In this paper, we address the problem of precisely recovering the 3-D pose of 3-D shape fiducials from images obtained by means of an uncalibrated Computed Tomography (CT) imaging device. The main goal in this work is to model and estimate the geometric transformation relating line fiducials to their projections in cross-sectional images. To do so, we propose techniques which solve the points to lines correspondence using closed-form and numerical algorithms. A geometric transformation with eight degrees of freedom (rotation, translation and anisotropic scaling) is used to model both a rigid-body transformation and a scaling transformation accounting for CT scan intrinsic parameters. Furthermore, an estimation of error bounds in space is given when image data are affected by noise. Real experiments show that the proposed method provides good results on a set of CT images from many viewpoints.