Volume Rendering

Tag: Computer Graphic; Date: 08 April 2020

What is Volume Rendering?

It is a method to create a 2D projection from a discretely sampled 3D data.
3D data: CT, a set of voxel, a group of 2D slice images.
Ex: From the figure below, we have an Image Space(2D) and Object Space(3D). Volume Rendering calculates the pixel value by projecting 3D object onto Image Space.

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Of course, the 3D object is often discretized into voxel. Each voxel have an intensity value corresponding to its density or material.
Form each pixel, we cast a ray into the object space. The ray will across the object and hit different voxels. For example, ray may hits air, skin, soft tissue, eyeball, bones, brain, …, hair, air, then out of the Object Space.
This changes in ray depth vs intensity can be described in Intensity Profile as the following figure.

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The ray can return different kinds of information from the volume. It depends what we want to see and what we want to get from the volume data. We can use different Ray Functions to help with that.
There are many Ray Functions. Here are some 4 basic ways:
1. Max Intensity Projection(MIP): return the maximum along the way. It often returns the densest part of the volume data. The object behind other object can be projected in front of them.
2. Accumulation Ray Function(ACC): adds up all the value it hits along the way
3. Average Ray Function(AVG): avg all the value it encounters along the way. The resulting image looks like a X-ray
4. First Hit Ray Casting(FIRS): return the first value that it encounters. The resulting image is corresponding to the iso-surface, e.g., skin of the face.
This different Ray Function results different kinds of images.

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So far, the ray traverse the volume data, and generate the Intensity Profile. But there is one thing we missed is how to sample the volume data.
Here are 3 basic approaches:
1. Regular Sampling: The distance $d$ between each sample point is always the same. However some sample point may not fall on the edges. So we need to interpolate those sample points. This approach is accurate but more computation required.
2. Scan Conversion: Simply take the value at he center of the voxel every time. It is the fastest among the three methods, but least accurate.
3. Voxel Intersections: This method try to balance between Regular Sampling and Scan Conversion. Samples the data every time the ray hits the edge. Therefore, the interpolation is simpler(only 1 linear interpolation on each edge).