Estimating the viewing parameters of random, noisy projections of asymmetric objects for tomographic reconstruction

Lauren, P.D.; Nandhakumar, N.

doi:10.1109/34.589202

Cited by 21 publications

(11 citation statements)

References 20 publications

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“…The common-line method is another reference-free algorithm based on the property that two projections of the same object from different directions must share a common line in Fourier space (Central-Slice Theorem). The search of the common line can be done by comparing the projection sinograms in the image space (Goncharov, 1990;Penczek et al, 1994;van Heel, 1987) or in the Fourier space (Goncharov, 1990;Lauren and Nandhakumar, 1997). The approach of Lauren and Nandhakumar (1997) is particularly interesting since shifts and noise are explicitly considered during the commonline search.…”

Section: Introductionmentioning

confidence: 99%

A multiresolution approach to orientation assignment in 3D electron microscopy of single particles

Sorzano

Jonić

El-Bez

et al. 2004

Journal of Structural Biology

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Three-dimensional (3D) electron microscopy (3DEM) aims at the determination of the spatial distribution of the Coulomb potential of macromolecular complexes. The 3D reconstruction of a macromolecule using single-particle techniques involves thousands of 2D projections. One of the key parameters required to perform such a 3D reconstruction is the orientation of each projection image as well as its in-plane orientation. This information is unknown experimentally and must be determined using image-processing techniques. We propose the use of wavelets to match the experimental projections with those obtained from a reference 3D model. The wavelet decomposition of the projection images provides a framework for a multiscale matching algorithm in which speed and robustness to noise are gained. Furthermore, this multiresolution approach is combined with a novel orientation selection strategy. Results obtained from computer simulations as well as experimental data encourage the use of this approach.

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Section: Introductionmentioning

confidence: 99%

A multiresolution approach to orientation assignment in 3D electron microscopy of single particles

Sorzano

Jonić

El-Bez

et al. 2004

Journal of Structural Biology

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“…We can classify all the techniques for the angular assignment into two groups: referencefree [5,6,8,9,12,14,16,18] and reference-based [7,10,11,13,15,17]. The goal of the reference-based methods is to refine a particle assignment with respect to a reference volume.…”

Section: Introductionmentioning

confidence: 99%

“…A 3D model of a particle is usually computed from its EM images in a twostep procedure. First, the in-plane coordinates of the center of the particle as well as its in-plane and out-of-plane rotations are determined and assigned to each particle image [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Second, a reconstruction algorithm is applied to compute the 3D model using the particle images and the previous angular and translational assignment [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Spline-based image-to-volume registration for three-dimensional electron microscopy

et al. 2005

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This paper presents an algorithm based on a continuous framework for a posteriori angular and translational assignment in three-dimensional electron microscopy (3DEM) of single particles. Our algorithm can be used advantageously to refine the assignment of standard quantized-parameter methods by registering the images to a reference 3D particle model. We achieve the registration by employing a gradient-based iterative minimization of a least-squares measure of dissimilarity between an image and a projection of the volume in the Fourier transform (FT) domain. We compute the FT of the projection using the central-slice theorem (CST). To compute the gradient accurately, we take advantage of a cubic B-spline model of the data in the frequency domain. To improve the robustness of the algorithm, we weight the cost function in the FT domain and apply a ''mixed'' strategy for the assignment based on the minimum value of the cost function at registration for several different initializations. We validate our algorithm in a fully controlled simulation environment. We show that the mixed strategy improves the assignment accuracy; on our data, the quality of the angular and translational assignment was better than 2 voxel (i.e., 6.54 Å ). We also test the performance of our algorithm on real EM data. We conclude that our algorithm outperforms a standard projection-matching refinement in terms of both consistency of 3D reconstructions and speed. r

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“…It is only expected to work well when the initial point is in the neighborhood of the optimal solution. A similar problem has been studied in the field of tomography when the rotation corresponding to a projection is not known [14,15]. In [15], the authors dealt with imaging noise using self consistency between four projections.…”

Section: Background and Related Workmentioning

confidence: 96%

“…On the other hand, in the tilted configuration, several images of the specimen are acquired by rotating the stage supporting the carbon film about a known axis by known angular increments. In this paper we focus our attention to the reconstruction of 3D density using a single exposure at zero tilt [5,6,10,15,19,20,22].…”

Section: Background and Related Workmentioning

confidence: 99%

Structure and View Estimation for Tomographic Reconstruction: A Bayesian Approach

Mallick

Agarwal

Kriegman

et al.

2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 2 (CVPR'06)

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This paper addresses the problem of reconstructing the density of a scene from multiple projection images produced by modalities such as x-ray, electron microscopy, etc. where an image value is related to the integral of the scene density along a 3D line segment between a radiation source and a point on the image plane. While computed tomography (CT) addresses this problem when the absolute orientation of the image plane and radiation source directions are known, this paper addresses the problem when the orientations are unknown -it is akin to the structure-from-motion (SFM) problem when the extrinsic camera parameters are unknown. We study the problem within the context of reconstructing the density of protein macro-molecules in Cryogenic Electron Microscopy (cryo-EM), where images are very noisy and existing techniques use several thousands of images. In a non-degenerate configuration, the viewing planes corresponding to two projections, intersect in a line in 3D. Using the geometry of the imaging setup, it is possible to determine the projections of this 3D line on the two image planes. In turn, the problem can be formulated as a type of orthographic structure from motion from line correspondences where the line correspondences between two views are unreliable due to image noise. We formulate the task as the problem of denoising a correspondence matrix and present a Bayesian solution to it. Subsequently, the absolute orientation of each projection is determined followed by density reconstruction. We show results on cryo-EM images of proteins and compare our results to that of Electron Micrograph Analysis (EMAN)-a widely used reconstruction tool in cryo-EM.

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Estimating the viewing parameters of random, noisy projections of asymmetric objects for tomographic reconstruction

Cited by 21 publications

References 20 publications

A multiresolution approach to orientation assignment in 3D electron microscopy of single particles

A multiresolution approach to orientation assignment in 3D electron microscopy of single particles

Spline-based image-to-volume registration for three-dimensional electron microscopy

Structure and View Estimation for Tomographic Reconstruction: A Bayesian Approach

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