Projection distortion analysis for flattened image mosaicing from straight uniform generalized cylinders

Abstract

This paper presents a new approach for reconstructing images mapped or painted on straight uniform generalized cylinders (SUGC). A set of monocular images is taken from different viewpoints in order to be mosaiced and to represent the entire scene in detail. The expressions of the SUGC's projection axis are derived from two cross-sections projected onto the image plane. Based on these axes we derive the SUGC localization in the camera coordinate system. We explain how we can find a virtual image representation when the intersection of the two axes is matched to the image center. We analyze the perspective distortions when flattening a scene which is mapped on a SUGC. We evaluate the lower and the upper bounds of the necessary number of views in order to represent the entire scene from a SUGC, by considering the distortions produced by perspective projection. A region matching based mosaicing method is proposed to be applied on the flattened images in order to obtain the complete scene. The mosaiced scene is visualized on a new synthetic surface by a mapping procedure. The proposed algorithm is used for the representation of mural paintings located on SUGCs with closed cross-sections (circles for columns), or opened cross-sections (ellipses or parabolas for vaults).