2D image

To describe the X-ray imaging system the projection of 3D object points onto the 2D image plane, and nonlinear distortions inherent in the image detector system have to, be modelled. A parametric camera model based on a simple pinhole model to describe the projection in combination with a polynomal model of the nonlinear distortions is used to describe the X-ray imaging system. The parameters of the model are estimated using a two step approach. First the distortion parameters for fixed source and detector positions are calculated without any knowledge of the projection parameters. In a second step, the projection parameters are calculated for each image taken with the same source and detector positions but with different sample positions. 

The projection model (equations 1, 2) describes the mapping of 3D points = m,yw,2wY to 2D image points Pi = (ii,j/i) in a virtual, undistorted image plane. The... 

Finally, the standard draft provides a detailed model of the acquisition data, which intends to describe all the possible shapes which can be taken by NDE data OD (scalar or complex), ID (sampled - cf ultrasonics A-scans - or unsampled - ef ultrasonics time/amplitude data), 2D (images) or 3D (volumes). 

Figure 10.3-16. Graphical representation of the chemical structure of the reactants and products of a chemical reaction a) as a 2D image b) with structure diagrams showing all atoms and bonds of the reactants and products to indicate how this information is stored in a connection table.

TEM is still the most powerful technique to elucidate the dispersion of nano-filler in rubbery matrix. However, the conventional TEM projects three-dimensional (3D) body onto two-dimensional (2D) (x, y) plane, hence the structural information on the thickness direction (z-axis) is only obtained as an accumulated one. This lack of z-axis structure poses tricky problems in estimating 3D structure in the sample to result in more or less misleading interpretations of the structure. How to elucidate the dispersion of nano-fillers in 3D space from 2D images has not been solved until the advent of 3D-TEM technique, which combines TEM and computerized tomography technique to afford 3D structural images, incidentally called electrontomography . 

In the following, we will discuss two-dimensional (2D)-to-3D conversion in this context. However, it should be emphasized that we do so only for the sake of brevity. In reality, none of the conversion programs uhlizes informahon of a 2D image of a chemical structure. Only the information on the atoms of a molecule and how they are cormected is used (i.e. the starhng informahon is the conshtution of the molecule). One could even refer to linear structure representations such as SMILES as one-dimensional. However this is not true since SMILES allows for branches and ring closure which makes its informahon content essentially 2D. Thus, all structure representahons which lack 3D atomic coordinates will in the following simply be referred to as 2D. 

Fig. 1.21 Echo Planar Imaging (EPI) pulse sequence. Gradient-echo based multiple echoes are used for fast single-shot 2D imaging. Slice selection along Gs and frequency encoding along C, are utilized. Phase encoding is realized using short blipped gradient pulses along Gp.

Cano Barrita [27] cast concrete specimens with w/c of 0.6, dried the specimens at 38 °C and 20% relative humidity, then measured the penetration of water in a capillary uptake type of experiment. A 3D centric scan SPRITE measurement was selected, as an image could be acquired in 150 s and the image would therefore be weighted only by the T2 decay. 3D images were acquired at various exposure times and the central 2D image slice was extracted from the data to measure the penetration depth with time. 

Our very first experiments with the reactor depicted in Figure 5.4.1 were carried out with a 15% Pt-Y-Al203 single cylindrical catalyst pellet [10-12], The acquisition time of 2D images of an axial slice at that time was about 260 s. Despite this, the first direct MRI visualization of the operation of a model gas-liquid-solid reactor has revealed the existence of large gradients of the liquid phase content within the catalyst pellet upon imbibition of liquid a-methylstyrene (AMS) under conditions... 

With these goals in mind, we have studied the distribution of the liquid phase in the course of the hydrogenation reaction in a catalyst bed comprised of 1-mm catalyst beads (Figure 5.4.5). The 2D images shown reflect the distribution of the liquid phase in a 2-mm thick axial slice upon variation of the liquid AMS flow rate. The results show that while the increase in the flow rate leads to larger liquid contents in the bed (and vice versa), a steady state operation of the catalyst bed with unchanging spatial distribution of the liquid is observed if the external conditions remain unchanged. 

Fig. 5.5.14 Schematic diagram showing how the double-phase encoded DEPT sequence achieves both spatial and spectral resolution within the reactor, (a) A spin-echo ]H 2D image taken through the column overlayed with a grid showing the spatial location within the column of the two orthogonal phase encoded planes (z and x) used in the modified DEPT sequence. The resulting data set is a zx image with a projection along y. In-plane spatial resol-ution is 156 [Am (z) x 141 [xm (x) for a 3-mm slice thickness. The center of each volume from which the data have been acquired is identified by the intersection of the white lines. The arrow indicates the direction of flow.

Thus in this favorable case the complete information on nanostructure is recorded in one 2D image. Mathematically the recorded image is a slice... 

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