Volume rendering
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Volume rendering is a technique used to display a 2D projection of a 3D discretely sampled data set.
A typical 3D data set is a group of 2D slice images acquired by a CT or MRI scanner. Usually these are acquired in a regular pattern (e.g., one slice every millimeter) and usually have a regular number of image pixels in a regular pattern. This is an example of a regular volumetric grid, with each volume element, or voxel represented by a single value that is obtained by sampling the immediate area surrounding the voxel.
To render a 2D projection of the 3D data set, one first needs to define a camera in space relative to the volume. Also, one needs to define the opacity and color of every voxel. This is usually defined using an RGBA (for red, green, blue, alpha) transfer function that defines the RGBA value for every possible voxel value.
A volume may be viewed by extracting surfaces of equal values from the volume and rendering them as polygonal meshes or by rendering the volume directly as a block of data. The Marching Cubes algorithm is a common technique for extracting a surface from volume data. Direct volume rendering is a computationally intensive task that may be performed in a several ways.
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Direct Volume Rendering
A direct volume renderer requires every voxel values to be mapped to an opacity and a colour. This is done with a transfer function which can be a simple ramp, a piecewise linear function or an arbitrary table. Once converted to an RGBA (for red, green, blue, alpha) value, voxels are composited into the frame buffer. The way this is done depends on the rendering technique.
Ray Casting
The simplest way to project the image is to cast rays through the volume using ray casting. In this technique, a ray is generated for each desired image pixel. Using a simple camera model, the ray starts at the center of the projection of the camera (usually the eye point) and passes through the image pixel on the imaginary image plane floating in between the camera and the volume to be rendered. The ray is clipped by the boundaries of the volume to save time then the ray is sampled at regular intervals throughout the volume. The data is interpolated at each sample point, the transfer function applied to form an RGBA sample, the sample is composited onto the accumulated RGBA of the ray, and the process repeated until the ray exits the volume. The RGBA color is converted to an RGB color and deposited in the corresponding image pixel. The process is repeated for every pixel on the screen to form the completed image.
Shear Warp
A new approach to volume rendering was developed by Philippe Lacroute and Marc Levoy and described in the paper "Fast Volume Rendering Using a Shear-Warp Factorization of the Viewing Transformation" [1] (http://graphics.stanford.edu/papers/shear/) In this technique, the viewing transformation is transformed such that the nearest face of the volume becomes axis aligned with an off-screen image buffer with a fixed scale of voxels to pixels. The volume is then renderered into this buffer using the far more favourable memory alignment and fixed scaling and blending factors. Once all slices of the volume have been rendered, the buffer is then warped into the desired orientation and scale in the displayed image.
This technique is relatively fast at the cost of less accurate sampling and potentially worse image quality compared to ray casting.
Texture Mapping
Many 3D graphics systems use texture mapping to apply images, or textures, to geometric objects. Commodity PC graphics cards are fast at texturing and can efficiently render slices of a 3D volume.
These slices can either be aligned with the volume and rendered at an angle to the viewer, or aligned with the viewing plane and sampled from unaligned slices through the volume. Graphics hardware support for 3D textures is needed for the second technique.
Volume aligned texturing produces images of reasonable quality, though there is often a noticeable transition when the volume is rotated. View aligned texturing creates images of similar high quality to those of ray casting, and indeed the sampling pattern is identical.
A combination of these techniques is possible. For instance, a shear warp implementation could use texturing hardware to draw the aligned slices in the off-screen buffer.
Optimisation Techniques
Empty Space Skipping
Often, a volume rendering system will have a system for identifying regions of the volume containing no visible material. This information can be used to avoid rendering these transparent regions.
Early Ray Termination
This is a technique used when the volume is rendered in front to back order. For a ray through a pixel, once sufficient dense material has been encountered, further samples will make no significant contribution to the pixel and so may be ignored.
Octree and BSP space subdivision
The use of hierarchical structures such as octree and BSP-tree could be very helpful for both compression of volume data and speed optimization of volumetric ray casting process.