Abstract: We present a novel approach for the decimation of triangle surface meshes. Our algorithm takes as input a triangle surface mesh and a set of planar proxies detected in a pre-processing analysis step, and structured via an adjacency graph. It then performs greedy mesh decimation through a series of edge collapse, designed to approximate the local mesh geometry as well as the geometry and structure of proxies. Such structure-preserving approach is well suited to planar abstraction, i.e. extreme decimation approximating well the planar parts while filtering out the others. Our experiments on a variety of inputs illustrate the potential of our approach in terms of improved accuracy and preservation of structure.