# Graph-Based Clustering for Apictorial Jigsaw Puzzles of Hand Shredded Content-less Pages

12 Dec 2016-pp 135-147

TL;DR: An efficient iterative framework to solve apictorial jigsaw puzzles of hand shredded content-less pages, using only the shape information is proposed, which shows the efficiency in the reconstruction of multiple content- less pages from arbitrarily torn fragments.

Abstract: Reassembling hand shredded content-less pages is a challenging task, with applications in forensics and fun games. This paper proposes an efficient iterative framework to solve apictorial jigsaw puzzles of hand shredded content-less pages, using only the shape information. The proposed framework consists of four phases. In the first phase, normalized shape features are extracted from fragment contours. Then, for all possible matches between pairs of fragments transformation parameters for alignment of fragments and three goodness scores are estimated. In the third phase, incorrect matches are eliminated based on the score values. The alignments are refined by pruning the set of pairwise matched fragments. Finally, a modified graph-based framework for agglomerative clustering is used to globally reassemble the page(s). Experimental evaluation of our proposed framework on an annotated dataset of shredded documents shows the efficiency in the reconstruction of multiple content-less pages from arbitrarily torn fragments.

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22 Jul 2018

TL;DR: A reassembly framework for a three-dimensional shell is proposed as a logical extension of the twodimensional framework that can handle fragments even with curved edges which can be reasonably approximated by a set of edges.

Abstract: A major bottleneck activity in the process of restoration of Heritage Structures is the reassembly of its fragments. Computer-aided reassembly could assist in finding the relation between them thereby reducing time, manpower and potential degradation to fragile fragments. Using geometric compatibility between the adjacent fragments as the central idea, a reassembly framework for a three-dimensional shell is proposed as a logical extension of the twodimensional framework. Edges are extracted as polygons and relevant features are computed at each of its vertices. Sequences of the match for two fragments in the feature space are found using a modified version of Smith-Waterman Algorithm. Each match is assessed using a connectivity score. The final choice of best match is left to the user by displaying the resultant assembled fragments of prospective candidates along with the score. After pairwise matching, the global reassembly is done through a clustering-based method. This framework can handle fragments even with curved edges which can be reasonably approximated by a set of edges. We verify the methodology using a simulated dataset for both 2D pieces and a shattered 3D

3 citations

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TL;DR: This paper presents a fully-automatic and general algorithm that addresses puzzle solving in archaeology, and shows that the state-of-the-art approach manages to correctly reassemble dozens of broken artifacts and frescoes.

Abstract: This paper focuses on the re-assembly of an archaeological artifact, given images of its fragments. This problem can be considered as a special challenging case of puzzle solving. The restricted case of re-assembly of a natural image from square pieces has been investigated extensively and was shown to be a difficult problem in its own right. Likewise, the case of matching “clean” 2D polygons/splines based solely on their geometric properties has been studied. But what if these ideal conditions do not hold? This is the problem addressed in the paper. Three unique characteristics of archaeological fragments make puzzle solving extremely difficult: (1) The fragments are of general shape; (2) They are abraded, especially at the boundaries (where the strongest cues for matching should exist); and (3) The domain of valid transformations between the pieces is continuous. The key contribution of this paper is a fully-automatic and general algorithm that addresses puzzle solving in this intriguing domain. We show that our approach manages to correctly reassemble dozens of broken artifacts and frescoes.

2 citations

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TL;DR: This paper proposes a method of completely clustering Chinese homologous pieces in which the distribution features of the characters in the pieces and the document layout are used to correlate adjacent pieces and cluster them in different areas of a document.

Abstract: When recovering a shredded document that has numerous mixed pieces, the difficulty of the recovery process can be reduced by clustering, which is a method of grouping pieces that originally belonged to the same page. Restoring homologous shredded documents (pieces from different pages of the same file) is a frequent problem, and because these pieces have nearly indistinguishable visual characteristics, grouping them is extremely difficult. Clustering research has important practical significance for document recovery because homologous pieces are ubiquitous. Because of the wide usage of Chinese and the huge demand for Chinese shredded document recovery, our research focuses on Chinese homologous pieces. In this paper, we propose a method of completely clustering Chinese homologous pieces in which the distribution features of the characters in the pieces and the document layout are used to correlate adjacent pieces and cluster them in different areas of a document. The experimental results show that the proposed method has a good clustering effect on real pieces. For the dataset containing 10 page documents (a total of 462 pieces), its average accuracy is 97.19%.

1 citations

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24 Nov 2022

TL;DR: PuzzleFusion as discussed by the authors proposes an end-to-end neural architecture based on Diffusion Models for spatial puzzle solving, particularly jigsaw puzzle and room arrangement tasks, which takes a set of room layouts as polygonal curves in the top-down view and aligns the room layout pieces by estimating their 2D translations and rotations.

Abstract: This paper presents an end-to-end neural architecture based on Diffusion Models for spatial puzzle solving, particularly jigsaw puzzle and room arrangement tasks. In the latter task, for instance, the proposed system ``PuzzleFusion'' takes a set of room layouts as polygonal curves in the top-down view and aligns the room layout pieces by estimating their 2D translations and rotations, akin to solving the jigsaw puzzle of room layouts. A surprising discovery of the paper is that the simple use of a Diffusion Model effectively solves these challenging spatial puzzle tasks as a conditional generation process. To enable learning of an end-to-end neural system, the paper introduces new datasets with ground-truth arrangements: 1) 2D Voronoi jigsaw dataset, a synthetic one where pieces are generated by Voronoi diagram of 2D pointset; and 2) MagicPlan dataset, a real one offered by MagicPlan from its production pipeline, where pieces are room layouts constructed by augmented reality App by real-estate consumers. The qualitative and quantitative evaluations demonstrate that our approach outperforms the competing methods by significant margins in all the tasks. We will publicly share all our code and data.

##### References

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TL;DR: This letter extends the heuristic homology algorithm of Needleman & Wunsch (1970) to find a pair of segments, one from each of two long sequences, such that there is no other Pair of segments with greater similarity (homology).

Abstract: The identification of maximally homologous subsequences among sets of long sequences is an important problem in molecular sequence analysis. The problem is straightforward only if one restricts consideration to contiguous subsequences (segments) containing no internal deletions or insertions. The more general problem has its solution in an extension of sequence metrics (Sellers 1974; Waterman et al., 1976) developed to measure the minimum number of “events” required to convert one sequence into another. These developments in the modern sequence analysis began with the heuristic homology algorithm of Needleman & Wunsch (1970) which first introduced an iterative matrix method of calculation. Numerous other heuristic algorithms have been suggested including those of Fitch (1966) and Dayhoff (1969). More mathematically rigorous algorithms were suggested by Sankoff (1972), Reichert et al. (1973) and Beyer et al. (1979) but these were generally not biologically satisfying or interpretable. Success came with Sellers (1974) development of a true metric measure of the distance between sequences. This metric was later generalized by Waterman et al. (1976) to include deletions/insertions of arbitrary length. This metric represents the minimum number of “mutational events” required to convert one sequence into another. It is of interest to note that Smith et al. (1980) have recently shown that under some conditions the generalized Sellers metric is equivalent to the original homology algorithm of Needleman & Wunsch (1970). In this letter we extend the above ideas to find a pair of segments, one from each of two long sequences, such that there is no other pair of segments with greater similarity (homology). The similarity measure used here allows for arbitrary length deletions and insertions.

9,761 citations

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TL;DR: An implementation is demonstrated that is able to align two range images in a few tens of milliseconds, assuming a good initial guess, and has potential application to real-time 3D model acquisition and model-based tracking.

Abstract: The ICP (Iterative Closest Point) algorithm is widely used for geometric alignment of three-dimensional models when an initial estimate of the relative pose is known. Many variants of ICP have been proposed, affecting all phases of the algorithm from the selection and matching of points to the minimization strategy. We enumerate and classify many of these variants, and evaluate their effect on the speed with which the correct alignment is reached. In order to improve convergence for nearly-flat meshes with small features, such as inscribed surfaces, we introduce a new variant based on uniform sampling of the space of normals. We conclude by proposing a combination of ICP variants optimized for high speed. We demonstrate an implementation that is able to align two range images in a few tens of milliseconds, assuming a good initial guess. This capability has potential application to real-time 3D model acquisition and model-based tracking.

3,673 citations

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01 Dec 1973-Cartographica: The International Journal for Geographic Information and Geovisualization

TL;DR: In this paper, two algorithms to reduce the number of points required to represent the line and, if desired, produce caricatures are presented and compared with the most promising methods so far suggested.

Abstract: All digitizing methods, as a general rule, record lines with far more data than is necessary for accurate graphic reproduction or for computer analysis. Two algorithms to reduce the number of points required to represent the line and, if desired, produce caricatures, are presented and compared with the most promising methods so far suggested. Line reduction will form a major part of automated generalization. Regle generale, les methodes numeriques enregistrent des lignes avec beaucoup plus de donnees qu'il n'est necessaire a la reproduction graphique precise ou a la recherche par ordinateur. L'auteur presente deux algorithmes pour reduire le nombre de points necessaires pour representer la ligne et produire des caricatures si desire, et les compare aux methodes les plus prometteuses suggerees jusqu'ici. La reduction de la ligne constituera une partie importante de la generalisation automatique.

3,476 citations

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TL;DR: This paper describes the development of a procedure that enables a digital computer to solve ``apictorial'' jigsaw puzzles, i.e., puzzles in which all pieces are uniformly gray and the only available information is the shape of the pieces.

Abstract: This paper describes the development of a procedure that enables a digital computer to solve ``apictorial'' jigsaw puzzles, i.e., puzzles in which all pieces are uniformly gray and the only available information is the shape of the pieces. The problem was selected because it provided an excellent vehicle to develop computer techniques for manipulation of arbitrary geometric patterns, for pattern identification, and for game solving. The kinds of puzzles and their properties are discussed in detail. Methods are described for characterizing and classifying piece contours, for selecting and ordering pieces that are ``most likely'' to mate with a given piece, for determining likelihood of fit, for overcoming ambiguities, and for evaluation of the progressive puzzle assembly. An illustration of an actual computer solution of a puzzle is given.

234 citations

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Brown University

^{1}TL;DR: R ridges of 3D fragments scanned using a laser range finder are detected using a dynamic programming method and a pair of ridges are matched using a generalization of the 2D curve matching approach to space curves by using an energy solution involving curvature and torsion.

Abstract: We approach the problem of 2D and 3D puzzle solving by matching the geometric features of puzzle pieces three at a time. First, we define an affinity measure for a pair of pieces in two stages, one based on a coarse-scale representation of curves and one based on a fine-scale elastic curve matching method. This re-examination of the top coarse-scale matches at the fine scale results in an optimal relative pose as well as a matching cost which is used as the affinity measure for a pair of pieces. Pairings with overlapping boundaries are impossible and are removed from further consideration, resulting in a set of top valid candidate pairs. Second, triples arising from generic junctions are formed from this rank-ordered list of pairs. The puzzle is solved by a recursive grouping of triples using a best-first search strategy, with backtracking in the case of overlapping pieces. We also generalize aspects of this approach to matching of 3D pieces. Specifically, ridges of 3D fragments scanned using a laser range finder are detected using a dynamic programming method. A pair of ridges are matched using a generalization of the 2D curve matching approach to space curves by using an energy solution involving curvature and torsion, which are computed using a novel robust numerical method. The reconstruction of map fragments and broken tiles using this method is illustrated.

171 citations

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