Hierarchical representation and coding of surfaces using 3D polygon meshes

This paper presents a novel procedure for the representation and coding of 3D surfaces using hierarchical adaptive triangulation. The proposed procedure is based on pyramidal analysis using the quincunx sampling minimum variance interpolation (QMVINT) filters. These are reduced pyramids with quincunx sampling applied to the parametric representation of the surface, chosen so as to minimize the variance of the interpolation error, and thus optimize the compression of the mesh information transmitted. At the same time, it produces a hierarchy of meshes based on quincunx sampling where coarse meshes are as similar to their finer versions as possible. This is very much desirable in progressive transmission. The result is a progressive sequence of meshes consisting of more triangles wherever large variations exist and fewer in uniform regions. Complete correspondence between triangles at each level is identified, resulting to an efficient hierarchical representation of the mesh. Experimental results demonstrate the efficient performance of the algorithm