Slicing for std calculation

[McHaillet]

This PR improves the calculation of the standard deviation over a template matching search. It closes #97.

First some background on why I updated this. Template matching has a huge search space (N_voxels * rotations) which is mainly false positives, and has in comparison a tiny fraction of true positives. If we have a Gaussian for the background (with expected mean 0 and some standard deviation), the false alarm rate can be calculated for a certain cut-off value, as it is dependent on the size of the search space. For example, a false alarm rate of (N_voxels * rotations)^(-1), indicates it would expect 1 false positive in the whole search. This can be calculated with error function,

$$N^{-1} = erfc( \theta / ( \sigma \sqrt{2} ) ) / 2$$

, where theta is the cut-off, sigma the standard deviation of the Gaussian, and N the search space.

The search space is easily calculated, the standard deviation can be kept tracked of for each orientation (which is what this custom square_sum_kernel is used for). However there were true problems:

• with the next_fast_len for ffts the volume was padded with zeros that were also incorporated in the square_sum_kernel.
• with subvolume splitting I added overhang between subvolumes, needed for accurate scores, but these regions were incorporated doubly in the standard deviation calculation.

I fixed it by passing a search_volume_roi to template matching which contains the actual region of interest wihout fft padding and without template overhang. The indexing is already calculated, so I just created a slicing for the cupy array.

I first added tests to check whether the search_space and std are consistent with subvolume splitting (and also rotation splitting), and realised there was a bug in tmjob.py in calculating the start of the subvolume (lines 380 to 384): I did not put brackets around template_size // 2 which messes with integer division with the minus sign in front 😩 . This is now fixed.

I also added plotting of an extraction graph which shows a histogram of extracted scores together with the background Gaussian (as this is now properly estimated). Which I think is nice for users to see.

Let me know if anything is unclear.

[sroet]

1 suggestion and 1 line was added twice, LGTM otherwise

[sroet]

(selected the wrong option)

[sroet]

LGTM, feel free to merge