Minimal Distortion using 2 Homographys
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hey folks, I've got quite a complex question for you... suppose I've got two triangles in different pictures. I can easily compute the homography between those. Is there a way to compute a Homography for each so that the distortion for each triangle is minimized??? I guess the aspect ratio (or diagonals in a square using this homography) can be used for measuring the amount of distortion. but how to compute those "points in the middle" where distortion is least?? Say, given are: x_1,x_2,x_3 (for one triangle) x_4,x_5,x_6 (for the other one) We want to know: x_7,x_8,x_9 ( our destination triangle ) We also know: H*x_i = x_j (where i = 1,2,3 and j=7,8,9) H = Homography (/Affine transformation) and G*x_i = x_j (where i = 4,5,6 and j=7,8,9) G = Homography (/Affine transformation) H = a b t_x c d t_y 0 0 1 a/d should be minimal... for H and G Is it true that b=-c because of rotation which gives no distortion?? any hints and links are appreciated