Progressive Low Bit Rate Coding of Simple 3D Objects with Matching Pursuit

Abstract

Summary form only given. The paper presents a low rate progressive 3D mesh compression scheme for simple, genus-zero 3D objects. The proposed scheme is based on signal representation using redundant expansions on the 2D-sphere. First, generic input data is re-sampled as a function on the 2D-sphere, and the signal value for each point on the regular grid is obtained by performing nearest neighbor interpolation within four points from the initial 3D model. The model representation is then constructed using a matching pursuit algorithm, with an over-complete dictionary of atoms, defined on a sphere. In order to capture the particular characteristics of the 3D models efficiently, we propose a dictionary construction based on two generating functions, a Gaussian to capture low-frequency components, and a modified combination of a Gaussian and its second derivative to capture high-frequency components of the input signal. Compared to state-of-the-art encoders, our method has been shown to offer very good compression efficiency, but the performance is limited by the resampling step that maps the input model on the 2D-sphere. Matching pursuit has, however, the advantage of providing an intrinsically progressive scheme, that is also very flexible.