How to "size-normalize" objects in a binary image? (e.g. make sizes of all non-zero objects to be the same)

Dear Community,

I have a binary image (attached in .jpg and .fig) with circles, pixel values inside circles =1 and outside =0. These circles look very similar, although they differ in size a little bit. For instance, the difference between two random circles in diameter can be about approx. 10 pixels. Is there a way to make all these circles to become of EXACTLY the same size? Size itself is not important btw, it can range from biggest possible (before circles start to overlap) to 1 pixel. Also a more general answer on how to make objects (not only circles) in a binary image equally sized will satisfy my needs.

I will appreciate any sugestions.

Thank you,

Vasilii

[Rik]

In response to your flag:

"I would like to remove my question. Reasons are the following: 1) The question hasn/t been answered. 2) I resolved the issue myself 3) The question contains no useful information for the community (since there's no answer)"

There actually is an answer: the answer is that it is not always possible. If that didn't help you, why did you mark it as accepted answer?

How I would approach this, is to attempt to define an anchor point (e.g. the centroid) for each binary object. Then you can mark only the anchor point for each object and use a convolution to insert the same shape into all points. The only tricky step in between would be to select the correct shape.

[Vasya Mika]

>> There actually is an answer: the answer is that it is not always possible.

This is indeed why I marked the answer as accepted.

[Rik]

Then removing this question will be a disservice to people with a similar question. Knowing something isn't possible is very valuable.

If you are still interested in my approach, you can post a comment. Otherwise I'll spend my time differently. You may also consider posting your own solution as an answer.

[Vasya Mika]

If I'd ask something like: "How can I count all stars in universe in MATLAB?" and get an answer "You cannot", would it be worth staying?..

Regarding your approach: is there a way to centroid every object without cropping these objects from the image first?

[Vasya Mika]

UPD: Sorry, Image Analyst have just answered that, thanks!

Answer 1

[Image Analyst]

Not if x and y can be anything (floating point) since you will have quantization error.

If you want to specify that the center or upper left corner is exactly on an integer coordinate, you can.

Just see the FAQ.

[Vasya Mika]

What I need is to have uniform peaks e.g. after cross-correlation I have some peaks with one pixel and some with 10 and so on. They all differ... I need them to be exact shape & size. Finding local maxima is close to what I want, but I still get some small anisotropy though...

>> If you want to specify that the center or upper left corner is exactly on an integer coordinate, you can.

>> Just see the FAQ.

I don't really understad what you mean by this but it's not helpful (

[Image Analyst]

If you want, you can use regionprops() to identfy the centroids of the existing circles. Then round them to the nearest integer. Next create a new, blank image and paste onto it a small template of the desired circle shape. I'm attaching a copy and paste demo.

[Vasya Mika]

Thank you for this nice solution!