There has been much interest recently in using invariant theory in computer vision. Most work has concentrated on recognition of 3-D objects from 2-D images using algebraic or differential invariants. In this work, we address the usage of a class of projective invariants and quasi-invariants for the segmentation and 3-D recovery of generalized cylinders from a monocular image. We derive important projective invariants of straight homogeneous generalized cylinders and describe an implemented system for their segmentation and recovery from a monocular intensity image. We then derive quasi-invariant properties of circular planar right generalized cylinders and describe another implemented system for recovering their 3-D shape from 2-D contours. This work shows that the problem of shape description and scene segmentation from a monocular image can be solved for a large class of objects in our environment. Examples of results of both systems are also given.