Resultants Approach to the Triple Three-dimensional Intersection Problem

概要

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The resultant algebraic approach is here applied to solve the triple three-dimensional intersection problem vital in Photogrammetry and Computer vision. From the observations of type horizontal directions T and vertical directions B<SUB>i</SUB>, with i = 1, 2, 3, we demonstrate that the three nonlinear system of equations can be decomposed using Strumfel's resultant method to three quartic polynomials whose roots are obtainable via MA TLAB-solve command. The advantage here is that when one is faced with the minimum number of known points, here three, one can still carry out an intersection to obtain the coordinates of the desired point. In Photo-grammetry, the procedure could be used to obtain the coordinates of pass points where known stations are limited only to the minimum number.
日本測地学会の論文