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The mapping from the coordinates of a 3D point P to the 2D image coordinates of the point's projection onto the image plane, according to the pinhole camera model, is given by
A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane.
The essence of an image is a projection from a 3D scene onto a 2D plane, during which process the depth is lost. The 3D point corresponding to a specific image point is constrained to be on the line of sight. From a single image, it is impossible to determine which point on this line corresponds to the image point.
The projection of point P onto the image plane, denoted Q. This point is given by the intersection of the projection line (green) and the image plane. In any practical situation we can assume that > 0 which means that the intersection point is well defined. There is also a 2D coordinate system in the image plane, with origin at R and with axes ...
The triangulation problem is in principle trivial. Since each point in an image corresponds to a line in 3D space, all points on the line in 3D are projected to the point in the image. If a pair of corresponding points in two, or more images, can be found it must be the case that they are the projection of a common 3D point x.
Since the optical centers of the cameras lenses are distinct, each center projects onto a distinct point into the other camera's image plane. These two image points, denoted by e L and e R, are called epipoles or epipolar points. Both epipoles e L and e R in their respective image planes and both optical centers O L and O R lie on a single 3D ...
The angled corner of the plane of projection is addressed later. Fig.3: Projectors emanate parallel from all points of the object, perpendicular to the plane of projection. Fig.4: An image is created thereby. Fig.5: A second, horizontal plane of projection is added, perpendicular to the first.
Planar projections are the subset of 3D graphical projections constructed by linearly mapping points in three-dimensional space to points on a two-dimensional projection plane. The projected point on the plane is chosen such that it is collinear with the corresponding three-dimensional point and the centre of projection .