Bài giảng Chapter 2: Projective geometry and camera models
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Chapter 2 – Camera Model
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Chapter 2
Projective Geometry and
Camera Models
James Hays, Brown University
Department of Mechatronics
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Contents
Mapping between image and world coordinates
• Projective geometry
Vanishing points and lines
• Pinhole camera model
• Cameras & lenses
• Projection matrix
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Camera and World Geometry
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Chapter 2 – Camera Model
Projection can be tricky…
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Chapter 2 – Camera Model
Projection can be tricky…
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Projective Geometry
• What is lost?
Length
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Length is not preserved
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Projective Geometry
• What is lost?
Length
Angles
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Projective Geometry
• What is preserved?
Straight lines are still straight
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Vanishing points and lines
• Parallel lines in the world intersect in the image at a
“vanishing point”.
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Vanishing points and lines
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Vanishing points and lines
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Vanishing points and lines
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Note on estimating vanishing points
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Camera obscura: the pre-camera
• Known during classical period in China and Greece
(e.g. Mo-Ti, China, 470BC to 390BC)
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Parallel light rays which pass through a small aperture
begin to diverge and interfere with one another. This
becomes more significant as the size of the aperture
decreases relative to the wavelength of light passing
through, but occurs to some extent for any size of
aperture or concentrated light source.
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Cameras and Lenses
• A lens focuses light onto the film
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Cameras and Lenses
• A lens focuses light onto the film
Rays passing through the center are not deviated.
All parallel rays converge to one point on a plane
located at the focal length f.
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Cameras and Lenses
• A lens focuses light onto the film
There is a specific distance at which objects are “in
focus” [other points project to a “circle of confusion”
in the image].
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