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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
Northwestern University
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 (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.)
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 (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 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?