Abstract: A process and apparatus are provided to characterize low-resolution partial point clouds for object recognition or query. A partial point cloud representation of an object is received. Zero and first order geometric moments of the partial point cloud are computed. A location of a center of a point cloud mass is computed using the geometric moments. A cubic bounding box is generated centered at the location of the mass center of the point cloud, with one side of the box bounding the point cloud at its longest semi-axis. The bounding box is divided into a three dimensional grid. A normalized voxel mass distribution is generated over the three dimensional grid. Tchebichef moments of different orders are calculated with respect to the voxel mass distribution in the grid. Low-order moments are collected to form TMSDs. Similarity is compared between the TMSD of the point cloud with TMSDs of other point clouds.