1. Abstract
   1. we introduce a procedural noise
      1. based on sparse convolution and the Gabor kernel
      2. offers accurate spectral control with intuitive parameters
      3. supports two-dimensional and solid noise
      4. also introduce setup-free surface noise
      5. requires only a few bytes of storage
2. Introduction
   1. The application of noise
      1. procedural modeling and texturing [Ebert et al. 2002]
   2. we want a procedural noise
      1. accurate spectral control
      2. setup-free surface texturing
      3. anisotropic
      4. allow high-quality anisotropic filtering
   3. Related Work
      1. Procedural
         1. Perlin Noise [Perlin 1985]
         2. Ebert et al. [2002]
      2. Spectral Control
         1. Perlin 1985,;Lewis 1989; Perlin and Hoffert 1989
            1. a weighted sum of band-limited octaves of noise
            2. only approximate
         2. Cook and DeRose 2005; Kensler et al. 2008
            1. focus on constructing band-limited noise
         3. Lewis [1989]
            1. introduced solid procedural noises with improved control over the power spectrum
      3. Surface Noise
         1. Perlin[1985] and Peachy[1985]
            1. solid texturing
            2. does not require a surface parameterization
            3. setup-free
         2. Cook and DeRose[2005]
            1. surface noise can not be obtained by simply mapping solid noise onto a surface
      4. anisotropy
         1. [Cook and DeRose 2005]
         2. [Hart et al. 1999]
         3. Goldberg et al.[2008]
      5. Fast to Evaluate
         1. interactive
            1. Hart 2001
            2. Olano 2005
            3. Frisvad and Wyvill 2007
            4. Goldberg et al. 2008
3. Band-Limited Anisotropic Noise
   1. Sparse Convolution Noise
   2. The Random Pulse Process
   3. The Gabor Kernel
      1. parameterized
      2. have compact support in the spatial domain
      3. have compact support in the frequency domain
   4. Band-Limited Anisotropic Noise
      1. intuitive parameters
         1. the magnitude K
         2. the orientation w_0
         3. the magnitude F_0 of the frequency
         4. the width a of the Gabor kernel
4. Noise with On-The-Fly Spectral Control
   1. band-limited isotropic noise
   2. noise with controllable band-limits
   3. interactive noise design
5. Procedural Evaluation
6. Anisotropically Filtered Surface Noise
   1. Setup-free surface noise
   2. Anisotropic Filtering
      1. can be formulated as a convolution of a texture with a filter in the spatial domain, or as a multiplication in the frequency domain.