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I am new to Mathematica and trying to figure out whether it is a good tool for algorithmic exploration. So I had the idea of implementing a simple OCR with Mathematica, just using standard algorithms.

I have this picture: Block of text

I'd like to apply the following steps:

  1. Finding the cells of the picture: Could one use a voronoi algorithm to recognize the grid in the picture?

After having the cells I'd like to apply these steps to each:

  1. Use Thinning to find the skeleton of the character.
  2. Use EditDistance to compare the character to a skeletized version of every possible character and then select the character which is closest.

I have seen in the documentation that Mathematica has all these algorithms I am just not sure whether it would actually be feasible to do what I want.

(If it's impossible to do without knowing the name of the font I used: It's "Osaka, Regular-Mono, 144 pt".)

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  • $\begingroup$ Yes, it's feasible. Can you show us your initial code? $\endgroup$ Commented Oct 15, 2012 at 21:48
  • $\begingroup$ I have no code, alas. E.g. VoronoiDiagram[] expects a list of points, so I would need to somehow convert all my characters to points. Maybe there is a similar function that works directly on images? (Partition?). Once I have an image for each character, I could loop over them (via Table[]) and then apply Thinning[image]. EditDistance[] expects a vector. I would need to create that vector by making changes to a picture and then comparing for equality, not sure if I could do that in Mathematica on a pixel or vector level (Thinning[] only returns an image right? Not the vector data). $\endgroup$
    – Sven K
    Commented Oct 15, 2012 at 22:00
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    $\begingroup$ Look at the help for ImageCorrelate, under Applications i.sstatic.net/3tjDp.png $\endgroup$ Commented Oct 15, 2012 at 22:09
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    $\begingroup$ @belisarius just hope he's not looking for Schroedinger or Wilson $\endgroup$
    – acl
    Commented Oct 15, 2012 at 23:24
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    $\begingroup$ @acl Everybody knows Schrödinger. He is the one with the Cheshire Cat on his lap. $\endgroup$ Commented Oct 15, 2012 at 23:44

1 Answer 1

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Ok, here is a rather raw intent:

(*define a template font*)
i = Rasterize@Style[" A B C D E F G H I J K L M N O P Q R S T U V W X Y Z ",  
                   FontFamily -> "Courier", FontSize -> 24];

(*separate characters*)
cn = ColorNegate /@ Flatten@ImagePartition[i, ImageDimensions[i]/{26, 1}]

(*define a function for size adjustment*)
let[u_] := Function[{x}, ImageTake[x, Sequence @@ Reverse@Transpose@(u + 
                    ComponentMeasurements[x, "BoundingBox"][[1, 2]])]][#] & /@ cn;

(*set of images for size scaling *)
forSize = let[0];

(*set of images for matching*)
forMatch = let[3 {{-1, -1}, {1, 1}}];

(*Mean template char size*)
sz = N@Mean[ImageDimensions /@ forSize]

(*----------------------*)
(*Now test it*)
i1 = ColorNegate@Rasterize[
   Style[" M Y  L I T T L E  H O U S E  I N  T H E   P R A I R I E   \
                            W A S   A   M E S S   O F   R A T S   A N D  B A T S  ", 
    FontFamily -> "Courier", FontSize -> 25], ImageSize -> 1000]

(* Compute a size factor*)
sizeFactor = -Mean[Mean[Subtract@@@(Range@38/. ComponentMeasurements[i1, "BoundingBox"])]/sz];

(* resize the image to match the template's char size*)
r = Rasterize[i1, ImageSize -> ImageDimensions@i1/sizeFactor];

(*Perform the matching*)
c[t_] := List @@ (ColorData[60][t[[1]]]);
xx = (ImageCorrelate[ r, #, NormalizedSquaredEuclideanDistance] & /@ (Binarize /@ forMatch));
cc = MapIndexed[ImageMultiply[
     With[{k = c[#2]}, Image@Array[k &, Reverse@ImageDimensions[#1]]],
      Dilation[Binarize[ColorNegate@#1, 0.8], DiskMatrix[15]]] &, xx];
rcc = Image[ImageAdd[cc[[#]], r], ImageSize -> {849, 60}] & /@  Range@Length@forMatch;
Fold[ImageAdd[#1, #2] &, rcc[[1]], rcc]

As you can see below the results aren't perfect. There are two obvious improvements to test:

  1. Accept a match after comparing the goodness of all other matchings over a character
  2. Refine the sensibility (0.95 in this test)

Mathematica graphics

Mathematica graphics

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    $\begingroup$ looks good, but it may not be copy/pasting correctly: "ImageCorrelate::klcst: The distance function NormalizedSquaredEuclideanDistance is not defined for constant kernels. >>" $\endgroup$
    – cormullion
    Commented Oct 17, 2012 at 8:38
  • $\begingroup$ @cormullion Believe it or not, the culprit is the window size of the notebbok. I never saw something like this! Trying to fix it. $\endgroup$ Commented Oct 17, 2012 at 10:45

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