Projection Orientations Research Articles

Feature-Oriented CBCT Self-Calibration Parameter Estimator for Arbitrary Trajectories: FORCAST-EST

Background: For the reconstruction of Cone-Beam CT volumes, the exact position of each projection is needed; however, in some situations, this information is missing. Purpose: The development of a self-calibration algorithm for arbitrary CBCT trajectories that does not need initial positions. Methods: Projections are simulated in a spherical grid around the center of rotation. Through using feature detection and matching, an acquired projection is compared to each simulated image in this grid. The position with the most matched features was used as a starting point for a fine calibration with a state-of-the-art algorithm. Evaluation: This approach is compared with the calibration of nearly correct starting positions when using FORCASTER and CMA-ES minimization with a normalized gradient information (NGI) objective function. The comparison metrics were the normalized root mean squared error, structural similarity index, and the dice coefficient, which were evaluated on the segmentation of a metal object. Results: The parameter estimation for a regular Cone-Beam CT with a 496 projection took 1:26 h with the following metric values: NRMSE = 0.0669; SSIM = 0.992; NGI = 0.75; and Dice = 0.96. FORCASTER with parameter estimation took 3:28 h with the following metrics: NRMSE = 0.0190; SSIM = 0.999; NGI = 0.92; and Dice = 0.99. CMA-ES with parameter estimation took 5:39 h with the following metrics: NRMSE = 0.0037; SSIM = 1.0; NGI = 0.98; and Dice = 1.0. Conclusions: The proposed algorithm can determine the parameters of the projection orientations for arbitrary trajectories with enough accuracy to reconstruct a 3D volume with low errors.

Single-Particle Cryo-EM Data Collection with Stage Tilt using Leginon.

Single-particle analysis (SPA) by cryo-electron microscopy (cryo-EM) is now a mainstream technique for high-resolution structural biology. Structure determination by SPA relies upon obtaining multiple distinct views of a macromolecular object vitrified within a thin layer of ice. Ideally, a collection of uniformly distributed random projection orientations would amount to all possible views of the object, giving rise to reconstructions characterized by isotropic directional resolution. However, in reality, many samples suffer from preferentially oriented particles adhering to the air-water interface. This leads to non-uniform angular orientation distributions in the dataset and inhomogeneous Fourier-space sampling in the reconstruction, translating into maps characterized by anisotropic resolution. Tilting the specimen stage provides a generalizable solution to overcoming resolution anisotropy by virtue of improving the uniformity of orientation distributions, and thus the isotropy of Fourier space sampling. The present protocol describes a tilted-stage automated data collection strategy using Leginon, a software for automated image acquisition. The procedure is simple to implement, does not require any additional equipment or software, and is compatible with most standard transmission electron microscopes (TEMs) used for imaging biological macromolecules.

Feature-based CBCT self-calibration for arbitrary trajectories

PurposeDevelopment of an algorithm to self-calibrate arbitrary CBCT trajectories which can be used to reduce metal artifacts. By using feature detection and matching we want to reduce the amount of parameters for the BFGS optimization and thus reduce the runtime.MethodsEach projection is 2D-3D registered on a prior image with AKAZE feature detection and brute force matching. Translational misalignment is calculated directly from the misalignment of feature positions, rotations are aligned using a minimization algorithm that fits a quartic function and determines the minimum of this function.EvaluationWe did three experiments to compare how well the algorithm can handle noise on the different degrees of freedom. Our algorithms are compared to Broyden–Fletcher–Goldfarb–Shanno (BFGS) minimizer with Normalized Gradient Information (NGI) objective function, and BFGS with distance between features objective function using SSIM, nRMSE, and the Dice coefficient of segmented metal object.ResultsOur algorithm (Feature ORiented Calibration for Arbitrary Scan Trajectories with Enhanced Reliability (FORCASTER)) performs on par with the state-of-the-art algorithms (BFGS with NGI objective). nRMSE: FORCASTER = 0.3390, BFGS+NGI = 0.3441; SSIM: FORCASTER = 0.83, BFGS + NGI = 0.79; Dice: FORCASTER = 0.86, BFGS + NGI = 0.87.ConclusionThe proposed algorithm can determine the parameters of the projection orientations for arbitrary trajectories with calibration quality comparable to state-of-the-art algorithms, but faster and with higher tolerance to errors in the initially guessed parameters.

Correlation-based view registration for 3D tomography.

This study reports a new, to the best of our knowledge, view registration method that can achieve high-quality tomographic reconstruction in spite of a large view registration (VR) error. The correlation-based view registration (CBVR) method is a directional orientation modification method based on the cross-correlation between measured projections and ray-tracings generated from the reconstruction, which can reduce the gross VR error to moderate levels by iterations. In the CBVR method, a traditional multi-camera VR process is first performed, based on the sensitivity of the projections to the VR error, and are evaluated and quantified for all cameras. Afterward, the orientation of each camera is iteratively updated based on the cross-correlation of the measured projections and the ray-tracings generated from the reconstruction calculated through all other cameras. The CBVR is consecutively validated by numerical and experimental studies. Through a numerical study on a controlled phantom introduced with 2% Gaussian noise, the CBVR method is proved to be able to reduce the large VR error (up to 4.8°) to 0.2° as well as to reduce the reconstruction error to ∼6.7% in 12 rounds of iterations, which is very close to that obtained without any VR error (6% caused by Gaussian noise only). The CBVR method is then demonstrated and validated by reconstructing a two-branch laminar flame. By implementing the method, the initial projection orientations are optimized from traditional multi-camera VR results within a range of ±3∘, leading to effectively improved tomographic reconstruction of flame chemiluminescence distribution.

SPREAD: A Fully Automated Toolkit for Single-Particle Cryogenic Electron Microscopy Data 3D Reconstruction with Image-Network-Aided Orientation Assignment.

For the past decade, cryogenic electron microscopy (cryo-EM) has become an important technology to determine three-dimensional (3D) structures of biomacromolecules. Many software tools have been developed for cryo-EM image processing and 3D reconstruction, covering various computational tasks in cryo-EM data analysis. Despite the recent progress, most of these software tools focus on a single task, such as automatic particle picking or image clustering, whereas software packages covering the whole pipeline of cryo-EM data processing are still few. In this study, we developed a fully automatic single-particle reconstruction and analysis toolkit for cryo-EM data, named SPREAD, which integrates 2D image classification, 3D initial model generation, model selection, and 3D refinement. In SPREAD, we adopt our previously proposed network-based clustering algorithm for 2D image classification, NCEM, and the reference-free resolution measurement method SRes to realize the automatic model ranking and selection procedure. Projection orientation assignment is one of the key steps in initial model generation and 3D refinement. In SPREAD, we use the network-based image similarity metric and introduce a new probabilistic-based orientation searching method, named peak finding, to enhance assignment of the projection orientations. For dealing with both the particle images and projection images in the 3D refinement using SPREAD, we build a mixture image network containing both of these types of images on the basis of the peak-finding results, and then similarities for node pairs are recomputed by a superposed random walk on the network. SPREAD achieves a fully automatic workflow in which nearly no expert domain knowledge and interactive manual operation are involved. Our software can accessed for free at http://www.csbio.sjtu.edu.cn/bioinf/SPREAD/ for academic use.

Learning principal orientations and residual descriptor for action recognition

In this paper, we propose an unsupervised representation method to learn principal orientations and residual descriptor (PORD) for action recognition. Our PORD aims to learn the statistic principal orientations and to represent the local features of action videos with residual values. The existing hand-crafted feature based methods require high prior knowledge and lack of the ability to represent the distribution of features of the dataset. Most of the deep learned feature based methods are data adaptive, but they do not consider the projection orientations of features nor the loss of locally aggregated descriptors of the quantization. We propose a method of principal orientations and residual descriptor considering that the principal orientations reflect the distribution of local features in the dataset and the residual of projection contains discriminative information of local features. Moreover, we propose a multi-modality PORD method by reducing the modality gap of the RGB channels and the depth channel at the feature level to make our method applicable to RGB-D action recognition. To evaluate the performance, we conduct experiments on five challenging action datasets: Hollywood2, UCF101, HMDB51, MSRDaily, and MSR-Pair. The results show that our method is competitive with the state-of-the-art methods.

Robust evaluation of 3D electron cryomicroscopy data using tilt-pairs.

Determining the structure of a protein complex using electron microscopy requires the calculation of a 3D density map from 2D images of single particles. Since the individual images are taken at low electron dose to avoid radiation damage, they are noisy and difficult to align with each other. This can result in incorrect maps, making validation essential. Pairs of electron micrographs taken at known angles to each other (tilt-pairs) can be used to measure the accuracy of assigned projection orientations and verify the soundness of calculated maps. Here we establish a statistical framework for evaluating images and density maps using tilt-pairs. The directional distribution of such angular data is modelled using a Fisher distribution on the unit sphere. This provides a simple, quantitative and easily comparable metric, the concentration parameter κ, for evaluating the quality of datasets and density maps that is independent of the data collection and analysis methods. A large κ is indicative of good agreement between the particle images and the 3D density map. For structure validation, we recommend and a p-value <0.01. The statistical framework herein allows one to objectively answer the question: Is a reconstructed density map correct within a particular confidence interval?

SU‐E‐I‐159: Delaunay Triangulation for Angular Interpolation and Single Stage Reconstruction of EPRI

Purpose: To employ Delaunay Triangulation of projection orientations in 3D electron paramagnetic resonance imaging (EPRI) for multidimensional angular interpolation and the duel tessellation (Voronoi diagram) for weighting coefficients enabling reconstruction by single stage inverse Radon Transform without the necessity of regridding data. Methods: Standard 3D pulsed EPR oxygen images were acquired of an OX063 phantom with projections in an approximately uniform but none rectilinear fashion. The projection orientation was mapped to a unit sphere, and the Delaunay triangulation was calculated for these points on the surface. Projections were interpolated to the incenter of each triangulation using a weighted mean of projections located at the vertices. The Voronoi diagram was then calculated, partitioning the surface of the sphere such that each projection was associated with a spherical polygon. The area of these polygons was used as a weighting coefficient for calculation of the discrete surface integral in the filtered backprojection (FBP) algorithm. Results: We were able to successfully reconstruct images using angular interpolation and the FBP algorithm without decomposition of the problem into stages of 1D interpolation and line integrals. Examination of images indicates improved ability to resolve oxygen concentration of phantoms Conclusions: Direct single stage reconstruction from non rectilinear sampling is an important progression in ERPI as it avoids the filtering effects of interpolation in regridding and multistage reconstruction. Proper analysis of the angular distributions of projections will allow for unrestricted sampling choices and potential optimization. Since sampling requirements of the discrete inverse Radon transform scale rapidly with higher dimension, angular projection interpolation is an important technique for artifact avoidance that must be reproduced in the move from single to multistage reconstruction. This work will form the basis for future investigation into the reconstruction of EPRI.

Computed tomographic‐dacryocystography (CT‐DCG) of the normal canine nasolacrimal drainage system with three‐dimensional reconstruction

The aims of the study were (1) to quantify the influence of selected imaging parameters on the image quality (slice thickness, mAs, and beam orientation) defining optimal conditions for scan protocols and (2) to evaluate the benefits of the 3D reconstruction techniques for visualization of NDS structures in dogs. CT-DCG was performed bilaterally in 32 heads of dogs. CT transverse images were obtained using a combination of two slice thickness values (0.8 mm and 2 mm) and two mAs values (50 mAs and 300 mAs). Two beam projection orientations were also tested: transverse plane (perpendicular to the hard palate) and oblique to the hard palate. Three-dimensional images were obtained using Volume Rendering (VR). Transverse beam projection proved to be superior for the assessment of the inferior and superior lacrimal canaliculi and lacrimal sac. In this study, there was no statistical difference regarding mAs values (50 mAs and 300 mAs) and slice thickness values (0.8 mm and 2 mm). Three-dimensional images were helpful for the assessment of topographic relationship between nasolacrimal structures and cranial landmarks.

An algorithm for recovering unknown projection orientations and shifts in 3-D tomography

It is common for example in Cryo-electron microscopy of viruses, that the orientations at which the projections are acquired, are totally unknown. We introduce here a moment based algorithm for recovering them in the three-dimensional parallel beam tomography. In this context, there is likely to be also unknown shifts in the projections. They will be estimated simultaneously. Also stability properties of the algorithm are examined. Our considerations rely on recent results that guarantee a solution to be almost always unique. A similar analysis can also be done in the two-dimensional problem.

A clustering approach to multireference alignment of single-particle projections in electron microscopy

Two-dimensional analysis of projections of single-particles acquired by an electron microscope is a useful tool to help identifying the different kinds of projections present in a dataset and their different projection directions. Such analysis is also useful to distinguish between different kinds of particles or different particle conformations. In this paper we introduce a new algorithm for performing two-dimensional multireference alignment and classification that is based on a Hierarchical clustering approach using correntropy (instead of the more traditional correlation) and a modified criterion for the definition of the clusters specially suited for cases in which the Signal-to-Noise Ratio of the differences between classes is low. We show that our algorithm offers an improved sensitivity over current methods in use for distinguishing between different projection orientations and different particle conformations. This algorithm is publicly available through the software package Xmipp.

Reference free structure determination through eigenvectors of center of mass operators

Recovering the three-dimensional structure of molecules is important for understanding their functionality. We describe a spectral graph algorithm for reconstructing the three-dimensional structure of molecules from their cryo-electron microscopy images taken at random unknown orientations. We first identify a one-to-one correspondence between radial lines in three-dimensional Fourier space of the molecule and points on the unit sphere. The problem is then reduced to determining the coordinates of points on the sphere given a subset of their pairwise geodesic distances. To recover those coordinates, we exploit the special geometry of the problem, as rendered by the Fourier projection–slice theorem, to construct a weighted graph whose vertices are the radial Fourier lines and whose edges are linked using the common line property. The graph organizes the radial lines on the sphere in a global manner that reveals the acquisition direction of each image. This organization is derived from a global computation of a few eigenvectors of the graph's sparse adjacency matrix. Once the directions are obtained, the molecule can be reconstructed using classical tomography methods. The presented algorithm is direct (as opposed to iterative refinement schemes), does not require any prior model for the reconstructed object, and is shown to have favorable computational and numerical properties. Moreover, the algorithm does not impose any assumption on the distribution of the projection orientations. Physically, this means that the algorithm is applicable to molecules that have unknown spatial preference.

Graph Laplacian Tomography From Unknown Random Projections

We introduce a graph Laplacian-based algorithm for the tomographic reconstruction of a planar object from its projections taken at random unknown directions. A Laplace-type operator is constructed on the data set of projections, and the eigenvectors of this operator reveal the projection orientations. The algorithm is shown to successfully reconstruct the Shepp-Logan phantom from its noisy projections. Such a reconstruction algorithm is desirable for the structuring of certain biological proteins using cryo-electron microscopy.

Unique recovery of unknown projection orientations in three-dimensional tomography

We consider uniqueness of three-dimensional parallel beam tomography in which both the object being imaged and the projection orientations are unknown. This problem occurs in certain practical applications, for example in cryo electron microscopy of viral particles, where the projection orientations may be completely unknown due to the random orientations of the particles being imaged. We show that only three projections are needed to guarantee unique recovery of the unknown projection orientations (up to a common orthogonal transformation), if the object belongs to a certain generic set of objects. In particular, the uniqueness holds for almost all objects. We also show that, if the object belongs to that generic set, $k+1$ projections at unknown orientations suffice to determine uniquely also the geometric moments of the object of order less or equal to $k$. As a consequence, the object belonging to that generic set, is uniquely determined (up to an orthogonal transformation) by almost any infinitely many projections at unknown orientations. We show that the uniqueness problem is related to some properties of certain homogeneous polynomials that depend on the projection orientations and the geometric moments of objects. Here certain theorems of algebraic geometry turn out to be useful. We also provide a system of equations, that is uniquely solvable and gives the desired projection orientations and object's geometric moments.