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xRobert Richmond

Light Field Mapping

September 2001

Page Two

Page One: Applications of Light Field Mapping
Synthetic Imaging
Real-World Imaging
Technical Analysis
Page Four: Triangle Centered Approximation
Triangle-Centered Light Field Mapping
Analysis of Triangle-Centered Approximation
Page Two: Data Acquisition
Resampling and Normalization
Page Five: Vertex-Centered Approximation
Vertex-Centered Light Field Mapping
Analysis of Vertex-Centered Approximation
Page Three: Surface Light Field Approximation Page Six: Hardware Acceleration
Light Field Map Compression
Final Thoughts

Data Acquisition

A surface map must first be defined before a quantitative analysis of the specific imaging features can be derived.  A surface map model simply describes the radiance values of every point on a measured surface from every possible direction. 

Trying to sample "every" point for a surface range would imply an infinite process, thus approximations of certain data ranges must be calculated  for performance to remain at acceptable levels during real-time rendering.  This compression process yields the final data, which is stored as two dimensional texture maps which can be processed through multi-textured blending operations to render the final light mapped image.

Gathering the information for surface light field data can be carried out through either of two processes.  Synthetic imaging is achieved through the usage of pre-generated data sets for the required input values.  Physical objects require a more complex acquisition routine.  Geometry is first scanned with aid from a structured light gathering system as used by professionals for real-world 3D modeling.  Then 200 to 400 images must be taken from various fixed points to acquire the surface texture features.  The data is then combined by a complex registration routine that matches the geometric and photo data sets to build an input dataset.

Resampling and Normalization

Next, the input dataset is processed through a visibility algorithm to determine un-occluded views.  The view-set is then decomposed through resampling and normalization into corresponding equal size triangle patterns while retaining characteristics for observation from multiple viewpoints for the texture being rendered.  While being computationally intensive, the resamping process can generally be processed by standard texture mapping hardware conventions.

A texture normalization method is utilized to build initial viewing patterns for later synthesis of associated rendered viewpoints.

In other suggested light mapping routines, an approximation of texture ranges is now employed as determination of an infinite number of viewpoints is not possible due to both hardware and real-world mathematical limitations.  The process presented above is referred to as the Eigen-Texture Approach.

Viewpoint synthesis is carried out to determine the aspects of both original and novel views.  Original views are easily determined, though novel views require extremely complex interpolation operations while performing texturing blending, thus limiting the effectiveness of real-time rendering.  The Eigen-Texture Approach also leads to image artifacts since this formula assumes a constant viewing angle per triangle without the capability of per sample interpolation.  

Intel has a defined a better approach through the resampling of viewing directions through direction parameterization.  Viewing direction resampling offers the ability to simply the synthesis of novel views.  This is accomplished by enabling per sample interpolation during the triangle rendering process, plus a new approximation pattern can be employed that allows for minimal image artifacting since root mean square errors can be minimized.  Also, resampling can be performed through 3D hardware acceleration unlike the Eigen-Texture Approach.  The question now is what type of parameterization operation should be utilized?

Parameterization according to spherical coordinates is possible, though this technique would not prove suitable for hardware acceleration due to limitations with available technology.

Parameterization through orthographic projection within the (x,y) plane is best suited for hardware acceleration as the values can be expressed in terms of a two dimensional space.

Now the viewing directions must be projected for visible triangle views.  Then the triangulation of the original views must be established.  Next, a dataset composed of a grid of regular viewpoints is derived through the blending of original views.

Referencing the original normalization formula that was presented earlier, the radiance data after sampling can be included.

The available data for the associated viewing directions can also be included to arrive at a combined formula to represent radiance across the range of resampled textures.

Page Three . . .


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