This example shows how to use imfindcircles to automatically detect circles or circular objects in an image. It also shows the use of viscircles to visualize the detected circles.
Step 1: Load Image
This example uses an image of round plastic chips of various colors.
rgb = imread('coloredChips.png');
figure
imshow(rgb)
Besides
having plenty of circles to detect, there are a few interesting things
going on in this image from a circle detection point-of-view:
- There are chips of different colors, which have different contrasts with respect to the background. On one end, the blue and red ones have strong contrast on this background. On the other end, some of the yellow chips do not contrast well with the background.
- Notice how some chips are on top of each other and some others that are close together and almost touching each other. Overlapping object boundaries and object occlusion are usually challenging scenarios for object detection.
Step 2: Determine Radius Range for Searching Circles
imfindcircles needs a radius range to search for the
circles. A quick way to find the appropriate radius range is to use the
interactive tool imdistline to get an approximate estimate of the radii of various objects.
d = imdistline;
imdistline
creates a draggable tool that can be moved to fit across a chip and the
numbers can be read to get an approximate estimate of its radius. Most
chips have radius in the range of 21-23 pixels. Use a slightly larger
radius range of 20-25 pixels just to be sure. Before that remove the imdistline tool.
delete(d);
Step 3: Initial Attempt to Find Circles
Call imfindcircles on this image with the search radius of
[20 25] pixels. Before that, it is a good practice to ask whether the
objects are brighter or darker than the background. To answer that
question, look at the grayscale version of this image.
gray_image = rgb2gray(rgb); imshow(gray_image);
The background is quite bright and most of the chips are darker than the background. But, by default, imfindcircles finds circular objects that are brighter than the background. So, set the parameter 'ObjectPolarity' to 'dark' in imfindcircles to search for dark circles.
[centers, radii] = imfindcircles(rgb,[20 25],'ObjectPolarity','dark')
centers =
[]
radii =
[]
Note that the outputs centers and radii are empty, which means that no circles were found. This happens frequently because imfindcircles is a circle detector, and similar to most detectors, imfindcircles has an internal detection threshold
that determines its sensitivity. In simple terms it means that the
detector's confidence in a certain (circle) detection has to be greater
than a certain level before it is considered a valid detection. imfindcircles
has a parameter 'Sensitivity' which can be used to control this
internal threshold, and consequently, the sensitivity of the algorithm. A
higher 'Sensitivity' value sets the detection threshold lower and leads
to detecting more circles. This is similar to the sensitivity control
on the motion detectors used in home security systems.
Step 4: Increase Detection Sensitivity
Coming back to the chip image, it is possible that at the default
sensitivity level all the circles are lower than the internal threshold,
which is why no circles were detected. By default, 'Sensitivity', which
is a number between 0 and 1, is set to 0.85. Increase 'Sensitivity' to
0.9.
[centers, radii] = imfindcircles(rgb,[20 25],'ObjectPolarity','dark', ... 'Sensitivity',0.9)
centers = 146.1895 198.5824 328.8132 135.5883 130.3134 43.8039 175.2698 297.0583 312.2831 192.3709 327.1316 297.0077 243.9893 166.4538 271.5873 280.8920 radii = 23.1604 22.5710 22.9576 23.7356 22.9551 22.9995 22.9055 23.0298
This time imfindcircles found some circles - eight to be precise. centers contains the locations of circle centers and radii contains the estimated radii of those circles.
Step 5: Draw the Circles on the Image
The function viscircles can be used to draw circles on the image. Output variables centers and radii from imfindcircles can be passed directly to viscircles.
imshow(rgb); h = viscircles(centers,radii);
The
circle centers seem correctly positioned and their corresponding radii
seem to match well to the actual chips. But still quite a few chips were
missed. Try increasing the 'Sensitivity' even more, to 0.92.
[centers, radii] = imfindcircles(rgb,[20 25],'ObjectPolarity','dark', ... 'Sensitivity',0.92); length(centers)
ans =
16
So increasing 'Sensitivity' gets us even more circles. Plot these circles on the image again.
delete(h); % Delete previously drawn circles
h = viscircles(centers,radii);
Step 6: Use the Second Method (Two-stage) for Finding Circles
This result looks better. Now, under the hood, imfindcircles has two different methods for finding circles. So far the default method, called the phase coding method, was used for detecting circles. There's another method, popularly called the two-stage method, that is available in imfindcircles. Use the two-stage method and show the results.
[centers, radii] = imfindcircles(rgb,[20 25], 'ObjectPolarity','dark', ... 'Sensitivity',0.92,'Method','twostage'); delete(h); h = viscircles(centers,radii);
The
two-stage method is detecting more circles, at the Sensitivity of 0.92.
In general, these two method are complementary in that have they have
different strengths. Phase coding method is typically faster and
slightly more robust to noise than the two-stage method. But it may also
need higher 'Sensitivity' levels to get the same number of detections
as the two-stage method. For example, the phase coding method also finds
the same chips if the 'Sensitivity' level is raised higher, say to
0.95.
[centers, radii] = imfindcircles(rgb,[20 25], 'ObjectPolarity','dark', ... 'Sensitivity',0.95,'Method','twostage'); delete(h); viscircles(centers,radii);
Note that both the methods in imfindcircles find the centers and radii of the partially visible (occluded) chips accurately.
Step 7: Why are Some Circles Still Getting Missed?
Looking at the last result, it is curious that imfindcircles
does not find the yellow chips in the image. The yellow chips do not
have strong contrast with the background. In fact they seem to have very
similar intensities as the background. Is it possible that the yellow
chips are not really 'darker' than the background as was assumed? To
confirm, show the grayscale version of this image again.
imshow(gray_image);
Step 8: Find 'Bright' Circles in the Image
Indeed! The yellow chips are almost the same intensity, maybe even
brighter, as compared to the background. Therefore, to detect the yellow
chips, change 'ObjectPolarity' to 'bright'.
[centersBright, radiiBright] = imfindcircles(rgb,[20 25],'ObjectPolarity', ... 'bright','Sensitivity',0.92);
Step 9: Draw 'Bright' Circles with Different Color
Draw the bright circles in a different color, say blue, by changing the 'Color' parameter in viscircles.
imshow(rgb); hBright = viscircles(centersBright, radiiBright,'Color','b');
Three
of the missing yellow chips were found. One yellow chip is still
missing. These yellow ones are hard to find because of they don't stand out as well as others on this background.
Step 10: Lower the Value of 'EdgeThreshold'
There is another parameter in imfindcircles which may be useful here, namely 'EdgeThreshold'. To find circles, imfindcircles
uses only the edge pixels in the image. These edge pixels are
essentially pixels with high gradient value. The 'EdgeThreshold'
parameter controls how high the gradient value at a pixel has to
be before it is considered an edge pixel and included in computation. A
high value (closer to 1) for this parameter will allow only the strong
edges (higher gradient values) to be included, whereas a low value
(closer to 0) is more permissive and includes even the weaker edges
(lower gradient values) in computation. In case of the missing yellow
chip, since the contrast is low, some of the boundary pixels (on the
circumference of the chip) are expected to have low gradient values.
Therefore, lower the 'EdgeThreshold' parameter to ensure that the most
of the edge pixels for the yellow chip are included in computation.
[centersBright, radiiBright, metricBright] = imfindcircles(rgb,[20 25], ... 'ObjectPolarity','bright','Sensitivity',0.92,'EdgeThreshold',0.1); delete(hBright); hBright = viscircles(centersBright, radiiBright,'Color','b');
Step 11: Draw 'Dark' and 'Bright' Circles Together
Now imfindcircles finds all of the yellow ones, and a green
one too. Draw these chips in blue, together with the other chips that
were found earlier (with 'ObjectPolarity' set to 'dark'), in red.
h = viscircles(centers,radii);
All
the circles are detected. A final word - it should be noted that
changing the parameters to be more aggressive in detection may find more
circles, but it also increases the likelihood of detecting false
circles. There is a trade-off between the number of true circles that
can be found (detection rate) and the number of false circles that are
found with them (false alarm rate).
Happy circle hunting!