# Catalogue of Artificial Intelligence Techniques

## 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:

where and , , and are the length, width and breadth respectively. and are the parameters which specify the shape of the superquadric. is the squareness parameter in the north-south direction. is the squareness parameter in the east-west direction. The advantage of this representation is that the normal vectors are given by:

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.

### References:

- Barr, A.H.,
*Superquadrics and angle-preserving transformations*IEEE Computer Graphics and Applications**1**, 1--20.

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