Single-view Metrology and Camera Calibration

Transcription

1 Sigle-iew Metrology ad Caera Calibratio Coputer Visio Jia-Bi Huag, Virgiia Tech May slides fro S. Seitz ad D. Hoie

2 Adiistratie stuffs HW 2 due :59 PM o Oct 9 th Ask/discuss questios o Piazza Office hour

3 Perspectie ad 3D Geoetry Projectie geoetry ad caera odels What s the appig betwee iage ad world coordiates? Sigle iew etrology ad caera calibratio How ca we estiate the caera paraeters? How ca we easure the size of 3D objects i a iage? Photo stitchig What s the appig fro two iages take without caera traslatio? Epipolar Geoetry ad Stereo Visio What s the appig fro two iages take with caera traslatio? Structure fro otio How ca we recoer 3D poits fro ultiple iages?

4 Last Class: Pihole Caera Pricipal Poit (u., ) f.. P. u u p Caera Ceter (t x, t y, t z ) 4

5 Last Class: Projectio Matrix t r r r t r r r t r r r f u s f u w z y x t x K R O w i w k w j w t R 5

6 Last class: Vaishig Poits Vertical aishig poit (at ifiity) Vaishig lie Vaishig poit Vaishig poit Slide fro Efros, Photo fro Criiisi 6

7 This class How ca we calibrate the caera? How ca we easure the size of objects i the world fro a iage? What about other caera properties: focal legth, field of iew, depth of field, aperture, f-uber? 7

8 How to calibrate the caera? * * * * * * * * * * * * w w wu t x K R 8

9 Calibratig the Caera Method : Use a object (calibratio grid) with kow geoetry Correspod iage poits to 3d poits Get least squares solutio (or o-liear solutio) Kow 2d iage coordiates Kow 3d locatios wu w w Ukow Caera Paraeters 9

10 s s su Kow 3d locatios Kow 2d iage coords Ukow Caera Paraeters u u u u u u u u

11 s s su Kow 3d locatios Kow 2d iage coords Ukow Caera Paraeters u u u u Method hoogeeous liear syste. Sole for s etries usig liear least squares u u u u u u u u [U, S, V] = sd(a); M = V(:,ed); M = reshape(m,[],3)';

12 Method 2 ohoogeeous liear syste. Sole for s etries usig liear least squares u u u u u u u u Ax=b for M = A\; M = [M;]; M = reshape(m,[],3)'; s s su Kow 3d locatios Kow 2d iage coords Ukow Caera Paraeters

13 Calibratio with liear ethod Adatages Easy to forulate ad sole Proides iitializatio for o-liear ethods Disadatages Does t directly gie you caera paraeters Does t odel radial distortio Ca t ipose costraits, such as kow focal legth Does t iiize projectio error No-liear ethods are preferred Defie error as differece betwee projected poits ad easured poits Miiize error usig Newto s ethod or other o-liear optiizatio 3

14 Ca we factorize M back to K [R T]? es! ou ca use RQ factorizatio (ote ot the ore failiar QR factorizatio). R (right diagoal) is K, ad Q (orthogoal basis) is R. T, the last colu of [R T], is i(k) * last colu of M. Need post-processig to ake sure that the atrices are alid. See Slide credit: J. Hays

15 Calibratig the Caera Method 2: Use aishig poits Fid aishig poits correspodig to orthogoal directios Vaishig lie Vertical aishig poit (at ifiity) Vaishig poit Vaishig poit 5

16 Calibratio by orthogoal aishig poits Itrisic caera atrix Use orthogoality as a costrait Model K with oly f, u, For aishig poits T j p KR i i i i = R K p i p i K (R)(R )(K )p i = What if you do t hae three fiite aishig poits? Two fiite VP: sole f, get alid u, closest to iage ceter Oe fiite VP: u, is at aishig poit; ca t sole for f 6

17 Calibratio by aishig poits Itrisic caera atrix p KR i i Rotatio atrix Set directios of aishig poits e.g., = [,, ] Each VP proides oe colu of R Special properties of R i(r)=r T Each row ad colu of R has uit legth p i = Kr i 7

18 How ca we easure the size of 3D objects fro a iage? 8 Slide by Stee Seitz

19 Slide by Stee Seitz Perspectie cues 9

20 Slide by Stee Seitz Perspectie cues 2

21 Slide by Stee Seitz Perspectie cues 2

22 Aes Roo 22

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24 Slide by Stee Seitz Coparig heights Vaishig Poit 24

25 Slide by Stee Seitz Measurig height Caera height

26 Which is higher the caera or the a i the parachute? 26

27 The cross ratio A Projectie Iariat Does ot chage uder projectie trasforatios P P 2 P 3 P P P P P P P P P The cross-ratio of 4 colliear poits Ca perute the poit orderig 4! = 24 differet orders (but oly 6 distict alues) This is the fudaetal iariat of projectie geoetry i i i i P P P P P P P P P Slide by Stee Seitz 27

28 r t b t r b r t b iage cross ratio Measurig height B (botto of object) T (top of object) R (referece poit) groud plae H C T R B R T B scee cross ratio P y x p scee poits represeted as iage poits as R H R H R Slide by Stee Seitz 28

29 Measurig height z r Slide by Stee Seitz aishig lie (horizo) x t H t R H y b t b r b r t iage cross ratio b 29

30 Measurig height z r Slide by Stee Seitz aishig lie (horizo) t x t y t b b What if the poit o the groud plae b is ot kow? Here the guy is stadig o the box, height of box is kow Use oe side of the box to help fid b as show aboe b 3

31 What about focus, aperture, DOF, FOV, etc?

32 Addig a les circle of cofusio A les focuses light oto the fil There is a specific distace at which objects are i focus other poits project to a circle of cofusio i the iage Chagig the shape of the les chages this distace

33 Focal legth, aperture, depth of field F optical ceter (Ceter Of Projectio) focal poit A les focuses parallel rays oto a sigle focal poit focal poit at a distace f beyod the plae of the les Aperture of diaeter D restricts the rage of rays Slide source: Seitz

34 The eye The hua eye is a caera Iris - colored aulus with radial uscles Pupil (aperture) - the hole whose size is cotrolled by the iris Retia (fil): photoreceptor cells (rods ad coes) Slide source: Seitz

35 Depth of field Slide source: Seitz f / 5.6 f / 32 Chagig the aperture size or focal legth affects depth of field Flower iages fro Wikipedia

36 Slide fro Efros Varyig the aperture Large aperture = sall DOF Sall aperture = large DOF

37 Shrikig the aperture Why ot ake the aperture as sall as possible? Less light gets through Diffractio effects Slide by Stee Seitz

38 Shrikig the aperture Slide by Stee Seitz

39 Relatio betwee field of iew ad focal legth Field of iew (agle width) fo ta d 2 f Fil/Sesor Width Focal legth

40 Dolly oo or Vertigo Effect How is this doe? oo i while oig away

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42 Variables that affect exposure /applets/exposure.htl

43 Reiew How tall is this woa? How high is the caera? What is the caera rotatio? What is the focal legth of the caera?

44 Thigs to reeber Calibrate the caera? Use a object with kow geoetry Use aishig poits Measure the size of objects i the world fro a iage? Use perspectie cues Caera properties focal legth, field of iew, depth of field, aperture, f-uber?

45 Next class Iage stitchig P Q Caera Ceter 45