The projective plane

Why do we need homogeneous coordinates? • represent points at infinity, homographies, perspective projection, multi-view relationships What is the geometric intuition? • a point in the image is a ray in projective space

y

(sx,sy,s)

(x,y,1)

x

z

image plane

• Each point (x,y) on the plane is represented by a ray (sx,sy,s) – all points on the ray are equivalent:  (x, y, 1) @ (sx, sy, s)