View Variation and Linear Invariants in 2-d and 3-d

abstract We present a systematic study of the relation between 2-D linear image invariants for point sets and their relation to camera viewpoint and linear 3-D invariants. For 5 points in general position there is a simple realtion between the a linear image invariant an a 3-D invaraint computed from the 5 points toghether with the camera viewpoint. We use this in order to derive the viewpoint independent relation between relative image and space invariants for 6 points in general position in terms of brackets in image and space coordnates. We demonstrate how constraints on point conngurations such as point coplanarity simpliies relations between invariants in 2-D and 3-D. The simple case of 4 point coplanarity has a dramatic eeect on the relation between invariants in 2-D and 3-D and is suggested as a good compromise for a recognition system of 3-D objects based on indexing using image invariants computed from a single image

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