Lecture 7: homogeneous Dr. Richard E. Turner (ret26@cam.ac.uk) October 31, 2013
House keeping webpage: http://cbl.eng.cam.ac.uk/public/turner/teaching
Recap of last lecture: Pin hole camera image plane pin hole camera world point real image focal length f optical centre optical axis Cheap mobile phone cameras: non-linear distortions distortions can be removed => pin hole model accurate
Recap of last lecture: Pin hole camera focal length f optical axis camera-centred
Recap of last lecture: Pin hole camera focal length f optical axis camera-centred world
Recap of last lecture: World optical axis world point focal length f camera-centred world
Recap of last lecture: World optical axis world point focal length f camera-centred world
Recap of last lecture: World optical axis world point focal length f camera-centred world - fixed
Recap of last lecture: Camera centred optical axis world point focal length f camera-centred - can change world - fixed
Recap of last lecture: Camera centred optical axis world point focal length f camera-centred - can change world - fixed
Recap of last lecture: Perspective projection optical axis world point focal length f camera-centred - can change image plane world - fixed
Recap of last lecture: Pixel pixel optical axis world point focal length f camera-centred - can change image plane world - fixed
Summary of coordinate transforms world
Summary of coordinate transforms world camera-centred linear (rotate & translate)
Summary of coordinate transforms world camera-centred image plane linear (rotate & translate) non-linear (perspective projection)
Summary of coordinate transforms world camera-centred image plane pixel linear (rotate & translate) non-linear (perspective projection) linear (stretch & translate)
Summary of coordinate transforms world difficult step camera-centred image plane pixel linear (rotate & translate) non-linear (perspective projection) linear (stretch & translate)
Summary of this lecture introduce new mathematical machinery to handle the projection step smart way to handle points at infinity (key to perspective projection) allows us to retain the matrix formulation apply non-linearity at the end (rather than in the middle) homogeneous initially feels like sleight of hand apply to all (world/camera-centred/image/pixel)
Homogeneous quiz cartesian homogeneous [0,0,1] [0,1,0] [1,0,0]
Homogeneous quiz cartesian homogeneous [0,0,1] [0,1,0] [1,0,0]
Homogeneous quiz cartesian homogeneous [0,0,1] [0,1,0] [,0] [1,0,0]
Homogeneous quiz cartesian [0, ] homogeneous [0,0,1] [0,1,0] [,0] [1,0,0]
Homogeneous quiz [0, ] cartesian homogeneous [0,0,1] [0,1,0] [0,0,0] [,0] [1,0,0]
Homogeneous quiz
Homogeneous quiz [0, ] [,0] half-lines get mapped to points at infinity: = 0 or 1 by convention
scale changes Homogeneous quiz
scale changes Homogeneous quiz
Homogeneous quiz scale changes have no effect maps to same point as
Homogeneous quiz 1 0 straight line
Homogeneous quiz 1 0 straight line
Homogeneous quiz 1 0 straight line plane
Homogeneous quiz 1 0 straight line plane
Homogeneous quiz 1 0 straight line
Homogeneous quiz 1 0 straight line
Homogeneous quiz 1 0 straight line planes that intersect at
Mobile eye http://www.youtube.com/watch?v=hxpiylueooy