Cryo-electron microscopy (cryo-EM), the subject of the 2017 Nobel Prize in Chemistry, is a technology for determining the 3-D structure of macromolecules from many noisy 2-D projections of instances of these macromolecules, whose orientations and positions are unknown. The molecular structures are not rigid objects, but flexible objects involved in dynamical processes. The different conformations are exhibited by different instances of the macromolecule observed in a cryo-EM experiment, each of which is recorded as a particle image. The range of conformations and the conformation of each particle are not known a priori; one of the great promises of cryo-EM is to map this conformation space. Remarkable progress has been made in determining rigid structures from homogeneous samples of molecules in spite of the unknown orientation of each particle image and significant progress has been made in recovering a few distinct states from mixtures of rather distinct conformations, but more complex heterogeneous samples remain a major challenge. We introduce the hyper-molecule'' framework for modeling structures across different states of heterogeneous molecules, including continuums of states. The key idea behind this framework is representing heterogeneous macromolecules as high-dimensional objects, with the additional dimensions representing the conformation space. This idea is then refined to model properties such as localized heterogeneity. In addition, we introduce an algorithmic framework for recovering such maps of heterogeneous objects from experimental data using a Bayesian formulation of the problem and Markov chain Monte Carlo (MCMC) algorithms to address the computational challenges in recovering these high dimensional hyper-molecules. We demonstrate these ideas in a prototype applied to synthetic data.
In addition to homogeneous reconstruction, many of the methods mentioned above also accommodate discrete heterogeneity through a 3-D classification framework, where each particle image is assigned to a separate 3-D reconstruction by maximizing a similarity measure. Expectation-maximization algorithms, such as RELION @cite_18 , generalize to discrete heterogeneity by estimating conditional joint distributions of orientations and discrete class assignment. While this approach has led to impressive results, it requires significant human intervention in a process of successive refinement of the datasets to achieve a more homogeneous sample, and structures that are not well represented in the data tend to be lost @cite_33 .
@cite_18 @cite_33
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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. We present a dense reconstruction approach that overcomes the drawbacks of traditional multiview stereo by incorporating semantic information in the form of learned category-level shape priors and object detection. Given training data comprised of 3D scans and images of objects from various viewpoints, we learn a prior comprised of a mean shape and a set of weighted anchor points. The former captures the commonality of shapes across the category, while the latter encodes similarities between instances in the form of appearance and spatial consistency. We propose robust algorithms to match anchor points across instances that enable learning a mean shape for the category, even with large shape variations across instances. We model the shape of an object instance as a warped version of the category mean, along with instance-specific details. Given multiple images of an unseen instance, we collate information from 2D object detectors to align the structure from motion point cloud with the mean shape, which is subsequently warped and refined to approach the actual shape. Extensive experiments demonstrate that our model is general enough to learn semantic priors for different object categories, yet powerful enough to reconstruct individual shapes with large variations. Qualitative and quantitative evaluations show that our framework can produce more accurate reconstructions than alternative state-of-the-art multiview stereo systems. This paper presents an efficient system for simultaneous dense scene reconstruction and object labeling in real-world environments (captured with an RGB-D sensor). The proposed system starts with the generation of object proposals in the scene. It then tracks spatio-temporally consistent object proposals across multiple frames and produces a dense reconstruction of the scene. In parallel, the proposed system uses an efficient inference algorithm, where object class probabilities are computed at an object-level and fused into a voxel-based prediction hypothesis modeled on the voxels of the reconstructed scene. Our extensive experiments using challenging RGB-D object and scene datasets, and live video streams from Microsoft Kinect show that the proposed system achieved competitive 3D scene reconstruction and object labeling results compared to the state-of-the-art methods. A novel method able to recover scene planes of arbitrary position and orientation from oriented images using homographies is presented. Planar regions are reconstructed using only sparse, affine-invariant sets of corresponding seed regions. These regions are iteratively expanded and refined using plane-induced homographies. Experiments on synthetic data show the high accuracy of the reconstruction and demonstrate that the reconstruction method can cope with large baseline changes. Experiments on real images show the performance of the method on practically relevant scenes.