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Multi-View Geometry

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- Points go to Points
- Lines go to Lines
- Planes go to whole image or Half-planes
- Polygons go to Polygons

Y

M

Image plane

C

Z

v

X

Focal plane

m

u

Y

M

Image plane

Y

C

Z

v

X

X

Z

Focal plane

m

u

By Rigid Body Transformation:

- What cues in the image provide 3D information?

- Shading

Merle Norman Cosmetics, Los Angeles

- Shading
- Texture

The Visual Cliff, by William Vandivert, 1960

- Shading
- Texture
- Focus

From The Art of Photography, Canon

- Shading
- Texture
- Focus
- Motion

- Shading
- Texture
- Focus
- Motion

- Shape From X
- X = shading, texture, focus, motion, ...

- 3D World Points

- Camera Centers

- Camera Orientations

Relates

- 3D World Points

- Camera Centers

- Camera Intrinsic Parameters

- Image Points

Relates

- Camera Orientations

scene point

image plane

optical center

- Basic Principle: Triangulation
- Gives reconstruction as intersection of two rays

- Requires
- calibration
- point correspondence

p’

?

p

Given p in left image, where can the corresponding point p’in right image be?

Epipolar Line

p’

Y2

X2

Z2

O2

Epipole

M

Image plane

Y1

p

O1

Z1

X1

Focal plane

P

p

p’

O’

O

P

p

p’

O’

O

Linear Constraint:Should be able to express as matrix multiplication.