On the geometries of conic section representation of noisy object boundaries

This paper studies some geometrical properties of conic sections and the utilization of these properties for the generation of conic section representations of object boundaries in digital images. Several geometrical features of the conic sections, such as the chord, the characteristic point, the guiding triangles, and their appearances under the tessellation and noise corruption of the digital images are discussed. The study leads to a noniterative algorithm that takes advantage of these features in the process of formulating the conic section parameters and generating the approximations of object boundaries from the given sequences of edge pixels in the images. The results can be optimized with respect to certain different criteria of the fittings.