Robot vision
Regularization of inverse visual problems involving discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
Diffusions for global optimizations
SIAM Journal on Control and Optimization
Weighted bicubic spline interpolation to rapidly varying data
ACM Transactions on Graphics (TOG)
Generalized stochastic subdivision
ACM Transactions on Graphics (TOG)
An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Computer rendering of stochastic models
Communications of the ACM
Optimal surface reconstruction from planar contours
Communications of the ACM
Bayesian modeling of uncertainty in low-level vision
Bayesian modeling of uncertainty in low-level vision
Regularization uses fractal priors
AAAI'87 Proceedings of the sixth National conference on Artificial intelligence - Volume 2
Dynamic NURBS with geometric constraints for interactive sculpting
ACM Transactions on Graphics (TOG) - Special issue on interactive sculpting
A fast Gibbs sampler for synthesizing constrained fractals
Proceedings of the 7th conference on Visualization '96
Anisotropic diffusion for Monte Carlo noise reduction
ACM Transactions on Graphics (TOG)
A Full Bayesian Approach to Curve and Surface Reconstruction
Journal of Mathematical Imaging and Vision
Sampling plausible solutions to multi-body constraint problems
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
A Fast Gibbs Sampler for Synthesizing Constrained Fractals
IEEE Transactions on Visualization and Computer Graphics
A Bayesian method for probable surface reconstruction and decimation
ACM Transactions on Graphics (TOG)
Terrain Synthesis from Digital Elevation Models
IEEE Transactions on Visualization and Computer Graphics
Physically based hydraulic erosion simulation on graphics processing unit
Proceedings of the 5th international conference on Computer graphics and interactive techniques in Australia and Southeast Asia
A fractal-based relaxation algorithm for shape from terrain image
Computer Vision and Image Understanding
A novel method for solving the shape from shading (SFS) problem
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part II
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Deterministic splines and stochastic fractals are complementary techniques for generating free-form shapes. Splines are easily constrained and well suited to modeling smooth, man-made objects. Fractals, while difficult to constrain, are suitable for generating various irregular shapes found in nature. This paper develops constrained fractals, a hybrid of splines and fractals which intimately combines their complementary features. This novel shape synthesis technique stems from a formal connection between fractals and generalized energy-minimizing splines which may be derived through Fourier analysis. A physical interpretation of constrained fractal generation is to drive a spline subject to constraints with modulated white noise, letting the spline diffuse the noise into the desired fractal spectrum as it settles into equilibrium. We use constrained fractals to synthesize realistic terrain models from sparse elevation data.