Find circles using circular Hough transform
Read the image into the workspace and display it.
A = imread('coins.png'); imshow(A)
Find all the circles with radius r such that 15 ≤ r ≤ 30.
[centers, radii, metric] = imfindcircles(A,[15 30]);
Retain the five strongest circles according to the metric values.
centersStrong5 = centers(1:5,:); radiiStrong5 = radii(1:5); metricStrong5 = metric(1:5);
Draw the five strongest circle perimeters.
Read the image into the workspace and display it.
A = imread('circlesBrightDark.png'); imshow(A)
Define the radius range.
Rmin = 30; Rmax = 65;
Find all the bright circles in the image within the radius range.
[centersBright, radiiBright] = imfindcircles(A,[Rmin Rmax],'ObjectPolarity','bright');
Find all the dark circles in the image within the radius range.
[centersDark, radiiDark] = imfindcircles(A,[Rmin Rmax],'ObjectPolarity','dark');
Plot bright circles in blue.
Plot dark circles in dashed red boundaries.
A— Input imagegrayscale image | truecolor image | binary image
Input image is the image in which to detect circular objects, specified as a grayscale, truecolor, or binary image.
radius— Circle radiusscalar numeric
Circle radius is the approximate radius of the circular objects you want to detect, specified as a scalar of any numeric type.
radiusRange— Range of radii two-element vector of integers
Range of radii for the circular objects you want to detect,
specified as a two-element vector,
of integers of any numeric type.
Specify optional comma-separated pairs of
Name is the argument
Value is the corresponding
Name must appear
inside single quotes (
You can specify several name and value pair
arguments in any order as
'ObjectPolarity','bright'specifies bright circular objects on a dark background.
'ObjectPolarity'— Object polarity
Object polarity indicates whether the circular objects are brighter
or darker than the background, specified as the comma-separated pair
'ObjectPolarity' and either of the
text strings in the following table.
|The circular objects are brighter than the background.|
|The circular objects are darker than the background.|
bright circular objects on a dark background.
'Method'— Computation method
Computation method is the technique used to compute the accumulator
array, specified as the comma-separated pair consisting of
either of the text strings in the following table.
|Atherton and Kerbyson's  phase coding method . This is the default.|
|The method used in two-stage circular Hough transform , .|
'Method','PhaseCode' specifies the
Atherton and Kerbyson's phase coding method.
'Sensitivity'— Sensitivity factor0.85 (default) | nonnegative scalar between 0 and 1
Sensitivity factor is the sensitivity for the circular Hough
transform accumulator array, specified as the comma-separated pair
'Sensitivity' and a nonnegative scalar
value in the range
[0,1]. As you increase the sensitivity
imfindcircles detects more circular objects,
including weak and partially obscured circles. Higher sensitivity
values also increase the risk of false detection.
'Sensitivity',0.3 sets the sensitivity
'EdgeThreshold'— Edge gradient thresholdnonnegative scalar between 0 and 1
Edge gradient threshold sets the gradient threshold for determining
edge pixels in the image, specified as the comma-separated pair consisting
'EdgeThreshold' and a nonnegative scalar value
in the range
set the threshold to zero-gradient magnitude. Specify
set the threshold to the maximum gradient magnitude.
more circular objects (with both weak and strong edges) when you set
the threshold to a lower value. It detects fewer circles with weak
edges as you increase the value of the threshold. By default,
the edge gradient threshold automatically using the function
'EdgeThreshold',0.5 sets the edge
gradient threshold to
centers— Coordinates of circle centerstwo-column matrix
Coordinates of the circle centers, returned as a
containing the x-coordinates of the circle centers
in the first column and the y-coordinates in the
second column. The number of rows,
P, is the number
of circles detected.
centers is sorted based on
the strength of the circles.
radii— Estimated radiicolumn vector
The estimated radii for the circle centers, returned as a column
vector. The radius value at
radii(j) corresponds to the circle centered at
metric— Circle strengthscolumn vector
Circle strengths is the relative strengths for the circle centers,
returned as a vector. The value at
metric(j) corresponds to the circle with radius
radii(j) centered at
Specify a relatively small
better accuracy. A good rule of thumb is to choose
rmax < 3*rmin and
The accuracy of
limited when the value of
is less than 10.
The radius estimation step is typically faster if
you use the (default)
'PhaseCode' method instead
Both computation methods,
limited in their ability to detect concentric circles. The results
for concentric circles can vary depending on the input image.
imfindcircles does not find circles
with centers outside the domain of the image.
imfindcircles preprocesses binary
(logical) images to improve the accuracy of the result. It converts
truecolor images to grayscale using the function
rgb2gray before processing them.
imfindcircles uses a Circular
Hough Transform (CHT) based algorithm for finding circles in images.
This approach is used because of its robustness in the presence of
noise, occlusion and varying illumination.
The CHT is not a rigorously specified algorithm, rather there are a number of different approaches that can be taken in its implementation. However, by and large, there are three essential steps which are common to all.
Accumulator Array Computation.
Foreground pixels of high gradient are designated as being candidate pixels and are allowed to cast ‘votes' in the accumulator array. In a classical CHT implementation, the candidate pixels vote in pattern around them that forms a full circle of a fixed radius. Figure 1a shows an example of a candidate pixel lying on an actual circle (solid circle) and the classical CHT voting pattern (dashed circles) for the candidate pixel.
Figure 1: classical CHT voting pattern
The votes of candidate pixels belonging to an image circle tend to accumulate at the accumulator array bin corresponding to the circle's center. Therefore, the circle centers are estimated by detecting the peaks in the accumulator array. Figure 1b shows an example of the candidate pixels (solid dots) lying on an actual circle (solid circle), and their voting patterns (dashed circles) which coincide at the center of the actual circle.
If the same accumulator array is used for more than one radius value, as is commonly done in CHT algorithms, radii of the detected circles have to be estimated as a separate step.
imfindcircles provides two algorithms
for finding circles in images: Phase-Coding (default) and Two-Stage.
Both share some common computational steps, but each has its own unique
aspects as well.
The common computational features shared by both algorithms are as follow:
Use of 2-D Accumulator Array:
The classical Hough Transform requires a 3-D array for storing votes for multiple radii, which results in large storage requirements and long processing times. Both the Phase-Coding and Two-Stage methods solve this problem by using a single 2-D accumulator array for all the radii. Although this approach requires an additional step of radius estimation, the overall computational load is typically lower, especially when working over large radius range. This is a widely adopted practice in modern CHT implementations.
Use of Edge Pixels
Overall memory requirements and speed is strongly governed by the number of candidate pixels. To limit their number, the gradient magnitude of the input image is threshold so that only pixels of high gradient are included in tallying votes.
Use of Edge Orientation Information:
Another way to optimize performance is to restrict the number of bins available to candidate pixels. This is accomplished by utilizing locally available edge information to only permit voting in a limited interval along direction of the gradient (Figure 2).
Figure 2: Voting mode: multiple radii, along direction of the gradient
|rmin||Minimum search radius|
|rmax||Maximum search radius|
|ractual||Radius of the circle that the candidate pixel belongs to|
|cmin||Center of the circle of radius rmin|
|cmax||Center of the circle of radius rmax|
|cactual||Center of the circle of radius ractual|
The two CHT methods employed by function
differ in the manner by which the circle radii are computed.
Radii are explicitly estimated utilizing the estimated circle centers along with image information. The technique is based on computing radial histograms; see references 1 & 2 for a detailed explanation.
The key idea in Phase Coding is the use of complex values in the accumulator array with the radius information encoded in the phase of the array entries. The votes cast by the edge pixels contain information not only about the possible center locations but also about the radius of the circle associated with the center location. Unlike the Two-Stage method where radius has to be estimated explicitly using radial histograms, in Phase Coding the radius can be estimated by simply decoding the phase information from the estimated center location in the accumulator array. (see reference 3).
 T.J Atherton, D.J. Kerbyson. "Size invariant circle detection." Image and Vision Computing. Volume 17, Number 11, 1999, pp. 795-803.
 H.K Yuen, .J. Princen, J. Illingworth, and J. Kittler. "Comparative study of Hough transform methods for circle finding." Image and Vision Computing. Volume 8, Number 1, 1990, pp. 71–77.
 E.R. Davies, Machine Vision: Theory, Algorithms, Practicalities. Chapter 10. 3rd Edition. Morgan Kauffman Publishers, 2005,