Frequency-Based Representation of 3D Models using Spherical Harmonics

3D meshes are the most common representation of 3D models. However, surfaces represented by 3D meshes may contain noise or some unrequired details. Multiresolution representations and filtering techniques are very useful in this case. In this paper, we propose a new and compact representation for the surface of a general 3D mesh using the spherical harmonics. This representation can be useful in many applications such as filtering, progressive transmission and compression of 3D surfaces. First, we present a basic framework for star-shaped objects. Then, we show how to extend this framework to general form meshes using certain segmentation techniques in combination with implicit surface techniques. An interesting feature of our approach is that the computation of the involved spherical harmonics transform is decomposed into the computation of spherical harmonics transforms based on elementary triangles which compose the mesh. This feature shows that the complexity of the computation of the used spherical harmonics transform linearly dependant on the number of triangles of the mesh. We present some experimental results which demonstrate our technique.