Dense semantic 3D reconstruction is typically formulated as a discrete or continuous problem over label assignments in a voxel grid, combining semantic and depth likelihoods in a Markov Random Field framework. The depth and semantic information is incorporated as a unary potential, smoothed by a pairwise regularizer. However, modelling likelihoods as a unary potential does not model the problem correctly leading to various undesirable visibility artifacts. We propose to formulate an optimization problem that directly optimizes the reprojection error of the 3D model with respect to the image estimates, which corresponds to the optimization over rays, where the cost function depends on the semantic class and depth of the first occupied voxel along the ray. The 2-label formulation is made feasible by transforming it into a graph-representable form under QPBO relaxation, solvable using graph cut. The multi-label problem is solved by applying alpha-expansion using the same relaxation in each expansion move. Our method was indeed shown to be feasible in practice, running comparably fast to the competing methods, while not suffering from ray potential approximation artifacts.
The silhouettes of objects in the input image contain important information about the geometry. They constrain the solution, such that for every ray passing through the silhouette there must be at least one occupied voxel, and every ray outside of the silhouette consists of free space voxels only. This constraint has been used in form of a convex relaxation in @cite_5 . @cite_19 proposes an intelligent unary ballooning visibility term based on the consensus from different views. In @cite_4 , the silhouettes are handled in a two-stage process, where the initial surface is reprojected into each image and the interior is heuristically corrected using the sets of erroneous pixels, by finding the most photo-consistent voxels along the ray. Recently, also approaches which jointly reason about geometry and semantic labels have been proposed @cite_0 . For volumetric 3D reconstruction in indoor environments a Conditional Random Field (CRF) model was proposed in @cite_9 . It includes higher order potentials over groups of voxels to include priors from 2D object detections and 3D surface detections in the raw input depth data. Furthermore, potentials over rays are used to enforce visibility of only one voxel along a ray.
@cite_4 @cite_9 @cite_0 @cite_19 @cite_5
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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. In this paper, we propose a non-local structured prior for volumetric multi-view 3D reconstruction. Towards this goal, we present a novel Markov random field model based on ray potentials in which assumptions about large 3D surface patches such as planarity or Manhattan world constraints can be efficiently encoded as probabilistic priors. We further derive an inference algorithm that reasons jointly about voxels, pixels and image segments, and estimates marginal distributions of appearance, occupancy, depth, normals and planarity. Key to tractable inference is a novel hybrid representation that spans both voxel and pixel space and that integrates non-local information from 2D image segmentations in a principled way. We compare our non-local prior to commonly employed local smoothness assumptions and a variety of state-of-the-art volumetric reconstruction baselines on challenging outdoor scenes with textureless and reflective surfaces. Our experiments indicate that regularizing over larger distances has the potential to resolve ambiguities where local regularizers fail. Dense semantic 3D reconstruction is typically formulated as a discrete or continuous problem over label assignments in a voxel grid, combining semantic and depth likelihoods in a Markov Random Field framework. The depth and semantic information is incorporated as a unary potential, smoothed by a pairwise regularizer. However, modelling likelihoods as a unary potential does not model the problem correctly leading to various undesirable visibility artifacts. We propose to formulate an optimization problem that directly optimizes the reprojection error of the 3D model with respect to the image estimates, which corresponds to the optimization over rays, where the cost function depends on the semantic class and depth of the first occupied voxel along the ray. The 2-label formulation is made feasible by transforming it into a graph-representable form under QPBO relaxation, solvable using graph cut. The multi-label problem is solved by applying α-expansion using the same relaxation in each expansion move. Our method was indeed shown to be feasible in practice, running comparably fast to the competing methods, while not suffering from ray potential approximation artifacts. 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.