1. Sampling Gabor Noise in the Spatial Domain
Victor Charpenay Bernhard Steiner Przemyslaw Musialski Vienna University of Technology

2. Gabor Noise - Motivation
Procedural noise extensively used, no ultimate noise definition. Gabor noise enables the design of an extremely large panel of textures (wood, skin, rust, fabric, marble).
Advantages:
Intuitive noise control
Isotropic/anisotropic
Does not require parameterization
Linear filtering
Real-time evaluation (in the GPU)
Image: [Lagae 09]
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Sampling Gabor Noise in the Spatial Domain

3. Sampling Gabor Noise in the Spatial Domain
Noise Classification
Spectral control over the noise function ?
Type of noise
Generation
Spectral Control
Lattice-based
(Perlin noise)
Fourier transform-based
Sparse convolution process
0.1
0.6
0.7
0.5
Interpolation
None
DFT
Intricate
Perlin Noise & Lattice-based noises
Fourier transform-based noises
Sparse convolution process
Noise parameters ? (function composition – Perlin, Probability distribution – Fourier-based, Kernel parameters – Sparse convolution)
Goal: provide spectral control over the noise
Lattice-based: Value, Gradient, Value-gradient, Lattice convolution noise (impulses are at the lattice nodes)
Fourier transform: pseudo-random discrete spetrum (following a probability distribution) -> FFT
Sparse convulution: Lewis (1984)
Gaussian
kernel
Easy
but limited
Noise classification: [Ebert 03]
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Sampling Gabor Noise in the Spatial Domain

4. + + Gabor Noise Definition Sparse Convolution Process
Orientation Randomization
Gabor Kernel + +
Did not show the frequency domain representation
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Sampling Gabor Noise in the Spatial Domain

5. Sampling Gabor Noise in the Spatial Domain
Definition 𝑦
Gabor noise parameters
𝐾, 𝑎, 𝐹 0 , 𝜔 0 , 𝜔 𝑠 ,( 𝐹 𝑠 )
1 𝑎
𝜔 0 𝑥
1 𝐹 0
Gaussian amplitude
Frequency spread
Gaussian width
Angle spread
Did not show the frequency domain representation
Sine frequency
Sine orientation
𝑔 𝑥,𝑦 =𝐾 𝑒 −𝜋 𝑎 2 ( 𝑥 2 + 𝑦 2 ) cos (2 𝜋 𝐹 0 (𝑥 cos 𝜔 0 +𝑦 sin (𝜔 0 ) ) )
Gaussian envelope
2D sine wave
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Sampling Gabor Noise in the Spatial Domain

6. Other Works on Gabor Noise
Filtering Solid Gabor Noise [Lagae 11a]
Continuous solid noise
Improving Gabor Noise [Lagae 11b]
Efficient isotropic noise
Noise error estimation function
Spatially varying noise (based on interpolation)
Gabor Noise by Example [Galerne 12]
Allows generation of noise functions from example textures
[Lagae 11a] phase-augmented Gabor noise (slicing instead of projecting)
[Lagae 11b] isotropic noise: new kernel that speeds up noise generation by 2 (radial sine wave)
Kernel truncation error estimation. Automatic kernel radius estimation according to the wanted level of error
Interpolation of a parameter
[Galerne 12] bandwidth quantization (a parameter defined as series of harmonic, then, during rendering, randomly chosen)
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Sampling Gabor Noise in the Spatial Domain

7. Sampling Gabor Noise in the Spatial Domain
Illustration
Sparse Convolution Process in Detail y
5 impulses 𝑥
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Sampling Gabor Noise in the Spatial Domain

8. Sampling Gabor Noise in the Spatial Domain
Illustration
Sparse Convolution Process in Detail y
15 impulses 𝑥
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Sampling Gabor Noise in the Spatial Domain

9. Sampling Gabor Noise in the Spatial Domain
Illustration
Sparse Convolution Process in Detail y
40 impulses 𝑥
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Sampling Gabor Noise in the Spatial Domain

10. Sampling Gabor Noise in the Spatial Domain
Illustration
Sparse Convolution Process in Detail y
80 impulses 𝑥
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Sampling Gabor Noise in the Spatial Domain

11. Spatially Varying Gabor Noise
Sparse Convolution Process
Lattice-Based Interpolation y y
𝑦 ′ 2
0.256
0.84
0.7
0.2
𝑦 2
0.44
0.8
0.1
𝑦 1
𝑦 ′ 1
0.29
0.5621
0.6 𝑥 𝑥
𝑥 1
𝑥 2
𝑥 ′ 1
𝑥 ′ 2
Noise aspect at ( 𝑥 1 , 𝑦 1 ) ? Noise aspect at ( 𝑥 ′ 1 , 𝑦 ′ 1 ) ?
Gabor noise is spatially controllable
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Sampling Gabor Noise in the Spatial Domain

12. Spatially Varying Gabor Noise
Surface Gabor noise defined without parameterization (setup-free)…
…but parameterization helps spatial control
Our idea: attach parameter values to model’s UV-space
Basic control map
Elaborated design tools
Image: [ZBrush]
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Sampling Gabor Noise in the Spatial Domain

13. Sampling Gabor Noise in the Spatial Domain
Spatial Variation in 2D
𝐹 0 (Sine frequency)
𝑎=59.0, 𝜔 0 =0, 𝐹 𝑠 =0, 𝜔 𝑠 =0 65
𝜔 𝑠 (Angle spread)
𝑎=26.9, 𝐹 0 =25.9, 𝜔 0 =0, 𝐹 𝑠 =0
𝜋 4
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Sampling Gabor Noise in the Spatial Domain

14. Our Perception of the Noise
Range on 𝐹 0 has been doubled 65
130
Image:
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Sampling Gabor Noise in the Spatial Domain

15. Our Perception of the Noise
Contrast sensitivity function [Landy 04]
Spatial frequency
contrast 𝑥 𝑦
𝜔 0
1 𝐹 0
𝑟 𝑘 ≈ 1 𝑎
𝐹 𝑘 ≈2
Image:
𝐹 0 represents an absolute frequency
Our perception is relative to the kernel radius
𝑟 𝑘 = 1 𝑎 ln⁡(20) 𝜋 𝐹 𝑘 = 𝐹 0 ∙ 𝑟 𝑘
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Sampling Gabor Noise in the Spatial Domain

16. Our Perception of the Noise
A more intuitive evolution of the parameter
𝐹 0 65
Image:
𝐹 𝑘 7
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Sampling Gabor Noise in the Spatial Domain

17. Sampling Gabor Noise in the Spatial Domain
Application
Procedural variation of 𝜔 0
Interlacing patches
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Sampling Gabor Noise in the Spatial Domain 17

18. Sampling Gabor Noise in the Spatial Domain
Application
Textures and 3D models
UV control mapping
Noise layers
Purely procedural
20-30 FPS
On the GPU
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Sampling Gabor Noise in the Spatial Domain

19. Sampling Gabor Noise in the Spatial Domain
Application
Textures and 3D models
More natural effects
Expressiveness of Gabor noise
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Sampling Gabor Noise in the Spatial Domain

20. Sampling Gabor Noise in the Spatial Domain
Conclusion
Contribution
UV spatial control over Gabor noise
A design-oriented set of parameters
𝑟 𝑘 = 1 𝑎 ln⁡(20) 𝜋 𝐹 𝑘 = 𝐹 0 ∙ 𝑟 𝑘
Underlines one advantage of Gabor noise, its controllability
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Sampling Gabor Noise in the Spatial Domain

21. Sampling Gabor Noise in the Spatial Domain
Future Work
Possible improvements on Gabor noise ?
Faster rendering
Optimal impulse density (perceived by humans)
Automatic parameter ranges
Based on Contrast Sensitivity function, Gestalt laws…
Non-linear filtering
Underlines one advantage of Gabor noise, its controllability
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Sampling Gabor Noise in the Spatial Domain

22. Thanks for your attention
Conclusion
Thanks for your attention ?
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Sampling Gabor Noise in the Spatial Domain

23. Sampling Gabor Noise in the Spatial Domain
References
[Ebert 03]
David S. Ebert, F. Kenton Musgrave, Darwyn Peachey, Ken Perlin, Steve Worley Texturing and Modeling: A Procedural Approach
[Lagae 09]
Ares Lagae, Sylvain Lefebvre, George Drettakis, and Philip Dutré Procedural noise using sparse Gabor convolution. ACM Trans. Graph. 28, 3, Article 54 (July 2009), 10 pages.
[Lagae 11a]
Ares Lagae and George Drettakis Filtering solid Gabor noise. ACM Trans. Graph. 30, 4, Article 51 (July 2011), 6 pages
[Lagae 11b]
Ares Lagae, Sylvain Lefebvre, and Philip Dutre Improving Gabor Noise. IEEE Transactions on Visualization and Computer Graphics 17, 8 (August 2011),
[Galerne 12]
Bruno Galerne, Ares Lagae, Sylvain Lefebvre, and George Drettakis Gabor noise by example. ACM Trans. Graph. 31, 4, Article 73 (July 2012), 9 pages.
[Landy 04]
Michael Landy Spatial Frequency Channels. Lecture notes. New York University Center for Neural Science. 22 May <
[ZBrush]
Josh Tiefer. UV Master in production - Case Study with Josh Tiefer. Pixologic. 27 May <
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Sampling Gabor Noise in the Spatial Domain