A Global Approach for Solving Edge-Matching Puzzles

We consider apictorial edge-matching puzzles, in which the goal is to arrange a collection of puzzle pieces with colored edges so that the colors match along the edges of adjacent pieces. We devise an algebraic representation for this problem and provide conditions under which it exactly characterizes a puzzle. Using the new representation, we recast the combinatorial, discrete problem of solving puzzles as a global, polynomial system of equations with continuous variables. We further propose new algorithms for generating approximate solutions to the continuous problem by solving a sequence of convex relaxations

Solving Image Puzzles With A Simple Quadratic Programming Formulation

We present a new formulation to automatically solve jigsaw puzzles considering only the information contained on the image. Our formulation maps the problem of solving a jigsaw puzzle to the maximization of a constrained quadratic function that can be solved by a numerical method. The proposed method is deterministic and it can handle arbitrary rectangular pieces. We tested the validity of the method to solve problems up to 3300 puzzle pieces, and we compared our results to the current state-of-the-art, obtaining superior accuracy. © 2012 IEEE.6370Demaine, E., Demaine, M., Jigsaw puzzles, edge matching, and polyomino packing: Connections and complexity (2007) Graphs and Combinatorics, 23, pp. 195-208Justino, E., Oliveira, L.S., Freitas, C., Reconstructing shredded documents through feature matching (2006) Forensic Science International, 160 (2-3), pp. 140-147. , DOI 10.1016/j.forsciint.2005.09.001, PII S0379073805004913McBride, J., Kimia, B., Archaeological fragment reconstruction using curve-matching (2003) Conference on Computer Vision and Pattern Recognition Workshop. (CVPRW), 1, pp. 3-3Freeman, H., Garder, L., Apictorial jigsaw puzzles: The computer solution of a problem in pattern recognition (1964) IEEE Transactions on Electronic Computers, (2), pp. 118-127Goldberg, D., Malon, C., Bern, M., A global approach to automatic solution of jigsaw puzzles (2002) Proceedings of the Annual Symposium on Computational Geometry, pp. 82-87Kosiba, D., Devaux, P., Balasubramanian, S., Gandhi, T., Kasturi, K., An automatic jigsaw puzzle solver (1994) Proceedings of the 12th International Conference on Pattern Recognition (IAPR), 1, pp. 616-618Nielsen, T., Drewsen, P., Hansen, K., Solving jigsaw puzzles using image features (2008) Pattern Recognition Letters, 29 (14), pp. 1924-1933Cho, T., Avidan, S., Freeman, W., A probabilistic image jigsaw puzzle solver (2010) Conference on Computer Vision and Pattern Recognition (CVPR), pp. 183-190Pomeranz, D., Shemesh, M., Ben-Shahar, O., A fully automated greedy square jigsaw puzzle solver (2011) IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 9-16Seneta, E., (2006) Non-negative Matrices and Markov Chains, , Springer VerlagRosen, J., The gradient projection method for nonlinear programming. Part I. linear constraints (1960) Journal of the Society for Industrial and Applied Mathematics, 8 (1), pp. 181-21