How do I find specific points on a image, regardless of the rotate?

Question

I have such a picture.

Here is the image

This is the numbers of the dots on the picture. I want the dot numbers to stay the same even if I turn the picture upside down. This rotation can be any angle value.

For example

Head up

Upside down

90 degree

45 degree

I tried a few things like Opencv camera calibration and Pose Estimation but I couldn't get the point numbers to be fixed.

Are you planning to share a video of the dots moving? Do you have the code to locate the centres of the 7 circles? — Mark Setchell, Mar 28 '21 at 15:27
Please show your code - https://stackoverflow.com/help/minimal-reproducible-example — Mark Setchell, Mar 28 '21 at 17:40

score 3 · Answer 1 · answered Mar 28 '21 at 07:20

I don't think this is a programming problem, but a basic geometry one.

You've got 7 points in that configuration and you want to find some geometric properties which are robust to rotation. The first thing I can think of is distance.

Compute the squared distance (SD) between all points, then find the one which maximizes the sum of squared distances (SSD) to all others. That point is P7.
Find the one with maximum SD from P7. That point is P1.
Find the one with minimum SD from P7. That point is P6.
Find the one with second minimum SD from P7. That point is P5.
Find the one with minimum SD from P1. That point is P2.

In order to find P3 and P4 you need to detect a side (left/right) with respect to a direction. Let's call Q and R the two unknown points and a direction we are already sure of, such as the one from 1 to 7. You can now look at the sign of the cross product between vector from P1 to P7 and the one from P1 to Q. If it's at the right, the value will be positive. So we are able to find its identity.

if ( (Q.x - P1.x) * (P2.y - P1.x) - (Q.y - P1.y) * (P2.x - P1.x) > 0) {
    P3 = Q;
    P4 = R;
}
else {
    P3 = R;
    P4 = Q;
}

I like your answer, even if no-one else can manage to drag their mouse all the way over to the "upvote" button — Mark Setchell, Mar 28 '21 at 15:29
@ÇağatayKARADEMİR If you have another question, it's better to post another question. Specifically, in the question write your existing solution and clarify what is the problem with the accuracy that you get. — Costantino Grana, Mar 29 '21 at 12:38
@ÇağatayKARADEMİR Moreover, if the answer solves your problem, remember to mark it as accepted. — Costantino Grana, Mar 29 '21 at 12:41

How do I find specific points on a image, regardless of the rotate?

1 Answers1