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How to find the angular coordinates of a rectangle in an image

I got this image after preprocessing the original image. Now, my question is how can I get the four angular coordinates of the rectangle (the largest). Sorry if this asks the question.

enter image description here

Update: since I am developing OpenCV, I ended up using this answer

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1 answer

One easy way:

  • find all connected components
  • calculate convex hull for each component
  • select the component where the convex hull has the largest area
  • simplify the polygon of a convex hull
  • the vertices of the simplified polygon are the points you are looking for.

Quick & dirty Mathematica solution:

(* find all connected components, calculate the convex hull for each component *)
convexHulls = ComponentMeasurements[ColorNegate[Binarize[src]], {"ConvexArea", "ConvexVertices"}];

(* pick the component where the convex hull has the largest area *)
vertices = SortBy[convexHulls[[All, 2]], First][[-1, 2]]

(* simplify the convex hull polygon, by iteratively removing the vertex with the lowest distance to the line through the vertex before and after it *)
distanceToNeighbors[vertices_] := MapThread[Abs[(#1 - #2).Cross[#1 - #3]/Norm[#1 - #3]]&, RotateLeft[vertices, #] & /@ {-1, 0, 1}]
removeVertexWithLowestDistance[vertices_] := With[{removeIndex = Ordering[distanceToNeighbors[vertices], 1]}, Drop[vertices, removeIndex]]
verticesSimplified = NestWhile[removeVertexWithLowestDistance, vertices, Min[distanceToNeighbors[#]] < 10&]

(* the vertices of the simplified polygon are the points you're looking for *)
Show[src, Graphics[
  {
   {EdgeForm[Red], Transparent, Polygon[verticesSimplified]},
   {Red, PointSize[Large], Point[verticesSimplified]}
   }]]

Result

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