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Geometry of the triangulation procedure.

Geometry of the triangulation procedure.

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This paper addresses the problem of computing the three-dimensional (3-D) path of a moving rigid object using a calibrated stereoscopic vision setup. The proposed system begins by detecting feature points on the moving object. By tracking these points over time, it produces clouds of 3-D points that can be registered, thus giving information about...

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... Even if this approach, involving the minimization of algebraic quantities, works well in practice, a geometric triangulation formulation is often preferred. The method finds the 3-D point that minimizes its 3-D distance with two noncrossing lines in space. In other words, it returns the middle point of the segment perpendicular to both rays. Fig. 2 shows the geometry of two cameras projecting the images x 1 and x 2 of the 3-D point X. In an ideal situation, the extension of the ...
Context 2
... best solution is therefore to search for the point X that is the middle of the segment perpendicular to both lines. From Fig. 2, we have Expressing point X 2 in the reference frame of the first camera gives ...

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