Regularization of inverse visual problems involving discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generalized stochastic subdivision
ACM Transactions on Graphics (TOG)
The Computation of Visible-Surface Representations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computer Vision, Graphics, and Image Processing
A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Fast Surface Interpolation Using Hierarchical Basis Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
On Three-Dimensional Surface Reconstruction Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Multiresolution stochastic hybrid shape models with fractal priors
ACM Transactions on Graphics (TOG) - Special issue on interactive sculpting
Computer rendering of stochastic models
Communications of the ACM
Scale Space Tracking and Deformable Sheet Models for Computational Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Surface Interpolation using Multiresolution Wavelet Transform
IEEE Transactions on Pattern Analysis and Machine Intelligence
IFS Fractal Interpolation for 2D and 3D Visualization
VIS '95 Proceedings of the 6th conference on Visualization '95
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
An Introduction to the Conjugate Gradient Method Without the Agonizing Pain
Sampling plausible solutions to multi-body constraint problems
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Terrain modeling: a constrained fractal model
AFRIGRAPH '07 Proceedings of the 5th international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
Evolution of artificial terrains for video games based on accessibility
EvoApplicatons'10 Proceedings of the 2010 international conference on Applications of Evolutionary Computation - Volume Part I
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It is well known that the spatial frequency spectrum of membrane and thin plate splines exhibit self-affine characteristics and, hence, behave as fractals. This behavior was exploited in generating the constrained fractal surfaces, which were generated by using a Gibbs sampler algorithm in the work of Szeliski and Terzopoulos. The algorithm involves locally perturbing a constrained spline surface with white noise until the spline surface reaches an equilibrium state.In this paper, we introduce a fast generalized Gibbs sampler that combines two novel techniques, namely, a preconditioning technique in a wavelet basis for constraining the splines and a perturbation scheme in which, unlike the traditional Gibbs sampler, all sites (surface nodes) that do not share a common neighbor are updated simultaneously. In addition, we demonstrate the capability to generate arbitrary order fractal surfaces without resorting to blending techniques. Using this fast Gibbs sampler algorithm, we demonstrate the synthesis of realistic terrain models from sparse elevation data.