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 s ampling 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 er ror, and thus, when combined with the appropriate encoding of the coefficie nts, optimize the compression of the mesh information transmitted. At the s ame time, it produces a hierarchy of meshes based on quincunx sampling wher e coarse meshes are as similar to their liner versions as possible, This is very much desirable in progressive transmission. Depending on its interpol ation 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 few er in uniform regions. Complete correspondence between triangles at each le vel is identified, resulting to an efficient hierarchical representation of the mesh. The algorithm can be also used for the triangulation of a specif ic region of interest. Experimental results demonstrate that the proposed s cheme provides improvement in quality (MSE) by a factor of two when compare d with other well known adaptive triangulation schemes.