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The recognition of motions is very important for understanding dynamic actions and extracting events from video sequences. We propose invariants on object motions, which can be extracted from image sequences, and are invariant even if the motions are viewed from arbitrary viewpoints. We call them space-time invariants since they are defined under space-time projections. We show that these invariants are very useful for extracting specific motions from video sequences. The proposed space-time invariants are implemented and tested on real image sequences.