Solving a Special Type of Jigsaw Puzzles: Banknote Reconstruction From a Large Number of Fragments

In this paper, we propose a method to solve a special type of jigsaw puzzles, reconstructing banknotes from a large number of fragments based on fragments´ images. Existing jigsaw puzzle assembly algorithms have difficulty solving this problem effectively. A main limitation of these methods is that they do not leverage the following important observations: 1) an intact banknote´s image is known and thus can be used as prior information; 2) if two aligned fragments overlap each other, they must not be from a same banknote. Based on these two important observations, a three-step method is proposed to reconstruct banknotes from their fragments. Each fragment is first aligned to its original position on the banknote by a RANSAC method. After evaluating every two aligned fragments´ relationships, all fragments are embedded into a lower dimensional space and then clustered into small groups using a modified agglomerative clustering method. Fragments in a same cluster are likely to be from a same banknote. Experiments on both synthetic and real data demonstrate the effectiveness of our proposed method.