Efficient algorithms for determining 3D biplane imaging geometry
A key problem in biplane projection imaging is to determine the imaging geometry (i.e., the relative rotation and translation) of two projections so that the 3D structure can be accurately reconstructed. Based on interesting observations and efficient geometric techniques, the authors present new algorithmic solutions for this problem: given two sets of 2D points \(A=\{a_1,\dots,a_n \}\) and \(B=\{b_1,\dots,b_n \}\) on two image screens (or planes) resp. with each corresponding pair of points \(a_i\) and \(b_i\) being the approximations of the projections of an unknown 3-D point \(p_i\), also given the 3D coordinate system of \(A\), find the most likely position of the origin of \(o_B\) and the orientation of the 3D coordinate system of \(B\) in the coordinate system of \(A\). The authors' approach first reduces the imaging geometry determination problem to an optimal cell search problem in an arrangement of surfaces in \(\mathbb R^6\), then each of surfaces is simplified in aim to obtain explicit expression by an equation (in general non-algebraic). Comparing with existing optimization-based approaches, the presented techniques yield better accuracy and have bounded execution time, thus is more suitable for online applications.
scientific article; zbMATH DE number 5005137