Abstract
We present a novel algorithm based on “loop constraints” for assembling non-overlapping square-piece jigsaw puzzles where the rotation and the position of each piece are unknown. Our algorithm finds small loops of puzzle pieces which form consistent cycles. These small loops are in turn aggregated into higher order “loops of loops” in a bottom-up fashion. In contrast to previous puzzle solvers which avoid or ignore puzzle cycles, we specifically seek out and exploit these loops as a form of outlier rejection. Our algorithm significantly outperforms state-of-the-art algorithms in puzzle reconstruction accuracy. For the most challenging type of image puzzles with unknown piece rotation we reduce the reconstruction error by up to 70%. We determine an upper bound on reconstruction accuracy for various data sets and show that, in some cases, our algorithm nearly matches the upper bound.
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Alajlan, N.: Solving square jigsaw puzzles using dynamic programming and the hungarian procedure. American Journal of Applied Science 5(11), 1941–1947 (2009)
Cho, T.S., Avidan, S., Freeman, W.T.: The patch transform. PAMI (2010)
Cho, T.S., Avidan, S., Freeman, W.T.: A probabilistic image jigsaw puzzle solver. In: CVPR (2010)
Demaine, E.D., Demaine, M.L.: Jigsaw puzzles, edge matching, and polyomino packing: Connections and complexity. Graphs and Combinatorics 23(suppl.) (June 2007)
Andal, F.A., Taubin, G., Goldenstein, S.: Solving image puzzles with a simple quadratic programming formulation. In: Conference on Graphics, Patterns and Images (2012)
Freeman, H., Garder, L.: Apictorial jigsaw puzzles: the computer solution of a problem in pattern recognition. Electronic Computers 13, 118–127 (1964)
Gallagher, A.C.: Jigsaw puzzles with pieces of unknown orientation. In: CVPR (2012)
Garfinkel, S.L.: Digital forensics research: The next 10 years. Digit. Investig. 7, S64–S73 (2010), http://dx.doi.org/10.1016/j.diin.2010.05.009
Joseph, B., Kruskal, J.: On the shortest spanning subtree of a graph and the traveling salesman problem. American Mathematical Society (1956)
Liu, H., Cao, S., Yan, S.: Automated assembly of shredded pieces from multiple photos. In: ICME (2010)
Olmos, A., Kingdom, F.A.A.: A biologically inspired algorithm for the recovery of shading and reflectance images (2004)
Pomeranz, D., Shemesh, M., Ben-Shahar, O.: A fully automated greedy square jigsaw puzzle solver. In: CVPR (2011)
Sharp, G.C., Lee, S.W., Wehe, D.K.: Multiview registration of 3D scenes by minimizing error between coordinate frames. PAMI 26(8), 1037–1050 (2004)
Sholomon, D., David, O., Netanyahu, N.: A genetic algorithm-based solver for very large jigsaw puzzles. In: CVPR (2013)
Son, K., Almeida, E.B., Cooper, D.B.: Axially symmetric 3D pots configuration system using axis of symmetry and break curve. In: CVPR (2013)
Williams, B., Cummins, M., Neira, J., Newman, P., Reid, I., Tardós, J.: A comparison of loop closing techniques in monocular slam. Robotics and Autonomous Systems (2009)
Willis, A., Cooper, D.B.: Computational reconstruction of ancient artifacts. IEEE Signal Processing Magazine, 65–83 (2008)
Yang, X., Adluru, N., Latecki, L.J.: Particle filter with state permutations for solving image jigsaw puzzles. In: CVPR (2011)
Zach, C., Klopschitz, M., Pollefeys, M.: Disambiguating visual relations using loop constraints. In: CVPR (2010)
Zhu, L., Zhou, Z., Hu, D.: Globally consistent reconstruction of ripped-up documents. PAMI 30(1), 1–13 (2008)
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Son, K., Hays, J., Cooper, D.B. (2014). Solving Square Jigsaw Puzzles with Loop Constraints. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds) Computer Vision – ECCV 2014. ECCV 2014. Lecture Notes in Computer Science, vol 8694. Springer, Cham. https://doi.org/10.1007/978-3-319-10599-4_3
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DOI: https://doi.org/10.1007/978-3-319-10599-4_3
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