How to detect corresponding locations from images related by rotation about camera center?

I have two images (I and I’) from a camera (intrinsics K is known). The second image has been captured w.r.t. the first by rotating the camera about the camera center by theta (known rotation matrix R). There is no overlap between the images. The homography can be computed as (K and R known)


My question is given a location in image 1, how do I find the location in image 2. The homography equation has a factor s. How do I determine this factor?

you’re operating in a Projective space - Wikipedia

you do not “determine” s.

when you have some screen space coordinate (x,y), all projective coordinates (xw, yw, w), or (x,y,1)*w, or (xs,ys,s), or (x,y,1)*s, represent that SAME coordinate.

So how do I find the point (x’,y’) in image I’ if the corresponding location in image I is (x,y). Do I just ignore s while using the equation above?

are you asking what to do with a 3-dimensional vector that represents a 2D coordinate in homogeneous coordinates?

if you have a vector, the last dimension is the projective one. you take that value and divide the entire vector by that.

(xw, yw, w) / w = (x, y, 1)

and that’s it.

please find a book or other teaching materials that explain this to you.

if you have questions based on that, feel free to ask.

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