If the object is has a relatively simple geometry and you want to get a compact description of its shape, one of the following representations could work: superquadratic [1], hyperqurdaric [2], so-called "supershape" [3]. If the object isn't so simple, you can represent it in terms polynomial bases or radial basis functions. There is a vast number of other possibilities, however.
[1] Zhou & Kambhamettu, 2000, Extending superqudratics with exponent functions [2] Ohuchi & Saito, 2001, 3D shape modeling with extended hyperqudratics [3] Fougerolle et al., 2006, Rational supershapes for surface reconstruction
