Multiresolution Wavelet Representations for Arbitrary Meshes

Wavelets and multiresolution analysis are instrumental for developing ee-cient methods for representing, storing and manipulating functions at various levels of detail. Although alternative methods such as hierarchical quadtrees or pyramidal models have been used to that eeect as well, wavelets have picked up increasing popularity in recent years due to their energy compactness, ee-ciency, and speed. Wavelet representations have achieved a great success in a wide variety of applications, including graphics, data compression, signal processing , physical simulation, hierarchical optimization, and numerical analysis, among others. This paper gives an overview of wavelets and their construction, as well as some applications to graphics and 3-D mesh processing at multiple levels of detail. The emphasis is on meshes of arbitrary topology and their multiresolution analysis by means of subdivision wavelets and their generalizations. In particular , both the traditional ((rst generation) wavelets and the more recent second generation wavelets are considered, together with the lifting scheme for their construction. Examples of such wavelets and their use for representation of arbitrary meshes are given, along with a survey of applications of wavelet-based multiresolution analysis to graphics problems.