3D shape coding with superquadrics

We present a geometric coding method for 3D real and virtual objects transmission and visualization. We describe object surfaces with a set of superellipsoids which are structured with a constructive solid geometry (CSG) tree. An unstructured cloud of 3D points lying on the original object surface is considered as initial data. The tree is obtained using a split and merge algorithm. At each splitting step, the set of points is partitioned into two superellipsoids. The parameters of each ellipsoid is computed with a nonlinear regression technique (Levenberg-Marquardt). This decomposition is stopped when the estimation error reaches a given threshold (the accepted distortion). The objective of the merging algorithm is to reduce the number of superellipsoids used to describe the complex 3D object without increasing the global distortion. This algorithm allows one to merge both connected and non-connected elements of the superellipsoids set obtained from the decomposition step. The whole scheme is applied to synthetic objects