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Homography, Mosaicing and Stabilization Computer Vision Some Slides are from Prof. Robert Collins, Penn State Univ.

Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4

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Page 1: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4

Homography, Mosaicing and

Stabilization

Computer Vision

Some Slides are from Prof. Robert Collins, Penn State Univ.

Page 2: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 3: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 4: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 5: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 6: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 7: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 8: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 9: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 10: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 11: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 12: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 13: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 14: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 15: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 16: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 17: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4

Scale~

Page 18: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 19: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 20: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 21: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 22: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4

This is know to be optimal in L.S sense

Page 23: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 24: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 25: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 26: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4

(Singular Value Decomposition)

Solution in SVD is proportional to the eigenvector

corresponding to the zero eigenvalue of ATA

Page 27: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 28: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 29: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 30: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 31: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 32: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 33: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 34: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 35: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 36: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 37: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4

https://www.youtube.com/watch?v=i5keG1Y810U

https://www.youtube.com/watch?v=i5keG1Y810U
https://www.youtube.com/watch?v=i5keG1Y810U
Page 38: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 39: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 40: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 41: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 42: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 43: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 44: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 45: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 46: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 47: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 48: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 49: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 50: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4
Page 51: Homography, Mosaicing and Stabilizationcvlab.khu.ac.kr/CVLecture12.pdf · 2018-10-23 · 8 x 1 2N x 1 100 100 100 100 o 1 o 1 o 1 o 1 —xlYl —X2V2 —x2Y2 —X3Y3 — xW4 — .X4Y4

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