Analytical formulations for reconstruction of a line in 3-D space from two arbitrary perspective views

Objects in nature as well as man made are bound by planar as well as curvilinear surfaces. Hence the reconstruction process of three dimensional objects involves obtaining the geometrical attributes of these planar as well as curvilinear surfaces, lines, points etc. The work presented in this paper deals with the process of reconstruction of a line in 3-D space from two arbitrary perspective views. If a line in 3-D space is viewed from two arbitrary positions, two different images of the same line are obtained. The correspondence between this pair of projections of the line is assumed to be established in this work. The parameters of the line in 3-D space are obtained from the parameters of this pair of projections of the line on the image planes. The mathematical formulations for the parameters of the reconstructed line are analytically solved.