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Debugging my app I have noticed that minRepDistance inside detectCharucoDiamond is growing in squared proportion to the image width, and then its value is squared again for the thresholding using closestCandidateDistance inside of refineDetectedMarkers. So to supress this escalation 'to the fourth' of the image size, I have implemented the following patch in charuco.cpp (in the aruco module folder)

--- charuco.cpp 2017-08-09 14:01:38.583984613 +0200
+++ charuco.1.cpp   2017-08-09 14:01:08.972215628 +0200 @@ -738,7
+738,7 @@

     CV_Assert(_markerIds.total() > 0 && _markerIds.total() ==
_markerCorners.total());

-    const float minRepDistanceRate = 0.12f;
+    const float minRepDistanceRate = 1.3024550356922115f;

     // create Charuco board layout for diamond (3x3 layout)
     Ptr<Dictionary> dict = getPredefinedDictionary(PREDEFINED_DICTIONARY_NAME(0)); @@ -771,7 +771,7 @@
           perimeterSq += edge.x*edge.x + edge.y*edge.y;
         }
         // maximum reprojection error relative to perimeter
-        float minRepDistance = perimeterSq * minRepDistanceRate * minRepDistanceRate;
+        float minRepDistance = sqrt(perimeterSq) * minRepDistanceRate;

         int currentId = _markerIds.getMat().at< int >(i);

I came out with that (unneccesarily long) float minRepDistanceRate by trying to maintain the same threashold for a resolution of 640x480 when making the minRepDistance not quadratic anymore. Now when using it for 1920x1080, it works great!