Problem when extracting data of a closed curve from a black and white image: how to find the correct transformation of coordinates?

Question

I am trying to extract the data of the closed curve from a black and white image.

But the coordinates of the curve I extraced are wrong, as seen in my result .

For example, the x-coordinate of my result ranges from -150 to 0, which is different from the true range, i.e., -6 to 6.

I found some very useful discussions here about extracting data from images.

However, when I tried to apply the techniques discussed to extract data from a black and white image, the results were incorrect.

Here is my naive try. Where did I go wrong?

It seems I didn't find a correct transformation?

Any suggestions? Thank you.

imgImport = Import["https://i.sstatic.net/c0KCa.png"];
img = ImageTake[imgImport, {55, 286}, {125, 469}]

cor = ImageValuePositions[img, {0., 0., 0.}];
{o, x, y} = {{6.56169201921564`, 
    22.11360816415005`}, {28.934949660676992`, 
    5.2325141690732515`}, {6.679185088841892`, 6.554693779835269`}};
trans = FindGeometricTransform[{o, y}, {{-6, -14}, {-6, 16}}][[2]];

ListPlot[trans /@ cor]

Answer 1

Here is an approximation.

Identify axes

ls = ImageLines[ColorNegate@imgImport, .2];
HighlightImage[imgImport, ls]

Find the origin

origin = Flatten[MeshPrimitives[RegionIntersection[MeshRegion /@ ls], 0] /. 
   Point -> List]
  (* {111.145, 85.2972} *)

Crop the image at the axes

{w, h} = ImageDimensions[imgImport];
img = ImageTake[imgImport, {0, h - origin[[2]]}, {origin[[1]], w}]

Get the coordinates from the cropped image and transform according to a manual inspection of the axes

d = ImageValuePositions[img, {0., 0., 0.}];
{w2, h2} = ImageDimensions[img];
dtxf = {(#[[1]]/w2) 12 - 6, (#[[2]]/h2) 34 - 16} & /@ d;

ListPlot[dtxf, AspectRatio -> 1]