We present a novel method for building a multi-resolution representation of large digital surface models. The surface points coincide with the nodes of a planar graph which can be processed using a critically sampled, invertible lifting scheme. To drive the lazy wavelet node partitioning, we employ an attribute aware cost function based on the generalized quadric error metric. The resulting algorithm can be applied to multivariate data by storing additional attributes at the graph’s nodes. We discuss how the cost computation mechanism can be coupled with the lifting scheme and examine the results by evaluating the root mean square error. The algorithm is experimentally tested using two multivariate LiDAR sets representing terrain surface and vegetation structure with different sampling densities.