Lecture 8 Camera Models

Transcription

1 Lecture 8 Caera Models Professor Silvio Savarese Coputational Vision and Geoetr Lab Silvio Savarese Lecture 8-5-Oct-4

2 Lecture 8 Caera Models Pinhole caeras Caeras & lenses The geoetr of pinhole caeras Other caera odels Reading: Silvio Savarese [FP] Chapter Caeras [FP] Chapter 2 Geoetric Caera Models [HZ] Chapter 6 Caera Models Soe slides in this lecture are courtes to Profs. J. Ponce, S. Seit, F-F Li Lecture 8-5-Oct-4

3 How do we see the world? Let s design a caera Idea : put a piece of fil in front of an object Do we get a reasonable iage?

4 Pinhole caera Add a barrier to block off ost of the ras This reduces blurring The opening known as the aperture

5 Soe histor Milestones: Leonardo da Vinci (452-59): first record of caera obscura

6 Soe histor Milestones: Leonardo da Vinci (452-59): first record of caera obscura Johann Zahn (685): first portable caera

7 Soe histor Milestones: Leonardo da Vinci (452-59): first record of caera obscura Johann Zahn (685): first portable caera Joseph Nicephore Niepce (822): first photo - birth of photograph Photograph (Niepce, La Table Servie, 822)

8 Soe histor Milestones: Leonardo da Vinci (452-59): first record of caera obscura Johann Zahn (685): first portable caera Joseph Nicephore Niepce (822): first photo - birth of photograph Daguerréotpes (839) Photographic Fil (Eastan, 889) Cinea (Luière Brothers, 895) Color Photograph (Luière Brothers, 98) Photograph (Niepce, La Table Servie, 822)

9 Let s also not forget Motu ( BC) Oldest eistent book on geoetr in China Aristotle ( BC) Also: Plato, Euclid Al-Kindi (c ) Ibn al-haitha (965-4)

10 Pinhole caera Pinhole perspective projection f o f = focal length o = aperture = pinhole = center of the caera

11 f ' f ' P P Pinhole caera Derived using siilar triangles

12 Pinhole caera k f i P = [, ] P =[, f ] O f

13 Pinhole caera f f Coon to draw iage plane in front of the focal point. What s the transforation between these 2 planes? ' ' f f

14 Pinhole caera Is the sie of the aperture iportant? Kate lauka

15 Shrinking aperture sie - Ras are ied up -Wh the aperture cannot be too sall? -Less light passes through -Diffraction effect Adding lenses!

16 Caeras & Lenses A lens focuses light onto the fil

17 Caeras & Lenses circle of confusion A lens focuses light onto the fil There is a specific distance at which objects are in focus Related to the concept of depth of field

18 Caeras & Lenses A lens focuses light onto the fil There is a specific distance at which objects are in focus Related to the concept of depth of field

19 Caeras & Lenses focal point f A lens focuses light onto the fil All parallel ras converge to one point on a plane located at the focal length f Ras passing through the center are not deviated

20 Caeras & Lenses Z - f o Fro Snell s law: ' ' ' ' f ' f R 2(n ) o

21 Thin Lenses o ' f o f R 2(n ) Snell s law: Focal length n sin = n 2 sin 2 Sall angles: n n 2 2 n = n (lens) n = (air) ' ' ' '

22 Issues with lenses: Radial Distortion Deviations are ost noticeable for ras that pass through the edge of the lens No distortion Pin cushion Barrel (fishee lens) Iage agnification decreases with distance fro the optical ais

23 Lecture 2 Caera Models Pinhole caeras Caeras & lenses The geoetr of pinhole caeras Intrinsic Etrinsic Other caera odels Silvio Savarese Lecture 8-5-Oct-4

24 Pinhole caera Pinhole perspective projection f o f = focal length o = center of the caera (,, ) 3 E 2 (f,f )

25 Fro retina plane to iages Piels, botto-left coordinate sstes

26 Coordinate sstes c c

27 Converting to piels c. Off set C=[c, c ] c (,, ) (f c, f c )

28 Converting to piels c c. Off set 2. Fro etric to piels (,, ) (f k c, f l c ) C=[c, c ] Units: k,l : piel/ f : Non-square piels, : piel

29 Converting to piels c (,, ) ( c, c ) C=[c, c ] c Matri for? A related question: Is this a linear transforation?

30 (,, ) (f,f ) Is this a linear transforation? No division b is nonlinear How to ake it linear?

31 Hoogeneous coordinates hoogeneous iage coordinates hoogeneous scene coordinates Converting fro hoogeneous coordinates

32 Caera Matri ) c, c ( ),, ( c c c c X c c C=[c, c ]

33 Perspective Projection Transforation f f f f X f f X i X M X M 3 H 4

34 X M X X K I Caera Matri c c X Caera atri K

35 Finite projective caeras c c s X Skew paraeter c c C=[c, c ] K has 5 degrees of freedo!

36 Lecture 2 Caera Models Pinhole caeras Caeras & lenses The geoetr of pinhole caeras Intrinsic Etrinsic Other caera odels Silvio Savarese Lecture 8-5-Oct-4

37 World reference sste R,T j w k w O w i w The apping so far is defined within the caera reference sste What if an object is represented in the world reference sste

38 3D Rotation of Points Rotation around the coordinate aes, counter-clockwise: cos sin sin cos ) ( cos sin sin cos ) ( cos sin sin cos ) ( R R R p Y p

39 World reference sste R,T j w X k w O w X i w In 4D hoogeneous coordinates: X R T 4 4 X w I X X K Internal paraeters R T ' K I X w 44 K Eternal paraeters R T X w M

40 Projective caeras R,T j w X k w O w X i w 3 w 4 X 3 M 34 X w K 3 R T 34 X K s c c How an degrees of freedo? =!

41 Caera calibration More details in CS23A Estiate intrinsic and etrinsic paraeters fro or ultiple iages 3 w 4 X 3 M 34 X w K 3 R T 34 X K s c c How an degrees of freedo? =!

42 Projective caeras O w i w k w j w R,T w 3 X X M w X T R K 3 2 M W W W W X X X X ), ( w w w w X X X X E X X

43 Properties of Projection Points project to points Lines project to lines Distant objects look saller

44 Properties of Projection Angles are not preserved Parallel lines eet! Parallel lines in the world intersect in the iage at a vanishing point

45 Horion line (vanishing line) l horion

46 Horion line (vanishing line)

47 One-point perspective Masaccio, Trinit, Santa Maria Novella, Florence, Credit slide S. Laebnik

48 Lecture 2 Caera Models Pinhole caeras Caeras & lenses The geoetr of pinhole caeras Intrinsic Etrinsic Other caera odels Silvio Savarese Lecture 8-5-Oct-4

49 Projective caera p q r f O Q R P

50 Weak perspective projection When the relative scene depth is sall copared to its distance fro the caera p f q r Q Q O o R R P P

51 Weak perspective projection When the relative scene depth is sall copared to its distance fro the caera f p R q r Q Q O o R P P ' ' f f ' ' ' ' f ' f ' Magnification

52 Weak perspective projection f o p R q r Q Q O R P M P w P P M A b M K Instead of R T A v b

53 2 3 2 P P P W 2 W W 3 2 ) P, P ( 2 w w E P M P w b A M agnification 3 2 P M P w v b A M W 3 W 2 W W 3 2 P P P P ) P P, P P ( w w w w E Perspective Weak perspective

54 Orthographic (affine) projection Distance fro center of projection to iage plane is infinite f f ' ' ' ' ' '

55 Pros and Cons of These Models Weak perspective uch sipler ath. Accurate when object is sall and distant. Most useful for recognition. Pinhole perspective uch ore accurate for scenes. Used in structure fro otion.

56 Weak perspective projection The Kangi Eperor's Southern Inspection Tour (69-698) B Wang Hui

57 Weak perspective projection The Kangi Eperor's Southern Inspection Tour (69-698) B Wang Hui

58 Things to reeber

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