GEOMETRIC CAMERA MODELS

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Presentation transcript:

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.

Quantitative Measurements and Calibration Euclidean Geometry

Euclidean Coordinate Systems

Planes

OBP = OBOA + OAP , BP = AP + BOA Coordinate Changes: Pure Translations OBP = OBOA + OAP , BP = AP + BOA

Coordinate Changes: Pure Rotations

Coordinate Changes: Rotations about the z Axis

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.

Coordinate Changes: Pure Rotations

Coordinate Changes: Rigid Transformations

Rigid Transformations as Mappings

The Intrinsic Parameters of a Camera Units: k,l : pixel/m f : m a,b : pixel Physical Image Coordinates Normalized Image Coordinates

The Intrinsic Parameters of a Camera Calibration Matrix The Perspective Projection Equation

Extrinsic Parameters

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