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.

https://docs.opencv.org/4.x/d9/dab/tutorial_homography.html