first you have to determine the center, then you can map the use the equation 4 * pi * Area/(r2)

There are circle detection methods in computer vision, e.g.,

https://gist.github.com/martinsik/a3d6142b0392d77c13ab

https://dsp.stackexchange.com/questions/44152/detect-circles-in-image

Changming Sun,

Thanks for yor response. Both the links are informative.

In first link what I could understand that the shape is analysed by some in built Hough function in the program. In the second the same technique and fitting algorithms are reffered. Both are complex analysis with lots of calculation.

I am looking for any such algorithm which can do some simple computation on an image to understand its circularity.

Foran example, if radius of image is equal to the redius of equivalent circle, the image is ⭕️ circle.

Edge detection followed by Hough transform is used a lot.

In case you have a segmented blob, you could calculate the radius in two ways, using the area of the blob, and using the circumference of the blob.

Area = Pi x r x r

Circum = 2 x Pi x r

The more the two computed radii are alike, the more the blob is circular.

Lambert Zijp

great help. I am looking for such easy ways. Thank you For this clue.

Further to Lambert Zijp's suggestion, there is the concept of compactness or FormFactor which is defined as: (4 * pi * Area/Circum). For a circular object, this value is close to 1, otherwise this value is smaller.

4 * pi * Area/(Circum*Circum)

you can use the following code to identify the circles in an gray image

[centers,radii]=imfindcircles(rgb,[20 25],'ObjectPolarity','dark')

Further to Muhammad Rashid, which is the MATLAB function that applies the Hough transform cited by Lambert Zijp, you can do the same with the OpenCV library: https://docs.opencv.org/3.4/d4/d70/tutorial_hough_circle.html

As it is said, edge detection and Hough transform would be far enough. For color images, I also suggest you to use color differentiation. In this link: https://startthelifeyouwant.blogspot.com/2018/09/color-differentiation-by-rgb-to-hsi.html I told how to do it by transforming rgb images to HSI-HSV image then expose the color you want. After that, you can find the circles which have the specific color you want to find.

You can use saturation channel from the HSV colour space to segment the ball easily because it is yellow:

i=imread('ball.jpg');

ii=rgb2hsv(i);

bw = im2bw(ii(:,:,2),graythresh(ii));

Then you can get help from this link to identify the rounding metric:

https://uk.mathworks.com/help/images/identifying-round-objects.html;jsessionid=4f8d63bdb433cfc2c18b6bf7627e

You can apply several methods. One which usually works very well for circles is the so called *Hough transform*. In MATLAB, for instance, it is already implemented, you just have to use the *embedded* version.

I hope it might be of some help.

As they mentioned using the edge you get the circle.

If the question is how to prove that it is a circle in the science of images processing , you can follow the following steps:

After you get the edge image and convert the image into a binary image

Calculate the longest distance between points and it will be the diameter of the circle

Divide into the middle and extract its coordinates.

If the distant between points and the center are equal it is a circle.

If not equal it isnot a circle it is possible to be an oval

Dr. Zyad Al-Thalji

colour segmenation->canny edge detection-> Hough Algorithm to identify circle

first you have to determine the center, then you can map the use the equation 4 * pi * Area/(r2)

You use circular hough transform to basically identify circular objects in images.

You can use hough circles for that...

Visit this link for documentations:-

https://docs.opencv.org/2.4/doc/tutorials/imgproc/imgtrans/hough_circle/hough_circle.html

If the image is color, first you convert it to the grayscale; find edges of the objects in the image using a good edge detection method; check whether the object is closed. If it is closed, find distance from a pixel in the boundary to its straight opposite side of the boundary, similarly measure the distance in all directions. If all the distances are equal, then it can be concluded that the shape is circular. The distance can be identified as a diameter of the circle (closed shape).

Dr. K. Seetharaman , thank you for your response. It is a great help.

Can you please help me with some best established methods to check whether an object is closed or not?

Thank you

There have already been several answers.

If your input image has a good contrast, and less noise (including other lines or objects); then Canny edge is your best bet. It will look for best continuity of edge elements.

To detect whether it's a circle or not-

1. Hough circle transform. OR

2. Find centroid of edge points; exclude outliers; check smoothness of boundary.

You can improve the connectivity of edge pixels by preprocessing (smoothing operation) the image before edge detection.

For example, you take an image with size 256X256, remove noise using any filtering technique; and find out the edges. Now, your objective is to identify whether a shape/object is closed or not. To achieve this, you mark a pixel along the edge/boundary of the shape, you move from the pixel on the direction of the pixel connectivity, based on the chain code/adjacent pixels concept; if the ending point finishes at the starting point, then we can conclude that the shape is closed (it may be circle/contour)

For object identification with color detection, I transformed rgb values to eighth sphere (1/8 sphere) coordinates. System works so well. The color you want to expose can be found even though there is a shadow noise.

After you exposed the color of the object, you can do edge-detection and Hough transform.

In edge detection, I suggest you to threshold and skeletonize the edges. It would output better results in Hough transform.

In the black and white image and say a black circle, the detection is as follows:

1. Search from top to bottom, and from left to right, until you find black pixels, mark it as START pixel coordinates.

2. by using the beach tracing algorithm (the left hand in the white pixel and the right hand in the black pixel) move the next direction until you find it with START. (each move to a neighbor pixel gives a direction code; there are eight directions of code; each code encountered is recorded in the counter direction)

3. If all eight counters are equal, it means that the object is a circle.

This method can also be applied to other standard geometric shapes.

I hope this can be useful for you.

You can decide for yourself when the computer should recognize a circle. If the distance to the center is always the same, then it's a perfect circle. If a certain number of points deviate 5% from perfection, it can still be a circle. If there are more than 50% distance deviations, but the average of the positive and negative ones is nearly zero, then it can still be a circle for the computer. From my point of view it depends on the distance and the distribution of points compared to the center.

Dear Soumi Ray,

Look the link, maybe useful.

https://ieeexplore.ieee.org/document/7533040

https://arxiv.org/ftp/arxiv/papers/1405/1405.5406.pdf

Regards,

Shafagat

I would suggest color detection first. In my profile I have a presentation that explains a color detection technique. I convert the rgb colors to eighth spherical coordinate system. Then it becomes pretty easy to detect specific colors in a determined range. The detection process is like converting the image to gray scale. In contrast to normal gray scale conversion, your max illumination is not 255, 255, 255 to 255. Your max illumination is accepted as the color values you want, for example 155, 167,255.

Secondly hough transform can be used after the conversion.

Another technique that I actually plan is to find coordinates of edges in the converted image. Then take the mean of these coordinates. after that find the angles between mean coordinate and all the edge coordinates. Save these angles as a pattern and use them to detect the circle later. It could be a interesting method to detect the shapes.

The most commen techniques are the Hough transform. In the method, for each pixel the set of all possible circles are considered. Then, with a histogram the best instances are selected. In theory, such high values would correspond to the circles present in the image

For your sample image, using Hough transformation using this parameters (Python) :

circles = cv.HoughCircles(gray, cv.HOUGH_GRADIENT, 1, 20, param1=20, param2=50, minRadius=0, maxRadius=0)

will produce the correct answer : one circle found.

Hough Transformations method may not always work. There are other newer methods available in the internet.

You can map the use the equation 4 * pi * Area/(r2)

For more details we have:

https://arxiv.org/ftp/arxiv/papers/1405/1405.5406.pdf

https://www.pyimagesearch.com/2014/07/21/detecting-circles-images-using-opencv-hough-circles/