# Adaptive Mesh Compression in 3D Computer Graphics using Multiscale Manifold Learning

This paper investigates compression of 3D ob jects in computer graphics using manifold learning. Spectral compression uses the eigenvectors of the graph Laplacian of an object's topology to adaptively compress 3D objects. 3D compression is a challenging application domain: ob ject models can have > 105 vertices, and reliably computing the basis functions on large graphs is numerically challenging. In this paper, we introduce a novel multiscale manifold learning approach to 3D mesh compression using diffusion wavelets, a general extension of wavelets to graphs with arbitrary topology. Unlike the "global" nature of Laplacian bases, diffusion wavelet bases are compact, and multiscale in nature. We decompose large graphs using a fast graph partitioning method, and combine local multiscale wavelet bases computed on each subgraph. We present results showing that multiscale diffusion wavelets bases are superior to the Laplacian bases for adaptive compression of large 3D ob jects.

*Author: Sridhar Mahadevan, University of Massachusetts Amherst*