Aug 6, 2014

I have an image which i have reduced to a mathematical representation of light intensities. We can consider each cell in my spreadsheet as a pixel, the value within the cell corresponding to how much light that pixel it took in during an exposure. There is a trend along the pixels that i would like to isolate as exactly as possible: a diagonal line, not quite straight from the bottom left corner to the top right.

What I would like to do, if possible, is to treat each cell in my spreadsheet as a point on a coordinate plane, and to use some type of formula or macro to give me a line of best fit using the positions of the highest valued cells as the data points in my extrapolation.

The tool I'm looking for would take data organized like this:

1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 200 1 1 1

1 1 1 1 1 1 200 1 1 1 1

1 1 1 1 1 200 1 1 1 1 1

1 1 1 1 200 1 1 1 1 1 1

1 1 1 200 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1 1 1

And give me an equation of the form y=1x + b (describing where to find the maximum values among the cells), although my actually data will need to be fit to a higher order polynomial.

Once I can do this, I will also need a way to take perpendicular sums automatically along the line of best fit at distance of two pixels in both directions and a width of one pixel. You can imagine drawing a rectangular box perpendicular to the line of maximum values and adding the proportions of each cell enclosed by that box. This means that for the example above, i would get 209 for all five points of interest: the maximum value plus the two values of one in the upper left perpendicular direction, the two values of one in the lower right perpendicular direction, half the values of the two cells neighboring the exactly perpendicular cells and a quarter of the outermost cells touched by our imaginary pixel box.

The following image may be useful in clarifying what I'm looking for. The red bar represents the imaginary box containing perpendicular pixel sums, where the green beam is the line of best fit derived from my maximum values.

Attachment 337419

Also, here is a snippet of my actual data to experiment with in solving these strange and exotic problems

Attachment 337420

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