In this paper, we propose an efficient and accurate scheme for the integration of multiple stereo-based depth measurements. For each provided depth map a confidence-based weight is assigned to each depth estimate by evaluating local geometry orientation, underlying camera setting and photometric evidence. Subsequently, all hypotheses are fused together into a compact and consistent 3D model. Thereby, visibility conflicts are identified and resolved, and fitting measurements are averaged with regard to their confidence scores. The individual stages of the proposed approach are validated by comparing it to two alternative techniques which rely on a conceptually different fusion scheme and a different confidence inference, respectively. Pursuing live 3D reconstruction on mobile devices as a primary goal, we demonstrate that the developed method can easily be integrated into a system for monocular interactive 3D modeling by substantially improving its accuracy while adding a negligible overhead to its performance and retaining its interactive potential.

In this paper, we propose a complete on-device 3D reconstruction pipeline for mobile monocular hand-held devices, which generates dense 3D models with absolute scale on-site while simultaneously supplying the user with real-time interactive feedback. The method fills a gap in current cloud-based mobile reconstruction services as it ensures at capture time that the acquired image set fulfills desired quality and completeness criteria. In contrast to existing systems, the developed framework offers multiple innovative solutions. In particular, we investigate the usability of the available on-device inertial sensors to make the tracking and mapping process more resilient to rapid motions and to estimate the metric scale of the captured scene. Moreover, we propose an efficient and accurate scheme for dense stereo matching which allows to reduce the processing time to interactive speed. We demonstrate the performance of the reconstruction pipeline on multiple challenging indoor and outdoor scenes of different size and depth variability.

We propose a probabilistic formulation of joint silhouette extraction and 3D reconstruction given a series of calibrated 2D images. Instead of segmenting each image separately in order to construct a 3D surface consistent with the estimated silhouettes, we compute the most probable 3D shape that gives rise to the observed color information. The probabilistic framework, based on Bayesian inference, enables robust 3D reconstruction by optimally taking into account the contribution of all views. We solve the arising maximum a posteriori shape inference in a globally optimal manner by convex relaxation techniques in a spatially continuous representation. For an interactively provided user input in the form of scribbles specifying foreground and background regions, we build corresponding color distributions as multivariate Gaussians and find a volume occupancy that best fits to this data in a variational sense. Compared to classical methods for silhouette-based multiview reconstruction, the proposed approach does not depend on initialization and enjoys significant resilience to violations of the model assumptions due to background clutter, specular reflections, and camera sensor perturbations. In experiments on several real-world data sets, we show that exploiting a silhouette coherency criterion in a multiview setting allows for dramatic improvements of silhouette quality over independent 2D segmentations without any significant increase of computational efforts. This results in more accurate visual hull estimation, needed by a multitude of image-based modeling approaches. We made use of recent advances in parallel computing with a GPU implementation of the proposed method generating reconstructions on volume grids of more than 20 million voxels in up to 4.41 seconds.

We introduce a spatially dense variational approach to estimate the calibration of multiple cameras in the context of 3D reconstruction. We propose a relaxation scheme which allows to transform the original photometric error into a geometric one, thereby decoupling the problems of dense matching and camera calibration. In both quantitative and qualitative experiments, we demonstrate that the proposed decoupling scheme allows for robust and accurate estimation of camera parameters. In particular, the presented dense camera calibration formulation leads to substantial improvements both in the reconstructed 3D geometry and in the super-resolution texture estimation.

We propose a convex formulation for silhouette and stereo fusion in 3D reconstruction from multiple images. The key idea is to show that the reconstruction problem can be cast as one of minimizing a convex functional, where the exact silhouette consistency is imposed as convex constraints that restrict the domain of feasible functions. As a consequence, we can retain the original stereo-weighted surface area as a cost functional without heuristic modifications of this energy by balloon terms or other strategies, yet still obtain meaningful (non-empty) reconstructions which are guaranteed to be silhouette-consistent. We prove that the proposed convex relaxation approach provides solutions that lie within a bound of the optimal solution. Compared to existing alternatives, the proposed method does not depend on initialization and leads to a simpler and more robust numerical scheme for imposing silhouette consistency obtained by projection onto convex sets. We show that this projection can be solved exactly using an efficient algorithm. We propose a parallel implementation of the resulting convex optimization problem on a graphics card. Given a photo-consistency map and a set of image silhouettes, we are able to compute highly accurate and silhouette-consistent reconstructions for challenging real-world data sets. In particular, experimental results demonstrate that the proposed silhouette constraints help to preserve fine-scale details of the reconstructed shape. Computation times depend on the resolution of the input imagery and vary between a few seconds and a couple of minutes for all experiments in this paper.

We introduce a convex relaxation framework to optimally minimize continuous surface ratios. The key idea is to minimize the continuous surface ratio by solving a sequence of convex optimization problems. We show that such minimal ratios are superior to traditionally used minimal surface formulations in that they do not suffer from a shrinking bias and no longer require the choice of a regularity parameter. The absence of a shrinking bias in the minimal ratio model is proven analytically. Furthermore we demonstrate that continuous ratio optimization can be applied to derive a new algorithm for reconstructing three-dimensional silhouette-consistent objects from multiple views. Experimental results confirm that our approach allows to accurately reconstruct deep concavities even without the specification of tuning parameters.