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, S j, i 1 L, i 1 R,i 2 L, i 2 R, … i j L, i j 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 = T 11 x + T 12 y + T 13 z + T 14 V = T 21 x + T 22 y + T 23 z + T 24 W = T 31 x + T 32 y + T 33 z + T 34 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 = b 1 X 1 + b 2 X 2 +…+b 0 Where the b’s are coefficients And X’s are some combination of the coordinates. Kriging: Y =  W i Y i

Trace contour line Line smooth Another algorithm

Application Interactive Surgical Planning Earthvision Rendering Volumetric data in molecular system Animated 3D CT imaging

Reference Volume visualization Arie kaufman IEEE computer Society Press 1991 Statistics and data analysis in Geology John C. Davis John Wiley and Sons, inc