Many global shape recognition techniques, such as moments and Fourier Descriptors, are used almost exclusively with two-dimensional images. It would be desirable to extend these global shape recognition concepts to three dimensional images. Specifically, the concepts associated with Fourier Descriptors will be extended to both three dimensional object representation and recognition and the representation and recognition of objects which are described by depth data. With Fourier Descriptors, two dimensional shape boundaries are described in terms of a set of complex sinusoidal basis functions. Extending this concept to three dimensions, the surface of a shape will be described in terms of a set of three .dimensional basis functions. The basis functions which will be used are known as spherical harmonics. Spherical harmonics can be used to describe a function on the surface of the unit sphere. In this application, the function on the unit sphere will describe the shape to be represented. The representation presented here is restricted to the class of objects for which each ray from the origin intersects the surface of the object only once. Basic definitions and properties of spherical harmonics will be discussed. A distance measure for shape discrimination will be derived as a function of the spherical harmonic coefficients for two shapes. The question of representation of objects described by depth data will then be addressed. A functional description for the objects will be introduced, along with methods of normalizing the spherical harmonic coefficients for scale, translation, and orientation so that meaningful library comparisons might be possible. Classification results obtained with a set of simple objects will be discussed.