pooling-windows

PyTorch implementation of pooling windows like those used in Freeman and Simoncelli, 2011¹.

Matlab code for these windows exist as part of Jeremy Freeman's repo for the original paper. This repo is not a direct port of that code, but a conceptual reimplementation, following the math outlined in the supplemental materials, and also includes a version using Gaussian windows. Note this means we do not test whether our outputs match the original implementation (and, as pointed out by Wallis et al, 2019², there is a minor bug in that code).

The included Guassian windows overlap more than the original windows (which used a raised-cosine falloff), and thus give a smoother representation. They were created by William Broderick for his foveated metamer project (VSS 2020 poster, VSS 2023 poster, preprint), and notably improved the quality of V1 and retinal metamers. A more detailed discussion of the differences between the Gaussian and raised-cosine windows can be found at the top of pooling.py.

Requirements

This code works with python 3.7, 3.8, 3.9, and 3.10. The packages required to use this code can be found in requirements.txt. In order to install them in your virtual environment of choice, run pip install -r requirements.txt; you will then be able to use the code here from within this directory (pooling is not itself installed, and thus will not be on your path). There is one function, PoolingWindows.plot_windows(), which requires plenoptic -- if you wish to use it, you must install that package as well (follow the instructions in its README).

If you wish to view the included notebook (which contains a simple demonstration of some sampling and aliasing issues), you will also need to install jupyter.

Usage

The PoolingWindows class is the main way of interacting with this code. To use, you instantiate it and then call it on a 4d image-like tensor. Let's break that down:

• First, load in an image. This can be either grayscale or color. In the following code snippet, we treat it as if it were 8-bit integers (which is generally the case) and divide it by 255 because we need all values to lie between 0 and 1.

import torch
import matplotlib.pyplot as plt
import numpy as np
import pooling

img = torch.from_numpy(plt.imread('path/to/image.png').astype(np.float32)) / 255

• Unsqueeze the image until it's 4d. Like many pytorch modules, PoolingWindows operate on 4d images as input: batch by channel by height by width. The batch dimension is used for multiple images and channel for RGB(A) (or different channels in convolution layers). PoolingWindows supports both single- and multi-batch and channel inputs, operating independently along batch and channel dimensions.

# if this is a grayscale image, it will be unsqueezed twice; if it's RGB, it will be unsqueezed once.
while img.ndim < 4:
    img = img.unsqueeze(0)

• Construct the PoolingWindows object. There are several possible initialization arguments, and you are encouraged to investigate them yourself. The only necessary ones are scaling, which sets the relationship between the width of the windows and eccentricity, and img_res, which gives the height and width of the input. In the example below, we construct Gaussian windows. To instead construct raised-cosine ones, set window_type='cosine' and remove the std_dev argument.

pw = pooling.PoolingWindows(.5, img.shape[-2:], window_type='gaussian', std_dev=1)

• Call PoolingWindows.forward() on the image! Note that pw(img) and pw.forward(img) are the same.

pooled = pw(img)

You can also run PoolingWindows on dictionaries of 4d tensors, like that created by the steerable pyramid implementation found in plenoptic (in this case, the keys of the input dictionary must be tuples where the first value is an int, giving the scale):

import torch
import matplotlib.pyplot as plt
import numpy as np
import pooling
import plenoptic as po

img = torch.from_numpy(plt.imread('path/to/image.png').astype(np.float32)) / 255
while img.ndim < 4:
    img = img.unsqueeze(0)
# create the pyramid
pyr = po.simul.Steerable_Pyramid_Freq(img.shape[-2:], height=4)
# get the pyramid coefficients
pyr_coeffs = pyr(img)
# remove the residuals, which PoolingWindows doesn't support natively
for k in ['residual_highpass', 'residual_lowpass']:
    pyr_coeffs.pop(k)
# let's see their shape
for k, v in pyr_coeffs.items():
    print(f'scale {k[0]}, orientation band {k[1]}: {v.shape}')
# create the windows. Note that we're now setting the number of scales! 
# This must be the same as the height of the pyramid
pw = pooling.PoolingWindows(.5, img.shape[-2:], window_type='gaussian', 
                            std_dev=1, num_scales=4)
# pooled_coeffs will have the same keys as pyr_coeffs, and its values will 
# be the pooled versions of the corresponding value in pyr_coeffs
pooled_coeffs = pw(pyr_coeffs)
for k, v in pooled_coeffs.items():
    print(f'scale {k[0]}, orientation band {k[1]}: {v.shape}')

For an example of a more elaborate usage of these windows, see the PooledVentralStream models (note that these are no longer part of plenoptic and so will not be found on the master branch).

Notes

1. These windows are exact, and so are incredibly memory-intensive for small scaling values and large resolutions -- creating windows with scaling=.01 and img_res=(2048, 2600), for example, can take 15 minutes to an hour (depending on your machine) and more than 100 GB of RAM, and a single forward() call can take 4 minutes. This is something to be aware of. It is possible to come up with more memory-efficient approximations of foveation, but it is likely that synthesis will exploit the approximation errors.
2. Because creating the windows can take so long, we have a cache_dir argument: set this to a directory on your machine and the windows will be saved there during creation and, if the appropriate windows are found when instantiating a new instance, they will loaded in. If the directory does not exist, we raise a FileNotFoundError.
3. PoolingWindows supports multi-scale windows (by setting num_scales argument). To do this, we independently construct the windows at each scale (note this is different from [1], which constructed the windows at the input resolution and then blurred them).
4. PoolingWindows works on the GPU. If you have a CUDA-compliant GPU available and have properly installed pytorch to make use of it, call the .to(torch.device('cuda')) method of an instantiated PoolingWindows object to send it to the GPU (note that you will also need to send over your input images to the same device).
5. We construct windows smaller than a pixel -- this is a bit of an implementation detail and changed back and forth over development. Doing so gives a more gradual transition during metamer synthesis from the "pixel match" region at the center to the pooled region. Setting the min_eccentricity will set the eccentricity (in degrees) where we start creating the windows, regardless of their size (in pixels) at that point.
6. These windows have only been used on the output of plenoptic's steerable pyramid (as described above) and images. Any other use-case will probably require some modification.
7. PoolingWindows has a variety of helper methods to help understand what it's doing, including several that create plots. For example pw.plot_windows() will create contour plots showing the windows at each eccentricity and a small number of angles, and pw.plot_window_areas() will show the area of the windows (in pixels or degrees) in each eccentricity ring. They should all have complete docstrings, so you are encouraged to explore.
8. The code in this repo was originally part of plenoptic but removed in March 2021. In moving over the code, I broke the git history; if, for some reason, you wish to see the history or git blame, this plenoptic commit contains all the code before transferring it to this repo.

Code structure

• tests/test_pooling.py: some tests (run on every push using Github actions) to make sure pooling windows don't change drastically. They're not a complete suite of tests for these windows.
• pooling/: python module containing the code for the pooling windows.
  • pooling_windows.py: contains the PoolingWindows class, which is how users should interact with this code.
  • pooling.py: variety of calculations used for constructing and investigating the windows, used by PoolingWindows.
  • utils.py: miscellaneous utility functions.
  • __init__.py: boilerplate file for making pooling a module.
  • sampling.py: checks sampling and aliasing issues, used by the Sampling_and_aliasing.ipynb notebook, but not by PoolingWindows.
• Sampling_and_aliasing.ipynb: example of how to check for sampling / aliasing issues. I would recommend you do something similar to this if you construct your own windows or modify these in a significant way.

References

Footnotes

1. Freeman, J., & Simoncelli, E. P. (2011). Metamers of the ventral stream. Nature Neuroscience, 14(9), 1195–1201. http://dx.doi.org/10.1038/nn.2889. reprint ↩

2. Wallis, T. S., Funke, C. M., Ecker, A. S., Gatys, L. A., Wichmann, F. A., & Bethge, M. (2019). Image content is more important than bouma's law for scene metamers. eLife, 8(), . http://dx.doi.org/10.7554/elife.42512 ↩