How to find circular objects in an image?

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:

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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
This blog post might be useful. – VLC Oct 8 '12 at 11:06
Also this one – cormullion Oct 8 '12 at 12:01
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

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"]


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


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]
]
]


{, , , , }

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,
minhoughvoxels_Integer: 4] :=
Module[{edgeimage, hough3dbin, hough3dbinlabels, coords, arraydim},

edgeimage =
SelectComponents[
DeleteBorderComponents[
],
"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]][#] &,
]
]
],
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];

ParallelMap[
Function[{level, offx, offy},
ImageMultiply[
image,
{{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]


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
]


Here we find two more or less concentric hits.

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


Oblique views are a matter of luck, of course.

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


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
]


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.

-
Very nice. Perhaps a link to a good explanation of the Circular Hough Transform may help future readers – Dr. 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
This is realy great, but I fail at getting the coordinates of the circles: eg. if I take coords[[All,{2,3}]] and place them with points on the image, they don't align with the circles I then obtain with ParallelMap that follows... Probably this is just me being dumb, sorry, but some help? – mgm Aug 4 '15 at 9:49
@mgm Run this, I guess you will notice how differently coordinates may need to be handled: Module[{image, coords = {{2, 2}, {10, 20}, {20, 30}, {30, 40}}, corrcoords, data}, image = Import["ExampleData/rose.gif"]; corrcoords = Map[{#[[1]], ImageDimensions[image][[2]] + 1 - #[[2]]} &, Reverse[coords, 2]]; Map[(image = ImageCompose[image, Graphics[{Red, PointSize[0.05], Point[{0, 0}]}], # - {1, 0}]) &, corrcoords]; data = ImageData[image]; Map[(data[[#[[1]] - 1 ;; #[[1]] + 1, #[[2]] - 1 ;; #[[2]] + 1]] = Table[{0, 0, 1}, {3}, {3}]) &, coords]; Image@data ] – UDB Aug 22 '15 at 12:39

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"}))]


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 – Dr. 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 :) – Dr. belisarius Oct 8 '12 at 17:58
will an amphibian do? – cormullion Oct 8 '12 at 18:59

Basically, you import the image:

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


Tidy it up:

mb = MorphologicalBinarize[i]


Isolate the areas of interest:

cn = ColorNegate[Closing [mb, 10]]


Use component analysis:

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


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

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


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