Lecture 9: inverting the imaging process calibration, recovery of world position, mosaicing

Transcription

1 Lecture 9: inverting the imaging process calibration, recovery of world position, mosaicing Dr. Richard E. Turner November 7, 2013

2 House keeping examples sheet solutions will be put on the website today webpage:

3 Recap: perspective camera world pixel

4 Recap: perspective camera world pixel

5 Recap: perspective camera world pixel

6 Recap: perspective camera world pixel

7 Recap: perspective camera world pixel

8 Recap: perspective camera world pixel

9 Recap: perspective camera world pixel

10 Recap: perspective camera world pixel perspective camera projection matrix camera calibration matrix rigid body motion matrix

11 Recap: perspective camera world pixel 10 d.o.f. perspective camera projection matrix complex structure camera calibration matrix rigid body motion matrix

12 Recap: perspective camera world pixel projective camera projection matrix

13 Recap: perspective camera world pixel 11 d.o.f. projective camera projection matrix simple structure

14 Recap: perspective camera world pixel viewing a wlg can be set to 0

15 Recap: perspective camera world pixel viewing a wlg can be set to 0

16 Recap: perspective camera world pixel viewing a can be removed wlg can be set to 0

17 Recap: perspective camera world pixel viewing a nb: this is exact

18 Recap: perspective camera world pixel viewing a line wlg can be set to 0

19 Recap: perspective camera world pixel viewing a line wlg can be set to 0

20 Recap: perspective camera world pixel viewing a line can be removed wlg can be set to 0

21 Recap: perspective camera world pixel viewing a line

22 Outstanding problems how do we calibrate cameras from known world/ points? (3D,2D,1D) how do we recover world position from a calibrated camera? how do we do mosaicing? (how do we calibrate and recover world position from multiple s)

23 Problems with standard fitting methods parameter fitting methods strongly affected by outliers

24 Problems with standard fitting methods parameter fitting methods strongly affected by outliers X 2 X 1

25 Problems with standard fitting methods parameter fitting methods strongly affected by outliers linear regression solution X 2 X 1

26 Problems with standard fitting methods parameter fitting methods strongly affected by outliers linear regression solution desired solution X 2 X 1

27 RANSAC Algorithm computationally cheap way of approximating desired solution linear regression solution desired solution X 2 X 1

28 RANSAC Algorithm initialise count of number of points fit X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

29 RANSAC Algorithm begin loop X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

30 RANSAC Algorithm: RAndom SAmple pick a subset of K points randomly (here K=2) X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

31 RANSAC Algorithm fit parameters to subset S X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

32 RANSAC Algorithm count number of points which are inliers X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

33 RANSAC Algorithm count number of points which are inliers, here ninliers = 4 X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

34 RANSAC Algorithm: Consensus if number of inliers is larger than before, save parameters & ninliers X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

35 RANSAC Algorithm pick a subset of K points randomly (here K=2) X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

36 RANSAC Algorithm fit parameters X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

37 RANSAC Algorithm count number if inliers, here ninliers = 6 X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

38 RANSAC Algorithm if number of inliers larger than best, update parameters etc. X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

39 RANSAC Algorithm pick a subset of K points randomly (here K=2) X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

40 RANSAC Algorithm fit parameters X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

41 RANSAC Algorithm count inliers X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

42 RANSAC Algorithm no need to update as not an improvement X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

43 RANSAC Algorithm pick a subset of K points randomly (here K=2) X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

44 RANSAC Algorithm fit parameters X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

45 RANSAC Algorithm count number of inliers X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

46 RANSAC Algorithm update stored parameters X 2 nbest = 0 while i<niterations S = selectrandsubset(x) = fitparams(s) ninliers = countinliers(x, ) if ninliers>nbest = nbest = ninliers endif endwhile X 1

47 RANSAC for mosaicing H = eye(3,3) homography, H = KRK 1, initialised to identity nbest = 0 for int i = 0; i < niterations; i++ do P4 = SelectRandomSubset(P) select subset of points (e.g. 4) Hi = ComputeHomography(P4) compute homography from subset ninliers = ComputeInliers(Hi) compute no. of consistent points if ninliers > nbest then H = Hi nbest = ninliers end if end for