Mathematical model for shape coding with B-splines

A major problem in object-oriented video coding is the efficient encoding of the shape information of arbitrarily shaped objects. Efficient shape coding schemes are also needed in encoding the shape information of video object (VO) in the upcoming MPEG-4 standard. Furthermore, there are many applications where only the shape needs to be encoded, such as CAD, 3D modeling and signature encoding. In this paper, we present an efficient method for the lossy encoding of object shapes which are given as 8-connect chain codes using a mathematical model. We approximate a boundary by a second-order B-spline curve and consider the problem of finding the curve with the lowest bit-rate for a given distortion. The presented scheme is optimal, efficient and offers complete control over the trade-off between bit-rate and distortion. It is an extension of our previous research where we used polygons to approximate a boundary. The main reason for using curves rather than polygons is that curves have a more natural appearance than polygons and can give better coding efficiencies. We present results of the proposed scheme using objects boundaries in different shapes and sizes as well as an MPEG-4 test sequence.