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.
 In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces—Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.   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. Jigsaw puzzle algorithm is important as it can be applied to many areas such as biology, image editing, archaeology and incomplete crime-scene reconstruction. But, still, some problems exist in the process of practical application, for example, when there are a large number of similar objects in the puzzle fragments, the error rate will reach 30 –50 . When some fragments are missing, most algorithms fail to restore the images accurately. When the number of fragments of the jigsaw puzzle is large, efficiency is reduced. During the intelligent puzzle, mainly the Sum of Squared Distance Scoring (SSD), Mahalanobis Gradient Compatibility (MGC) and other metrics are used to calculate the similarity between the fragments. On the basis of these two measures, we put forward some new methods: 1. MGC is one of the most effective measures, but using MGC to reassemble the puzzle can cause an error image every 30 or 50 times, so we combine the Jaccard and MGC metric measure to compute the similarity between the image fragments, and reassemble the puzzle with a greedy algorithm. This algorithm not only reduces the error rate, but can also maintain a high accuracy in the case of a large number of fragments of similar objects. 2. For the lack of fragmentation and low efficiency, this paper uses a new method of SSD measurement and mark matrix, it is general in the sense that it can handle puzzles of unknown size, with fragments of unknown orientation, and even puzzles with missing fragments. The algorithm does not require any preset conditions and is more practical in real life. Finally, experiments show that the algorithm proposed in this paper improves not only the accuracy but also the efficiency of the operation. An important step in automatic reassembly of 2D fragments is to find candidate matching pairs for adjacent fragments. In this paper, we propose a new partial curve matching method to find the candidate matches. In this method, the fragment contours are represented by their turning functions. The matching segments between two fragment contours are found by analyzing the difference curve between two turning functions directly. The performance of our method is illustrated with randomly shredded document fragments. 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.