Progressive graph-signal sampling and encoding for static 3D geometry representation

Compression of arbitrary 3D geometry like a human figure in 3D space is challenging. Existing 3D representations like point cloud require encoding of input-specified 3D coordinates, resulting in a large overhead. In this paper, assuming that there exists an underlying smooth 2D manifold in 3D space that describes the geometric shape of a target object, we develop a new progressive 3D geometry representation that signal-adaptively identifies new samples on the manifold surface and encodes them efficiently as graph-signals. Specifically, at each iteration, using previous encoded samples in 3D space, the encoder and decoder first synchronously interpolate a continuous sampling kernel (a 3D mesh) - an approximation of the target surface. We next distribute new sample locations on the continuous kernel based on locally computed kernel curvatures, and compute the signed distances between sample locations and the target surface as sample values. Finally, we connect new discrete samples into a graph for graph-based transform coding of the sample values, which are transmitted to the decoder to refine 3D reconstruction. Experimental results show that our coding scheme outperforms an existing mesh-bsed approach significantly at the low-bitrate region for two different datasets.