Transcript Polynomial Texture Mapping

Technology Transition Workshop
Evaluation and Application of
Polynomial Texture Mapping
(PTM) for Footwear and Tire
Impression Comparisons
(NIJ Grant# 2004-IJ-CX-K008)
Project Manager: Lab Director John S. Yoshida
Principal Investigator: Senior Criminalist James S. Hamiel
[email protected]
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Polynomial Texture Mapping (PTM)
PTM is basically a simple idea. Light striking a surface
at an angle will reveal texture on that surface. PTM is a
new way of increasing the photorealism of texture maps.
Light coming from different angles and directions will
disclose different parts of the texture. In PTM, the light
sources are precisely placed to cover a lighting
hemisphere. The point sources impinge from near the
horizon to near vertical and from all points of the
compass. Mathematically, one needs at least six lights
with more lights providing more detail.
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PTM (cont.)
• Polynomial Texture Mapping (PTM) is a new method
for increasing the photorealism of texture maps.
• Coefficients of a biquadratic polynomial are stored per
pixel, and used to reconstruct the surface color under
varying lighting conditions.
• Like bump mapping, this allows the perception of
surface deformations. However, the Hewlett-Packard
method is image-based, and photographs of a surface
under varying lighting conditions can be used to
construct these maps.
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PTM Equation
Typically in a PTM there are nine values
stored per texel. The first three are the red,
green, and blue chrominance values. The
next six values are coefficients to a biquadratic
equation seen in [1]. This equation takes a
given light position in relation to the texture
(project the light vector onto the texture plane)
and calculates the luminance for that texel.
The final color value for the texel is the
chrominance modulated by the luminance.
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[1] The Biquadratic:
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PTM Equation (cont.)
A PTM can be constructed from real world data by taking
multiple pictures of some texture of interest, from a fixed
camera position, with a light placed in different positions.
The position of the light should be known for each
picture taken. Next, we represent each pixel
independently with a simple biquadratic polynomial. This
is done by using the polynomial to approximate the
luminance of each texel and keeping the chrominance
constant. The result is a texture map that properly
reproduces the effects of surface variations in the
illuminant direction relative to the object.
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The known light vectors are used to find a
least squares fit to the linear system seen
below:
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History
• Software developed by Tom Malzbender and
Dan Gelb of Hewlett-Packard Labs.
• Designed to increase the photorealism of
images.
• Utilizes digital images from multiple light source
positions to increase texture information.
• Additional information at
http://www.hpl.hp.com/research/ptm/
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Applications
• Archeology and Paleontology have utilized PTMs to
improve visualization of clay tablets and fossils
• Art World Applications
• Forensics
– Footwear/tire impressions
– Cartridge case comparisons
– Indented writing
• PTM technique can be applied to most applications
utilizing oblique light
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Examples
1.
2.
3.
4.
One virtual light source
normal to the shale
surface.
Oblique virtual light source
from SE, inverted image.
This image can be
regarded as a “traditional”
film-based photographic
image for comparison with
the enhanced versions.
Specular Enhancement
Addition (overlaying) of
images 2 and 3.
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Specular Enhancement
One light source
normal to the
surface
vs.
Specular
Enhancement
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Seeds
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Depth of Field
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PTM Design
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PTM Dome