Lecture 7: homogeneous coordinates
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1 Lecture 7: homogeneous Dr. Richard E. Turner October 31, 2013
2 House keeping webpage:
3 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
4 Recap of last lecture: Pin hole camera focal length f optical axis camera-centred
5 Recap of last lecture: Pin hole camera focal length f optical axis camera-centred world
6 Recap of last lecture: World optical axis world point focal length f camera-centred world
7 Recap of last lecture: World optical axis world point focal length f camera-centred world
8 Recap of last lecture: World optical axis world point focal length f camera-centred world - fixed
9 Recap of last lecture: Camera centred optical axis world point focal length f camera-centred - can change world - fixed
10 Recap of last lecture: Camera centred optical axis world point focal length f camera-centred - can change world - fixed
11 Recap of last lecture: Perspective projection optical axis world point focal length f camera-centred - can change image plane world - fixed
12 Recap of last lecture: Pixel pixel optical axis world point focal length f camera-centred - can change image plane world - fixed
13 Summary of coordinate transforms world
14 Summary of coordinate transforms world camera-centred linear (rotate & translate)
15 Summary of coordinate transforms world camera-centred image plane linear (rotate & translate) non-linear (perspective projection)
16 Summary of coordinate transforms world camera-centred image plane pixel linear (rotate & translate) non-linear (perspective projection) linear (stretch & translate)
17 Summary of coordinate transforms world difficult step camera-centred image plane pixel linear (rotate & translate) non-linear (perspective projection) linear (stretch & translate)
18 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)
19 Homogeneous quiz cartesian homogeneous [0,0,1] [0,1,0] [1,0,0]
20 Homogeneous quiz cartesian homogeneous [0,0,1] [0,1,0] [1,0,0]
21 Homogeneous quiz cartesian homogeneous [0,0,1] [0,1,0] [,0] [1,0,0]
22 Homogeneous quiz cartesian [0, ] homogeneous [0,0,1] [0,1,0] [,0] [1,0,0]
23 Homogeneous quiz [0, ] cartesian homogeneous [0,0,1] [0,1,0] [0,0,0] [,0] [1,0,0]
24 Homogeneous quiz
25 Homogeneous quiz [0, ] [,0] half-lines get mapped to points at infinity: = 0 or 1 by convention
26 scale changes Homogeneous quiz
27 scale changes Homogeneous quiz
28 Homogeneous quiz scale changes have no effect maps to same point as
29 Homogeneous quiz 1 0 straight line
30 Homogeneous quiz 1 0 straight line
31 Homogeneous quiz 1 0 straight line plane
32 Homogeneous quiz 1 0 straight line plane
33 Homogeneous quiz 1 0 straight line
34 Homogeneous quiz 1 0 straight line
35 Homogeneous quiz 1 0 straight line planes that intersect at
36 Mobile eye
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