Compressive Representation of Three-dimensional Models

Abstract

Due to recent developments in data acquisition mechanisms, called 3d scanners, mesh compression has become an important tool for manipulating geometric data in several areas. In this context, a recent approach to the theory of signs called Compressive Sensing states that a signal can be recovered from far fewer samples than those provided by the classical theory. In this paper, we investigate the applicability of this new theory with the purpose of to obtain a compressive representation of geometric meshes. We developed an experiment which combines sampling, compression and reconstruction of various mesh sizes. Besides figuring compression rates, we also measured the relative error between the original mesh and the recovered mesh. We also compare two measurement techniques through their processing times, which are: the use of Gaussian matrices; and the use of Noiselet matrices. Gaussian matrices performed better in terms of processing speed, with equivalent performance in compression capacity. The results indicate that compressive sensing is very useful for mesh compression showing quite comparable results with traditional mesh compression techniques.