A volumetric method for building complex models from range images

Abstract

A number of techniques have been developed for reconstructing surfaces by integrating groups of aligned range images. A desirable set of properties for such algorithms includes: incremental updating, representation of directional uncertainty, the ability to fill gaps in the reconstruction, and robustness in the presence of outliers. Prior algorithms possess subsets of these properties. In this paper, we present a volumetric method for integrating range images that possesses all of these properties.Our volumetric representation consists of a cumulative weighted signed distance function. Working with one range image at a time, we first scan-convert it to a distance function, then combine this with the data already acquired using a simple additive scheme. To achieve space efficiency, we employ a run-length encoding of the volume. To achieve time efficiency, we resample the range image to align with the voxel grid and traverse the range and voxel scanlines synchronously. We generate the final manifold by extracting an isosurface from the volumetric grid. We show that under certain assumptions, this isosurface is optimal in the least squares sense. To fill gaps in the model, we tessellate over the boundaries between regions seen to be empty and regions never observed.Using this method, we are able to integrate a large number of range images (as many as 70) yielding seamless, high-detail models of up to 2.6 million triangles.

Real-time scene reconstruction and triangle mesh generation using multiple RGB-D cameras

“…We also may wish to include backgrounds in reconstructions, but this is generally not supported. Curless and Levoy [15] use a visual hull concept together with range images and define a space carving method. Thanks to the range images, background segmentation becomes a simple task.…”

A Probabilistic Theory of Occupancy and Emptiness

“…From an informal standpoint, this occurs because the set of voxel visibility strings that are carving sequences does not adequately cover the space of all possible visibility assignments for voxels in Î Ë, resulting in an under-estimation of the "probability mass" for the event Empty(Î Ë Á). Fortunately, the following proposition tells us that this mass can be correctly accounted for by a slightly expanded set of voxel visibility strings, all of which are mutually disjoint, which consider all sets of visibility assignments for voxels in Î Ë and contain every voxel in Î Ë at most Î Ë times: 2 A simple way to verify this fact is to expand the sum in Eq. (7) ʴȵ ´È µ (6) where È´¦µ is the set of strings È Ô½ ¡ ¡ ¡ Ô Ð with the following properties: (1) È is created by adding voxels in their Ú-form to a carving sequence ¦, (2) each voxel Ú occurs at most once between any two successive voxels appearing in their Ú-form, (3) no voxel in È can occur in its Ú-form after it has occurred in its Ú-form; and ´È µ and ʴȵ are given by Proposition 1 tells us that the "extra" mass needed to establish the emptiness of a region consists of the ´È µ-terms in Eq.…”

“…Many applications, from robotics [1] to computer graphics [2] and virtual reality, rely on probabilistic representations of occupancy to express uncertainty about the physical layout of the 3D world. While occupancy has an intuitive and well-defined physical interpretation for every 3D point (i.e., a point is occupied when the scene's volume contains it), little is known about what probabilistic information regarding occupancy is theoretically computable from a set of Ò noisy images.…”

Construction object identification from LADAR scans:

“…Many, however, involve scans of relatively small objects or modeling of available point cloud datasets. The following references describe some of these methods: Sourlier and Bucher [75], Bajaj, et al [2], Curless and Levoy [19], Bernardini et al [8], Lu and Yun [61], Juarez et al [48], Boughorbal et al [12], Chatzis and Pitas [14], Levy and Lindenbaum [58], Marshall et al [65], Barhak and Fischer [3], Whitaker and Gregor [82]. There are a few references that describe modeling of point clouds obtained from large scale scans, such as buildings and statuary.…”