introduction to volume visualization
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Introduction to Volume Visualization. Mengxia Zhu Fall 2007. Volume Visualization. Volume visualization is used to create images from volumetric data defined on multiple dimensional grids - PowerPoint PPT PresentationTRANSCRIPT
Introduction to Volume Visualization
Mengxia Zhu
Fall 2007
Volume Visualization
Volume visualization is used to create images from volumetric data defined on multiple dimensional grids
volumetric data is typically a set of samples f(x,y,z,d) with d representing the data property at a location determined by (x,y,z).
Timing varying volumetric data f(x, y, z, t, d)
Data Type d can take the form of scalar, vector, or even tensor.
Scalar, Single valued at each location in a dataset. Examples are temperature, pressure, density, and elevation etc. Simplest and most common form. i.e. f of type real, integer
Vector, data with magnitude and direction. In 3D, it is represented as a triplet of values ( u,v,w). Examples include flow velocity, particle trajectory, wind motion, and gradient function.
Tensor, complex mathematical generalizations of vectors and matrices. A tensor of rank 0 is a scalar. Rank 1 is vector, rank 2 is 3x3 matrix.
E.g. stress and strain in FEM modeling, which represent the stress and strain at a point in an object under load
Data Elements
Volumetric data is usually defined on a cartesian grid
two alternative methods defining data elements. Voxels: sample values are
called voxel Cells: a cuboidal region
with voxels at 8 grid corners.
Regular and Irregular Structure A dataset consists of an organizing structure and
associated attribute data Characterized according to whether its structure
is regular or irregular. If there is a single mathematical relationship
within the composing points and cells, a dataset is regular. Regular data can be implicitly represented efficiently. Irregular data must be explicitly represented since
there is no inherent pattern that can be compactly described. Unstructured data tends to be more general, but requires greater memory and computational resources.
Grid and Lattice
Cartesian grids: all elements are identical axis-aligned cubes
Regular grid: identical rectangular elements aligned along the axes of the dataset.
Rectilinear Grids: aligned along the axes of the dataset. However arbitrary spacing and the data elements themselves are no longer identical.
curvilinear Grids: Elements are no longer axis aligned, and again the elements can be non-identical.
Grid Types
uniform rectilinearregular curvilinear
Structured Grids:
regular irregular hybrid curved
Unstructured Grids:
Examples
Regular grid
Rectilinear grid
Methods
The fundamental algorithms are of two types: direct volume rendering (DVR) algorithms surface-fitting (SF) algorithms.
DVR methods map elements directly into screen space without using intermediate geometric primitives as an intermediate representation.
SF methods are also called feature-extraction or iso-surfacing and fit planar polygons or surface patches to constant-value contour surfaces.
www.cs.sunysb.edu/.../ WeiWeb/research.htmwww.mpa-garching.mpg.de/ gadget/hydrosims/www-vis.lbl.gov/.../ ChomboVis99/sharedvrend.html
DVR versus SF Volume rendering is a process of creating a 2D image directly from
3D volumetric data Mapping the entire 3D data into a 2D image
SF is a process of creating an image of a surface contained within the volume data using geometric primitives Marching Cubes algorithm (triangles as primitives) Dividing Cubes algorithm (3D points as primitives)
DVR conveys more information than surface rendering images at the cost of increased algorithm complexity and rendering times
Volume rendering to display amorphous phenomena such as clouds, fog
Direct Volume Rendering Techniques Object-order technique
Uses a forward mapping scheme where the volume data is mapped into the image plane
Image-order techniqueUses a backward mapping scheme where rays are
cast from each pixel in the image plane through the volume data to determine the pixel value
Hybrid technique Combines the two approaches
Data Classification
Threshold value (Iso-value) for an SF method or the color and opacity values (transfer function) for a DVR method.
The DVR color table is used to map data values to meaningful colors. The opacity table is used to expose the part of the volume most interesting to the user and to make transparent the uninteresting parts.
Common Steps in SF Data acquisition either via empirical
measurement or computer simulation. Put the data into a format that can be easily
manipulated. This may entail scaling the data for a better value distribution, enhancing contrast, filtering out noise, and removing out-of-range data.
The data is mapped onto geometric or display primitives.
The primitives are stored, manipulated, and displayed.
Interpolation
Interpolation assumes that the value of the data element varies across the element. some combination of the surrounding grid points.
For example, with trilinear interpolation the value at a arbitrary point in the data element is calculated from the surrounding eight grid points.
Trilinear Interpolation
Trilinear Interpolation
Trilinear interpolation is the process of taking a three-dimensional set of numbers and interpolating the values linearly, finding a point using a weighted average of eight values.
Shading To create a realistic image, shading with light
define how much light each data point received. The gradient is used to approximate the surface
normal to an imaginary surface touching the point.
Central difference method:
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