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3D camera pose x= u v 1 1 1 P 2 P F 2D correspondences X= X Y Z Optical Flow: 2D point correspondences

Optical Flow: 2D point correspondencescis580/Spring2016/Lectures/coursera-18... · Optical Flow: 2D point correspondences. Optical Flow: 2D point correspondences. Optical Flow: 2D

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Page 1: Optical Flow: 2D point correspondencescis580/Spring2016/Lectures/coursera-18... · Optical Flow: 2D point correspondences. Optical Flow: 2D point correspondences. Optical Flow: 2D

3D camera pose

x =uv

11

1

P2

PF

2D correspondences

X=XYZ

Optical Flow: 2D point correspondences

Page 2: Optical Flow: 2D point correspondencescis580/Spring2016/Lectures/coursera-18... · Optical Flow: 2D point correspondences. Optical Flow: 2D point correspondences. Optical Flow: 2D

Optical Flow: 2D point correspondences

Page 3: Optical Flow: 2D point correspondencescis580/Spring2016/Lectures/coursera-18... · Optical Flow: 2D point correspondences. Optical Flow: 2D point correspondences. Optical Flow: 2D

Optical Flow: 2D point correspondences

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Page 5: Optical Flow: 2D point correspondencescis580/Spring2016/Lectures/coursera-18... · Optical Flow: 2D point correspondences. Optical Flow: 2D point correspondences. Optical Flow: 2D

d

Page 6: Optical Flow: 2D point correspondencescis580/Spring2016/Lectures/coursera-18... · Optical Flow: 2D point correspondences. Optical Flow: 2D point correspondences. Optical Flow: 2D

When d=0

=-

E(d=0)

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Three steps for solving this problem

Page 8: Optical Flow: 2D point correspondencescis580/Spring2016/Lectures/coursera-18... · Optical Flow: 2D point correspondences. Optical Flow: 2D point correspondences. Optical Flow: 2D

Step 1: Solve for

Page 9: Optical Flow: 2D point correspondencescis580/Spring2016/Lectures/coursera-18... · Optical Flow: 2D point correspondences. Optical Flow: 2D point correspondences. Optical Flow: 2D

Step 1: Solve for

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Step 1: Solve for

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Page 12: Optical Flow: 2D point correspondencescis580/Spring2016/Lectures/coursera-18... · Optical Flow: 2D point correspondences. Optical Flow: 2D point correspondences. Optical Flow: 2D

= +

Step 2: Taylor expansion

+

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Putting all together

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2D unknowns flow vector per pixel2 equations

Page 17: Optical Flow: 2D point correspondencescis580/Spring2016/Lectures/coursera-18... · Optical Flow: 2D point correspondences. Optical Flow: 2D point correspondences. Optical Flow: 2D

Also known as second moment matrix

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2 × 2 matrix

Summing over pixels

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2 × 1 matrix

Summing over pixels

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Error

Page 30: Optical Flow: 2D point correspondencescis580/Spring2016/Lectures/coursera-18... · Optical Flow: 2D point correspondences. Optical Flow: 2D point correspondences. Optical Flow: 2D

Error

Page 31: Optical Flow: 2D point correspondencescis580/Spring2016/Lectures/coursera-18... · Optical Flow: 2D point correspondences. Optical Flow: 2D point correspondences. Optical Flow: 2D

Error

d=(-7.1, -8.8)

d=(-6.8, -8.9)

d=(-1.4, -3.0)

Page 32: Optical Flow: 2D point correspondencescis580/Spring2016/Lectures/coursera-18... · Optical Flow: 2D point correspondences. Optical Flow: 2D point correspondences. Optical Flow: 2D
演示者
演示文稿备注
the difference between two images are too large, so I manually shift one image and try to recover the patch size is chosen so that we have a meaningful object in it
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Error

d=(-4.9, -0.4)

演示者
演示文稿备注
t = 11
Page 37: Optical Flow: 2D point correspondencescis580/Spring2016/Lectures/coursera-18... · Optical Flow: 2D point correspondences. Optical Flow: 2D point correspondences. Optical Flow: 2D

Error

d=(-4.9, -0.4)

d=(-0.1, -5.8)

d=(0, -3.7)

演示者
演示文稿备注
t = 0, 11, 41, 61