Rewrite Footprint Frame Update

[raymondwjang]

Currently, footprint update has a few issues:

• boundary expansion - feature missing. unsure if needed since merging is in place. This operation is also expensive, costing tens of microseconds within each loop.
• tolerance - need some kind of graceful failure for when footprint estimate just isn't good enough at the moment, and we have to wait until more frames have come in.

[raymondwjang]

• boundary expansion - only perform once per process, with an option to entirely skip it.
• tolerance - add max_iter for exit when it's just not gonna converge. (need more test cases here. separate issue)

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!! Source of Error in Original Alg !!

when the traces of one cell is more than an order of magnitude smaller than of an overlapping cell, the footprint_update step can cannibalize the inactive cell.

i.e. simulating a situation where the original footprint estimate was too large. so

1. simulating 5 overlapping cells in an x-shape arrange (one in each corner with one in the center)
2. the footprints are dilated from the correct simulation
3. the sufficient statistics are "correct" (they don't directly depend on footprints anyway)
4. update footprints to see if the excess meat is whittled down

dilated:

expected:

result:

here, a visible "bite mark" is present in the cell with a smaller trace. this phenomenon is not present in other cells with larger traces that are roughly equal in magnitude to other cells. Also, this bite-mark disappears if the magnitude of the cell trace is amplified.

[raymondwjang]

made sense of it

Ã[p, i] = max(Ã[p, i] + (W[p, i] - Ã[p, :]M[:, i])/M[i, i], 0)

means:
from brightness correlation history of a pixel p and component i (W[p, i]), we subtract contributions from cells other than i at p (Ã[p, :]M[:, i])

since we "overestimate" the contribution of another component via dilation, this gets subtracted, creating the empty pixels.