1 Background

In computer graphics, a Bidirectional Reflection Distribution Function (BRDF) is one of the classic models used describe the appearance property of object surface in computer graphics [PH04]. These functions take in two parameters, θ_i and θ_o, describing the angle of incoming and outgoing light at the incident point on the material. The result of the function is the fraction of light that is reflected along the specified angles. In general, it is helpful to think of a BRDF as a vector in a high-dimensional space.

In the real world, the physical processes and aging effects that apply to an object vary between different materials, and often have non-linear properties. Thus, linearly blending two BRDFs may generate unnatural results. Physic-based simulations can generate plausible results, but are computationally intensive and require knowledge of underlying physical and biological principles [WTL⁺06].

Nonlinear dimensionality reduction techniques provide tools to discover underlying structure of the given data without knowing the function itself, making it possible to approximate a nonlinear appearance manifold from known spatially- and temporally-varying BRDF data.

Wang et al. [WTL⁺06] made the observation that the BRDF data is largely self-similar across a material. They conjectured that the BRDF data of a particular material will cluster in the high-dimensional space of all possible BRDFs, where all the BRDF vectors lie on an appearance manifold. They implemented a variant of Isomap [BST⁺02] to discover an appearence manifold for a material’s BRDF data.

2 Goals

Our goals for this project are the following:

1.

Implement the Isomap variant algorithm proposed by [WTL⁺06] as a reference. We will use the BRDF metric proposed in the paper for optimizing the manifold.

2.

Implement another nonlinear dimensionaly reduction technique, such as Locally Linear Embedding (LLE) [RS00] or Manifold Scultping [GVM07]e

3.

Alternative BRDF metrics may result in better appearance manifolds. We will explore these.

4.

Compare the results of the variations above. This includes comparing quality appearance manifold outputs, performances, etc. Note: In order to compare the quality of the manifolds, we will need to develop an appearance manifold metric. This is still open for discussion.

We plan to meet the first two items by the milestone date (2010 May 11).

If time allows, we would like to further extend our project to include the following:

• Implement an appearance manifold visualization tool.
• Implement an interactive tool to view the BRDF on a given surface.
• Explore the interpolation of BRDF data along the appearance manifold.
• Transfer BRDF data of one particular material to the manifold of another.

Because a highly accurate data set can be large in size (several gigabytes), running the machine learning algorithms could become a computationally expensive process. We are aware of the availability of running Matlab on the Computer Science department’s cluster, and hence are going to explore this option. The remaining code will be written in C#.

3 Methods

We will implement the variant of Isomap as proposed by, as well as at least one other nonlinear dimensionaly reduction technique, such as LLE or Manifold Sculpting. Both of these algorithms will run unsupervised.

4 Dataset

We will use spatially-varying BRDF data available through the computer graphics lab. Additionally, we will contact [WTL⁺06] to see if we may use their data.

5 Timeline

References