This supplemental material provides additional information on the core elements of the PPTBF model, i.e. the point process, the window and feature functions.

Observation of texture databases, e.g., the well-known Brodatz album [Brodatz 1966], reveals that many natural textures embed spatial stochastic structures like cells, cracks, grains, scratches, spots, stains or waves, with some spatial geometric variations. Most of these types of textures can be characterized through three components: 1) the distribution of its elements, which can be modeled as a spatial point process, 2) the local visual pattern of the elements, modeled as a feature function and 3) the interaction among elements, i.e., how they blend with each others or stay localized in isolated regions, modeled as a window function.

Observation of texture databases, e.g., the well-known Brodatz album [Brodatz 1966], reveals that many natural textures embed spatial stochastic structures like cells, cracks, grains, scratches, spots, stains or waves, with some spatial geometric variations. Most of these types of textures can be characterized through three components:

- [1] the distribution of its elements, which can be modeled as a spatial
*point process***P**, - [2] the local visual pattern of the elements, modeled as a
*feature function***F** - [3] and the interaction among elements, i.e., how they blend with each others
or stay localized in isolated regions, modeled as a
*window function***W**.

This supplemental material provides additional information on *reverse engineering* procedural textures designed by artist from the Substance Designer tool.

As can be seen from the node graph, artist started to create a pattern of a single *fish scale*, then use different tiling generator to distribute it on the plane, by mixing (i.e. blending) distributions. The main drawback is the lack of control of the resulting distribution.

As can be seen from the node graph, artist...

The key idea is to separate the structure synthesis from the color synthesis. Structures can be modeled as procedural modeling, inspired from Blumenthal implicit fucntions and the signed distance field distance functions demoscene (e.g. NVScene, shadertoy) and VFX industry.

We compare to:

- Sparse convolution noise
- LRP Noise
- Cellular texture basis functions
- Texture bombing
- Patch-based approaches

From left to right: (1) input exmplar, (2) output grid of selected patchs from input (patch contents are the *features*, the grid is resulting from a *point process* with regular distribution),
(3) optimal cuts between overlapping patches [regions delimited by cuts are the *windows*], (4) resulting synthesis.

The *Point Process* **P** controls the spatial distributions of elements through 2 parameters:

- tiling: tile the plan in different configurations
- jitter: add some jittering in cell

Tiling | Jitter |

- Cellular Window
- Tapered Cosine Window

Cellular Window |
Tapered Cosine Window |

- Anisotropic Gabor Kernels
- Operators: bombing, voronoise

Anisotropic Gabor Kernels |
Operators: bombing, voronoise |

Spatial distortions significantly increase the range of structures: on the left, no distortion applied to the PPTBF, on the right adding noise-based spatial warping, aiming at simulating natural Brownian motion, a very frequent stochastic process in nature.

Binary Structure Maps (thresholding) |

Few samples of structures generated with PPTBF. These images have been obtained by binary thresholding. Unlike noise, PPTBF covers a large variety of different structural appearances.

Complex structures can be obtained by mixing cellular and regular windows (left: no blend, middle: 50%, right: 100%).

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