Width of plot profile at selected value

[coregis]

I'm new to plugins and Java, but I think what I'd like to accomplish should
be relatively simple in ImageJ. Please let me know if this can be done and
any potential pitfalls to look out for. And any advice would be greatly
appreciated.

I will have an RGB image with thick areas of darkness running across the
image against the background. I'd like to first open and use only the red
channel. I'd then like to transform the entire image's pixel values
according to a simple formula of the form y=1/(a+bx)+c or even a lookup
table. (I'm converting pixel values to another unit)

The user will draw one line across one area, and this first line will simply
establish an index value at the maximum across the line.

Then, the user will draw another line across a second area, and we calculate
the length of that line which was above the index value.

I hope this is clear- I have attached an example image with annotations.

Thanks for any advice.