GEOMETRIC CAMERA MODELS

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GEOMETRIC CAMERA MODELS

• Elements of Euclidean Geometry
• The Intrinsic Parameters of a Camera
• The Extrinsic Parameters of a Camera
• The General Form of the Perspective Projection
  Equation

Reading Chapter 2.
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Quantitative Measurements and Calibration
Euclidean Geometry
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Euclidean Coordinate Systems
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Planes
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Coordinate Changes Pure Translations
OBP OBOA OAP , BP AP BOA
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Coordinate Changes Pure Rotations
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Coordinate Changes Rotations about the z Axis
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A rotation matrix is characterized by the
following properties

• Its inverse is equal to its transpose, and
• its determinant is equal to 1.

Or equivalently

• Its rows (or columns) form a right-handed
• orthonormal coordinate system.

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Coordinate Changes Pure Rotations
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Coordinate Changes Rigid Transformations
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Rigid Transformations as Mappings
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The Intrinsic Parameters of a Camera
Units
k,l pixel/m
f m
a,b
pixel
Physical Image Coordinates
Normalized Image Coordinates
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The Intrinsic Parameters of a Camera
Calibration Matrix
The Perspective Projection Equation
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Extrinsic Parameters