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The main problems in
Projective geometry, camera models and calibration
Subhashis Banerjee
Dept. Computer Science and Engineering
IIT Delhi
The main problems in computer vision
An infinitely strange perspective
The pin-hole camera model
Standard perspective projection
In terms of projective coordinates
Basics of Projective Geometry
Affine and Euclidean geometries
Spherical geometry
Projective geometry
Canonical injection of
into
and Points at infinity
Lines and conics in
Planes and lines in
Lines is
: Pl
cker coordinates
Projective basis
Collineations
Preserves straight lines and cross ratios
Illustration of perspectivity
Projective mappings of lines and conics in
The affine subgroup
The Euclidean subgroup
Decomposition of a projective transformation
Affine calibration of a plane
Euclidean calibration of a plane
How to compute a homography
Camera models
The Projective Camera
The Perspective Camera
The Affine Camera
The Weak-Perspective Camera
The orthographic camera
Anatomy of a projective camera
The optical center
The column vectors of the camera matrix
The row vectors of the camera matrix
The focal plane:
The axes planes:
The Principal axis and the principal point
Pin-hole camera revisited
Camera calibration
Tsai camera model and calibration
Linear estimation of parameters
Nonlinear optimization
Camera calibration and absolute conic
What does calibration give?
The image of the absolute conic
A simple calibration device
Vanishing points and vanishing lines
Camera rotation from vanishing points
Determining calibration from vanishing points and lines
Zhang's camera calibration
About this document ...
Subhashis Banerjee 2008-01-20
into
and Points at infinity
