Hierarchical representation and coding of surfaces using 3-D polygon meshes

This paper presents a novel procedure for the representation and coding of three-dimensional (3-D) 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, when combined with the appropriate encoding of the coefficients, 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. Depending on its interpolation error and the available bitrate, each filtered sample is a candidate for becoming a vertex of the mesh. 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 in an efficient hierarchical representation of the mesh. The algorithm can be also used for the triangulation of a specific region of interest. Experimental results demonstrate that the proposed scheme provides an improvement in quality (MSE) by a factor of two when compared with other well known adaptive triangulation schemes.