Adaptive mesh generation for surface reconstruction—parallel hierarchical triangulation without cracks

Abstract

This paper describes a method of precisely and effectively visualizing a complex 3-dimensionally curved surface from a set of range data by using meshes (parallel hierarchical triangulation) which are adaptive to the degree of its complexity. The method can reconstruct the curved surface without cracks by approximating its intrinsic shape and discontinuity with a polygon. The algorithm used can be processed by fact parallel local calculations with an upper limit in time and space. This paper proposes a parallel recursive algorithm for generating an adaptive mesh using a 3D-curvature based on the intrinsic shape of an object, and another parallel recursive algorithm to avoid the formation of a crack which occurs between two subdivisions. Experimental results applied to range images of human faces are shown. The proposed method can be applied to general images (e.g., gray-level image and color images) other than range images so that the compression or reconstruction of an image can be carried out by adaptively using its geometrical features (e.g., the pixel value, its first-order differential, and second order differential).