Topological evaluation of volume reconstructions by voxel carving

Abstract

a b s t r a c tSpace or voxel carving (Broadhurst et al., 2001;Culbertson et al., 1999;Kutulakos and Seitz, 2000;Seitz et al., 2006) is a technique for creating a three-dimensional reconstruction of an object from a series of two-dimensional images captured from cameras placed around the object at different viewing angles. However, little work has been done to date on evaluating the quality of space carving results. This paper extends the work reported in (Gutierrez et al., 2012), where application of persistent homology was initially proposed as a tool for providing a topological analysis of the carving process along the sequence of 3D reconstructions with increasing number of cameras. We give now a more extensive treatment by: (1) developing the formal framework by which persistent homology can be applied in this context; (2) computing persistent homology of the 3D reconstructions of 66 new frames, including different poses, resolutions and camera orders; (3) studying what information about stability, topological correctness and influence of the camera orders in the carving performance can be drawn from the computed barcodes.

An entropy-based persistence barcode

“…A typical persistence barcode contains short-lived intervals representing topological holes (homology classes) which may not represent real features of the space being analyzed. In such cases one has to set a "threshold" of significance on the length of the intervals of the persistence barcode, and this is normally carried out a posteriori (see, for example, [14] where authors consider a "simplified" barcode). On the other hand, if someone examines in depth typical cases where persistent homology is used, one will be faced with the inherent problem of "noise" in the persistence barcodes.…”

Three-dimensional volume reconstruction from slice data using phase-field models

“…Then, the volume is obtained by the zero isosurface [7]. For other approaches to 3D reconstruction, refer to [8][9][10][11].…”

Cereal Grain 3D Point Cloud Analysis Method For Shape Extraction And Filled/Unfilled Grain Identification Based On Structured Light Imaging

“…Since the grain size are small, high quality and complete point cloud of which is needed. Point clouds obtained by binocular stereo vision, structure from motion and space carving are relatively sparse [15][16][17][18] , on the contrary the structured light imaging, an active three-dimensional vision technology, can obtain high-precision point clouds, which is widely used in industrial detection, reverse engineering and cultural relic protection 19 , and it provides an effective method for high precision analysis of cereal grain 3D traits.…”