Acquiring Scattering Properties of Participating Media by Dilution SIGGRAPH Conference July 2006, Boston, USA Sponsors: NSF, ONR, Sloan Srinivasa Narasimhan Mohit Gupta Carnegie Mellon University Craig Donner Henrik Wann Jensen UC San Diego Ravi Ramamoorthi Shree Nayar Columbia University

Accurate Rendering of Media Critical for Realism Scattering in Participating Media

Accuracy Limited by the Input Medium Parameters Significant Progress in Volumetric Rendering [Jensen et al, 01][Donner, 03] [Fedkiw et al, 01] [Jensen, 02]

Measuring Surface Reflectance [’95 - ’06] BRDF [Matusik et al, 03]BTF [Dana et al, 97] Time varying BTF [Gu et al, 06]

Measurement Work in Graphics Attenuation of Laser Beams [Hawkins et al, 05] No Scattering Directional Scattering using a Mirror [Hawkins et al, 05] No Attenuation Diffusion-based BSSRDF Measurement [Jensen et al, 01; Joshi et al, 05] High Scattering

Measurement Work in Graphics Attenuation of Laser Beams [Hawkins et al, 05] No Scattering Directional Scattering using a Mirror [Hawkins et al, 05] No Attenuation Diffusion-based BSSRDF Measurement [Jensen et al, 01; Joshi et al, 05] High Scattering One Simple Setup Robust Parameter Estimation from a Photograph Cover Entire Parameter Space

Our Measurement Setup Camera Glass Tank

Frosted Glass Bulb Anti-reflection Glass Our Measurement Setup Dimensions of Tank: 25cm x 30 cm x 30 cm

Problem: Multiple Scattering Causes significant Blurring of Incident Light Inverse Estimation is Ill-conditioned and Not Unique [Ishimaru 75,97; McCormick et al., 79-83] Photo of Milk in Setup

Problem: Multiple Scattering Causes significant Blurring of Incident Light Inverse Estimation is Ill-conditioned and Not Unique [Ishimaru 75,97; McCormick et al., 79-83] Key Idea: Avoid Multiple Scattering - Single Scattering dominant At “low” concentrations: - Multiple Scattering negligible [Ishimaru 97; Narasimhan et al 99-03] Increasing Milk Concentrations Photo of Milk in Setup

So…dilute media “sufficiently” with water to simplify light transport.

Single Scattering Ray Geometry Physical Apparatus Captured Ortho-Photo Range of Scattering Angles: [ 0 deg, 175 deg ] Range of Path-lengths: [ 125 mm, 610mm ] All Path-length and Angle Combinations Source Medium

Single Scattering Model and Estimation Source Image Formation Model: Medium Phase function Scattering Coefficient Extinction Coefficient

Single Scattering Model and Estimation Source Parameter Estimation: Nelder-Meade Search in Matlab Medium Image Formation Model: Phase function Scattering Coefficient Extinction Coefficient

Single Scattering Model and Estimation Source Parameter Estimation: Nelder-Meade Search in Matlab Medium Image Formation Model: Phase function Scattering Coefficient Extinction Coefficient Unique and Robust!

How Much to Dilute? Multiple Scattering Single Scattering 9 ml 15 ml 26 ml Multiple Scattering Single Scattering 9 ml18 ml 20 ml 23 ml15 ml26 ml4 ml Increasing Milk Concentration

Database of 40 Common Materials Alcoholic Beverages – 3 wines, 3 beers… Coffees – black, with cream, cappuccino,… Milks – chocolate, whole, 2% fat, vitamin A & D,… Juices – grape, apple, cranberry,… Soft-drinks – coke, pepsi, lemonade… Cleaning supplies – detergents, shampoos,… Powders and Crystals – sugar, salt, tang,… Pacific Ocean Water – bay, different depths,…

BudweiserCoors LightYuengling BeerOrange PowderGatoradePink LemonadeClorox DetergentEra Detergent CappuccinoEspressoMint MochaCokePepsiSpriteSuisse MochaLemon Tea Apple JuiceSugar PowderRuby Gfruit JuiceGrape JuiceWhite ZinfandelCranberry JuiceChardonnayMerlot Reg Choc MilkLow Fat Choc MilkLow Fat MilkReduced MilkRegular MilkLow Fat Soy MilkReg Soy MilkWhite Gfruit Juice Mission Bay (10ft, 8 hrs) Mission Bay (10ft, 30 mins) Mission Bay (Surface, 1 hr) Salt Powder Balancing Shampoo Strawberry Shampoo Heads & Shoulders Pacific Ocean (Surface, 1 hr)

Orange Powder Pink Lemonade Powder Regular Milk Cappuccino Powder Ruby Grapefruit Juice Low Fat Milk Salt PowderRegular Chocolate Milk Espresso Coffee Low Fat Choc Milk Sample Photographs: Highly Scattering Media

Merlot Wine Yuengling Beer Era Detergent Grape Juice Lemon Tea Powder Strawberry Shampoo Coke Brown Sugar Pacific Ocean Water Chardonnay Wine Sample Photographs: Highly Absorbing Media

MediumVolume Extinction Coefficient (  ) (x mm -1 ) Scattering Coefficient (  ) (x mm -1 ) Average Cosine (g) Low-Fat Milk 16 ml R G B Regular Milk15 ml R G B Regular Chocolate Milk 16 ml R G B Sample Parameters: Highly Scattering Media

MediumVolume Extinction Coefficient (  ) (x mm -1 ) Scattering Coefficient (  ) (x mm -1 ) Average Cosine (g) Yuengling Beer 2900 ml R G B Merlot Wine1500 ml R G B Era Detergent 2300 ml R G B Sample Parameters: Highly Absorbing Media

Regular Milk Low Fat Milk Regular Choc Milk Low Fat Choc Milk Coors Light Sprite Strawberry Shampoo Chardonnay Merlot Wine Coke Era Detergent Orange Powder Pink Lemonade Powder Ruby Grape Fruit Juice Absorption Coefficient Scattering Coefficient Ocean Water

Regular Milk Low Fat Milk Absorption Coefficient Scattering Coefficient Regular Choc Milk Low Fat Choc Milk Coors Light Sprite Chardonnay Merlot Wine Coke Orange Powder Pink Lemonade Powder Ruby Grape Fruit Juice Highly Scattering Media Strawberry Shampoo Era Detergent Ocean Water

Regular Milk Low Fat Milk Regular Choc Milk Low Fat Choc Milk Coors Light Sprite Chardonnay Merlot Wine Coke Orange Powder Pink Lemonade Powder Ruby Grape Fruit Juice Highly Absorbing Media Absorption Coefficient Scattering Coefficient Strawberry Shampoo Era Detergent Ocean Water

Regular Milk Low Fat Milk Regular Choc Milk Low Fat Choc Milk Coors Light Sprite Chardonnay Merlot Wine Coke Orange Powder Pink Lemonade Powder Ruby Grape Fruit Juice Low Scattering & Absorption Absorption Coefficient Scattering Coefficient Strawberry Shampoo Era Detergent Ocean Water

Regular Milk Low Fat Milk Regular Choc Milk Low Fat Choc Milk Coors Light Sprite Chardonnay Merlot Wine Coke Orange Powder Pink Lemonade Powder Ruby Grape Fruit Juice Moderate Scattering & Absorption Absorption Coefficient Scattering Coefficient Strawberry Shampoo Era Detergent

Distance from the Source (mm) Intensity (0-255) R G B Experimental Validation: Fits to Measurements Orange Powder

Sample Fits: Highly Absorbing Media Era Detergent Pacific Ocean Surface Water Yuengling BeerMerlot Wine Dist. from Source Brightness

Sample Fits: Highly Scattering Media Regular MilkLow Fat Milk Clorox DetergentRegular Chocolate Milk Dist. from Source Brightness

Renderings with the “Kitchen” Environment Map [Debevec et al]

Merlot Wine Chardonnay Wine

Coca-Cola Yuengling Beer

Milk Yuengling Beer

Renderings with a Single Directional Light Source

Coca-cola Yuengling Beer

Chardonnay Wine Orange Powder

Era Detergent Strawberry Shampoo

+= 75% EspressoLight Coffee25% Milk Blending Parameters

+= 50% Wine50% Milk?

Wine  Water  Milk  Espresso Transitions between Media

Concentrations at which Parameters Measured

Real Concentrations

Robust Parameter EstimationSimple Apparatus Render Any ConcentrationMixing Media + = Summary