Not sure why this happens, probably the default 'reflect' mode of the scipy gaussian_filter, but a simple solution is creating something slightly larger and then crop the edges.

I have been meaning to address this bug, but just always too busy. The guassian blur function that is used has a mode argument which controls how the edges are handled. This should be a pretty simple thing to fix just by specifying either reflect or mirror. Interestingly, there is also the wrap mode...I wonder if that would allow for periodic boundaries?

I played with this and even created a PR, but my solution did not work. Using wrap solves the problem and has the added benefit of making a periodic image, which is quite handy. However, I am not sure why mirror and or reflect create this problem. In my understanding, both reflect and mirror should ensure the convolution does not suffer edge effects since the interior values are reflected outward, so the phase fraction at the edges should be representative. We are not doing anything fancy in the code, it's just gaussian_filter followed by any_to_uniform, followed by a threshold.

I spent a bit of time on this and reached the following conclusions:

• Something is happening during the gaussian_blur which seems like a bug (maybe?). All of the edge modes, except 'wrap' result in the edge effects noted above. I am sure that reflect and mirror should not cause this.
• When looking at the density distribution of the blurred image along the x-axis (i.e. summing up all the values for a given x and looking at the yz plane), there is no noticeable edge effect, but when I take a threshold THEN the edge effect appears. This seems to tell me that there is a minor bias in the edge values which is only noticeable once the values are booleaned.

why not use 'wrap'?

I was thinking that making the image periodic would not always be desired (though tbh I would prefer it). Also, it just bothers me that it's happening so I want to know why and how to fix it.

I think the answer is that the mirror and reflect modes make the edges have less variation in every square/cube, because the same numbers are used. This causes less smoothing by the gaussian filter because the filter is applied to less numbers and so the result is higher variation in the edges.

np.std(im[:1])
0.013613445803553578
np.std(im[20:21])
0.010896353309892862

This higher variation makes many of these pixels larger after all_to_uniform.

I think the solution is making a slightly bigger volume and then crop the edges affected by the mirror/reflect.