Departament
of Geometry and Topology, Universidad
Complutense de Madrid Image Processing Group (GTI), Universidad Politécnica de Madrid |
A very short camera autocalibration dictionary |
Absolute conic: The conic that in a
Euclidean coordinate system has equations T=X2+Y2+Z2=0, in homogeneous coordinates. Thus it
lies at the plane at infinity. Absolute quadric: The
set of planes tangent to the absolute conic. The homogeneous
coordinates of these planes have equation U2+V2+W2=0. Autocalibration: Literally,
obtainment of the extrinsic parameters (positions and orientation) and
intrinsic parameters (pixel shape, focal length, principal point) of a
set of cameras on the exclusive basis of images taken with them.
Equally often it has this more specific meaning. Homography: A geometric transformation that, in homogenous coordinates, is given by the multiplication of the coordinate vector of each point by a regular matrix. Homogeneous
coordinates: The homogeneous coordinates of a spatial point of
affine coordinates (X,Y,Z) are (X,Y,Z,1) or any non-null proportional
vector. In homogeneous coordinates we also have points at infinity,
corresponding to the set of lines parallel to a given line. If these
lines have direction vector (A,B,C), the associated point has
homogeneous coordinates (A,B,C,0). Euclidean
homogeneous coordinates are those that result from a Euclidean
reference. Horopter curve: The
set of 3D points that project onto two points of identical coordinates
in two cameras. It is a cubic curve that intersects the plane at
infinity at two points of the absolute conic plus a third point which
is the pole with respect to the absolute conic of the line given by the
other two. Absolute line
quadric: The set of lines that intersect the absolute conic. In
(suitable) Euclidean Plücker coordinates it is given by the
equation A12+A22+A32=0. Plane at infinity: The set of points that, in Euclidean homogeneous coordinates, have equation T=0. Plücker
coordinates: Lines in space (projective 3-space P3) form a 4-dimensional space and can be represented in algebraic geometry by six homogeneous coordinates satisfying a quadratic constraint (i.e., by points in P5 that lie on Klein's quadric). Projective
reconstruction: A 3D reconstruction that differs from the
original one by a spatial homography. |
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