On recognizing and positioning curved 3D objects from image contours

The authors present an approach for explicitly relating the shape of image contours to models of curved three-dimensional objects. This relationship is used for object recognition and positioning. Object models consist of collections of parametric surface patches and their intersection curves; this includes nearly all representations used in computer-aided geometric design and computer vision. The image contours considered are the projections of surface discontinuities and occluding contours. Elimination theory provides a method for constructing the implicity equation of the image contours of an object observed under orthographic or perspective projection. This equation is parameterized by the object´s position and orientation with respect to the observer. Determining these parameters is reduced to a fitting problem between the theoretical contour and the observed data points. The approach readily extends to parameterized models. It has been implemented for a simple world composed of various surfaces of revolution and successfully tested on several real images