Question

I have to detect the pattern of 6 circles using opencv. I have detected the circles and their centroids by using thresholding and contour function in opencv.

Now I have to define the relation between these circles in a way that should be invariant to scale and rotation. With this I would be able to detect this pattern in various views. I have to use this pattern for determining the object pose.

How can I achieve scale/rotation invariance? Do you have any reference I could read about it?

Answer 1

To make your pattern invariant toward rotation & scale, you have to normalize the direction and the scale when detecting your pattern. Here is a simple algorithm to achieve this

• detect centers and circle size (you say you have already achieved this – good!)
• compute the average center using a simple mean. Express all the centers from this mean
• find the farthest center using a simple norm (euclidian is good enough)
• scale the center position and the circle sizes so that this maximum distance is 1.0
• rotate the centers so that coordinates of the farthest one is (1.0, 0)

you’re done. You are now the proud owner of a scale/rotation invariant pattern detector!! Congratulations!

Now you can find patterns, transform them as suggested, and compare center position & circle sizes.