Three-dimensional descriptions based on the analysis of the invariant and quasi-invariant properties of some curved-axis generalized cylinders

We address the recovery of object-level 3D descriptions of some classes of curved-axis generalized cylinders. For this, the first part of the paper analyzes the projective properties of two common generic shapes, planar right constant generalized cylinders (PRCGCs) and circular planar right generalized cylinders (circular PRGCs). The properties we analyze include new geometric invariant and quasi-invariant properties of the orthographic projection of the above shapes and a useful classification of their structural properties as functions of their pose. The second part of the paper describes an implemented system which detects and recovers PRCGCs and circular PRGCs from an intensity image in the presence of noise, surface markings, shadows, and partial occlusion. The methods exploit the projective properties to hypothesize and verify relevant curved-axis objects, thus explicitly using the three-dimensionality of the objects and of the desired descriptions. This work extends past work on the recovery of volumetric shapes from an intensity image by addressing new primitives, deriving new properties and by developing a system that recovers them from an intensity image. We demonstrate our method on several real intensity images.