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Multiview Stereo and Silhouette Consistency via Convex Functionals over Convex Domains

机译:通过凸域上的凸功能实现多视图立体声和轮廓一致性

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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 (nonempty) 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 photoconsistency 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.
机译:我们针对从多个图像进行3D重建提出了一种轮廓和立体融合的凸公式。关键思想是表明重构问题可以看作是最小化凸函数的一种,其中精确的轮廓一致性被强加为限制可行函数域的凸约束。结果,我们可以保留原始的立体加权表面积作为成本函数,而无需通过气球项或其他策略试探性地修改此能量,但仍可以获得有意义的(非空)重建,保证了轮廓一致。我们证明了所提出的凸松弛方法提供了在最优解的范围内的解。与现有的替代方法相比,所提出的方法不依赖于初始化,并且导致了一种更简单,更可靠的数值方案,用于将通过投影到凸集上而获得的轮廓一致性强加于人。我们表明,使用有效的算法可以准确地解决此投影问题。我们提出了在图形卡上并行生成的凸优化问题。给定一个光一致性贴图和一组图像轮廓,我们就能够计算出高度准确且轮廓一致的重构,以应对具有挑战性的真实数据集。特别是,实验结果表明,提出的轮廓约束有助于保留重构形状的精细尺度细节。对于本文中的所有实验,计算时间取决于输入图像的分辨率,并且在几秒钟到几分钟之间变化。

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