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.
More recently, the RELION framework has been extended to include multi-body refinement @cite_24 (also see @cite_0 @cite_6 @cite_34 @cite_34 @cite_1 @cite_64 ). In this approach, the user selects different rigid 3-D models that are to be refined separately from the main, or consensus, model. Each separate sub-model is then refined separately, with its own viewing direction and translation, allowing it to move with respect to the consensus model in a rigid-body fashion. This method is limited to rigid-body variability in a few sub-volumes, and cannot handle non-rigid deformations or other types of variability. In particular, the structure found at the interface between the sub-models is likely to vary as their relative positions vary, and it is therefore lost in this method.
@cite_64 @cite_1 @cite_6 @cite_24 @cite_0 @cite_34
2075402943 1981985525 1976363785 2004734153
We present a combined hardware and software solution for markerless reconstruction of non-rigidly deforming physical objects with arbitrary shape in real-time. Our system uses a single self-contained stereo camera unit built from off-the-shelf components and consumer graphics hardware to generate spatio-temporally coherent 3D models at 30 Hz. A new stereo matching algorithm estimates real-time RGB-D data. We start by scanning a smooth template model of the subject as they move rigidly. This geometric surface prior avoids strong scene assumptions, such as a kinematic human skeleton or a parametric shape model. Next, a novel GPU pipeline performs non-rigid registration of live RGB-D data to the smooth template using an extended non-linear as-rigid-as-possible (ARAP) framework. High-frequency details are fused onto the final mesh using a linear deformation model. The system is an order of magnitude faster than state-of-the-art methods, while matching the quality and robustness of many offline algorithms. We show precise real-time reconstructions of diverse scenes, including: large deformations of users' heads, hands, and upper bodies; fine-scale wrinkles and folds of skin and clothing; and non-rigid interactions performed by users on flexible objects such as toys. We demonstrate how acquired models can be used for many interactive scenarios, including re-texturing, online performance capture and preview, and real-time shape and motion re-targeting. This paper studies segmentation of multiple rigid-body motions in a 3-D dynamic scene under perspective camera projection. We consider dynamic scenes that contain both 3-D rigid-body structures and 2-D planar structures. Based on the well-known epipolar and homography constraints between two views, we propose a hybrid perspective constraint (HPC) to unify the representation of rigid-body and planar motions. Given a mixture of K hybrid perspective constraints, we propose an algebraic process to partition image correspondences to the individual 3-D motions, called Robust Algebraic Segmentation (RAS). Particularly, we prove that the joint distribution of image correspondences is uniquely determined by a set of (2K)-th degree polynomials, a global signature for the union of K motions of possibly mixed type. The first and second derivatives of these polynomials provide a means to recover the association of the individual image samples to their respective motions. Finally, using robust statistics, we show that the polynomials can be robustly estimated in the presence of moderate image noise and outliers. We conduct extensive simulations and real experiments to validate the performance of the new algorithm. The results demonstrate that RAS achieves notably higher accuracy than most existing robust motion-segmentation methods, including random sample consensus (RANSAC) and its variations. The implementation of the algorithm is also two to three times faster than the existing methods. The implementation of the algorithm and the benchmark scripts are available at http: perception.csl.illinois.edu ras . We propose a framework for the full two-way coupling of rigid and deformable bodies, which is achieved with both a unified time integration scheme as well as individual two-way coupled algorithms at each point of that scheme. As our algorithm is two-way coupled in every fashion, we do not require ad hoc methods for dealing with stability issues or interleaving parts of the simulation. We maintain the ability to treat the key desirable aspects of rigid bodies (e.g. contact, collision, stacking, and friction) and deformable bodies (e.g. arbitrary constitutive models, thin shells, and self-collisions). In addition, our simulation framework supports more advanced features such as proportional derivative controlled articulation between rigid bodies. This not only allows for the robust simulation of a number of new phenomena, but also directly lends itself to the design of deformable creatures with proportional derivative controlled articulated rigid skeletons that interact in a life-like way with their environment. This paper addresses the problem of obtaining 3d detailed reconstructions of human faces in real-time and with inexpensive hardware. We present an algorithm based on a monocular multi-spectral photometric-stereo setup. This system is known to capture high-detailed deforming 3d surfaces at high frame rates and without having to use any expensive hardware or synchronized light stage. However, the main challenge of such a setup is the calibration stage, which depends on the lights setup and how they interact with the specific material being captured, in this case, human faces. For this purpose we develop a self-calibration technique where the person being captured is asked to perform a rigid motion in front of the camera, maintaining a neutral expression. Rigidity constrains are then used to compute the head's motion with a structure-from-motion algorithm. Once the motion is obtained, a multi-view stereo algorithm reconstructs a coarse 3d model of the face. This coarse model is then used to estimate the lighting parameters with a stratified approach: In the first step we use a RANSAC search to identify purely diffuse points on the face and to simultaneously estimate this diffuse reflectance model. In the second step we apply non-linear optimization to fit a non-Lambertian reflectance model to the outliers of the previous step. The calibration procedure is validated with synthetic and real data.