Pressing: Smooth Isosurfaces with Flats from Binary Grids

Abstract

We explore the automatic recovery of solids from their volumetric discretizations. In particular, we propose an approach, called Pressing, for smoothing isosurfaces extracted from binary volumes while recovering their large planar regions ( ats). Pressing yields a surface that is guaranteed to contain the samples of the volume classi ed as interior and exclude those classi ed as exterior. It uses global optimization to identify ats and constrained bilaplacian smoothing to eliminate sharp features and high-frequencies from the rest of the isosurface. It recovers sharp edges between at regions and between at and smooth regions. Hence, the resulting isosurface is usually a much more accurate approximation of the original solid than isosurfaces produced by previously proposed approaches. Furthermore, the segmentation of the isosurface into at and curved faces and the sharp/smooth labelling of their edges may be valuable for shape recognition, simpli cation, compression, and various reverse engineering and manufacturing applications.

Two Plane-Probing Algorithms for the Computation of the Normal Vector to a Digital Plane

“…The segmentation of the shape boundary into linear parts is thus generally greedy [14,19,5], for instance by extracting first the biggest plane, and then repeat the process [23]. In 3D, the main problem is that there is no more an implication between "being a maximal plane" and "being a tangent plane" as it is in 2D.…”

“…• (1,2,5). Images (e) to (h) show iterations 0 (initial), 2, 5 and 7 (final) of the algorithm from [17].…”

“…Images (e) to (h) show iterations 0 (initial), 2, 5 and 7 (final) of the algorithm from [17]. The initial tetrahedron (a) is placed at the origin and the final one (h) has an upper triangle with normal vector (1,2,5).…”

Regularization of voxel art

“…), the overall reconstruction is highly sensitive to normal and position errors, as illustrated in the supplementary. On binary grids, [Chica et al 2008] proposes a complex two-step algorithm combining a decomposition of the surface into maximal flat patches and a specific smoothing step. We propose a GPU friendly simpler yet robust formulation.…”

Dual Marching Tetrahedra: Contouring in the Tetrahedronal Environment

“…Due to the wide spread need for such techniques, there continues to be a fair amount of published literature on this topic. See [2], [4], [6], [9], [13] and [19] for example. Here we discuss the tetrahedronal version of this method or, in other words, the dual marching tetrahedra (DMT) method.…”