Poisson Texture Tiling

Overview

This tool converts an input image into a seamlessly tileable texture.

This program contains following three steps to generate the texture.

1. Build the sparse linear system from the input image ( $Ax = b$ )

   • Compute a Laplacian from the input image ( $b$ )

   • Construct a sparse Laplacian matrix with periodic boundary conditions ( $A$ )

2. Solve the sparse linear system

3. Adjust the global color offset

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This program uses Eigen::SimplicialLDLT with Eigen::SparseMatrix to solve Poisson equation.

It seems time complexity is O(N^1.5), where N is the number of pixels in the image.

So make sure not to input too large images.

DEMO

Input image	Output image
Tiling without poisson	Tiling with poisson

TODO

• FFT-based Poisson solver

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Requirements

• OpenCV (4.13.0_6)
• CMake (4.2.3)
• GNU Make (3.81)

This project has been developed and tested only with the versions above.

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Usage

# clone
git clone --recursive https://github.com/poisson-texture-tiling
cd poisson-texture-tiling

# build
mkdir build
cmake -S . -B build/
cmake --build build/

# execute
./build/poisson_texture_tiling <path-to-target-image>

# output two images, "poisson_texture_tiling_output.png" and "poisson_texture_tiling_output_tiled3x3.png".
# the former is a tileable texture, and the latter is an image showing an example of tiling.

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Note

TODO

write mathematical explanation