This is a set of simple python scripts that test a method for generating spatially correlated noise.
This will generate an (n * m) pixels intensity image (i.e. between 0 and 1) with an underlying noise structure.
Run the scripts in your console using
> python spacenoise.py
> python spacenoise_reduced.py
For the original implementation,
- Generate an image with a specific initial condition (e.g. random or uniform(0.5) )
- Define an underlying coupling structure using pixel position information, to return a "similarity measure"
- Normalize the similarity measure to get coupling weights
- Iteratively sample a random pixel from the image
- Use the coupling weights to sample another pixel to which it couples strongly
- Sample the new pixel intensity from some distribution based on sampled pixel intensities, similarity and other params.
Note that this is very slow, since coupling is calculated for all pixels to all pixels, and we sample accordingly. To make this faster, another version was written (spacenoise_reduced) that only samples from the strongest coupling pixels.
We require a definition of:
- Initial Condition
- Similarity Measure
- Sampling Distribution
for the algorithm to work. A few examples have been implemented!
- Uniformly Random
- Uniform 0.5
- Exponentiated euclidean pixel distance squared
- Exponentiated euclidean pixel distance non-squared
- Sine squared of euclidean pixel distance
- Gaussian centered around neighbor with fixed variance
- Gaussian centered around average of neighbor and sampled pixel with fixed variance
- Gaussian centered around neighbor with variance determined by coupling strength
I forgot exactly what parameters generated these results, but in general a long-distance coupling function (i.e. sine) worked best. Picking appropriate coupling scales for the image size is also important. Choosing smaller coupling numbers will give more "cut off" results, and larger ones will give smoother results.
If the results are too grainy, you can pass a gaussian filter over it.
Average sampling gaussian also gives smoother results.
Note: These were all generated with different parameter sets.
