Shape geometric invariant play an important role in model- based vision (MBV). However, in many MBV scenarios, shape information may not be sufficiently reliable and hence other types of invariant need to be considered. This paper addresses motion-based classification of objects based on unique motion or activity characteristics in long-sequence of images. To date, the techniques developed in motion-based recognition are inherently sensitive to (a) object's shape, (b) Euclidean group actions and (c) time scale, i.e., velocity and acceleration of motion. We propose the development of a set of motion-based invariant that capture geometric aspects of object's kinematic constraints during distinctive motions and activities. Algebraic and differential invariant of curves and surfaces in a projective space, the kinematic image space, are proposed for motion and activity classification. The proposed approach established parallelism between space and motion geometric invariance.