Charlie-san,

I'm sorry I've not built an abnormal route in my tool. I don't know if the following is the problem you're facing, but an endless loop may occur when locator2coordinate function does not have unique solution from given two red points.

You may avoid the loop by changing the function to the following. Please change the location of two red points and try again.

locator2coordinate[list_, sample_] := 
 Module[{l1x, l1y, l2x, l2y, s1x, s1y, s2x, s2y, d, c, ysolve, xlist, 
   ylist},
  {l1x, l1y} = list[[1]]; {l2x, l2y} = list[[2]];
  If[l1x === l2x || l1y === l2y, Beep[]; Return[{}]];
  {s1x, s1y} = sample[[1]]; {s2x, s2y} = sample[[2]];
  ysolve = Solve[d*l1y + c == s1y && d*l2y + c == s2y, {d, c}];
  {{d, c}} = {d, c} /. ysolve;
  ({Exp[(#[[1]] - l1x)/(l2x - l1x)*(Log[s2x] - Log[s1x]) + Log[s1x]], 
       d*#[[2]] + c} & /@ list) // Sort
  ]

Charlie-san,

Thanks for your comment. To work for graphs that have a logarithmic scaling on the x-axis, change the locator2coordinate function below.

locator2coordinate[list_, sample_] := 
 Module[{l1x, l1y, l2x, l2y, s1x, s1y, s2x, s2y, d, c, ysolve, xlist, 
   ylist},
  {l1x, l1y} = list[[1]]; {l2x, l2y} = list[[2]];
  {s1x, s1y} = sample[[1]]; {s2x, s2y} = sample[[2]];
  ysolve = Solve[d*l1y + c == s1y && d*l2y + c == s2y, {d, c}];
  {{d, c}} = {d, c} /. ysolve;
  ({Exp[(#[[1]] - l1x)/(l2x - l1x)*(Log[s2x] - Log[s1x]) + Log[s1x]], 
       d*#[[2]] + c} & /@ list) // Sort
  ]

This is my result of your example.

For your reference:

• GraphImage2List for multi-colored graph-image-data
• GraphImage2List : more automatically
• presentation(Japanese) at Wolfram Conference Japan 2018

- Congratulations! This post is now a Staff Pick as distinguished by a badge on your profile! Thank you, keep it coming!