Reflectance Function Approximation

Ted Wild

CS 766

Thursday, December 11, 2003

Motivation

• Material recognition

• Classification Problem– Dror et al.– Recognizing materials with known reflectance

functions– CUReT, Dana et al.

Example

• Denim + Cotton + Skin = Person

• Can make feature tracking, segmentation, etc. easier

• Would work under different pose, lighting

Reflectance

• How light and surface interact

• Depends on angle at which light hits surface and view angle

• Figure by Wallace and Price

Bidirectional Reflectance Distribution Functions

• Scalar function of 4 variables:– Incident light (2 angles)– View direction (2 angles)

• CUReT data– BRDF’s of 61 materials– 205 measurements per material

CUReT

CUReT

CUReT

BRDF Approximation

• Kernel regression

• Gaussian kernels

• 2 parameters

•

€

min ν K(A,A')α + be − y + α

(K(A,B))ij = e−μ A i '−B⋅ j

2

Approximation Results

BRDF Classification

• Given:– Set of known BRDF functions– Set of BRDF measurements for a material

• Determine what material the measurements are taken from

Method

• Approximate known reflectance functions from data– Kernel regression

• Use nearest-neighbor classification to identify new function

• Evaluation: Leave out random data from CUReT measurements, try to classify left out data

Questions

• How accurate does reflectance function approximation have to be for classification?

• How many points are needed to get sufficient accuracy?– Known BRDF approximation– Classification

• What models of reflectance work well?

Classification Results

Problems

• Need to know:– Geometry

• Discussed in class

– Illumination• Ramamoorthi and Hanrahan

• Factorization technique to recover BRDF and lighting in some cases

• Can only recognize “known” materials

Recognizing Unseen Materials

• If input is sufficiently different from known BRDF’s, create a new class for it

• Use linear combination of known BRDF’s for further recognition– May need less points for recognition than for

approximation– Can improve approximation of new class as

more of its measurements are identified

Very Early Results

• Leave one material out:– When testing, classify material as unseen if the

distance to its nearest neighbor >= tol

• tol = 0.25– Average error: 0.40, Predicting unseen: 0.51

• tol = 0.20– Average error: 0.45, Predicting unseen: 0.29

• Trials only run once!

Influences

• Dror et al. (2001)– Material classification based on reflectance

• Lensch et al. (2001)– Representation of BRDF’s as combination of a

few basis BRDF’s.

• Dana et al. (1997)– Use of CUReT data to evaluate reflectance

function approximation

Future Work

• Complete and test method for unseen material recognition

• Reduce error for approximation and classification methods

• Recognition of materials under unknown geometry and/or illumination

• Evaluate other reflectance models