26.
The
twin perspective 4 point (twin P4P) problem – also called the combined three dimensional resection-intersection problem – is the problem of finding
the position of a scene object from 4 correspondence points and a scene stereopair. While the
perspective centers of the left and right scene image are positioned by means of a
double three dimensional resection, the position of the scene object imaged on the left and right photograph is determined by a
three dimensional intersection based upon given
resected perspective centers. Here we present a new
algorithm solving the
twin P4P problem by means of
M?bius barycentric coordinates. In the
first algorithmic step we determine the distances between the perspective centers and the unknown intersected point by solving a linear system of
equations. Typically, area elements of the left and right image build up the linear equation system. The
second algorithmic step allows for the computation of the
M?bius barycentric coordinates of the
unknown intersected point which are
thirdly converted into three dimensional object space coordinates
{X,Y,Z} of the intersected point. Typically, this
three-step algorithm based upon
M?bius barycentric coordinates takes advantage of the primary double resection problem from which
only distances from four correspondence points to the left and right perspective centre are needed. No orientation parameters and no coordinates
of the left and right perspective center have to be made available.
Received 1 May 1996; Accepted 13 September 1996
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