Voxel Based method

Three different groups of reconstruction algorithms have been used. These groups have been differentiated on the basis of implementation in voxel-based methods (VBM), pixel-based methods (PBM) and function-based methods (FBM) by Solberg et al. (2007). 

Voxel-based methods imply the comparison of image gray levels to be registered. 

Acosta, O., et al.. Automated voxel-based 3D cortical thickness measurement in a combined Lagrangian-Eulerian PDE approach using partial volume maps. Med Image Anal, 2009. 13(5) p. 730-43. Wright, I.C., et al., A voxel-based method for the statistical analysis of gray and white matter density applied to schizophrenia. Neuroimage, 1995. 2(4) p. 244-52. 

Fig. 2. (Continued) method (regression model) third row SUV image (SUV), global metabolic rate (influx), and distribution volume (DV). The parametric images are obtained by applying the Patlak model to the data fourth row SUV image (SUV), phosphorylation rate (k3), and transport rate (kl). The images are obtained by a voxel-based application of the two-compartment model.

DTI identifies the motion of water that is quantified by voxel and region-based methods measuring diffusivity and fractional anisotropy. Diffusivity, a measurement of amplitude of diffusional motion, is increased with neuronal loss and gliosis. 

Function-based methods choose a particular function (like a polynomial) and determine coefficients to make one or more functions pass through the input pixels. Afterwards, the functions are used to create a regular voxel array by evaluating the functions at regular intervals. 

Noninvasive prediction of strength in vertebral bodies can provide valuable information for the assessment of the risk of fracture in human vertebrae [1-6], The aim of this study was to present an effective specimen-specific approach for predicting failure initiation locus in cadaveric vertebrae using a quantitative computed tomography (QCT) voxel-based finite element method (FEM). 

With the new voxel-based workflow two alternatives are possible the first one consists in creating seismically derived porosity and permeability cubes. That can be done by using the same methods as in classical workflows. Then the voxelization process will assign porosity and permeability values to all the voxels making up the voxel grid. 

The study presented a new tomographic method based on 3D reconstruction from a single 180 exposure. The method is based on the summation principle and the 3D voxel image is generated almost in real-time. 

Another approach to obtain spatially selective chemical shift information is, instead of obtaining the entire image, to select only the voxel of interest of the sample and record a spectrum. This method called Volume Selective spectroscopY (VOSY) is a ID NMR method and is accordingly fast compared with a 3D sequence such as the CSI method displayed in Figure 1.25(a). In Figure 1.25(b), a VOSY sequence based on a stimulated echo sequence is displayed, where three slice selective pulses excite coherences only inside the voxel of interest. The offset frequency of the slice selective pulse defines the location of the voxel. Along the receiver axis (rx) all echoes created by a stimulated echo sequence are displayed. The echoes V2, VI, L2 and L3 can be utilized, where such multiple echoes can be employed for signal accumulation. 

The stochastic reconstruction method is based on the idea that an arbitrarily complex porous structure can be described by a binary phase function which assumes a value 0 in the pore space and 1 in the solid matrix29 The intrinsic randomness of the phase function can be adequately qualified by the low order statistical moments, namely porosity and two-point autocorrelation function.29 The porosity is the probability that a voxel is in the pore space. The two-point autocorrelation function is the probability that two... 

Besides the compartment analysis, non-compartment models can be used. One frequently used procedure is the regression method. This method performs a linear regression fit on a voxel basis. The slope image provides information about the trapping of the tracer, while the intercept image reflects the distribution volume of the radiopharmaceutical. Another non-compartment model is based on the calculation of the fractal dimension (FD) (17). FD is a parameter for the heterogeneity and is calculated for the time-activity data of each individual VOI. The values of FD vary from 0 to 2 showing the deterministic or chaotic distribution of the tracer activity. We use a subdivision of 7 x 7 and a maximal SUV of 20 for the calculation of FD. 

In general, a regularization parameter should be chosen for each voxel. Since there may be thousands of voxels, the use of graphical or other methods requiring intervention is prohibitive. In the present work, an automatic, data-driven method is utilized to obtain a reliable estimate of the regularization parameter for each voxel. It is based on nonparametric statistical theory, which can incorporate a number of performance criteria, including unbiased prediction risk (UBPR),9 cross-validation (CV),15 and generalized cross-validation (GCV).16... 

For the dynamic lung impedance model to be useable in Finite Difference Method or Finite Element Method impedance signal simulations, the dynamic tissue sample model is discretized into volume data. At first 3D data with 35 x 35 x 35 voxel resolution is prepared from each of the 40 time frames. This allows for easy import into MATLAB or COMSOL based calculation. The volume data includes percentage of blood vessels (blood) for each of the 35 X 35 X 35 X 40 voxels. It can readily be transformed into electric/dielectric properties for each voxel with tissue data available on the internet. But data can also be exported with arbitrary resolution depending on calculation-simulation requirements. The simulations are run separately for each of the 40 time-frames to get full frequency characteristic of impedance measurement across the tissue sample. Finally we can get 40 frequency characteristics—one for each time-frame and to see a dynamic electrical impedance signal on a certain frequency, we just need to plot the impedance value at the chosen frequency from the 40 time-frames. 

Three-dimensional postprocessing method based on a weighted display of all voxels along each ray in the view direction. Transfer functions assign opacity and color to each CT number. 

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