Reconstruction from three orthographic views

Summary As Ullman (1979) showed, an object can be reconstructed uniquely from three orthographic views, if at least four homologous tripels of points are known. If only three homologous tripels of points are observed, the reconstruction problem has a finite number of solutions (cf. Huang and Lee (1989)). In this article the 3-point-problem is reduced to a quadratic problem: If the squares of the sides of the considered triangles are interpreted as coordinates in a three-dimensional parameter space, the reconstruction problem is equivalent to the determination of the intersection of three parallelly shifted cones subject to certain constraints.