Accuracy-Based Sampling and Reconstruction with Adaptive Meshes for Parallel Hierarchical Triangulation

Abstract

Recent advances in range finding techniques have made the task of acquiring surface data for 3-D objects easier and more accurate. With most advanced techniques, range and color data are acquired simultaneously. Since the number of such acquired data is generally very large, a surface model capable of compressing data while maintaining a specified accuracy is required. The objective of this work is to construct a polyhedral representation of input data for surfaces. This representation adapts to local intrinsic surface properties while preserving their discontinuities. In this paper, we present an accuracy-based adaptive sampling and reconstruction technique for hierarchical triangulation of 3D objects. We have developed a parallel algorithm for adaptive mesh generation that recursively bisects mesh elements by increasing the number of mesh nodes according to local surface properties, such as surface orientation, curvature, and color. The recursive subdivision based on such viewpoint-invariant properties yields a hierarchical surface triangulation that is intrinsic to the surface. This approach also satisfies the absolute accuracy criteria, since nodes are generated as required until the entire surface has been approximated within a specified level of accuracy. We have also developed a parallel algorithm that detects and preserves both depth (C0) and orientation (C1) discontinuities, without the formation of cracks which normally occur during independent subdivision. The algorithm has been successfully applied to adaptive sampling and reconstruction of both range and color images of human faces and Japanese antique dolls with fine grained color-texture.