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This paper presents an algorithmic approach to the problem of detecting independently moving objects in 3D scenes that are viewed under camera motion. There are two fundamental constraints that can be exploited for the problem: 1) two/multiview camera motion constraint (for instance, the epipolar/trilinear constraint) and 2) shape constancy constraint. Previous approaches to the problem either use only partial constraints, or rely on dense correspondences or flow. We employ both the fundamental constraints in an algorithm that does not demand a priori availability of correspondences or flow. Our approach uses the plane-plus-parallax decomposition to enforce the two constraints. It is also demonstrated that for a class of scenes, called sparse 3D scenes in which genuine parallax and independent motions may be confounded, how the plane-plus-parallax decomposition allows progressive introduction, and verification of the fundamental constraints. Results of the algorithm on some difficult sparse 3D scenes are promising.