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Compatible Embedding for 2D Shape Animation
September/October 2009 (vol. 15 no. 5)
pp. 867-879
ASCII Text
x 
 
William V. Baxter, III, Pascal Barla, Ken-ichi Anjyo, "Compatible Embedding for 2D Shape Animation," IEEE Transactions on Visualization and Computer Graphics, vol. 15, no. 5, pp. 867-879, September/October, 2009.
 
 
BibTex
x
 
@article{ 10.1109/TVCG.2009.38,
author = {William V. Baxter, III and Pascal Barla and Ken-ichi Anjyo},
title = {Compatible Embedding for 2D Shape Animation},
journal ={IEEE Transactions on Visualization and Computer Graphics},
volume = {15},
number = {5},
issn = {1077-2626},
year = {2009},
pages = {867-879},
doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2009.38},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Visualization and Computer Graphics
TI - Compatible Embedding for 2D Shape Animation
IS - 5
SN - 1077-2626
SP867
EP879
EPD - 867-879
A1 - William V. Baxter, III,
A1 - Pascal Barla,
A1 - Ken-ichi Anjyo,
PY - 2009
KW - Matching
KW - interpolation
KW - morphing
KW - in-betweening
KW - cross-parameterization
KW - multiscale analysis
KW - scale-space
KW - compatible triangulation.
VL - 15
JA - IEEE Transactions on Visualization and Computer Graphics
ER -
 
William V. Baxter, III, OLM Digital, Inc., Tokyo
Pascal Barla, INRIA Bordeau University, France
Ken-ichi Anjyo, OLM Digital, Inc., Tokyo
We present new algorithms for the compatible embedding of 2D shapes. Such embeddings offer a convenient way to interpolate shapes having complex, detailed features. Compared to existing techniques, our approach requires less user input, and is faster, more robust, and simpler to implement, making it ideal for interactive use in practical applications. Our new approach consists of three parts. First, our boundary matching algorithm locates salient features using the perceptually motivated principles of scale-space and uses these as automatic correspondences to guide an elastic curve matching algorithm. Second, we simplify boundaries while maintaining their parametric correspondence and the embedding of the original shapes. Finally, we extend the mapping to shapes' interiors via a new compatible triangulation algorithm. The combination of our algorithms allows us to demonstrate 2D shape interpolation with instant feedback. The proposed algorithms exhibit a combination of simplicity, speed, and accuracy that has not been achieved in previous work.

[1] L. Kavan, S. Dobbyn, S. Collins, J. Zara, and C. O'Sullivan, “Polypostors: 2D Polygonal Impostors for 3D Crowds,” Proc. ACM SIGGRAPH Symp. Interactive 3D Graphics and Games, Feb. 2008.
[2] T. Igarashi, T. Moscovich, and J.F. Hughes, “As-Rigid-As-Possible Shape Manipulation,” Proc. ACM SIGGRAPH '05, pp. 1134-1141, 2005.
[3] T. Beier and S. Neely, “Feature-Based Image Metamorphosis,” Proc. ACM SIGGRAPH '92, pp. 35-42, 1992.
[4] S.-Y. Lee, K.-Y. Chwa, and S.Y. Shin, “Image Metamorphosis Using Snakes and Free-Form Deformations,” Proc. ACM SIGGRAPH '95, pp. 439-448, 1995.
[5] G. Wolberg, “Image Morphing: A Survey,” The Visual Computer, vol. 14, no. 8, pp. 360-372, 1998.
[6] S. Schaefer, T. McPhail, and J. Warren, “Image Deformation Using Moving Least Squares,” Proc. ACM SIGGRAPH '06, pp. 533-540, 2006.
[7] H. Fang and J.C. Hart, “Detail Preserving Shape Deformation in Image Editing,” Proc. ACM SIGGRAPH '07, vol. 26, no. 3, p. 12, 2007.
[8] T.W. Sederberg, P. Gao, G. Wang, and H. Mu, “2D Shape Blending: An Intrinsic Solution to the Vertex Path Problem,” Proc. ACM SIGGRAPH '93, pp. 15-18, 1993.
[9] E. Goldstein and C. Gotsman, “Polygon Morphing Using a Multiresolution Representation,” Proc. Graphics Interface Conf., pp. 247-254, 1995.
[10] A. Tal and G. Elber, “Image Morphing with Feature Preserving Texture,” Computer Graphics Forum (Proc. Eurographics '99), vol. 18, no. 3, pp. 339-348, 1999.
[11] M. Alexa, D. Cohen-Or, and D. Levin, “As-Rigid-As-Possible Shape Interpolation,” Proc. ACM SIGGRAPH '00, pp. 157-164, 2000.
[12] V. Surazhsky and C. Gotsman, “High Quality Compatible Triangulations,” Eng. with Computers, vol. 20, no. 2, pp. 147-156, July 2004.
[13] M. Eitz, O. Sorkine, and M. Alexa, “Sketch Based Image Deformation,” Proc. Workshop Vision, Modeling, and Visualization, pp. 135-142, 2007.
[14] T.W. Sederberg and E. Greenwood, “A Physically Based Approach to 2D Shape Blending,” Proc. ACM SIGGRAPH '92, pp. 25-34, 1992.
[15] T.B. Sebastian, P.N. Klein, and B.B. Kimia, “Recognition of Shapes by Editing Their Shock Graphs,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 26, no. 5, pp. 550-571, May 2004.
[16] 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.
[17] X. Zabulis, J. Sporring, and S.C. Orphanoudakis, “Perceptually Relevant and Piecewise Linear Matching of Silhouettes,” Pattern Recognition, vol. 38, no. 1, pp. 75-93, 2005.
[18] M. van Eede, D. Macrini, A. Telea, C. Sminchisescu, and S.S. Dickinson, “Canonical Skeletons for Shape Matching,” Proc. 18th Int'l Conf. Pattern Recognition (ICPR '06), pp. 64-69, 2006.
[19] C. Gotsman and V. Surazhsky, “Guaranteed Intersection-Free Polygon Morphing,” Computers and Graphics, vol. 25, no. 1, pp. 67-75, 2001.
[20] T. Surazhsky, V. Surazhsky, G. Barequet, and A. Tal, “Blending Polygonal Shapes with Different Topologies,” Computers and Graphics, vol. 25, no. 1, pp. 29-39, 2001.
[21] M. Alexa, “Recent Advances in Mesh Morphing,” Computer Graphics Forum, vol. 21, no. 2, pp. 173-197, 2002.
[22] J. Schreiner, A. Asirvatham, E. Praun, and H. Hoppe, “Inter-Surface Mapping,” Proc. ACM SIGGRAPH '04, pp. 870-877, 2004.
[23] D. Xu, H. Zhang, Q. Wang, and H. Bao, “Poisson Shape Interpolation,” Proc. 2005 ACM Symp. Solid and Physical Modeling (SPM '05), pp. 267-274, 2005.
[24] R.W. Sumner, M. Zwicker, C. Gotsman, and J. Popović, “Mesh-Based Inverse Kinematics,” Proc. ACM SIGGRAPH '05, pp. 488-495, 2005.
[25] T.B. Sebastian, P.N. Klein, and B.B. Kimia, “Alignment-Based Recognition of Shape Outlines,” Proc. Fourth Int'l Workshop Visual Form (IWVF-4), pp. 606-618, 2001.
[26] R.C. Veltkamp and M. Hagedoorn, State of the Art in Shape Matching, pp. 87-119. Springer-Verlag, 2001.
[27] D. Douglas and T. Peucker, “Algorithms for the Reduction of the Number of Points Required to Represent a Digitized Line or Its Caricature,” Canadian Cartographer, vol. 10, no. 2, pp. 112-122, 1973.
[28] A. Finkelstein and D.H. Salesin, “Multiresolution Curves,” Proc. ACM SIGGRAPH '94, pp. 261-268, 1994.
[29] P. Barla, J. Thollot, and F. Sillion, “Geometric Clustering for Line Drawing Simplification,” Proc. Eurographics Symp. Rendering, 2005.
[30] P.V. Sander, X. Gu, S.J. Gortler, H. Hoppe, and J. Snyder, “Silhouette Clipping,” Proc. ACM SIGGRAPH '00, pp. 327-334, 2000.
[31] B. Aronov, R. Seidel, and D. Souvaine, “On Compatible Triangulations of Simple Polygons,” Computational Geometry: Theory and Applications, vol. 3, pp. 27-35, 1993.
[32] H. Gupta and R. Wenger, “Constructing Piecewise Linear Homeomorphisms of Simple Polygons,” J. Algorithms, vol. 22, no. 1, pp.142-157, 1997.
[33] S. Suri, “On Some Link Distance Problems in a Simple Polygon,” IEEE Trans. Robotics and Automation, vol. 6, no. 1, pp. 108-113, Feb. 1990.
[34] S. Suri, “A Linear Time Algorithm with Minimum Link Paths Inside a Simple Polygon,” Computer Vision, Graphics, and Image Processing, vol. 35, no. 1, pp. 99-110, 1986.
[35] L. Guibas, J. Hershberger, D. Leven, M. Sharir, and R. Tarjan, “Linear Time Algorithms for Visibility and Shortest Path Problems Inside Simple Polygons,” Proc. Symp. Computational Geometry (SCG '86), pp. 1-13, 1986.
[36] L. Guibas, E. McCreight, M. Plass, and J. Roberts, “A New Representation for Linear Lists,” Proc. Ninth ACM Symp. Theory of Computing, pp. 49-60, 1977.
[37] B. Chazelle, “Triangulating a Simple Polygon in Linear Time,” Discrete and Computational Geometry, vol. 6, no. 5, pp. 485-524, 1991.
[38] N.M. Amato, M.T. Goodrich, and E.A. Ramos, “A Randomized Algorithm for Triangulating a Simple Polygon in Linear Time,” Discrete and Computational Geometry, vol. 26, no. 2, pp. 245-265, 2001.
[39] B. Joe and R.B. Simpson, “Corrections to Lee's Visibility Polygon Algorithm,” Behaviour and Information Technology, vol. 27, no. 4, pp.458-473, 1987.
[40] C.A. Hipke, “Computing Visibility Polygons with LEDA,” http://ad.informatik.uni-freiburg.de/mitarbeiter/ hipke_hipke. work.vis_polygon.ps.gz , 1996.
[41] “Applets for Visibility in Simple Polygons,” Univ. of Bonn, http://web.informatik.uni-bonn.de/I/GeomLab VisPolygon/, 2008.
[42] H. Hoppe, “Progressive Meshes,” Proc. ACM SIGGRAPH '96, pp.98-108, 1996.
[43] P.V. Sander, J. Snyder, S.J. Gortler, and H. Hoppe, “Texture Mapping Progressive Meshes,” Proc. ACM SIGGRAPH '01, pp.409-416, 2001.
[44] W. Baxter, P. Barla, and K. Anjyo, “Notes on Compatible Mapping of 2D Shapes,” Technical Report OLMTRE-2008-002, OLM Digital, Inc., http://www.olm.co.jp/en/rd/2008/06 compatible_embedding_notes.html , 2008.
[45] W. Baxter, P. Barla, and K.-i. Anjyo, “Rigid Shape Interpolation Using Normal Equations,” Proc. Symp. Nonphotorealistic Animation and Rendering, pp. 59-64, 2008.
[46] V. Surazhsky, Personal Comm., June 2008.
[47] W. Baxter and K. Anjyo, “Latent Doodle Space,” Computer Graphics Forum, vol. 25, no. 3, pp. 477-485, 2006.
[48] W. Baxter, P. Barla, and K. Anjyo, “N-Way Morphing for 2D Animation,” Computer Animation and Virtual Worlds, 2009.

Index Terms:
Matching, interpolation, morphing, in-betweening, cross-parameterization, multiscale analysis, scale-space, compatible triangulation.
Citation:
William V. Baxter, III, Pascal Barla, Ken-ichi Anjyo, "Compatible Embedding for 2D Shape Animation," IEEE Transactions on Visualization and Computer Graphics, vol. 15, no. 5, pp. 867-879, Sept.-Oct. 2009, doi:10.1109/TVCG.2009.38
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