Using extremal boundaries for 3-D object modeling

The extremal boundaries, of 3-D curved objects are the images of special curves drawn on the object and are called rims. They are viewpoint dependent and characterized by the fact that the optical rays of their points are tangential to the surface of the object. The mathematics of the relationship between the extremal boundaries and the surface of the object is studied. This study makes it possible to design an algorithm for detecting those boundaries in the images that are likely to be extremal. Once this has been done, one can reconstruct the rims and compute the differential properties of the surface of the object along them up to the second order. If a qualitative description is sufficient, the sign of the Gaussian curvature of the surface along the rim can be computed in a much simpler way. Experimental results are presented on synthetic and real images. The work provides a better understanding of the relationship between the apparent and real shape of a 3-D object as well as algorithms for reconstructing the local shape of such an object along the rims