Persistent Homology for 3D Reconstruction Evaluation

Abstract

Abstract. Space or voxel carving is a non-invasive technique that is used to produce a 3D volume and can be used in particular for the reconstruction of a 3D human model from images captured from a set of cameras placed around the subject. In [1], the authors present a technique to quantitatively evaluate spatially carved volumetric representations of humans using a synthetic dataset of typical sports motion in a tennis court scenario, with regard to the number of cameras used. In this paper, we compute persistent homology over the sequence of chain complexes obtained from the 3D outcomes with increasing number of cameras. This allows us to analyze the topological evolution of the reconstruction process, something which as far as we are aware has not been investigated to date.

Topological evaluation of volume reconstructions by voxel carving

“…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.…”

“…Persistent homology [5,17] studies homology classes and their life-times (persistence) in the belief that significant topological attributes must have a long life-time in a filtration (an increasing nested sequence of subcomplexes). In this paper, we work upon the previous paper of the same authors [8] to apply persistence theory for the evaluation of a 3D reconstruction process, providing a wide experimental support to the initial ideas set down there. We want to clarify that the application described here is not the classical use of persistent homology; it is more an experimental use of it.…”

“…This investigation was motivated by the fact that very little work had been done to date on evaluating the quality of space carving results. A new insight into the voxel carving work by homologically characterising the sequence of reconstruction volumes was initiated in [8]. Given the nature of the carvings, a homology-based approach was presented as a more appropriate mathematical quantification than the relatively simple NMSE-based approach used previously.…”

“…This way, the associated barcode provides a global topological description of the process, that enriches the numerical comparison against the ground truth model. Although the idea of using persistent homology in this context was first proposed in [8], a more formal and detailed presentation of the method is given in this section. Besides, a considerable amount of experiments presented in next section, will support the proposed method.…”

Towards Minimal Barcodes

“…This problem can be seen as a view planning problem (see [19], a survey of computer vision sensor planning, [18], a more recent survey of view planning for 3-D vision). In our case, [9], starting from a compact block of voxels, each time a camera is added, a set of voxels are deleted (carved) from the 3D reconstruction, so the sequence of 3D reconstructions along decreasing number of cameras gives place to a filter of the corresponding cubical complexes. This allows to analyze the topological evolution of the reconstruction process.…”