Test: ensure that `phase_cross_correlation` ('cc') and Gaussian fit ('fit') methods give same drift correction direction and accord with usage later in processing

[vreuter]

Updated -- to test:

• [ ] PBT for the equivalent direction of drift for 'cc' and 'fit'
• [ ] computation of fine drifts: check that it correctly uses already-computed coarse drifts.
• [ ] check that drifts are additive (total = coarse + fine), rather than some difference between these
• [ ] check that spot image extraction for tracing correctly uses the coarse drift correction (#proximi
• [ ] check that proximity-based filtration of spots correctly uses both coarse and fine drift information
• [ ] check that coordinates are properly computed in the end, adding the fine drifts after the tracing
• [x] #195

Original: In particular, check that the addition/subtraction would be the same, e.g. template = offset + drift or template = offset - drift would be the same in either case.

[vreuter]

For cross-correlation, we have the relation that offset = reference_image - offset_image: https://scikit-image.org/docs/stable/auto_examples/registration/plot_register_translation.html#image-registration

This means that using an observed bead image and a reference bead image, we get an offset that represents how to recover a hypothetical original spot image (at time of reference) from an empirical spot image (not at time of reference). Then hypothetical = drift + empirical.

See below for docs:

[vreuter]

Our offset / shift / drift vector for the difference between centroids of Gaussian fits is here: https://github.com/gerlichlab/looptrace/blob/5b783bc5ea78cc2611329cfb0b4554caeb8dc2d6/looptrace/Drifter.py#L129-L134 which accords with the scikit-learn implementation of cross-correlation, good!

[vreuter]

As noted in #130, the coarse drifts are used for extracting spot images for tracing, where each extraction amounts to cutting out an ROI, detected in a regional barcode imaging timepoint, from another imaging timepoint. We then need to find the shift of the timepoint from which to extract relative to the timepoint in which the ROI-defining spot was detected.

In particular, we're computing coordinates for an extraction in an offset (relative to a spot detection timepoint) space. So again keeping with the offset = reference_image - offset_image equation, we want to compute something like offset_coords_vector = reference_coords_vector - (relative_)offset. We do that here:

https://github.com/gerlichlab/looptrace/blob/5b783bc5ea78cc2611329cfb0b4554caeb8dc2d6/looptrace/SpotPicker.py#L281-L283

where we have something like:

coarse_drift = int(frame_drift) - int(ref_drift)
                     = int(ref_time_coord - locus_time_coord) - int(ref_time_coord - region_time_coord)
                     = int(region_time_coord) - int(locus_time_coord)
                     = offset with region_time as reference, locus_time as moving

==> target_min = roi_min - coarse_drift 
~=~ offset_image = reference_image - offset

Hence the coarse_drift we compute there acts appropriately to compute coordinates in the locus-specific timepoint space from coordinates in the ROI detection (regional barcode imaging timepoint) space, by virtue of analogy with the equation used to compute the coarse drift correction itself. This is the same for target_max.

[vreuter]

Fine-scale drift correction also accords with drift = ref - mov, as we recover the images in "ref" space, so ref = mov + drift: https://github.com/gerlichlab/looptrace/blob/5b783bc5ea78cc2611329cfb0b4554caeb8dc2d6/looptrace/Tracer.py#L341-L346

[vreuter]

Coarse drift correction information is also used in single-bead extraction: https://github.com/gerlichlab/looptrace/blob/5b783bc5ea78cc2611329cfb0b4554caeb8dc2d6/looptrace/bead_roi_generation.py#L68