Object restoration is an unsolved problem in computer vision. We apply the concept of Straight Homogeneous Generalized Cylinders (SHGCs) as a significant model to constrain a variety of 3-D objects for viewpoint independent shape recovery. The SHGCs are represented with a straight axis and cross-section that have constant shape but vary in size. This paper presents a new approach to recover the 3-D shape of the SHGCs from their projected 2-D contour images with a single view. In addition, the analytical form of the SHGCs applied to various shapes, such as the Circular SHGC, the Polygonal SHGC., and the Ellipsoidal SHGC, is also discussed.