Shape constraints from parametric and non-parametric models

An important focus of research in computer vision is that of shape recovery. If machines are to be made intelligent so that they can understand the scene around them, they must have shape models with which to describe the objects that they encounter. These shape models must be capable of describing the wide class of shapes that occur in the real world. This thesis is interested in using models to constrain and recover 3D shape from images. Shape models can vary greatly in their degree of parametrization. Three shape model classes are considered in this thesis: fully parametric, partially parametric, and non-parametric. A fully parametric model is defined as a shape model that is completely specified by some finite set of parameters. A partially parametric model is one that can be described in a parametric form but cannot necessarily be described by a predetermined finite set of parameters. Non-Parametric shape models are those for which we do not have a parametric form, although one may exist. This thesis presents new methods for constraining and recovering 3D shape for both parametric and non-parametric shape models. For the class of fully parametric models, the recovery of superquadric solids from range data is studied and we show that there is a relationship between the EOF measure used in the recovery algorithm and the values of the recovered superquadric parameters. Moreover, ad hoc selection of an EOF measure is shown to bias the solution; parameter values are either under- or over-estimated. The solution to this problem of bias in the recovered parameters is shown to be in finding meaningful EOF measures and we propose an EOF measure that is an actual distance metric from a point to the surface and show that this EOF measure reduces the effects of bias on the recovered solution. Next, we consider the class of partially parametric models known as straight homogeneous generalized cylinders (hereafter SHGCs). We show that there are exactly two SHGC parameters unconstrained by contour. A lambertian intensity-based algorithm is then derived to uniquely recover the 3D SHGC modulo scale. The algorithm generalizes to multiple light sources and does not require prior knowledge of light source positions or intensities. Results of the algorithm are given for synthetic SHGC images. In the last part of this thesis, we consider recovering shape constraints for non- parametric models. Since symmetry is pervasive in both man-made objects and nature, we selected objects of symmetry as the non-parametric shape model to study. We develop SYMAN, a symmetry analyzer, that includes two new methods for recovering axes of skew symmetry. Examples are given using both real and synthetic image contours. Object-based heuristics are then introduced and are used to recover 3D surface normal information for symmetric object contours.