By considering all 2D transformations on image patterns, Otsu has shown that the moment feature is a kind of linear feature extractor from patterns and they are closed under such transformations. But the projections from 3D space onto 2D space are not considered. In order to recognize 3D motions from 2D images, the projections should be considered. So in this paper, the representation of the projected motion group is considered through Lie algebraic methods. We give the explicit formula of the bases of its representation. It is shown that the bases can be orthonormal bases. The quasi moments are defined and also shown to be closed in their order under the projected rotation group.