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How could I use morphological processing to find circular objects in an image? More specifically, I need to detect road signs.

I need to get the "80 speed limit" sign from this image:

enter image description here

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3  
Welcome to Mathematica.SE, Elfet! It would help if you described what you have tried so far and where you got stuck. –  Verbeia Oct 8 '12 at 10:47
5  
This blog post might be useful. –  VLC Oct 8 '12 at 11:06
2  
Also this one –  cormullion Oct 8 '12 at 12:01
2  
Because the road signs will rarely be seen head-on, you probably want to generalize the question to detecting elliptical objects--perhaps just ellipses with near-vertical major axes. –  whuber Oct 8 '12 at 16:13
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3 Answers

Circular Hough Transform

I have had fun implementing a circular Hough transform based solution for this question (in part using some MMA9 Image3D functionality which has become available in between). By this shape-related approach we can overcome the color restrictions of the approaches tried so far.

The method starts with an edge detection, followed by a circular Hough transform (also see this Java applet demonstration, or these lecture slides, or this paper).

In the following this is demonstrated using a test picture (with inscribed radius numbers) taken from www.markschulze.net/java/hough/. For this implementation the core part is the extensive use of ListConvolve, while the convolution is being done using annulus-shaped kernels.

markschulze = Import["http://i.stack.imgur.com/XoqbW.png"]

Mathematica graphics

markschulzeedges=EdgeDetect[markschulze, 10, Method -> "Sobel"]

Mathematica graphics

ParallelMap[Image@
 Divide[
  ListConvolve[
   #, 
   ImageData@markschulzeedges, 
   Ceiling[(Length@#)/2]
  ],
  Total[#, 2]
 ] &, 
 Map[
  Function[{r}, DiskMatrix[r] - ArrayPad[DiskMatrix[r - 1], 1]][#] &, 
  Range[14, 18, 1]
 ]
]

{Mathematica graphics, Mathematica graphics, Mathematica graphics, Mathematica graphics, Mathematica graphics }

These five images represent the circular Hough transform within the radius interval [14,18].

In order to utilize the transform for circle or circular area detection this transform is both binarized and labeled. According to the detected coordinates of candidate circles inside the 3D Hough transform volume, radii and image positions are determined, so that masks for the original image can be computed:

HoughCircleDetection[image_Image, radiusmin_Integer: 1, 
   radiusmax_Integer: 40, edgedetectradius_Integer: 10, 
   minfitvalue_Real: .25, radiusstep_Integer: 1, 
   minhoughvoxels_Integer: 4] := 
  Module[{edgeimage, hough3dbin, hough3dbinlabels, coords, arraydim},

   edgeimage = 
    SelectComponents[
     DeleteBorderComponents[
      EdgeDetect[image, edgedetectradius, Method -> "Sobel"]
     ],
     "EnclosingComponentCount", # == 0 &
    ];

   hough3dbin = 
    DeleteSmallComponents[
     Image3D[
      ParallelMap[
       Binarize[Image@
        Divide[
         ListConvolve[#, ImageData@edgeimage, Ceiling[(Length@#)/2]], 
         Total[#, 2]
        ],
        minfitvalue
       ] &,
       Map[
        Function[{r}, DiskMatrix[r] - ArrayPad[DiskMatrix[r - 1], 1]][#] &, 
        Range[radiusmin, radiusmax, radiusstep]
       ]
      ]
     ],
     minhoughvoxels
    ];

   hough3dbinlabels = MorphologicalComponents[hough3dbin];

   coords = 
    ParallelMap[
     Round[Mean[Position[hough3dbinlabels, #]]] &, 
     Sort[Rest@Tally@Flatten@hough3dbinlabels, #1[[2]] > #2[[2]] &][[All, 1]]
    ];

   arraydim = Rest@Dimensions[hough3dbinlabels];

   Print["Radii: ", radiusmin + coords[[All, 1]] - 1];

   ParallelMap[
    Function[{level, offx, offy},
     ImageMultiply[
      image,
      Image@ArrayPad[
       DiskMatrix[radiusmin + level - 1],
       {{offx - radiusmin - level, First@arraydim - offx - radiusmin - level + 1},
        {offy - radiusmin - level, Last@arraydim - offy - radiusmin - level + 1}}
      ]
     ]
    ][Sequence @@ #] &,
    coords
   ]

  ];

Practically it is useful to restrict the method to eligible radii. Also, sometimes parameters, like the edge detection radius, and the minimum fit value might be adapted:

Show[ImageApply[Plus, HoughCircleDetection[#, 14, 18, 10, .3]], 
   ImageSize -> ImageDimensions[#]] &[markschulze]

Radii: {16,15,17,14,14}

Mathematica graphics

The method appears to work quite specifically, though 13 is included here.

Let us see the results for the four images already used above:

Show[ImageApply[Plus, HoughCircleDetection[Import["http://tinyurl.com/aw74tvc"], 30, 50]],
     ImageSize -> 200
]

Radii: {39,33}

Mathematica graphics

Here we find two more or less concentric hits.

Show[ImageApply[Plus, HoughCircleDetection[Import["http://tinyurl.com/aycppg4"], 20, 30, 
   15]],
    ImageSize -> 200
]

Radii: {22}

Mathematica graphics

Oblique views are a matter of luck, of course.

Show[ImageApply[Plus, HoughCircleDetection[Import["http://tinyurl.com/9vnfrko"], 20, 40]],
     ImageSize -> 200
]

Radii: {24,24,24,23,24,24,22,24,24,22,22,24,23,24,22,22,24}

Mathematica graphics

While the No-U-turn sign is missed, the stop sign is included...

Show[ImageApply[Plus, HoughCircleDetection[Import["http://tinyurl.com/bak4uzx"], 20, 60]],
     ImageSize -> 200
]

Radii: {54,38}

Mathematica graphics

For the No-parking sign again the inner and outer circle is found.

For real life applications like road sign detection, for reasons of robustness feature combination is always being recommended.

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Very nice. Perhaps a link to a good explanation of the Circular Hough Transform may help future readers –  belisarius Oct 22 '13 at 20:15
    
Thanks, have added some references, and also have added some more or less didactic example. Sorry for a wrong Floor call inside ListConvolve for kernel alignmend, this was replaced by a Ceiling now, so all resulting images were replaced as well (I noticed a strange shift, this is now gone). –  UDB Oct 23 '13 at 14:26
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The following method doesn't require parameters and discovers also oblique views.

obl[transit_Image] :=
  (SelectComponents[
      MorphologicalComponents[
       DeleteSmallComponents@ChanVeseBinarize[#, "TargetColor" -> Red],
       Method -> "ConvexHull"],
      {"Count", "SemiAxes"}, Abs[Times @@ #2 Pi - #1] < #1/100 &]) & @ transit;

GraphicsGrid[{#, obl@# // Colorize, ImageMultiply[#, Image@Unitize@obl@#]} & /@ 
  (Import /@ ("http://tinyurl.com/" <> # &/@ {"aw74tvc", "aycppg4", "9vnfrko", "bak4uzx"}))]

Mathematica graphics

If you want to detect non-reddish edged ellipses just remove the "TargetColor" -> Red option.

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That's more like it...! Will it work with red birds on signs, though? :) –  cormullion Oct 8 '12 at 16:19
    
@cormullion Your raven is one of my examples :D –  belisarius Oct 8 '12 at 17:07
    
:) I meant that, if the bird was bright red (like a parrot) it might upset things. But your code is too clever to be fooled, I think! –  cormullion Oct 8 '12 at 17:46
    
@cormullion Now we only have to find a photograph of a bright red bird sitting on a transit signal and test it :) –  belisarius Oct 8 '12 at 17:58
    
will an amphibian do? –  cormullion Oct 8 '12 at 18:59
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Basically, you import the image:

i = Import["http://upload.wikimedia.org/wikipedia/commons/2/2c/Crow_on_the_sign_of_no_parking.jpg"]

image from wikimedia

Tidy it up:

mb = MorphologicalBinarize[i]

mbinarize

Isolate the areas of interest:

cn = ColorNegate[Closing [mb, 10]]

color negate

Use component analysis:

sc = SelectComponents[
  cn, {"Eccentricity", 
   "Circularity"}, #1 < .5  && #2 < 0.8 &];
Colorize[sc]

select components

Now use this information to process your original image...

ImageApply[# * 0.25 &, i, Masking -> ColorNegate[sc]]

apply

Of course, I've cheated in this answer: to process arbitrary images - or to detect crows on road signs - is much much harder!

(I chose this image because, when I wrote this answer, you hadn't supplied your example.)

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This is good! Try to do this also for image in my question. Is there are is way to use EdgeDetect? –  Elfet Oct 8 '12 at 12:00
4  
Have a go, show us what happens ... :) –  cormullion Oct 8 '12 at 12:01
    
How now get using this information (Colorized) to select sign from original image? –  Elfet Oct 8 '12 at 12:34
    
have a look at some of the relevant tutorials and videos: reference.wolfram.com/mathematica/tutorial/ImageProcessing.html should be built-in to the help; wolfram.com/broadcast/video.php?channel=97&video=839 is a good video introduction –  cormullion Oct 8 '12 at 14:04
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