The geometric invariants are very useful for recognizing objects in the scene from arbitrary viewpoints. Recently, it has been shown that some geometric invariants can be defined in the space with time domain, and they can be applied for recognizing dynamic motions from arbitrary viewpoints. However, the existing invariants on motions are computed from multiple points in the sequence of images, and thus accurate tracking of image features is required. As a result, if tracking of image features fails, these invariants cannot be computed. In this paper, we propose invariants on motions, which are defined by using image moments. We show that by using the proposed moment invariants on motions, we can recognize non-rigid motions from arbitrary viewpoints without tracking image features. We also show that they can reflect entire changes in object shapes and motions in image sequences.