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Superquadrics

Categories: Vision


Author(s): H.W. Hughes

Superquadrics are a set of parameterised volumetric shapes used for computer vision applications. They are useful because a wide range of solid shapes can be generated by use of only a few parameters. Surface patches can be defined by the surface of a superquadric volume. Additionally, more complex objects can be defined by combinations of simpler volumes using union, intersection and complement. Any superquadric may be expressed by the equation:

χ(η,ω)=(a1cosε1ηcosε2ωa2cosε1sinε2ωa3sinε1)

where -π/2ηπ/2 and -πω<π, a1, a2 and a3 are the length, width and breadth respectively. ϵ1 and ϵ2 are the parameters which specify the shape of the superquadric. ϵ1 is the squareness parameter in the north-south direction. ϵ2 is the squareness parameter in the east-west direction. The advantage of this representation is that the normal vectors are given by:

n(η,ω)=(1a1cos2ε1ηcos2ε2ω1a2cos2ε1ηsin2ε2ω1a3sin2ε1η)

enabling the shape parameters to be recovered via surface normal information from image intensity, contour shape and the like. These mathematical solids are a subset of the more general family of Generalised Cylinders.


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