Take the 2-minute tour ×
Mathematica Stack Exchange is a question and answer site for users of Mathematica. It's 100% free, no registration required.

How can I get the co-ordinates of the convex hull of a piece of Text?

share|improve this question
2  
Anyone would have a method that doesn’t first rasterize the text? –  F'x Apr 1 '12 at 18:13
add comment

3 Answers

The question could be rephrased: how do we get a vector graphic from a bitmap? The solution is pretty simple by using the code we can find here.

p = Image[Graphics[Text[Style["Get Convex Hull points.", Large]]]];
img = Thinning@EdgeDetect@p;
points = N@Position[ImageData[img], 1];
pts = Union@Flatten[FindCurvePath[points] /. c_Integer :> points[[c]], 1];
Needs["ComputationalGeometry`"]
chp = ConvexHull[pts];
Show[
Graphics@{Red, Thick, Line[Append[pts[[chp]], pts[[chp]][[1]]]]},
ListPlot[pts]]

enter image description here

share|improve this answer
add comment

Another method:

text = Rasterize["Text"];
data = Position[text[[1, 1]], {0, 0, 0}];
rotated = RotationMatrix[90 Degree].# & /@ data;
data2D = {-#1, #2} & @@@ rotated;
<< ComputationalGeometry`
Quiet[convexhull = ConvexHull[data2D]];
hull = PlanarGraphPlot[data2D, convexhull];
Graphics[{Black, Point[data2D], hull[[1, 2]]}]

enter image description here

Working it a bit more:

t = Text[Style["Text", FontFamily -> "Times", FontSize -> 48]];
text = Rasterize[t, ImageResolution -> 80];
data = Position[text[[1, 1]], Table[Except@255, {3}]];
rotated = RotationMatrix[90 Degree].# & /@ data;
data2D = {-#1, #2} & @@@ rotated;
<< ComputationalGeometry`
Quiet[convexhull = ConvexHull[data2D]];
hull = PlanarGraphPlot[data2D, convexhull];
Graphics[{Black, Point[data2D], hull[[1, 2]]}]

enter image description here

{{xmin, xmax}, {ymin, ymax}} = {Min@#, Max@#} & /@ Transpose[data2D];
Graphics[{Black, 
  Inset[text, {xmin + (xmax - xmin)/2 - 1, ymin + (ymax - ymin)/2},
   Center, Reverse@Most[Dimensions[text[[1, 1]]]]],
  Red, hull[[1, 2]]}, 
 PlotRange -> {{xmin - 3, xmax + 3}, {ymin - 3, ymax + 3}}]

enter image description here

share|improve this answer
add comment

An alternative approach that does not require the ComputationalGeometry package: You can use a combination of ClusteringComponents and ComponentMeasurements as follows:

Define

  chVertices[txtimg_] := 
  Insert[#, First@#, -1] &@
  ComponentMeasurements[ClusteringComponents[Binarize@txtimg, 2], 
  "ConvexVertices"][[2, 2]]

Example data:

  textimg1 = Image[Graphics[
  Text[Style["'., ab cgixyz,...", Green, FontFamily -> "Times", FontSize -> 72]]], 
  ImageSize -> {600, 100}];
  textimg2 = Image[Graphics[{EdgeForm[], Brown, 
  ImportString[ExportString[
  Style[".t e q s t,", Italic, FontFamily -> "Times", FontSize -> 36], 
  "PDF"], "PDF", "TextMode" -> "Outlines"][[1, 1]]}], ImageSize -> {600, 100}];
  textimg3 = Image[Graphics[
  Text[Style["Get Convex Hull points.", Orange, 56]]], 
  ImageSize -> {600, 100}];

Input pictures:

input text images

Results:

 Row[Show[#, Graphics@{Red, Thick, Line[chVertices[#]]}] & 
 /@ {textimg1, textimg2, textimg3}]

enter image description here

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.