Visual Computing - Volume Rendering

Volume rendering

Rendering data where we don’t have explicit surfaces

Most familiar example of volume rendering

Computed Axial Tomography (CAT scan)

Hounsfield unit

Standardised way to measure radiodensity in CT scans

Important point about CAT scans

No classification data. Data returned from the CAT scan is just radiodensity and we can use Hounsfield scale to convert.

Transfer function

Relating value in dataset to visuals

How to do more sophisticated direct volume rendering

Raycast. Fire ray from pixel on viewpoint into the volume. March along the ray in tiny steps and look at the colour and opacity associated with the voxel. Accumulate the opacity and colour. Repeat process.

Unlike raytracing. Single ray, not tracing path

Basic algorithm of direct volume rendering

Step 1: Apply a transfer function to classify data points and give them a colour and alpha value
Step 2: Raycast through the viewplane to determine the colour of each pixel.

Additive reprojection

“Reversing the process” of a CAT scanner. Name of the direct volume rendering algorithm.

Making fake “surfaces” on our voxel structure

Create fake surface normals from the data by interpreting the changes in the voxel value over 3 different dimensions.
Direction should vary smoothly.

Can then plug into local illumination calculations.

Isoline

Line that represents a constant value. Most familiar with contour line on a map—isoline representing constant height

Finding an isoline in two dimensions

Trace where the line is along the points. We can then classify objects/materials at opposite sides of the line

Isosurface

3D equivalent of the 2D isoline

Purpose of using an isosurface

Find the surface that differentiates between two different types of artefact in our data.

Algorithm for finding an isosurface

Marching cubes.
For every set of 8 data points, determine what combination of triangles contributes to the overall surface that separates out the two types of data points.

Marching cubes algorithm explanation

v = f(x,y,z). Gives some point in 3D space and gives a single value.
Use that function to sample function at regular intervals inside a given space

Surface level is the threshold for the values. Points below surface level are “empty space”.

We simplify all cubes points inside the volume to a single cube - 8 corner points inside. Triangulation configurations for those points that are active. Interpolate based on value and how close the value is to the surface value for a smoother surface.

Proxy geometry

Imagine a stack of glass panes. The colours from the voxels are being splattered like paint. Small number of polygons with a particular texture.

Mapping between volume and texture coordinates for proxy geometry

Use barocentric interpolation—weighted distance from the vertices of the triangle to give the coordinate in the triangle.

Map with linear interpolation to give RGBA value.