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Computational Methods for Three-Dimensional Microscopy by Gabor T. Herman

By Gabor T. Herman

Approaches to the restoration of third-dimensional info on a organic item, that are frequently formulated or carried out at the beginning in an intuitive means, are concisely defined right here in accordance with actual types of the thing and the image-formation approach. either third-dimensional electron microscopy and X-ray tomography should be captured within the similar mathematical framework, resulting in closely-related computational methods, however the methodologies vary intimately and for this reason pose assorted demanding situations. The editors of this quantity, Gabor T. Herman and Joachim Frank, are specialists within the respective methodologies and current learn on the leading edge of organic imaging and structural biology.

Computational tools for third-dimensional Microscopy Reconstruction will function an invaluable source for students attracted to the advance of computational equipment for structural biology and mobilephone biology, rather within the region of 3D imaging and modeling.

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Extra resources for Computational Methods for Three-Dimensional Microscopy Reconstruction

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6). In the following, we provide a “manual” rule of how to determine the projection direction and its in-plane rotation given . ; Â; /. An easy way to do this is depicted in Fig. 12. First, the tilt angle is applied, moving the projection coordinate system 2 Interchanging Geometry Conventions in 3DEM a 39 b 100 50 0 −50 −100 100 50 0 −50 −100 X ( pixels ) 100 100 50 50 0 −50 −50 −100 −100 c Y ( pixels ) Y ( pixels ) 0 d 100 50 0 −50 100 −100 X ( pixels ) 50 0 −50 −100 X ( pixels ) 100 100 50 50 0 −50 −50 −100 −100 Y ( pixels ) Y ( pixels ) 0 Fig.

Haar features are closely related to Haar wavelets [28] (the simplest possible wavelet, essentially a square function of the input signal). A Haar feature sums pixel intensities in two adjacent regions and then calculates the difference between those two sums; such a difference is maximized at the edge of an object. Similar to template matching, Haar features also have an efficient implementation, which uses what is generally known as an integral image (or summed-area tables) [7]. Thus, this method can both be used to simultaneously locate and verify [22] particles in the micrograph, when combined with fast Haar features, or simply verify subsets of candidates already located by template matching [38].

First, the tilt angle is applied, moving the projection coordinate system 2 Interchanging Geometry Conventions in 3DEM a 39 b 100 50 0 −50 −100 100 50 0 −50 −100 X ( pixels ) 100 100 50 50 0 −50 −50 −100 −100 c Y ( pixels ) Y ( pixels ) 0 d 100 50 0 −50 100 −100 X ( pixels ) 50 0 −50 −100 X ( pixels ) 100 100 50 50 0 −50 −50 −100 −100 Y ( pixels ) Y ( pixels ) 0 Fig. 11 Example of rotation about the transformed axes: (a) Original, unrotated volume. (b) Volume after rotating 90ı about Z (blue arrow in (a)).

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