoretical analysis of the classical Kaczmarz's projection method in the case of an inconsistent linear least-squares problem and we prove that the approximations so obtained are at a certain distance from the set of exact least-squares solutions. This distance is controlled by the component of the right hand side of the problem lying in the orthogonal complement of the range of problem's matrix, i.e. exactly the component that makes the problem inconsistent. For overcoming this difficulty we consider an extended version of Kaczmarz's algorithm, previously analyzed by one of the authors. In the numerical experiments described in the last part of the paper we compare the above mentioned extension with two well known (ART) type algorithms for image reconstruction in two electromagnetic geotomography problems. The results indicate that the extended Kaczmarz algorithm gives much better results than the other two. This thesis describes a general method for automatic reconstruction of accurate, concise, piecewise smooth surfaces from unorganized 3D points. Instances of surface reconstruction arise in numerous scientific and engineering applications, including reverse-engineering--the automatic generation of CAD models from physical objects. Previous surface reconstruction methods have typically required additional knowledge, such as structure in the data, known surface genus, or orientation information. In contrast, the method outlined in this thesis requires only the 3D coordinates of the data points. From the data, the method is able to automatically infer the topological type of the surface, its geometry, and the presence and location of features such as boundaries, creases, and corners. The reconstruction method has three major phases: (1) initial surface estimation, (2) mesh optimization, and (3) piecewise smooth surface optimization. A key ingredient in phase 3, and another principal contribution of this thesis, is the introduction of a new class of piecewise smooth representations based on subdivision. The effectiveness of the three-phase reconstruction method is demonstrated on a number of examples using both simulated and real data. Phases 2 and 3 of the surface reconstruction method can also be used to approximate existing surface models. By casting surface approximation as a global optimization problem with an energy function that directly measures deviation of the approximation from the original surface, models are obtained that exhibit excellent accuracy to conciseness trade-offs. Examples of piecewise linear and piecewise smooth approximations are generated for various surfaces, including meshes, NURBS surfaces, CSG models, and implicit surfaces.