Abstract
We present a novel approach for compressing relatively small unordered data sets by means of combinatorial optimization. The application background comes from the field of biometrics, where the embedding of fingerprint template data into images by means of watermarking techniques requires extraordinary compression techniques. The approach is based on the construction of a directed tree, covering a sufficient subset of the data points. The arcs are stored via referencing a dictionary, which contains “typical” arcs w.r.t. the particular tree solution. By solving a tree-based combinatorial optimization problem we are able to find a compact representation of the input data. As optimization method we use on the one hand an exact branch-and-cut approach, and on the other hand heuristics including a greedy randomized adaptive search procedure (GRASP) and a memetic algorithm. Experimental results show that our method is able to achieve higher compression rates for fingerprint (minutiae) data than several standard compression algorithms.
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References
Bentley, J.L.: Multidimensional binary search trees used for associative searching. Commun. ACM 18(9), 509–517 (1975)
Burrows, M., Wheeler, D.J.: A block-sorting lossless data compression algorithm. Technical report 124, Digital SRC Research Report (1994)
Chang, R.-S., Leu, S.-J.: The minimum labeling spanning trees. Inf. Process. Lett. 63(5), 277–282 (1997)
Cherkassky, B.V., Goldberg, A.V.: On implementing the push-relabel method for the maximum flow problem. Algorithmica 19(4), 390–410 (1997)
Chwatal, A.M., Raidl, G.R.: Applying branch-and-cut for compressing fingerprint templates (short abstract). In: Proceedings of the European Conference on Operational Research (EURO) XXII, Prague (2007)
Chwatal, A.M., Raidl, G.R., Dietzel, O.: Compressing fingerprint templates by solving an extended minimum label spanning tree problem. In: Proceedings of the Seventh Metaheuristics International Conference (MIC), Montreal (2007)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT, Cambridge (2001)
Dietzel, O.: Combinatorial optimization for the compression of biometric templates. Master’s thesis, Vienna University of Technology, Institute of Computer Graphics and Algorithms (2008)
Feo, T., Resende, M.: Greedy randomized adaptive search procedures. J. Glob. Optim. 6, 109–133 (1995)
Garris, M.D., McCabe, R.M.: NIST special database 27: fingerprint minutiae from latent and matching tenprint images. Technical report, National Institute of Standards and Technology (2000)
Hochbaum, D.S., Maass, W.: Approximation schemes for covering and packing problems in image processing and vlsi. J. ACM 32(1), 130–136 (1985)
ILOG Concert Technology, CPLEX: ILOG. http://www.ilog.com. Version 11.0 (2009)
Jain, A., Uludag, U.: Hiding fingerprint minutiae in images. In: Proceedings of Third Workshop on Automatic Identification Advanced Technologies, pp. 97–102 (2002)
Krumke, S.O., Wirth, H.-C.: On the minimum label spanning tree problem. Inf. Process. Lett. 66(2), 81–85 (1998)
Library for Efficient Datastructures and Algorithms (LEDA): Algorithmics Solutions Software GmbH. http://www.algorithmic-solutions.com/. Version 5.1 (2009)
Magnanti, T., Wolsey, L.: Optimal trees. In: Network Models. Handbook in Operations Research and Management Science, pp. 503–615. North Holland, Amsterdam (1995)
Maltoni, D., Maio, D., Jain, A.K., Prabhakar, S.: Handbook of Fingerprint Recognition. Springer, New York (2003)
Moffat, A., Neal, R.M., Witten, I.H.: Arithmetic coding revisited. ACM Trans. Inf. Sys. 16(3), 256–294 (1998)
Nummela, J., Julstrom, B.A.: An effective genetic algorithm for the minimum-label spanning tree problem. In: GECCO ’06: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, pp. 553–558. ACM, New York (2006)
Raidl, G.R., Chwatal, A.: Fingerprint template compression by solving a minimum label k-node subtree problem. In: Simos, E. (ed.) Numerical Analysis and Applied Mathematics. AIP Conference Proceedings, vol. 936, pp. 444–447. American Institute of Physics, New York (2007)
Saleh, A., Adhami, R.: Curvature-based matching approach for automatic fingerprint identification. In: Proceedings of the Southeastern Symposium on System Theory, pp. 171–175 (2001)
Sayood, K.: Introduction to Data Compression, 3rd edn. Morgan Kaufmann, San Mateo (2006)
Varshney, L.R., Goyal, V.K.: Benefiting from disorder: source coding for unordered data. arXiv, abs/0708.2310 (2007)
Vitter, J.S.: Design and analysis of dynamic huffman codes. J. ACM 34(4), 825–845 (1987)
Wolsey, L.A., Nemhauser, G.L.: Integer and Combinatorial Optimization. Wiley-Interscience, New York (1999)
Xiong, Y., Golden, B., Wasil, E.: A one-parameter genetic algorithm for the minimum labeling spanning tree problem. IEEE Trans. Evol. Comput. 9(1), 55–60, 2 (2005)
Ziv, J., Lempel, A.: A universal algorithm for sequential data compression. IEEE Trans. Inf. Theory 23(3), 337–343 (1977)
Ziv, J., Lempel, A.: Compression of individual sequences via variable-rate coding. IEEE Trans. Inf. Theory 24(5), 530–536 (1978)
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Chwatal, A.M., Raidl, G.R. & Oberlechner, K. Solving a k-Node Minimum Label Spanning Arborescence Problem to Compress Fingerprint Templates. J Math Model Algor 8, 293–334 (2009). https://doi.org/10.1007/s10852-009-9109-1
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DOI: https://doi.org/10.1007/s10852-009-9109-1