Locating the end points of a bridge-like structure in an image

Question

How do I locate the end points of a bridge-like structure in an image?

Below is a generalized representation.

Answer 1

Here you have a code example in Mathematica, probably not optimal:

f[i_] := 
   Module[{t, i2, w, z, neighbours, i3, cRed}, 
  (t = Thinning[ColorNegate@i, 15]; 
   i2 = ImageData@Binarize[ DeleteSmallComponents[
        ImageSubtract[t, Dilation[Erosion[t, 1], 1]], 100], .1];

    For[w = 2, w < Dimensions[i2][[1]], w++,
     For[z = 2, z < Dimensions[i2][[2]], z++,
      If[i2[[w, z]] == 1 && i2[[w + 1, z + 1]] == 1, 
         i2[[w, z + 1]] = i2[[w + 1, z]] = 0];
      If[i2[[w, z]] == i2[[w - 1, z - 1]] == 1, 
         i2[[w, z - 1]] = i2[[w - 1, z]] = 0];
      If[i2[[w, z]] == i2[[w + 1, z - 1]] == 1, 
         i2[[w, z - 1]] = i2[[w + 1, z]] = 0];
      If[i2[[w, z]] == i2[[w - 1, z + 1]] == 1, 
         i2[[w, z + 1]] = i2[[w - 1, z]] = 0];
      ]
     ];

    neighbours[l_, k_, j_] := 
      l[[k - 1, j]] +     l[[k + 1, j]] +     l[[k, j + 1]] + l[[k, j - 1]] + 
      l[[k + 1, j + 1]] + l[[k + 1, j - 1]] + l[[k - 1, j + 1]] + 
      l[[k - 1, j - 1]];

    i3 = Table[
      If[i2[[w, z]] ==1,neighbours[i2, w, z], 0],{w,2,Dimensions[i2][[1]]-1}, 
                                                 {z,2,Dimensions[i2][[2]]-1}];
    cRed = 
     ColorNegate@Rasterize[Graphics[{Red, Disk[]}], ImageSize -> 15];

    ImageCompose[
     ImageCompose[i, 
      cRed, {#[[2]], Dimensions[i2][[1]] - #[[1]]} &@
       Position[i3, 1][[1]]], 
      cRed, {#[[2]], Dimensions[i2][[1]] - #[[1]]} &@
       Position[i3, 1][[2]]])];