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Calibration with saturated images

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Please read the calibration page first if you have not already. This page won't make a great deal of sense otherwise.

I have not included a graph for this recipe - it's largely the same as the calibration recipe.

In the calibration recipe page we looked at how to calibrate an image to produce R^\star (reflectance) from DNs or radiance. This requires a calibration target to be present in the image1.

However, some of the patches in the reflection target may be saturated. This data cannot be used for calibration, because it is false - the saturated patches are brighter than the recorded image can show.

Consider the image below:

Image showing saturated patch and its spectrum
Figure: Image showing saturated patch and its spectrum. Click on image to expand.

The top-right patch on the ColorChecker target has two saturated bands, shown as "1.00" in the spectrum. In the case of this particular image, it's not saturated in any of the bands which make up the RGB image shown in the canvas, but by visual inspection many other patches are saturated in these bands.

If we try to get reflectance parameters m and c by fitting a line to these points, we end up with this mess:

Measured/known reflectances and line fits without saturated pixels removed
Figure: Measured/known reflectances and line fits without saturated pixels removed. Click on image to expand.

The points for each patch do not fall on a straight line. The saturated points count more in the line fit because they have lower uncertainty, which is particularly bad for the G0a and G0b filters, in which the saturated points dominate so strongly we fit a horizontal line!

Ideally, the image should be captured again at a shorter exposure time but this is often2 not possible. However, the reflectance patch will ignore pixels which have been marked as saturated. To do this, insert an expr node immediately after the input, and set the expression in that node to 

marksat(a,0,0.9997)
We're using 0.9997 rather than 1, because typically we're only using 12 bits of the input; for technical reasons this means that the maximum value from the camera scales to 0.9997711 (65520/65535) inside PCOT. You should see areas of the image turn magenta, indicating pixels with saturated data in any band (see the main PCOT docs for more details on how this works)3.

The calibration pipeline should look now something like this:

Image showing the calibration pipeline with the "marksat" expr node
Figure: Image showing the calibration pipeline with the "marksat" expr node. Click on image to expand.

Looking at the reflectance node, we can see the lines fitted to the patches in each band:

Measured/known reflectances and line fits with saturated patches removed
Figure: Measured/known reflectances and line fits with saturated patches removed. Click on image to expand.

The points are reasonably well aligned for each filter, indicating a good fit.

  1. Or at least some image; we can always import calibration data from one image to another by using multiple inputs. ↩

  2. Usually! ↩

  3. A future version of PCOT will fix this very slight inaccuracy by taking account of the camera bit depth in PNG image load. The raw loader should already do this. ↩