Some cells' a.tot equals their a.tot.p1

[naikymen]

Example pics:

a.tot: "Area of the cell in pixels"

a.tot.p1: "Area of all the pixels interior to the boundary that is one pixel wider than the cell boundary. Numbers thus include the original cell plus an annular region one pixel around the outside of the cell."

Since the perim variable is not actually the number of pixels in the perimeter, there is no good way of estimating it.

A workaround is to derive it from the pixel boundary masks.

For example, this creates a num.pix.perim column with the actual number of pixels in the boundary:

cdata.perim <- left_join(
  cdata,
  cell.boundaries %>% group_by(pos, cellID, t.frame) %>% 
    summarise(num.pix.perim = n()), 
  by = c("cellID", "t.frame", "pos")
  )

[naikymen]

Sample cells, with a.tot.p1 - a.tot < 0.

Thus, unfortunately, a.tot.p1 is not a reliable measure of the "outer" perimeter length when cells are not entirely convex.

Furthermore, this error likely propagates to other variables which depend on it, such as f.tot.p1 (needs checking).

[naikymen]

It is possible that a dilation operation on the mask pixels closes the holes on these weird / non-convex shapes. That would explain the shrinking of the a.tot.p1 relative to a.tot.

[naikymen]

For the record, i foundthis problem by trying to calculate a ratio between "inner" and "boundary" signal intensities in the TFP channel.

I was hoping it would be useful as an out-of-focus sensitive variable.

Using something like this:

cdata.perim <- left_join(
  cdata,
  cell.boundaries %>% group_by(pos, cellID, t.frame) %>% 
    summarise(num.pix.perim = n()), 
  by = c("cellID", "t.frame", "pos")
  )

# cdata.p1m2 <- cdata %>%
cdata.perim <- cdata.perim %>%
  mutate(
    # a.p1 = abs(a.tot.p1 - a.tot),
    a.p0 = num.pix.perim,
    a.m0 = a.tot - num.pix.perim,
    f.p1.tfp = f.tot.p1.tfp - f.tot.tfp,
    f.m2.tfp = f.tot.m2.tfp - f.tot.tfp
  ) %>% 
  mutate(
    # cf.p1.tfp = f.p1.tfp / a.p1,
    cf.p1.tfp = f.p1.tfp / a.p0,
    cf.m2.tfp = f.m2.tfp / a.m0
  ) %>% 
  mutate(cf.tfp.p1_m2 = cf.p1.tfp / cf.m2.tfp)