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Chapter 4 Voxels and Cells

Volumes of data are usually treated as either an array of voxels or an array of cells. These two approaches stem from the need to resample the volume between grid points during the rendering process. Resampling, requiring interpolation, occurs in almost every volume visualization algorithm. Since the underlying function is not usually known, and it is not known whether the function was sampled above the Nyquist frequency, it is impossible to check the reliability of the interpolation used to find data values between discrete grid points. It must be assumed that common interpolation techniques are valid for an image to be considered valid.

                 

Figure 1.2:Voxels. Each grid point has a sample value. Data values do not vary within voxels

The voxel approach dictates that the area around a grid point has the same value as the grid point (Figure 1.2). A voxel is, therefore, an area of non-varying value surrounding a central grid point. The voxel approach has the advantage that no assumptions are made about the behavior of data between grid points, only known data values are used for generating an image.

Figure 1.3: Cells. Data values do vary within cells. It is assumed that values between grid points can be estimated. Interpolation is used

The cell approach views a volume as a collection of hexahedra whose corners are grid points and whose value varies between the grid points (Figure 1.3). This technique attempts to estimate values inside the cell by interpolating between the values at the corners of the cell. Trilinear and tricubic are the most commonly used interpolation functions. Images generated using the cell approach, appear smoother than those images created with the voxel approach. However, the validity of the cell-based images cannot be verified [16].

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Expand Neural Networks and Pattern Recognition Using MATLABNeural Networks and Pattern Recognition Using MATLAB
Ch.1 Pattern Classification
Ch.2 Matrix Theory Applications
Ch.3 Network Object Reference
Ch.4 Bayesian Decision Theory
Ch.5 Principal Component Analysis
Ch.6 Intro to Neural Networks
Ch.8 Classical Models of NN
Ch.9 Linear Discriminant Functions
Ch.11 Non-Parametric Techniques
Ch.10 Multilayer Neural Networks
Ch.7 Neural Networks
Collapse Volume Rendering TemelleriVolume Rendering Temelleri
Ch.1 Introduction to Volume Rendering
Ch.2 Volume Rendering
Ch.3 Volumetric Data
Ch.4 Voxels and Cells
Ch.5 Classification of VR Algorithms
Ch.6 Optimization in Volume Rendering
Ch.7 References
Expand Accelerating Volume Rendering by DSP Hardware ImplementationAccelerating Volume Rendering by DSP Hardware Implementation
Ch.1 Volume Rendering
Ch.2 Optimization in VR
Ch.3 Framework
Ch.4 Choosing the Appropriate DSP Processor
Ch.5 Implementation
Expand A Review of Floating Point Basics and Comparison of Dedicated ProcessorsA Review of Floating Point Basics and Comparison of Dedicated Processors
Ch.1 Binary Systems
Ch.2 Digital Signal Processors
Ch.3 Introduction to DSP
Ch.4 Memory Architectures
Ch.5 Review of DSP Processors
Ch.6 Appropriate DSP Processor
Ap.A - IEEE Floating Point Arithmetic
Ap.B - IEEE Radix-Independent Floating Point
Ap.C - Calculation of Emax and Bias


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