In this article, we introduce a new global optimization method to the field of multiview 3D reconstruction. While global minimization has been proposed in a discrete formulation in form of the maxflow-mincut framework, we suggest the use of a continuous convex relaxation scheme. Specifically, we propose to cast the problem of 3D shape reconstruction as one of minimizing a spatially continuous convex functional. In qualitative and quantitative evaluation we demonstrate several advantages of the proposed continuous formulation over the discrete graph cut solution. Firstly, geometric properties such as weighted boundary length and surface area are represented in a numerically consistent manner: The continuous convex relaxation assures that the algorithm does not suffer from metrication errors in the sense that the reconstruction converges to the continuous solution as the spatial resolution is increased. Moreover, memory requirements are reduced, allowing for globally optimal reconstructions at higher resolutions.We study three different energy models for multiview reconstruction, which are based on a common variational template unifying regional volumetric terms and on-surface photoconsistency. The three models use data measurements at increasing levels of sophistication. While the first two approaches are based on a classical silhouette-based volume subdivision, the third one relies on stereo information to define regional costs. Furthermore, this scheme is exploited to compute a precise photoconsistency measure as opposed to the classical estimation. All three models are compared on standard data sets demonstrating their advantages and shortcomings. For the third one, which gives the most accurate results, a more exhaustive qualitative and quantitative evaluation is presented.

Recent work has demonstrated that it is possible to learn deep neural networks for monocular depth and ego-motion estimation from unlabelled video sequences, an interesting theoretical development with numerous advantages in applications. In this paper, we propose a number of improvements to these approaches. First, since such selfsupervised approaches are based on the brightness constancy assumption, which is valid only for a subset of pixels, we propose a probabilistic learning formulation where the network predicts distributions over variables rather than specific values. As these distributions are conditioned on the observed image, the network can learn which scene and object types are likely to violate the model assumptions, resulting in more robust learning. We also propose to build on dozens of years of experience in developing handcrafted structure-from-motion (SFM) algorithms. We do so by using an off-the-shelf SFM system to generate a supervisory signal for the deep neural network. While this signal is also noisy, we show that our probabilistic formulation can learn and account for the defects of SFM, helping to integrate different sources of information and boosting the overall performance of the network.

Abstract. Shape optimization is a problem which arises in numerous computer vision problems such as image segmentation and multiview reconstruction. In this paper, we focus on a certain class of binary labeling problems which can be globally optimized both in a spatially discrete setting and in a spatially continuous setting. The main contribution of this paper is to present a quantitative comparison of the reconstruction accuracy and computation times which allows to assess some of the strengths and limitations of both approaches. We also present a novel method to approximate length regularity in a graph cut based framework: Instead of using pairwise terms we introduce higher order terms. These allow to represent a more accurate discretization of the L2-norm in the length term.

Abstract. In this work, we introduce a robust energy model for multiview 3D reconstruction that fuses silhouette-and stereo-based image information. It allows to cope with significant amounts of noise without manual pre-segmentation of the input images. Moreover, we suggest a method that can globally optimize this energy up to the visibility constraint. While similar global optimization has been presented in the discrete context in form of the maxflow-mincut framework, we suggest the use of a continuous counterpart. In contrast to graph cut methods, discretizations of the continuous optimization technique are consistent and independent of the choice of the grid connectivity. Our experiments demonstrate that this leads to visible improvements. Moreover, memory requirements are reduced, allowing for global reconstructions at higher resolutions.