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Scattered data interpolation for computer graphics

Published: 27 July 2014 Publication History
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References

[1]
Ken Anjyo and J. P. Lewis. RBF interpolation and Gaussian process regression through an RKHS formulation. Journal of Math-for-Industry., 3: 63--71, 2011.
[2]
N. Aronszajn. Theory of reproducing kernels. Trans. Amer. Math. Soc., 68: 337--404, 1950.
[3]
W. Baxter and K. Anjyo. Latent doodle space. Computer Graphics Forum, 25: 477--485, 2006.
[4]
R. K. Beatson, W. A. Light, and S. Billings. Fast solution of the radial basis function interpolation equations: Domain decomposition methods. SIAM J. Sci. Comput., 22(5): 1717--1740, 2000.
[5]
R. K. Beatson, J. B. Cherrie, and C. T. Mouat. Fast fitting of radial basis functions: Methods based on preconditioned gmres iteration. Advances in Computational Mathematics, 11: 253--270, 1999.
[6]
Julien Cohen Bengio and Rony Goldenthal. Simplicial interpolation for animating The Hulk. In ACM SIGGRAPH 2013 Talks, SIGGRAPH '13, pages 7:1--7:1, New York, NY, USA, 2013. ACM.
[7]
S. Bergman. The kernel function and the conformal mapping. Mathematical Surveys, 5, 1950.
[8]
Bernd Bickel, Mario Botsch, Roland Angst, Wojciech Matusik, Miguel Otaduy, Hanspeter Pfister, and Markus Gross. Multi-scale capture of facial geometry and motion. ACM Trans. Graph., 26(3): 33, 2007.
[9]
Christopher Bishop. Pattern Recognition and Machine Learning. Springer, 2007.
[10]
Christopher M. Bishop. Neural Networks for Pattern Recognition. Oxford University Press, Inc., New York, NY, USA, 1995.
[11]
Jean-Daniel Boissonnat and Frédéric Cazals. Smooth surface reconstruction via natural neighbour interpolation of distance functions. In SCG '00: Proceedings of the sixteenth annual symposium on Computational geometry, pages 223--232, New York, NY, USA, 2000. ACM.
[12]
Martin D. Buhmann. Radial Basis Functions: Theory and Implementations. Cambridge University Press, 2003.
[13]
J. C. Carr, R. K. Beatson, J. B. Cherrie, T. J. Mitchell, W. R. Fright, B. C. McCallum, and T. R. Evans. Reconstruction and representation of 3d objects with radial basis functions. In SIGGRAPH '01: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pages 67--76, New York, NY, USA, 2001. ACM.
[14]
Z.-Q. Cheng, Y.-Z. Wang, K. Xu B. Li, G. Dang, and S. Y.-Jin. A survey of methods for moving least squares surfaces. In IEEE/EG Symposium on Volume and Point-Based Graphics, 2008.
[15]
Scott Davies. Multidimensional triangulation and interpolation for reinforcement learning. In NIPS, pages 1005--1011, 1996.
[16]
Gianluca Donato and Serge Belongie. Approximate thin plate spline mappings. In Proceedings of the 7th European Conference on Computer Vision-Part III, ECCV '02, pages 21--31, London, UK, UK, 2002. Springer-Verlag.
[17]
Gregory Fasshauer. Solving differential equations with radial basis functions: multilevel methods and smoothing. Advances in Computational Mathematics, 11: 139--159, 1999. 10.1023/A:1018919824891.
[18]
Gregory E. Fasshauer and Larry L. Schumaker. Scattered data fitting on the sphere. In Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997, pages 117--166, Nashville, TN, USA, 1998. Vanderbilt University.
[19]
Gregory F. Fasshauer. Meshfree Approximation Methods with MATLAB. World Scientific Publishing Co., Inc., River Edge, NJ, USA, 2007.
[20]
Shachar Fleishman, Daniel Cohen-Or, and Cláudio T. Silva. Robust moving least-squares fitting with sharp features. In SIGGRAPH '05: ACM SIGGRAPH 2005 Papers, pages 544--552, New York, NY, USA, 2005. ACM.
[21]
R. Franke and G. Nielson. Smooth interpolation of large sets of scattered data. International Journal of Numerical Methods in Engineering, 15: 1691--1704, 1980.
[22]
Edward J. Fuselier. Refined error estimates for matrix-valued radial basis functions. PhD thesis, Texas A & M University, College Station, Texas, 2006.
[23]
Edward J. Fuselier and Grady B. Wright. Stability and error estimates for vector field interpolation and decomposition on the sphere with rbfs. SIAM J. Numer. Anal., 47(5): 3213--3239, 2009.
[24]
Eitan Grinspun, Mathieu Desbrun, and et al. Discrete differential geometry: An applied introduction. SIGGRAPH Course, 2006.
[25]
Keith Grochow, Steven L. Martin, Aaron Hertzmann, and Zoran Popovic. Style-based inverse kinematics. ACM Trans. Graph., 23(3): 522--531, 2004.
[26]
T. Hastie, R. Tibshirani, and J. Friedman. The Elements of Statistical Learning: Data Mining, Inference and Prediction. Springer Verlag, New York, NY, 2009.
[27]
T. Hatanaka, N. Kondo, and K. Uosaki. Multi-objective structure selection for radial basis function networks based on genetic algorithm. In The 2003 Congress on Evolutionary Computation, 2003. CEC '03., pages 1095--1100 Vol. 2.
[28]
Y. C. Hon, R. Schaback, and X. Zhou. Adaptive greedy algorithm for solving large RBF collocation problems. Numer. Algorithms, 32: 13--25, 2003.
[29]
Pushkar Joshi, Wen C. Tien, Mathieu Desbrun, and Frédéric Pighin. Learning controls for blend shape based realistic facial animation. In SCA '03: Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation, pages 187--192, Aire-la-Ville, Switzerland, Switzerland, 2003. Eurographics Association.
[30]
Tsuneya Kurihara and Natsuki Miyata. Modeling deformable human hands from medical images. In Proceedings of the 2004 ACM SIGGRAPH Symposium on Computer Animation (SCA-04), pages 357--366, 2004.
[31]
Gene S. Lee. Evaluation of the radial basis function space. In ACM SIGGRAPH ASIA 2009 Sketches, SIGGRAPH ASIA '09, pages 42:1--42:1, New York, NY, USA, 2009. ACM.
[32]
J. Lewis, H.-J. Hwang, U. Neumann, and R. Enciso. Smart point landmark distribution for thin-plate splines. In Proc. SPIE Medical Imaging, pages 1236--1243, San Diego, 2004.
[33]
J. P. Lewis. Generalized stochastic subdivision. ACM Transactions on Graphics, 6(3): 167--190, July 1987.
[34]
J. P. Lewis, Matt Cordner, and Nickson Fong. Pose space deformation: a unified approach to shape interpolation and skeleton-driven deformation. In SIGGRAPH '00: Proceedings of the 27th annual conference on Computer graphics and interactive techniques, pages 165--172, New York, NY, USA, 2000. ACM Press/Addison-Wesley Publishing Co.
[35]
J. P. Lewis. Lifting detail from darkness. In SIGGRAPH '01: Proceedings of the SIGGRAPH 2001 conference Sketches & applications. ACM Press, 2001.
[36]
J. P. Lewis, Ken Anjyo, Taehyun Rhee, Mengjie Zhang, Fred Pighin, and Zhigang Deng. Practice and theory of blendshape facial models. In Eurographics, 2014.
[37]
J. Meinguet. Multivariate interpolation at arbitrary points made simple. Z. Angew. Math., 30: 292--304, 1979.
[38]
Francis J. Narcowich and Joseph D. Ward. Generalized hermite interpolation via matrix-valued conditionally positive definite functions. Math. Comput., 63(208): 661--687, 1994.
[39]
Jun-yong Noh and Ulrich Neumann. Expression cloning. In SIGGRAPH '01: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pages 277--288, New York, NY, USA, 2001. ACM.
[40]
Yutaka Ohtake, Alexander Belyaev, Marc Alexa, Greg Turk, and Hans-Peter Seidel. Multi-level partition of unity implicits. ACM Trans. Graph., 22(3): 463--470, 2003.
[41]
Jason Osipa. Stop Staring: Facial Modeling and Animation Done Right, 2nd Ed. Sybex, 2007.
[42]
Sung W. Park, Lars Linsen, Oliver Kreylos, John D. Owens, and Bernd Hamann. Discrete Sibson interpolation. IEEE Transactions on Visualization and Computer Graphics, 12(2): 243--253, 2006.
[43]
Patrick Pérez, Michel Gangnet, and Andrew Blake. Poisson image editing. ACM Trans. Graph., 22(3): 313--318, 2003.
[44]
Frédéric Pighin, Jamie Hecker, Dani Lischinski, Richard Szeliski, and David H. Salesin. Synthesizing realistic facial expressions from photographs. In SIGGRAPH '98: Proceedings of the 25th annual conference on Computer graphics and interactive techniques, pages 75--84, New York, NY, USA, 1998. ACM.
[45]
Taehyun Rhee, Youngkyoo Hwang, James Dokyoon Kim, and Changyeong Kim. Real-time facial animation from live video tracking. In Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA '11, pages 215--224, New York, NY, USA, 2011. ACM.
[46]
Taehyun Rhee, J. P. Lewis, Ulrich Neumann, and Krishna Nayak. Scan-based volume animation driven by locally adaptive articulated registrations. IEEE Trans. Visualization and Computer Graphics, 2011.
[47]
C. F. Rose, I. Peter-Pike, J. Sloan, and M. F. Cohen. Artist-directed inverse-kinematics using radial basis function interpolation. In EUROGRAPHICS, 2001.
[48]
Sam T. Roweis and Lawrence K. Saul. Nonlinear dimensionality reduction by locally linear embedding. SCIENCE, 290: 2323--2326, 2000.
[49]
M. Sato. Theory of hyperfunctions. I, Fac. Sci. Univ. Tokyo Sect. 1, 8, 139--193, 1959; II, ibid, 8, 387--437, 1960.
[50]
Scott Schaefer, Travis McPhail, and Joe Warren. Image deformation using moving least squares. In SIGGRAPH '06: ACM SIGGRAPH 2006 Papers, pages 533--540, New York, NY, USA, 2006. ACM.
[51]
B. Schölkopf and A. J. Smola. Learning with Kernels. MIT Press, 2002.
[52]
L. Schwartz. Théory des Distributions, vol. I et II. Hermann, 1950, 1951.
[53]
Jaewoo Seo, Geoffrey Irving, J. P. Lewis, and Junyong Noh. Compression and direct manipulation of complex blendshape models. ACM Trans. Graph., 30(6): 164:1--164:10, December 2011.
[54]
Yeongho Seol, J. P. Lewis, Jaewoo Seo, Byungkuk Choi, Ken Anjyo, and Junyong. Noh. Spacetime expression cloning for blendshapes. ACM Trans. Graph., 31(2): Article 14, 2012.
[55]
Yeongho Seol, Jaewoo Seo, Paul Hyunjin Kim, J. P. Lewis, and Junyong Noh. Weighted pose space editing for facial animation. The Visual Computer, 28(3): 319--327, 2012.
[56]
Donald Shepard. A two-dimensional interpolation function for irregularly-spaced data. In ACM '68: Proceedings of the 1968 23rd ACM national conference, pages 517--524, New York, NY, USA, 1968. ACM.
[57]
Yuhei Shibukawa, Yoshinori Dobashi, and Tsuyoshi Yamamoto. Interactive editing of volumetric objects by using feature-based transfer function. In Mathematical Progress in Expressive Image Synthesis I, pages 55--62, Tokyo, JAPAN, 2014. Springer Verlag.
[58]
Robert Sibson. A brief description of natural neighbor interpolation. In V. Barnett, editor, Interpreting Multivariate Data, chapter 2, pages 21--36. John Wiley, Chichester, 1981.
[59]
Peter-Pike J. Sloan, Charles F. Rose, and Michael F. Cohen. Shape by example. In SI3D '01: Proceedings of the 2001 symposium on Interactive 3D graphics, pages 135--143, New York, NY, USA, 2001. ACM Press.
[60]
J. B. Tenenbaum, V. de Silva, and J. C. Langford. A global geometric framework for nonlinear dimensionality reduction. Science, 290: 2319--2323, 2000.
[61]
Hideki Todo, Ken Anjyo, Williams Baxter, and Takeo Igarashi. Locally controllable stylized shading. ACM Trans. Graph., 26(3): Article17, 2007.
[62]
Karel Uhlir and Vaclav Skala. Radial basis function use for the restoration of damaged images. In Max Viergever, K. Wojciechowski, B. Smolka, H. Palus, R. S. Kozera, W. Skarbek, and L. Noakes, editors, Computer Vision and Graphics, volume 32 of Computational Imaging and Vision, pages 839--844. Springer Netherlands, 2006.
[63]
R. Peter Weistroffer, Kristen R. Walcott, Greg Humphreys, and Jason Lawrence. Efficient basis decomposition for scattered reflectance data. In EGSR07: Proceedings of the Eurographics Symposium on Rendering, Grenoble, France, June 2007.
[64]
Holger Wendland. Scattered Data Approximation. Cambridge, 2005.
[65]
Holger Wendland. Divergence-free kernel methods for approximating the Stokes problem. SIAM J. Numer. Anal., 47(4): 3158--3179, 2009.
[66]
Lexing Ying. Short note: A kernel independent fast multipole algorithm for radial basis functions. J. Comput. Phys., 213(2): 451--457, 2006.
[67]
Yuanchen Zhu and Steven J. Gortler. 3d deformation using moving least squares. Harvard Computer Science Technical Report: Tr-10-07. Technical report, Harvard University, Cambridge, MA, 2007.
[68]
Todd Zickler, Ravi Ramamoorthi, Sebastian Enrique, and Peter N. Belhumeur. Reflectance sharing: Predicting appearance from a sparse set of images of a known shape. IEEE Trans. Pattern Anal. Mach. Intell., 28(8): 1287--1302, 2006.

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cover image ACM Conferences
SIGGRAPH '14: ACM SIGGRAPH 2014 Courses
July 2014
2191 pages
ISBN:9781450329620
DOI:10.1145/2614028
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