Northwestern University Polynomial Texture Maps Dan Hazen Based on the paper: Malzbender, T., Gelb, D., Wolters, H., “Polynomial Texture Maps”, Computer.

Northwestern University

Polynomial Texture Maps

Dan Hazen

Based on the paper:

Malzbender, T., Gelb, D., Wolters, H., “Polynomial Texture Maps”, Computer Graphics (SIGRAPH 01 PROCEEDINGS), August 2001.

www.hpl.hp.com/ptm

CS 395: Advanced Computer Graphics

January 22, 2002

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Introduction

What are Polynomial Texture Maps (PTM’s)?

Image based texture maps used for more accurate texturization of fine details.

What are Polynomial Texture Maps (PTM’s)?

Image based texture maps used for more accurate texturization of fine details.

Why use PTM’s?

More Realistic Textures!

Why use PTM’s?

More Realistic Textures!

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Background

Bi-directional Texture Function:

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Background

Bi-directional Texture Function (Cont.):Conventional ConventionalBTF BTF

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Polynomial Texture Mapping

),(),(),( 0 vuRvuLvuR

),(),(),( 0 vuBvuLvuB

Store coefficients at EACH TEXEL. Coefficients derived from series of photographs.

),(),(),( 0 vuGvuLvuG

L(u,v) = a0(u,v)lu2 + a1(u,v)lv

2 + a2(u,v)lulv + a3(u,v)lu +

a4(u,v)lv + a5(u,v)

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Polynomial Texture Mapping (Cont.)

DEMO!

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Polynomial Texture Mapping (Cont.)

Capture images using devices to get the coefficients

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Polynomial Texture Mapping (cont.)

Storage Concerns:

1 Byte: Red

1 Byte: Blue

1 Byte: Green

6 Bytes: Coefficient a0-5

9 Bytes/Texel:

Best Case: Worst Case:

1 Byte: Red

1 Byte: Blue

1 Byte: Green

6 Bytes: a0-5 Red

21 Bytes/Texel:

6 Bytes: a0-5 Blue

6 Bytes: a0-5 Green

500x500 Image: ~2.2 Megs 500x500 Image: ~5.1 Megs

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PTM Applications

Specular Highlighting

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PTM Applications (Cont.)

Contrast Enhancement: Method 1 – Specular Highlights

Original

Photo

Specular

Highlight

PTM

Reconstruction

PTM + Highlight

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PTM Applications (Cont.)

Contrast Enhancement: Method 2 – Diffuse Gain

Original

Photograph

Diffuse

Gain = 1.9

PTM Reconstruction

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PTM Applications (Cont.)

Contrast Enhancement: Method 3 – Light Extrapolation

Original Photograph Extrapolated PTM

Reconstruction

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PTM Applications (Cont.)

Video: http://www.hpl.hp.com/ptm/

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PTM Applications (Cont.)

Northwestern University

PTM Applications (Cont.)

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PTM Applications (Cont.)

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PTM Applications (Cont.)

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PTM Applications (Cont.)

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PTM Applications (Cont.)

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PTM Advantages and Issues

Advantages1. Only images needed

to form the texture2. Texture maps

maintain roughness3. Neat lighting and

viewing tricks 4. Efficient enough for

interactive speeds once coefficients are obtained

Issues1. Storage Costs2. Using biquadratic

polynomial: in some cases may not be precise enough

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PTM Research Expansion

Suggestions for research expansion:

• Use a higher order polynomial for better representation

• Use basis functions to reduce storage costs

• Get rid of fixed camera constraint to get a higher number of free dimensions

• Add modeling surface opacity to the list of features

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Conclusions

• Polynomial Texture Maps (PTM’s) portray rough surfaces based on a set of input images

• Polynomial Texture Maps can be used for more than just interactively moving a light source around a texture; there are methods that improve image definition

• Easy to do in hardware but storage could be a problem

QUESTIONS?