A fast gibbs sampler for synthesizing constrained fractals

IEEE Transactions on Visualization and Computer Graphics

Volumn 3, Issue 4, 1997, Pages 337-351

  Vemuri, Baba C ^a   Mandai, Chhandomay ^b   Lai, Shang Hong ^c  

^a Department of Computer and Information Science and Engineering ^*  (United States)

^b UNIVERSITY OF FLORIDA   (United States)

^c SIEMENS CORPORATE RESEARCH   (United States)

Author keywords

Conjugate gradient algorithm; Fractal surfaces; Gibbs sampler; Preconditioning; Thin plate membrane splines; Wavelet basis

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; PERTURBATION TECHNIQUES;

FAST GIBBS SAMPLER;

FRACTALS;

EID: 0031246545     PISSN: 10772626     EISSN: None     Source Type: Journal    
DOI: 10.1109/2945.646237     Document Type: Article

References (36)

1. R. Szeliski and D. Terzopoulos, From Splines to Fractals, Proc. ACM S1CCRAPH '89, pp. 51-60, Aug. 1989.
2. G. Winkler, Image Analysis, Random Fields and Dynamic Monte Carlo Methods, pp. 168-170. Springer-Verlag, 1995.
3. A. Fournier, D. Fussel, and L. Carpenter, Computer Rendering of Stochastic Models, Comm. ACM, vol. 25, no. 6, pp. 371-384, 1982.
4. B. Mandelbrot, The Fractal Geometry of Nature. San Francisco: Freeman, 1977.
5. R.F. Voss, Random Fractal Forgeries, Fundamental Algorithms for Computer Graphics, R.A. Earnshaw, ed. Berlin: Springer-Verlag, 1985.
6. J.P. Lewis, Generalized Stochastic Subdivision, ACM Trans. Graphics, vol. 6, no. 3, pp. 167-190, July 1987.
7. N. Yokoya, K. Yamamoto, and N. Funakubo, Fractal-Based Analysis and Interpolation of 3D Natural Surfaces and Their Application to Terrain Modeling, Computer Vision, Graphics, and Image Processing, vol. 46, pp. 284-302, 1989.
8. W. Rümelin, Fractal Interpolation of Random Fields of Fractional Brownian Motion, Fractal Geometry and Computer Graphics, J.L. Encarnacao, H.O. Peitgen, G. Sakas, and G. Englert, eds., pp. 122-132. Springer-Verlag, 1992.
9. A. Pentland, Fractal Based Description of Natural Scenes, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 6, pp. 661674,1984.
10. S. Geman and D. Geman, Stochastic Relaxation, Gibbs Distribution, and Bayesian Restoration of Images, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 6, pp. 721-724, 1984.
11. K. Arakawa and E. Krotkov, Fractal Surface Reconstruction for Modeling Natural Terrain, Proc. IEEE Conf. Computer Vision and Pattern Recognition, 1993.
12. C.M. Wittenbrink, IPS Fractal Interpolation for 2D and 3D Visualization, Proc. Visualization 95 , pp. 77-84, Atlanta, Oct. 1995.
13. B.C. Vemuri and A. Radisavljevic, Multiresolution Stochastic Hybrid Shape Models with Fractal Priors, ACM Trans. Graphics, vol. 13, no. 2, pp. 177-207, Apr. 1994.
14. L.L. Schumaker, Fitting Surfaces to Scattered Data, Approximation II, G.G. Lorentz, C.K. Chui, and L.L. Schumaker, eds., pp. 203-267. New York: Academic, 1976.
15. R.M. Bolle and B.C. Vemuri, On Three-Dimensional Surface Reconstruction Methods, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, no. 1, Jan. 1991.
16. A.N. Tikhonov and V.A. Arsenin, Solutions of Ill-Posed Problems. Washington, D.C.: Winston, 1977.
17. W.E.L. Crimson, An Implementation of a Computational Theory of Visual Surface Interpolation, Computer Vision, Graphics, and Image Processing, vol. 22, pp. 39-69,1983.
18. D. Terzopoulos, Regularization of Inverse Visual Problems Involving Discontinuities, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, no. 4, pp. 413-424,1986.
19. J. Duchon, Splines Minimizing Rotation-Invariant Semi-Norms in Sobolev Spaces, Constructive Theory of Functions of Several Variables, A. Dodd and B. Eckmann, eds., pp. 85-100. Berlin: Springer-Verlag, 1977.
20. J. Meinguet, An Intrinsic Approach to Multivariate Spline Interpolation at Arbitrary Points, Polynomial and Spline Approximation: Theory and Applications, B.N. Sahney, ed. Dordrecht, The Netherlands: Reidel, 1979.
21. D. Terzopoulos, Multilevel Computational Processes for Visual Surface Reconstruction, Computer Vision, Graphics, and Image Processing, vol. 24, pp. 52-96,1983.
22. G. Kimeldorf and G. Wahba, A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by Splines, Annals Math. Statistics, vol. 41, no. 2, pp. 495-502, 1970.
23. G.H. Golub and V.H. Van Loan, Matrix Computations. Johns Hopkins Univ. Press, 1989.
24. R. Szeliski, Fast Surface Interpolation Using Hierarchical Basis Functions, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 6, pp. 513-528, June 1990.
25. J.R. Shewchuk, An Introduction to the Conjugate Gradient Method Without the Agonizing Pain, Technical Report CMUCS94-125, School of Computer Science, Carnegie Mellon Univ., 1994.
26. M.H. Yaou and W.T. Chang, Fast Surface Interpolation Using Multiresolution Wavelet Transform, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 7, pp. 673-688, July 1994.
27. S.G. Mallat, A Theory of Multi-Resolution Signal Decomposition: The Wavelet Representation, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp. 674-693, July 1989.
28. O. Rioul and M. Vitterli, Wavelets and Signal Processing, IEEE Signal Processing Magazine, vol. 8, pp. 14-38,1991.
29. S.H. Lai and B.C. Vemuri, Physically-Based Adaptive Preconditioners for Early Vision, Proc. IEEE Workshop Physics-Based Modeling in Computer Vision, pp. 151-157, Boston, 1995.
30. D. Terzopoulos, The Computation of Visible Surface Representations, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 10, no. 4, pp. 417-438, Apr. 1988.
31. M. Fiedler, Special Matrices and Their Applications in Numerical Mathematics. Dordrecht, The Netherlands: Martinus Nijhoff Publishers, 1986.
32. V. Torre and T.A. Poggio, On Edge Detection, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, no. 2, pp. 147-163, Mar. 1986.
33. G. Whitten, Scale Space Tracking and Deformable Sheet Models for Computational Vision, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 15, no. 7, pp. 697-706, July 1993.
34. M. Schroeder, Fractals, Chaos, Power Laws: Minutes From an Infinite Paradise. New York: W.H. Freeman, 1991.
35. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C. Cambridge Univ. Press, 1992.
36. J.A. Meijerink and H.A.V. Vorst, An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix Is a Symmetric M-Matrix, Mathematics of Computation, vol. 31, no. 137, pp. 148-162, Jan. 1977.