Processing and rendering of point sampled geometry

Abstract

Within the history of computer graphics a plenitude of sophisticated surface representations and graphics primitives have been devised, including splines, implicit surfaces, or hierarchical approaches. All of these methods aim at facilitating the creation, processing and display of graphics models with increasingly complex shape or surface detail. In spite of the sophistication of these methods the triangle has survived over decades as the major graphics primitive meeting a right balance between descriptive power and computational effort. As a consequence, today’s consumer graphics hardware is mostly tailored to high performance triangle processing. In addition, an upcoming repertoire of powerful geometric processing methods seems to foster the concept of triangle meshes for graphics modeling. In recent years, the emergence of affordable 3D scanning devices along with the demand for ever more geometric detail and rich organic shapes has created the need to process and render very large point sampled models efficiently. At data sizes where triangle based methods approach their limits point representations are receiving a growing attention. Unlike triangles, points have largely been neglected as a graphics primitive. Although being included in many APIs, it is only recently that point samples experience a renaissance in computer graphics. Conceptually, points provide a discretization of geometry without explicit storage of topology. Thus, point samples reduce the representation to the essentials needed for rendering and enable us to generate highly optimized object representations. Although the loss of topology poses great challenges for graphics processing, the latest generation of algorithms features high performance rendering, point/pixel shading, anisotropic texture mapping, and advanced signal processing of point sampled geometry. In this talk, I will introduce point samples as a versatile graphics primitive and present concepts for the acquisition, processing and rendering of large point sets. The first part of the talk discusses low-cost scanning devices and algorithms being used to reconstruct 3D point clouds from video image sequences. Powerful PC clusters allow for the real-time computation of the underlying image processing algorithms. Such concepts have been used within the ETH blue-c1 collaborative virtual environment. After the acquisition of raw point samples sophisticated postprocessing techniques are required to clean, denoise, enhance, or smooth the data. The second part of this talk presents our latest concepts for generalizing Fourier transforms to point sampled geometry. The method constitutes a partitioning of the point set and computes a local spectral decomposition for each patch using the FFT. The notion of frequency gives us access to a rich repertoire of signal processing methods including lowpass or highpass filtering, spectral estimation and resampling. The third part of my talk is dedicated to the concepts we developed for high performance rendering of point sampled geometry. A hierarchical data structure, called LDC tree stores point samples and renders them progressively. Holes, as appearing due to insufficient sampling, have to be detected and filled using image space filtering. Each point stores color values representing real or artificial texture information. The irregularity of the point sampling patterns on the object surface makes texture filtering and mip map computation highly nontrivial. The presented journey through point processing methods will demonstrate that point sets are a meaningful alternative concept complementing traditional triangle representations. 1 Find web resources at: blue-c.ethz.ch graphics.ethz.ch Proceedings of the 9th Pacific Conference on Computer Graphics and Applications (PG’01) 0-7695-1227-5/02 $17.00 © 2001 IEEE