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. >
['Jean Ponce', 'David J. Kriegman']
On recognizing and positioning curved 3D objects from image contours