Cartesian moments are frequently used global geometrical features in computer vision for object pose estimation and recognition. We derive a closed form expression for 3-D Cartesian moment of order p+q+r of a superellipsoid in its canonical coordinate system. We also show how 3-D Cartesian moment of a globally deformed superellipsoid in general position and orientation can be computed as a linear combination of 3-D Cartesian moments of the corresponding nondeformed superellipsoid in canonical coordinate system. Additionally, moments of objects that are compositions of superellipsoids can be computed as simple sums of moments of individual parts. To demonstrate practical application of the derived results we register pairs of range images based on moments of recovered compositions of superellipsoids. We use a standard technique to find centers of gravity and principal axes in pairs of range images while third-order moments are used to resolve the four-way ambiguity. Experimental results show expected improvement of recovered rigid transformation based on moments of recovered superellipsoids as compared to the registration based on moments of raw range image data. Besides object pose estimation the presented results can be directly used for object recognition with moments and/or moment invariants as object features.
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