Fast algorithm for 2D fragment assembly based on partial EMD

Abstract2D Fragment assembly is an important research topic in computer vision and pattern recognition, and has a wide range of applications such as relic restoration and remote sensing image processing. The key to this problem lies in utilizing contour features or visual cues to find the optimal partial matching. Considering that previous algorithms are weak in predicting the best matching configuration of two neighboring fragments, we suggest using the earth mover’s distance, based on length/property correspondence, to measure the similarity, which potentially matches a point on the first contour to a desirable destination point on the second contour. We further propose a greedy algorithm for 2D fragment assembly by repeatedly assembling two neighboring fragments into a composite one. Experimental results on map-piece assembly and relic restoration show that our algorithm runs fast, is insensitive to noise, and provides a novel solution to the fragment assembly problem.

[1]  Marshall W. Bern,et al.  A global approach to automatic solution of jigsaw puzzles , 2002, SCG '02.

[2]  Xiaoou Tang,et al.  2D Shape Matching by Contour Flexibility , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Wenyu Liu,et al.  A Unified Curvature Definition for Regular, Polygonal, and Digital Planar Curves , 2008, International Journal of Computer Vision.

[4]  Paul LaFollette,et al.  Isthmus critical points for solving jigsaw puzzles in computer vision , 1991, IEEE Trans. Syst. Man Cybern..

[5]  Tsuhan Chen,et al.  Feature-based Part Retrieval for Interactive 3D Reassembly , 2007, 2007 IEEE Workshop on Applications of Computer Vision (WACV '07).

[6]  Anuj Srivastava,et al.  Action Recognition Using Rate-Invariant Analysis of Skeletal Shape Trajectories , 2016, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[7]  H. Freeman,et al.  Apictorial Jigsaw Puzzles: The Computer Solution of a Problem in Pattern Recognition , 1964, IEEE Trans. Electron. Comput..

[8]  Zeyun Yu,et al.  Robust reconstruction of 2D curves from scattered noisy point data , 2014, Comput. Aided Des..

[9]  John Porrill,et al.  Curve matching and stereo calibration , 1991, Image and Vision Computing.

[10]  Xiaojun Wu,et al.  A novel contour descriptor for 2D shape matching and its application to image retrieval , 2011, Image Vis. Comput..

[11]  Yuan F. Zheng,et al.  Strategies for automatic assembly of deformable objects , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[12]  H. Pottmann,et al.  Reassembling fractured objects by geometric matching , 2006, SIGGRAPH 2006.

[13]  Trevor Darrell,et al.  Fast contour matching using approximate earth mover's distance , 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004..

[14]  Qiang Wang,et al.  An elastic partial shape matching technique , 2007, Pattern Recognit..

[15]  Yuqing Song,et al.  Matching sequences of salient contour points characterized by Voronoi region features , 2011, The Visual Computer.

[16]  Yasuo Kuniyoshi,et al.  Partial matching of real textured 3D objects using color cubic higher-order local auto-correlation features , 2010, The Visual Computer.

[17]  Joseph M. Miller,et al.  Automatic assembly planning with fasteners , 1989, Proceedings, 1989 International Conference on Robotics and Automation.

[18]  Rainer Lienhart,et al.  Learning to Reassemble Shredded Documents , 2013, IEEE Transactions on Multimedia.

[19]  David W. Jacobs,et al.  Approximate earth mover’s distance in linear time , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[20]  John Porrill,et al.  Curve matching and stereo calibration , 1991, Image Vis. Comput..

[21]  Xiang Pan,et al.  Geodesic Fourier Descriptor for 2D Shape Matching , 2008, 2008 International Conference on Embedded Software and Systems Symposia.

[22]  Wolfgang Stuerzlinger,et al.  A 3D desktop puzzle assembly system , 2011, 3DUI.

[23]  Helmut Alt,et al.  Comparison of Distance Measures for Planar Curves , 2003, Algorithmica.

[24]  Ahmad Faisal Mohamad Ayob,et al.  A novel evolutionary approach for 2D shape matching based on B-spline modeling , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[25]  Christopher Dyken,et al.  Simultaneous curve simplification , 2009, J. Geogr. Syst..

[26]  Peter Wonka,et al.  A new image registration scheme based on curvature scale space curve matching , 2007, The Visual Computer.

[27]  Peter Wonka,et al.  Curve matching for open 2D curves , 2009, Pattern Recognit. Lett..

[28]  Jianping Hu,et al.  Efficient EMD and Hilbert spectra computation for 3D geometry processing and analysis via space-filling curve , 2015, The Visual Computer.

[29]  Gareth M. James.  Curve alignment by moments , 2007, 0712.1425.

[30]  Kevin Buchin,et al.  Exact algorithms for partial curve matching via the Fréchet distance , 2009, SODA.

[31]  Zhaohui Huang,et al.  Affine-invariant B-spline moments for curve matching , 1996, IEEE Trans. Image Process..

[32]  Maike Buchin,et al.  Can We Compute the Similarity between Surfaces? , 2007, Discret. Comput. Geom..

[33]  Zoltan Kato,et al.  Realigning 2D and 3D Object Fragments without Correspondences , 2016, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[34]  Leonidas J. Guibas,et al.  The Earth Mover's Distance as a Metric for Image Retrieval , 2000, International Journal of Computer Vision.

[35]  Carlo Tomasi,et al.  Perceptual metrics for image database navigation , 1999 .

[36]  Ioannis Pratikakis,et al.  3D articulated object retrieval using a graph-based representation , 2010, The Visual Computer.

[37]  Sariel Har-Peled,et al.  Jaywalking your dog: computing the Fréchet distance with shortcuts , 2011, SODA 2012.

[38]  Nasir D. Memon,et al.  Automated reassembly of fragmented images , 2003, 2003 International Conference on Multimedia and Expo. ICME '03. Proceedings (Cat. No.03TH8698).

[39]  Peihua Gu,et al.  CAD-directed automatic assembly sequence planning , 1995 .

[40]  Enkhbayar Altantsetseg,et al.  Pairwise matching of 3D fragments using fast fourier transform , 2014, The Visual Computer.

[41]  Eric McCreath.  Partial Matching of Planar Polygons Under Translation and Rotation , 2008, CCCG.

[42]  Leonidas J. Guibas,et al.  Discrete Geometric Shapes: Matching, Interpolation, and Approximation , 2000, Handbook of Computational Geometry.

[43]  G. Taubin,et al.  Automatic reconstruction of ancient Portuguese tile panels , 2016 .

[44]  Laurence A. Baxter,et al.  Note: On the greedy algorithm for optimal assembly , 1992 .

[45]  Margaret M. Fleck,et al.  Jigsaw puzzle solver using shape and color , 1998, ICSP '98. 1998 Fourth International Conference on Signal Processing (Cat. No.98TH8344).

[46]  Cosmin Ancuti,et al.  An efficient two steps algorithm for wide baseline image matching , 2009, The Visual Computer.

[47]  Jörg-Rüdiger Sack,et al.  Improved Algorithms for Partial Curve Matching , 2011, ESA.