Digital Scanning

Yesterday, I was trying to figure out how to relate pixel location to real variables. The idea seemed familiar to me but I just can't remember. I had different solutions but they don't fit. In desperation, I asked Mabelle for some tips. She told me to use linear regression. She already had results and I have nothing. I was tempted to use programming but I hesitated. I am not that confident. While Mabelle was explaining to me the idea (how to solve the problem), it suddenly clicked to me that this was the very first thing Kirby taught me when I was in 3rd year. So, I immediately looked for my research notebook and there it is. Kirby's handwriting on my notebook. We already did this 2 years ago for the camera sensitivity experiment. My short-term amnesia is over. I can now perfectly remember how I did it 2 years ago. Thank you, Mabelle and Kirby for this. :)

So, here's how I did it.

1. Get the pixel location of the origin, x-coordinates and the y-coordinates. Write them down in Excel.
2. Make a table. One for the x-coordinates of the real and the pixel location in x and another one for the y-coordinates of the real and the pixel location in y.
3. Separately, graph the values. For my case, in the x-coordinate part of the image, my x was the pixel location and my y is the real values in the x-coordinate of the image. The same thing was done for the the Y-coordinate.

Displayed below are the graph, the equation and the R-squared value of the X and Y coordinates of the image.

4. Now, get the pixel location of points in the graph of the image. For my case, I took 60 points.
5. Using these points, insert the x and y value of points in the graph of the images to your equation in the X-coordinates. Then, using the same 60 points, do it also for the y-coordinates.
6. Once you have the value for the X and Y, graph these values.
7. Overlay the graph to the original image. Adjust the graph so that the x and y coordinates coincide.
8. See if you're able to perfectly reconstruct the original graph.

Here's what I got:

My best fit of the original graph

A small offset will result to a perfect reconstructed graph

It is not perfectly fit but it has the same shape as the original graph. This is the result after my 7th trial. The more points there are, the better the fit.

This skill is basic but very useful especially in preserving very old manuscripts. This activity made me realize something very important for a researcher: never forget everything that you have learned and always take notes of everything that you did in your experiment so as not to forget them the next time they are needed.

Because I took the points manually, I had to be very careful - a skill I don't usually possess but needed in research.

I think I just had a good start of the semester because of this activity. This activity slapped me hard in the face just to remind me that I should never forget everything that I learned and passed on to me in research. A helpful way to start my thesis year. :)


For this activity, I rate myself an 8 for doing my best despite the fact that I was not able to think of the solution to the problem on my own. Anyway, this is just the first. I'll improve next time. :)


The original graph used was from the PhD Dissertation in Physics of Minella C. Alarcon entitled Optical Remote Sensing using Low-Loss Optical Fiber Link in the Near Infrared Region last 1986.