Volume rendering is a technique used to display a 2D projection of a 3D discretely sampled data set. Texture mapping is a method for adding detail surface texture or colour to a computer-generated graphic or 3D model. Diffuse reflection is the reflection of Light from an uneven or granular surface such that an incident ray is seemingly reflected at a number of angles 3D projection is any method of mapping three-dimensional points to a two-dimensional plane In Signal processing, sampling is the reduction of a Continuous signal to a Discrete signal. A data set (or dataset) is a collection of Data, usually presented in tabular form
A typical 3D data set is a group of 2D slice images acquired by a CT or MRI scanner. Computed tomography (CT is a Medical imaging method employing Tomography. 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. In Digital imaging, a pixel ( pict ure el ement is the smallest piece of information in an image 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. A voxel (a Portmanteau of the words Volumetric and Pixel) is a volume element representing a value on a Regular grid in
To render a 2D projection of the 3D data set, one first needs to define a camera in space relative to the volume. A virtual camera is a series of Still cameras which are designed to behave as a motion camera or a simulated camera onto which a 3-D animation is projected when rendering 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. RGBA stands for R ed G reen B lue A lpha While it is sometimes described as a color space it is actually simply a use of the RGB color model with
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. A polygon mesh or Unstructured grid is a collection of vertices edges and faces that defines the shape of a polyhedral object in 3D computer The Marching Cubes algorithm is a common technique for extracting a surface from volume data. Marching cubes is a Computer graphics Algorithm, published in the 1987 SIGGRAPH proceedings by Lorensen and Cline for extracting a polygonal Direct volume rendering is a computationally intensive task that may be performed in several ways.
Contents |
Direct Volume Rendering
A direct volume renderer requires every sample value to be mapped to opacity and a color. 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, the composed RGBA result is projected on correspondent pixel of the frame buffer. The way this is done depends on the rendering technique.
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.
Volume Ray Casting
Main article: Volume ray casting. Volume ray casting, sometimes called volumetric ray casting, is an image based volume rendering technique. The technique of volume ray casting can be derived directly from the rendering equation. It provides results of very high quality, usually it is considered to provide the best image quality. Volume ray casting is classified as image based volume rendering technique, as the computation emanates from the output image, not the input volume data as is the case with object based techniques. 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 in order to save time. Then the ray is sampled at regular or adaptive 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.
Splatting
This is a technique which trades quality for speed. Here, every volume element is splatted, as Lee Westover said, like a snow ball, on to the viewing surface in back to front order. These splats are rendered as disks whose properties (color and transparency) vary diametrically in normal (Gaussian) manner. Flat disks and those with other kinds of property distribution are also used depending on the application.
Shear Warp
A new approach to volume rendering was developed by Cameron and Undrill, popularized by Philippe Lacroute and Marc Levoy, [1] 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. Marc Levoy is a Computer graphics researcher and Professor of Computer Science and Electrical Engineering at Stanford University. 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 in software at the cost of less accurate sampling and potentially worse image quality compared to ray casting. There is memory overhead for storing multiple copies of the volume, for the ability to have near axis aligned volumes. This overhead can be mitigated using run length encoding.
Texture Mapping
Many 3D graphics systems use texture mapping to apply images, or textures, to geometric objects. Texture mapping is a method for adding detail surface texture or colour to a computer-generated graphic or 3D model. Commodity PC graphics cards are fast at texturing and can efficiently render slices of a 3D volume, with realtime interaction capabilities. A video card, also known as a graphics accelerator card, display adapter, or graphics card, is a hardware component whose function is to Workstation GPUs are even faster, and are the basis for much of the production volume visualization used in medical imaging, oil and gas, and other markets (2007). In earlier years, dedicated 3D texture mapping systems were used on workstation systems such as Silicon Graphics Infinite Reality, HP Visualize FX, and others.
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.
Hardware-Accelerated Volume Rendering
A recently exploited technique to accelerate traditional volume rendering algorithms such as ray-casting, is the use of modern graphics cards. Starting with the programmable pixel shaders, people recognized the power of parallel operations on multiple pixels and began to perform general purpose computations on the graphics chip. A pixel shader is a shader program often executed on a Graphics processing unit. The pixel shaders are able to read and write randomly from video memory and perform some basic mathematical and logical calculations. A pixel shader is a shader program often executed on a Graphics processing unit. These SIMD processors were used to perform general calculations such as rendering polygons and signal processing. In Computing, SIMD ( S ingle I nstruction M ultiple D ata is a technique employed to achieve data level parallelism as in a Vector In recent GPU generations, the pixel shaders now are able to function as MIMD processors (now able to independently branch) utilizing up to 1GB of texture memory with floating point formats. In Computing, MIMD ( M ultiple I nstruction stream M ultiple D ata stream is a technique employed to achieve parallelism With such power, virtually any algorithm with steps that can be performed in parallel, such as volume ray casting or Tomographic reconstruction, can be performed with tremendous acceleration. The mathematical basis for tomographic imaging was laid down by Johann Radon. The introduction of languages like GLSL, it is possible for volume renderers such as Drishti to use their own algorithms optimised for the task at hand. GLSL ( OpenGL Shading Language) also known as GLslang, is a high level Shading language based on the C programming language. Drishti (meaning "vision" or "insight" in Sanskrit) is a multi-platform open-source Volume Exploration and Presentation Tool Custom shaders can be written for variations of the volume rendering process, such as multiple volume shaders, shadow and lighting, emissive colour and so forth.
Optimization 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. An octree is a Tree data structure in which each internal node has up to eight children Binary space partitioning ( BSP) is a method for recursively subdividing a space into Convex sets by Hyperplanes This subdivision gives rise to
Volume Segmentation
By sectioning out large portions of the volume that one considers uninteresting before rendering, the amount of calculations that have to be made by ray casting or texture blending can be significantly reduced. This reduction can be as much as from O(n) to O(log n) for n sequentially indexed voxels. Volume segmentation also has significant performance benefits for other ray tracing algorithms.
Multiple and Adaptive Resolution Representation
By representing less interesting regions of the volume in a coarser resolution, the data input overhead can be reduced. On closer observation, the data in these regions can be populated either by reading from memory or disk, or by interpolation. In the mathematical subfield of Numerical analysis, interpolation is a method of constructing new data points within the range of a Discrete set of
Pre-integrated volume rendering
Pre-integrated volume rendering is a method that can reduce sampling artifacts by pre-computing much of the required data. It is especially useful in hardware-accelerated applications because it improves quality without a large performance impact.
Sources
- ^ Marc Levoy, “Display of Surfaces from Volume Data”, IEEE CG&A, May 1988. Archive of Paper
- ^ Drebin, R. A. , Carpenter, L. , Hanrahan, P. , “Volume Rendering”, Computer Graphics, SIGGRAPH88. DOI citation link
- Barthold Lichtenbelt, Randy Crane, Shaz Naqvi, Introduction to Volume Rendering (Hewlett-Packard Professional Books) , Hewlett-Packard Company 1998.
- ^ Engel K. , Kraus M. , Ertl T. : High-quality pre-integrated volume rendering using hardware-accelerated pixel shading. In Proceedings of Eurographics/SIGGRAPH Workshop on Graphics Hardware (2001), pp. 9–16.
- ^ Lum E. , Wilson B. , Ma K. : High-Quality Lighting and Efficient Pre-Integration for Volume Rendering. In Eurographics/IEEE Symposium on Visualization 2004.
- ^ Max N. , Hanrahan P. , Crawfis R. : Area and volume coherence for efficient visualization of 3D scalar functions. In Computer Graphics (San Diego Workshop on Volume Visualization) (1990) vol. 24, pp. 27–33.
- ^ Sherbondy A. , Houston M. , Napel S. : Fast volume segmentation with simultaneous visualization using programmable graphics hardware. In Proceedings of IEEE Visualization (2003), pp. 171–176.
- ^ Stein C. , Backer B. , Max N. : Sorting and hardware assisted rendering for volume visualization. In Symposium on Volume Visualization (1994), pp. 83–90.
External links
Dapyx Software network: MP3 Explorer | Ebook Manager | Zenithic