Terminology

tCA or CA - transverse Chromatic Aberration. This is when the color channels in an image do not appear to line up well with each other. PTShift will allow the user to find the abcd parameters used by the PanoTools radial shift filter to reduce tCA in your images. A good introduction to CA can be found here.

abcd - The polynomial coefficients used by PanoTools Radial Shift filter to remove or reduce tCA. PTShift will calculate the values of abcd for you based on the channel shifts supplied by the user.

PanoTools Radial Shift Equation - The equation can be written as:

rs = a(rd^4) + b(rd^3) + c(rd^2) + d(rd)

where rs is the source pixel, and rd is the destination pixel.

A source image is transformed into the destination image using the above equation. The transformation result depends completely on what values you choose for the constants : a,b,c,d

By supplying the appropriate abcd constants for each color channel to the PanoTools Correctcion Radial Shift filter, you can reduce the tCA in an image. For the purpose of removing tCA from an image, the abcd values will NOT be the same for all color channels.

PanoTools Corrected Image - The resulting image you get when run the PanoTools Correction Radial Shift filter using the calculated abcd values from PTShift.

x,y - this is a horizontal,vertical location in your image where you wish to remove tCA. The user draws a rectangular selection box around a chosen x,y location, and then runs PTShift to remove the tCA at that location.

R - The radial distance of x,y from the image center, in units of pixels. Not to be confused with the 'R' in RGB (which stands for Red, Green, Blue).

Control Point - An x,y location with a user specified channel shift that has been saved by the user.

dR - the amount that a color channel will be radially SHIFTED (at a location x,y in the image) so that a color channel lines up with the other color channels. A positive dR means that you are shifting radially outwards, away from the image center. A negative dR means that you are shifting radially inwards, towards the image center.

dR[User] - This is the channel shift (in pixels) that the USER specifies in an attempt to remove the tCA at a location x,y.

dR[PT] - When you specify dR[User] values at numerous x,y locations throughout your image, PTShift attempts to find the abcd parameters that creates a best fit curve through all of your dR[User] data. dR[PT] is thus the *actual* dR value you will end up getting at a point x,y when you run the PanoTools Radial Shift with your abcd values - as opposed to your *user specified* dR[User].

Distance Error - Imagine you have a control point at x,y that is a distance R from the image center. You specify a dR[User] at that point, which means you want to shift a color channel from R to R+dR[User]. PTShift will calculate it's own dR[PTShift], meaning that the PanoTools Corrected image will show a shift at x,y from R to R+dR[PTShift].

I have thus defined distance error as follows:

Distance Error = R{transformed using the PTShift calculated abcd} - (R+dR[user]){transformed using the baseline abcd}

When you are using a baseline abcd=0001, the distance error is nothing more than (R+dR[PTShift]) - (R+dR[User]) , or just dR[PT] - dR[User].

The Distance Error will be displayed for each control point x,y in the INFO Window in PTShift.

Note that when you have 4 or fewer control points, the distance error for your points will essentially be ZERO. The reason for this is that the PanoTools Radial Shift equation is a 4th order polynomial and we are looking for 4 parameters: a,b,c, and d.

If you have 5 or more control points, then some (or all) of the distance errors you get will be non-zero because it is not possible to precisely satisfy 5 or more control points (each with a dR[User]) using a 4th order equation.

You are allowed, however, to specify as many or as few control points as you wish. PTShift will always try to get a least squares curve fit to minimize the overall distance errors.

Anchor Channel - A color channel in an image that will NOT be shifted. It will remain stationary while one or more other channels WILL be shifted, so that the shifted channels and the anchor channel all line up together to reduce tCA.

It is possible, however, to not have an anchor channel at all.

Baseline abcd - This is the abcd values that PTShift assumes are being applied to the Anchor Channel during optimization. The baseline abcd is specified in the Preferences Window of PTShift.

If the baseline abcd = 0,0,0,1 then this means that the anchor channel is not being transformed at all when we go from your Input Image to the PanoTools Corrected Image.

On the other hand, we can choose a baseline abcd such that the barrel/pincushion distortion is removed from the Anchor Channel when we transform the input image to the PanoTools Corrected Image. PTShift will then supply the abcd values for the NON anchored channels so that they line up with the Anchor channel.