One the measurements provided by regionprops is 'Centroid'. Here's an example of labeling binary objects, computing the centroid of each object, and plotting the centroid location on top of the image.
I = imread('text.png');
imshow(I)
L = bwlabel(I); s = regionprops(L, 'Centroid'); hold on for k = 1:numel(s) plot(s(k).Centroid(1), s(k).Centroid(2), 'r*') end hold off xlim([0 60]) ylim([0 60])
Last week, reader Daphne asked how to compute the intensity-weighted centroid. That is, if each labeled region corresponds to a region in a gray scale image, how do you compute the centroid weighted by the gray scale pixel values? The easiest way, I think, is to use the both the PixelIdxList and PixelList properties from regionprops. Let's try it with a simple synthetic image (download the image from here):
I = imread('spheres.png');
imshow(I)
Now let's threshold and label it:
bw = I < 255;
bw = imfill(bw, 'holes');
L = bwlabel(bw);
imshow(label2rgb(L, @jet, [.7 .7 .7]))
Next, get the PixelIdxList and PixelList for each labeled region:
s = regionprops(L, 'PixelIdxList', 'PixelList');
Each row of the PixelList for a region contains the x and y coordinates of a pixel in that region.
s(1).PixelList(1:4, :)
ans =
48 94
48 95
48 96
48 97
We can get the grayscale value of pixels in a region by indexing into I with PixelIdxList. By weighting those values with the x and y coordinates, we can compute the centroid.
idx = s(1).PixelIdxList; sum_region1 = sum(I(idx)); x = s(1).PixelList(:, 1); y = s(1).PixelList(:, 2); xbar = sum(x .* double(I(idx))) / sum_region1
xbar = 74.6128
ybar = sum(y .* double(I(idx))) / sum_region1
ybar = 92.5121
Let's do that in a loop and superimpose the centroid locations on the image.
imshow(I) hold on for k = 1:numel(s) idx = s(k).PixelIdxList; pixel_values = double(I(idx)); sum_pixel_values = sum(pixel_values); x = s(k).PixelList(:, 1); y = s(k).PixelList(:, 2); xbar = sum(x .* pixel_values) / sum_pixel_values; ybar = sum(y .* pixel_values) / sum_pixel_values; plot(xbar, ybar, '*') end hold off
Get
the MATLAB code
Published with MATLAB® 7.5
Hi Steve,
Thanks for the input. This works nicely and pretty quickly. However, it does require a binary image - i.e., a threshold value is needed. This is not so straightforward with an image that has less than perfect/clean background.
Will try to incorporate this, perhaps with the brightest pixel cutoff I had mentioned in my previous comment. That is, only blobs with a pixel > thresh will be considered at all.
A more general question, my original images just appear as nothing (plain gray) with imshow, but are beautiful with imagesc. Why is that ?
I can email a sample figure if you like.
Daphne
Daphne—The binary image is just a way to represent the set of pixels associated with each region. If you don’t know which pixels belong to each object, then I can’t think of a way to calculate the centroids. It’s like being asked to compute a definite integral without being told the limits of integration.
imshow assumes certain black-to-white dynamic ranges for gray scale images. For example, if the input image is uint8, then 0 is displayed as black and 255 is displayed as white. If the input image is uint16, then 65535 is displayed as white. For double and single images, 1 is displayed as white. imagesc, on the other hand, displayes the image in image-dependent fashion. The minimum pixel is displayed using the first colormap color, and the maximum pixel is displayed using the last colormap color. To get a similar effect using imshow, use this syntax:
See the imshow doc for an explanation. You might also want to look at my “All about pixel colors” posts between January and April 2006.
Hello Steve,
I wonder how i can find the proper threshold value of the picture.Could you please tell me how the theshold come and how i can get the proper threshold value ?
please explian to me.
I am new here and i’ve just started to study about Image Processing,so i do not know much about it but i want to learn about it.
Regards
suwanna
Suwanna—You might try using the function graythresh.
Hi Steve,
thanks for the nice solution to the gravity-center question. Just a minor issue: I noticed I cannot get the following line to work:
>> bw=I > bw = im2bw(I,0.9);
>> bw=1-bw;
sorry the line-breaks were messed up in the last post- feel free to delete it.
Regards,
Chaitanya.
Chaitanya—Where did that code come from? It doesn’t resemble any code in this post. Your first line has a syntax error (two equals signs).
Hello Steve
Thanks very much .
i will try to read it.
Regards
suwanna
Hi Steve,
Great tutorial. I wanted to ask you - the objects that I am trying to find the centroid of are not perfect spheres - is there anyway to manipulate a roughly spherical object into being represented as one. I’ve already applied a threshold to isolate the objects of interest, and i’ve also reduced noise by removing small objects [bw = bwareaopen(bw,30);]. However, due to the nature of the areas left, your code returns multiple centroids.
So in a nutshell is there anyway of approximating crude blobs as spheres?
Many thanks in advance.
Tariq—You might want to try a morphological closing step (imclose) prior to calling bwareaopen.
Thanks Steve. It works great.
Hi Steve
i doing project on “automatic signature verification system” .for that i am reading IEEE papers.in some papers authors are takeing “signature centroid” as feature.using above method i computed “Intensity-weighted centroids”.it is giving so many centroid points.but in IEEE papers they are showing only one centroid point.please tell me the difference between “signature centroid “, and “Intensity-weighted centroids”.
is their any difference between them.
K—The intensity-weighted centroids is giving you one centroid per connected component. You’ll need to preprocess the signature block to turn it into a single component. For the unweighted centroid, which is probably what you want, take the mean of the row coordinates and the mean of the columns coordinates for all the pixels belonging to the signature.
THANK YOU
STEVE
Hello Steve,
I tried your method with an image with regularly spaced spheres, but the centroids were not marked in an orderly manner (for example, centroids are not marked columnwise from left to right of image). If the spheres were arranged regularly in rows and columns, how can we ensure that the values in ‘xbar’ and ‘ybar’ are in an orderly manner?
Ana—The connected-components labeling functions (bwlabel and bwlabeln) do scan the image in columnwise order, from left to right. The particular object ordering that results, though, depends on where the scan first encountered a pixel belonging to each object. For example, an object below another object will get labeled first if the lower object sticks out even a tiny bit to the left. You can use functions such as sort and sortrows to rearrange the measurements however you wish.
hello sir,
i want to find centroid for my ultrasound breast image so as to find out the seed points to grow a region of interest..
Actually in the ultrasound image all lesion parts lye on the centre of the image only.
i calculated the feature values and got the seed points..
but some seed points are lying on the outside of the region of interest also..
so i thought of calculating the centroid and then find out the seed points in that particular area..
is my thought of doing this is write r not sir…
please give suggestions and send the centroid coding.
thank u..
Hi Steve,
I am working on hand written characters.
I am trying to import a 35*35 image and wanted to find the centroid of the character not for the whole image but according to the character aligment and its pixel intensity I wanted to calculate the cenroid based on the x-coordinate and y-coordinate distance using the formula:
Hence, Cx =(∑ xi) /N and Cy = (∑ yi)/N
for all 1 to N pixels. Since, Centroid (Cx, Cy) of a character is :
For a given character the summation of product of each pixels x-coordinate distance and its intensity value, divided by total no. of character pixels (N) gives x-coordinate of the centroid.
How to find the x-coordinate distance from a pixel and like-wise the y-cordinate distance?
Steve, Can you please let me know abt this…as this would be a great help to me.
Thanks in Advance,
Lakshmi
Sylvia—This post contains code and explanations for computing centroids.
Lakshmi—The centroid calculation involves the x-coordinate and y-coordinate of the pixel, not the distance from the pixel. This post shows how to do the calculation.
Thank you Steve.
My question was to find the pixel’s distance from x-axis.
I used
a=imread(’img.bmp’)
[y,x]=find(a)
and got the ans for tht!
Thanks once again
Thank u Steve..
Now i am working in ultrasound breast image.. my aim is to segment the leion area.. for this i used region growing technique.. i have found out seed point using texture features and grown the region by fixing the threshold(global thresholding).. but it works for only 2 images.. for the other images, other areas including the lesion area is segmented out..what i can i do for this type of problem. please clear my doubt and send me the coding to segment my lesion area alone.. waiting for your reply steve.. thank u.
Sylvia—I’m sorry, but image segmentation usually involves application- or data-set-specific algorithm development. It’s not something I can do for you or send you code for.
Dear Steve
I want to achieve the same results as Daphne, except in my case, I am using a real life actual image of crystal lattices showing many atoms in rows and columns. Your synthetic image was good quality; but on my image I can’t use the simple thresholding you used, in my image the atoms are all of different intensities, thus I have used multi-level thresholding using the grayslice function. Can one achieve the same results and obtain the centroide for each atom.
Hello Steve,
How could we use the MajorAxis and MinorAxis length to determine the location of an object in an image? I know that using the Centroid we could easily determine the location by using the x and y coordinates of the centroid.
But how could that be done using Major and Minor axis?
Shahnawaz—You will need to find a way to solve the segmentation problem somehow. If you can’t identify which pixels belong to each atom, then I don’t see how you can compute the centroids.
Mj—MajorAxisLength and MinorAxisLength give you no information about the location of an object in an image.
Then what are the properties (other than centroid) that could give me information about the location of an object in an image?
Mj—See the documentation for regionprops.
Dear Steve
How can I extract all the x and y coordinates in any image; then create separate images of Y and Y coordinates. I can at present extract certain X and Y coordinates but not all of them automatically.
Regards Shahnawaz
Shahnawaz—Extract the x and y coordinates of what? And what is an image of X and Y coordinates?
Dear Steve
Apologize for the lack of clarity, I meant extracting all the X and Y pixel coordinates from any image automatically; and create a pictorial representation (image) of all the X and Y pixel coordinates seperately. At present I can extract only certain pixel coordinates not all of them at once.
Regards Shahnawaz
Shahnawaz—You just repeated your question. I still don’t understand it.
Dear Steve
Sorry about this I understand but have not got it across well. I believe (imtool) in matlab does something similar but only one location and pixel value at a time using the mouse;
I want to do it as a global operation and extract all the coordinate locations and pixel values in my case for each atom; I think it should work for any image. I want to store x and y location information separately as an image of location values one for x and one for y. I hope this makes more sense.
P.S Can you delete the two which did not make sense.
I have managed to extract some of them x and y coordinates and pixel values I am dealing with a graylevel image.
Shahnawaz—Try meshgrid.
Dear steve
How can I find MaxIntensity,MeanIntensity from regionprops for grayscale image?
Suzie—MaxIntensity and MeanIntensity measurements are provided by regionprops in the latest release, R2008a. If you have an earlier version, see the techniques used in this post.
Steve, I have used regionprops to find centroids of objects in binary images for a class, and I am inquiring as to the algorithm used to do this because we have to explain all methods used. Is it safe to assume that groups of white pixels are found based on sharing common sides (no corner contact, that would result in 2 objects) then the common formula for finding the centroid is applied to each white pixel object? I have found reference to this on other sites but was wondering if you could offer me more insight to the algorithm this function uses.
Thanks again,
Josh
Josh—Presumably, you used bwlabel before you called regionprops. bwlabel computes connected components. By default, it uses “8-connectivity,” meaning that pixels connected at the corners are assumed to belong to the same object. You can also get bwlabel to use “4-connectivity,” meaning that pixels connected only at the corners belong to different objects. The reference page for bwlabel describes the algorithm used and gives a reference. And yes, regionprops uses the “common formula” for the centroid. You could look at the ComputeCentroid subfunction of regionprops to see the actual implementation.
hello sir
I want to calculate the centroid of edges/ Lines. I am working on image segmentation Project. I have obtained edge map of image by using Phase Congruency(Peter Kovesi). After getting binary image of edge map. I have used bwlabel to label each edge/ line in the image. Now I want to find the centroid of each edge. Then want to use K means clustering for clustering long edges. I am facing problem in finding the centroid of edge/ Line. How it could be done?
Thanks in advance
Patil Rajendra
Patil—Use regionprops.