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# Multi-View Geometry - PowerPoint PPT Presentation

Multi-View Geometry. Review: Pinhole Camera. Review: Perspective Projection. Review: Perspective Projection. Points go to Points Lines go to Lines Planes go to whole image or Half-planes Polygons go to Polygons. Perspective cues. Perspective cues. Perspective cues.

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## PowerPoint Slideshow about 'Multi-View Geometry' - doli

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Presentation Transcript

• 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?

Merle Norman Cosmetics, Los Angeles

• Texture

The Visual Cliff, by William Vandivert, 1960

• Texture

• Focus

From The Art of Photography, Canon

• Texture

• Focus

• Motion

• Texture

• Focus

• Motion

• Shape From X

• X = shading, texture, focus, motion, ...

• Camera Centers

• Camera Orientations

Multi-View Geometry

Relates

• Camera Centers

• Camera Intrinsic Parameters

• Image Points

Multi-View Geometry

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?

p’

Y2

X2

Z2

O2

Epipole

Stereo Constraints

M

Image plane

Y1

p

O1

Z1

X1

Focal plane

p

p’

O’

O

From Geometry to Algebra

p

p’

O’

O

From Geometry to Algebra

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