17
$\begingroup$

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

$\endgroup$
  • 2
    $\begingroup$ Anyone would have a method that doesn’t first rasterize the text? $\endgroup$ – F'x Apr 1 '12 at 18:13
21
$\begingroup$

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

$\endgroup$
15
$\begingroup$

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

$\endgroup$
11
$\begingroup$

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

$\endgroup$
9
$\begingroup$

In Version 10, this can be elegantly done in one line. First we create some text (stealing from @kguler) as follows:

img = Image[Graphics[Text[Style["'., ab cgixyz,...", Green, FontFamily -> "Times", 
                 FontSize -> 72]]], ImageSize -> {600, 100}];

Then:

cvx = ConvexHullMesh @ ImageValuePositions[EdgeDetect[img, 3], White];

Visualize:

Show[img, Graphics[GraphicsComplex[MeshCoordinates[cvx], {Thick, Red, MeshCells[cvx, 1]}]]]

Mathematica graphics

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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