A factorization-based approach to 3D reconstruction from multiple uncalibrated images

Obtaining the three-dimensional (3D) structure of negatively stained biological specimens at a resolution of, typically, 2 - 4 nm is becoming a relatively common practice in an increasing number of laboratories. A combination of new conceptual approaches, new software tools, and faster computers have made this situation possible. However, all these 3D reconstruction processes are quite computer intensive, and the middle term future is full of suggestions entailing an even greater need of computing power. Up to now all published 3D reconstructions in this field have been performed on conventional (sequential) computers, but it is a fact that new parallel computer architectures represent the potential of order-of-magnitude increases in computing power and should, therefore, be considered for their possible application in the most computing intensive tasks.We have studied both shared-memory-based computer architectures, like the BBN Butterfly, and local-memory-based architectures, mainly hypercubes implemented on transputers, where we have used the algorithmic mapping method proposed by Zapata el at. In this work we have developed the basic software tools needed to obtain a 3D reconstruction from non-crystalline specimens (“single particles”) using the so-called Random Conical Tilt Series Method. We start from a pair of images presenting the same field, first tilted (by ≃55°) and then untilted. It is then assumed that we can supply the system with the image of the particle we are looking for (ideally, a 2D average from a previous study) and with a matrix describing the geometrical relationships between the tilted and untilted fields (this step is now accomplished by interactively marking a few pairs of corresponding features in the two fields). From here on the 3D reconstruction process may be run automatically.

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Structural Studies on the Eukaryotic Ribosome

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100180033 ◽

1990 ◽

Vol 48 (1) ◽

pp. 256-257

Author(s):

Adriana Verschoor ◽

Ronald Milligan ◽

Suman Srivastava ◽

Joachim Frank

Keyword(s):

Chick Embryo ◽

3D Reconstruction ◽

Single Particle ◽

Mass Density ◽

Particle Surface ◽

Uranyl Acetate ◽

Electron Microscopic ◽

Eukaryotic Ribosome ◽

Negative Stain ◽

Reconstruction Methods

We have studied the eukaryotic ribosome from two vertebrate species (rabbit reticulocyte and chick embryo ribosomes) in several different electron microscopic preparations (Fig. 1a-d), and we have applied image processing methods to two of the types of images. Reticulocyte ribosomes were examined in both negative stain (0.5% uranyl acetate, in a double-carbon preparation) and frozen hydrated preparation as single-particle specimens. In addition, chick embryo ribosomes in tetrameric and crystalline assemblies in frozen hydrated preparation have been examined. 2D averaging, multivariate statistical analysis, and classification methods have been applied to the negatively stained single-particle micrographs and the frozen hydrated tetramer micrographs to obtain statistically well defined projection images of the ribosome (Fig. 2a,c). 3D reconstruction methods, the random conical reconstruction scheme and weighted back projection, were applied to the negative-stain data, and several closely related reconstructions were obtained. The principal 3D reconstruction (Fig. 2b), which has a resolution of 3.7 nm according to the differential phase residual criterion, can be compared to the images of individual ribosomes in a 2D tetramer average (Fig. 2c) at a similar resolution, and a good agreement of the general morphology and of many of the characteristic features is seen.Both data sets show the ribosome in roughly the same ’view’ or orientation, with respect to the adsorptive surface in the electron microscopic preparation, as judged by the agreement in both the projected form and the distribution of characteristic density features. The negative-stain reconstruction reveals details of the ribosome morphology; the 2D frozen-hydrated average provides projection information on the native mass-density distribution within the structure. The 40S subunit appears to have an elongate core of higher density, while the 60S subunit shows a more complex pattern of dense features, comprising a rather globular core, locally extending close to the particle surface.

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3D reconstruction and calculation of surface area and volume of bell pepper

Progress in Agricultural Engineering Sciences ◽

10.1556/progress.3.2007.5 ◽

2007 ◽

Vol 3 (1) ◽

pp. 89-113

Author(s):

Zoltán Gillay ◽

László Fenyvesi

Keyword(s):

3D Reconstruction ◽

Surface Area ◽

Three Dimensional ◽

Reference Method ◽

Bell Pepper ◽

Three Dimensional Model ◽

Acceptable Error ◽

Volume Calculation ◽

Bell Peppers ◽

Area And Volume

There was a method developed that generates the three-dimensional model of not axisymmetric produce, based on an arbitrary number of photos. The model can serve as a basis for calculating the surface area and the volume of produce. The efficiency of the reconstruction was tested on bell peppers and artificial shapes. In case of bell peppers 3-dimensional reconstruction was created from 4 images rotated in 45° angle intervals. The surface area and the volume were estimated on the basis of the reconstructed area. Furthermore, a new and simple reference method was devised to give precise results for the surface area of bell pepper. The results show that this 3D reconstruction-based surface area and volume calculation method is suitable to determine the surface area and volume of definite bell peppers with an acceptable error.

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