Volume Visualization

Presented by

Zhao, hai

What’ volume visualization

• Volume visualization is the creation of graphical representations of data sets that are defined on three-dimensional grids. Volume data sets are characterized by multidimensional arrays of scalar or vector data. These data are typically defined on lattice structures representing values sampled in 3-D space.

• many objects and natural phenomena are 3D volumes of data.

Contd..

• Volume visualization can be traced back to the beginning of the 1970s.

• Recently, volume visualization has matured as a primary field of computer graphics.

• Volume visualization is concerned with the representation, manipulation, and rendering of volumetric data.

Application Domains

• Spinal Cord/Neurology

• Earth and Atmospheric

• Visual human/medical images

• Molecular science

• Paleontology

• Aeronautics

• Joint simulation/ Engineering mechanical

• Oceanography

Taxonomy of Volume visualization

Volume Visualization Pipeline

Basic Concept

• A voxel is the 3D counterpart of the 2D pixel. Each voxel is a quantum unit of volume and has a numeric value associate with it that represents some measurable properties or independent variables of the real objects, i.e., color, density, time.

• volume rendering

To visualize the volume dataset, primitives can be directly projected into 2D pixel space and stored as a raster image in a frame buffer. It involves both the viewing and the shading of the volume image.

Basic Concept

• the volume data can be first converted into geometric primitives in a process called isosurfacing, isocontouring, and surface extraction.

Basic Concept

• surface rendering

the geometric primitives are rendered to the screen (I.e., conventional geometric rendering). It involves the isosurfacing, the viewing, and the shading stages

Basic Concept

• data acquisition.

The sources of volume data are sampled data of real objects. Sampled data are acquired by 2D or 3D multi-channel scanners that measure the real world object and usually produce a sequence of 2D cross sections of the object.

Enhancement

Is to change them into a form that is more informative, filtered and uniform.

Reconstruction

The missing data between slices or between scattered points are interpolated.

• Manipulation stage includes geometrics, domain transformations.

• Classification stage is either a thresholding step or a material classification step. Thresholding is used primarily in the surface-rending approach, i.e., all values below it are assigned “0”, while all those above are set to “1”.

• Mapping stage maps the 3D voxel data into geometric or display primitives.

The choice of display primitive depends on whether volume rendering or surface rendering is used.

• Volume viewing

Determines the parts of the 3D scene that are visible

• Volume shading

Shading techniques compute the intensity/color value that reaches the viewer’s eye from each point of the visible surface.

It has two goals: one is provide optimal visual recognition for discernment of the displayed objects. The other goal is show the natural appearance of real objects.

representation

• The binary-array representation

Scene is digitized that the density must be one of the integers between a lower limit L and an upper limit U. If L =0 and U =1, then we say that scene is binary scene.

• Segment Endpoint Representation

J, Sj, i1L, i1

R,i2L, i2

R, … ijL, ij

R

Directed contour representation

Display

• Ensuring only that part of the object that is visible from the given view is displayed

• Assigning a shade to the visible surface to impart a 3D illusion.

Display from the binary-array representation

• Back-to-front method

For any 3D scene, there is a 3*4 transformation matrix T

U = T11x + T12y + T13z + T14

V = T21x + T22y + T23z + T24

W = T31x + T32y + T33z + T34

Eliminationg x and y

W = a + bz

Earth models

The procedure of earth model

1. Contouring by Triangulation

2. Contouring by grid

Distance weighting

Tread surface Models:

Y = b1X1 + b2X2 +…+b0

Where the b’s are coefficients

And X’s are some combination of the coordinates.

Kriging:

Y = Wi Yi

• Trace contour line

• Line smooth

Another algorithm

Application

• Interactive Surgical Planning

• Earthvision

• Rendering Volumetric data in molecular system

• Animated 3D CT imaging

Reference

• Volume visualizationArie kaufman

IEEE computer Society Press 1991

• Statistics and data analysis in GeologyJohn C. Davis

John Wiley and Sons, inc 1986

• www.dgi.com