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A Multiscale Method for the Reassembly of Two-Dimensional Fragmented Objects
September 2002 (vol. 24 no. 9)
pp. 1239-1251

Abstract—We describe here an efficient procedure for reassembling unknown two-dimensional objects that have been broken or torn into a large number of irregular fragments—a problem that often arises in archaeology, art restoration, forensics, and other disciplines. The procedure compares the curvature-encoded fragment outlines, at progressively increasing scales of resolution, using an incremental dynamic programming sequence-matching algorithm. The total cost gets reduced by a factor proportional to the mean number of samples per segment, which makes the method viable for problems of practical size (thousands of fragments). The performance of our method is illustrated with an artificial but realistic example.

[1] K. Leutwyler, “Solving a Digital Jigsaw Puzzle,” Electronic article athttp://www.cns.nyu.edu/ftp/eero/portilla99.pdf/ /www.sciam.com/explorations/2001 062501fresco/, Feb. 2002.
[2] R. Winfield Smith and E. Kristof, “Computer Helps Scholars Recreate an Egyptian Temple,” National Geographic Magazine, vol. 138, no. 5, pp. 644-655, Nov. 1970.
[3] A.D. Kalvin, A. Remy, O. Ardito, K. Morla, E. Nolasco, J. Prado, A. Murga, and G. Wiese, “Using Visualization in the Archaeological Excavations of a Pre-Inca Temple in Peru,” Proc. IEEE Visualization Conf. '96, pp. 359-362, Oct. 1996.
[4] R. Halír and J. Flusser, “Estimation of Profiles of Sherds of Archaeological Pottery,” Proc. 1997 Czech Pattern Recognition Workshop (CPRW '97), pp. 126-130, Feb. 1997.
[5] C. Menard and R. Sablatnig, “On Finding Archaeological Fragment Assemblies Using a Bottom-Up Design,” Proc. 21st Workshop Austrian Assoc. for Pattern Recognition, pp. 203-207, 1997.
[6] R.A. Wagner and M.J. Fischer, "The String-to-String Correction Problem," J. ACM, vol. 21, no. 1, pp. 168-78, 1974.
[7] H.C.G. Leitão and J. Stolfi, “Automatic Reassembly of Irregular Fragments,” Technical Report IC-98-06, Inst. of Computing, Univ. of Campinas, Apr. 1998.
[8] H.C.G. Leitão, “Reconstrução Automática de Objetos Fragmentados,” PhD dissertation, Inst. of Computing, Univ. of Campinas (in Portuguese), Nov. 1999.
[9] H. Bunke and G. Kaufmann, “Jigsaw Puzzle Solving Using Approximate String Matching and Best-First Search,” Proc. Fifth Int'l Conf. Computer Analysis of Images and Patterns (CAIP '93), pp. 299-308, Sept. 1993.
[10] M. Levoy, “Scanning the Fragments of the Forma Urbis Romae,” Electronic document available at//www.graphics.stanford.edu/projects/mich/ forma-urbisforma-urbis.html, May 1999.
[11] G. Papaioannou, E.-A. Karabassi, and T. Theoharis, “Virtual Archaeologist: Assembling the Past,” IEEE Computer Graphics and Applications, vol. 21, no. 2, pp. 53-59, Mar. 2001.
[12] H.C.G. Leitão and J. Stolfi, “Information Contents of Fracture Lines,” Proc. WSCG '2000—Eighth Int'l Conf. in Central Europe on Computer Graphics, etc., vol. 2, pp. 389-395, Feb. 2000.
[13] G.C. Burdea and H.J. Wolfson, “Solving Jigsaw Puzzles by a Robot,” IEEE Trans. Robotics and Automation, vol. 5, no. 6, pp. 752-764, 1989.
[14] R.W. Webster, P.S. LaFollette, and R.L. Stafford, “Isthmus Critical Points for Solving Jigsaw Puzzles in Computer Vision,” IEEE Trans. Systems, Man, and Cybernetics, vol. 21, no. 5, pp. 1271-1278, 1991.
[15] H. Bunke and U. Buehler, “Applications of Approximate String Matching to 2-D Shape Recognition,” Pattern Recogniton, vol. 26, no. 12, pp. 1797-1824, 1993.
[16] A.R. Pope, “Model Based Object Recognition: A Survey of Recent Research,” Technical Report TR-94-04, Univ. of California, Berkeley, 1994.
[17] G. Barequet and M. Sharir, “Partial Surface and Volume Matching in Three Dimensions,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 9, pp. 929-948, Sept. 1997.
[18] F. Mokhtarian, “Silhouette-Based Isolated Object Recognition through Curvature Scale-Space,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 5, pp. 539-544, May 1995.
[19] F. Mokhtarian and A.K. Mackworth, “A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 8, pp. 789-805, Aug. 1992.
[20] A.P. Witkin, “Scale-Space Filtering,” Proc. Eighth Int'l Joint Conf. Artificial Intelligence (IJCAI '83), pp. 1019-1021, 1983.
[21] G. Üçoluk and I.H. Toroslu, “Automatic Reconstruction of Broken 3-D Surface Objects,” Computers&Graphics, vol. 23, no. 4, pp. 573-582, Aug. 1999.
[22] K. Hori, M. Imai, and T. Ogasawara, “Joint Detection for Potsherds of Broken Earthenware,” Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR '99), vol. 2, pp. 440-445, June 1999.
[23] K. Hori, M. Imai, and T. Ogasawara, “Data Model for Computer Reconstruction of Potsherds,” J. Computer Archaeology, (in Japanese), vol. 5, no. 2, pp. 1-10, Mar. 2000.
[24] K. Hori, M. Imai, and T. Ogasawara, “Hierarchical Description of a Contour for Reconstruction of Broken Earthenware,” The Trans. Electronics, Information and Comm. Engineers D-II (in Japanese), vol. J83-D-II, no. 5, pp. 1392-1394, May 2000.
[25] G.M. Radack and N.I. Badler, “Local Matching of Surfaces Using Boundary-Centered Radial Decomposition,” Computer Vision, Graphics, and Image Processing, vol. 45, no. 3, pp. 380-396, 1989.
[26] G. Turk and M. Levoy, “Zippered Polygon Meshes from Range Images,” Proc. SIGGRAPH '94, pp. 311-318, 1994.
[27] H.J. Wolfson, "On Curve Matching," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 5, pp. 483-489, May 1990.
[28] P. Rosin and S. Venkatesh, “Extracting Natural Scales Using the Fourier Description,” Pattern Recognition, vol. 26, no. 9, pp. 1383-1393, 1993.
[29] F. Boussofiane and G. Bertrand, “A New Method for Recognizing and Locating Objects by Searching Longest Paths,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 15, no. 12, pp. 445-448, Dec. 1993.
[30] A. Kalvin, E. Schonberg, J.T. Schwartz, and M. Sharir, “Two-Dimensional, Model-Based, Boundary Matching Using Footprints,” Int'l J. Robotics Research, vol. 5, no. 4, pp. 38-55, 1986.
[31] R. Legault and C.Y. Suen, “Optimal Local Weighted Averaging Methods in Contour Smoothing,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 8, pp. 801-817, 1997.
[32] H.C.G. Leitão and J. Stolfi, “A Multiscale Technique for Computer Assisted Reassembly of Fragmented Objects,” Technical Report IC-01-04, Inst. of Computing, Univ. of Campinas, Mar. 2001.
[33] J. Setubal and J. Meidanis, Introduction to Computational Molecular Biology. PWS Publishing, 1997.
[34] W.R. Pearson and W. Miller, “Dynamic Programming Algorithms for Biological Sequence Comparison,” Methods in Enzymology, vol. 210, pp. 575-601, 1992.

Index Terms:
Outline matching, planar shape matching, multiscale analysis, planar shape invariants, ceramic fragments, archaeology, fracture analysis.
Citation:
Helena Cristina da Gama Leitão, Jorge Stolfi, "A Multiscale Method for the Reassembly of Two-Dimensional Fragmented Objects," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 24, no. 9, pp. 1239-1251, Sept. 2002, doi:10.1109/TPAMI.2002.1033215
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