How do I translate pixel coordinates to real world coordinates using a calibration target?

I have a 2xN array of pixel coordinates = A that correspond to the dots on a dotted calibration target (a sheet with dots on it that are a known distance apart).

I have a 2xN array of real-world-unit coordinates = B which contains the positions of the dots on the target.

How do I find a way to smoothly translate any coordinate that falls into the area of the points contained in A onto B, so that I can find a given point in real space for any point on the target, not just the points where the dots are?

A linear translation is not possible as the image contains distortions. I have tried functions like estimateCameraParameters and estimateCameraMatrix, but these apparently either require multiple images or non-coplanar points, both of which I do not have.

Answer 1

[Image Analyst]

I think you can use scatteredInterpolant. Given a list of (xp, yp) pixel coordinates, and another separate list of real world (xr, yr) coordinates, you can essentially build a surface with scatteredInterpolant. So once you have that you can simply input the pixel coordinates and out pops the real world coordinates. Attached is a demo of scatteredInterpolant. I'm sure you can easily modify it, but the key is you need to know the real world coordinates for a certain set of image/pixel coordinates, but you said you know those.

[_NB_]

Thank you for the quick response. I have read into the documentation and the example you provided, but I do not seem to understand how scatteredInterpolant would even accept both of my coordinate lists to map them to each other.

As far as I understand only one list of coordinates, be they 2D or 3D, is accepted together with an assigned value for each point. I have tired simply plugging the second coordinate-array into the value input, but this expectedly threw an arror telling me to input a column vector.

[Image Analyst]

Upload your two lists and I'll do it. Upload the list of the points' pixel (x,y) coordinates, and the list of what their real world, spatially calibrated units are.

[_NB_]

Here you go and thank you for taking the time.

TargetDots are the pixel coordinates, TargetDotsReal are the real-world coordinates.

[_NB_]

Please note that these are not in order, if that is important for this function.

[Image Analyst]

This looks like it should be a perfect linear scaling:

s = load('export.mat')

TargetDots = s.TargetDots;

TargetDotsReal = s.TargetDotsReal;

% Show input

subplot(2, 1, 1);

scatter(TargetDots(:, 1), TargetDots(:, 2), 10, 'b', 'filled');

title('Target Dots')

subplot(2, 1, 2);

scatter(TargetDotsReal(:, 1), TargetDotsReal(:, 2), 10, 'r', 'filled');

title('Target Dots Real')

Why can't you simply do

estimatedY = 1 + 9 * (yTest - min(y)) / (max(y) - min(y));
estimatedX = 1 + 9 * (xTest - min(x)) / (max(x) - min(x));

???

[_NB_]

I cannot do a linear interpolation because for other images there may be more distortion, which could be along the X-axis, Y-Axis or random in nature.