A Symmetry Prior for Convex Variational 3D Reconstruction
We propose a novel prior for variational 3D reconstruction that favors symmetric solutions when dealing with noisy or incomplete data. We detect symmetries from incomplete data while explicitly handling unexplored areas to allow for plausible scene comple
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ETH Z¨ urich, Zurich, Switzerland [email protected] 2 Microsoft, Redmond, USA
Abstract. We propose a novel prior for variational 3D reconstruction that favors symmetric solutions when dealing with noisy or incomplete data. We detect symmetries from incomplete data while explicitly handling unexplored areas to allow for plausible scene completions. The set of detected symmetries is then enforced on their respective support domain within a variational reconstruction framework. This formulation also handles multiple symmetries sharing the same support. The proposed approach is able to denoise and complete surface geometry and even hallucinate large scene parts. We demonstrate in several experiments the benefit of harnessing symmetries when regularizing a surface. Keywords: Symmetry prior · 3D reconstruction · Variational methods · Convex optimization
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Introduction
One of the long-time goals of computer vision algorithms is to imitate the numerous powerful abilities of the human visual system to achieve better scene understanding. Many methods have actually been inspired by the physiology of the visual cortex of mammalian brains. One of the strongest cues that humans use in order to infer the underlying geometry of a scene despite having access to only a partial view is symmetry, as shown in [20]. Moreover, symmetry is a very strong and useful concept because it applies to many natural and man-made environments. Following this inspiration, we propose a method which leverages symmetry information directly within a 3D reconstruction procedure in order to complete or denoise symmetric surface regions which have been partially occluded or where the input information has low quality. In contrast to the majority of 3D reconstruction methods which fit minimal surfaces in order to fill unobserved surface parts, our method favors solutions which align with symmetries and adhere to required smoothness properties at the same time. Similarly to how humans extrapolate occluded areas and 3D information from just a few view points, our method can hallucinate entire scene parts in unobserved areas, fill small holes, or denoise observed surface geometry once a symmetry has been detected. An example of our approach is shown in Fig. 1. Equal contribution from P. Speciale and M.R. Oswald. c Springer International Publishing AG 2016 B. Leibe et al. (Eds.): ECCV 2016, Part VIII, LNCS 9912, pp. 313–328, 2016. DOI: 10.1007/978-3-319-46484-8 19
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Fig. 1. Example application of our approach. A model of a stool was scanned by a depth camera and the result is incomplete due to occlusions. With only two detected symmetries we can complete the 5-way symmetry of the model.
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Contributions
We propose to use symmetry information as a prior in 3D reconstruction in order to favor symmetric solutions when dealing with noisy and incomplete data. For this purpose, we extend standard symmetry detection algorithms to be able to exploit partially unexplore
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