Project Manager: Lab Director John S. Yoshida

1. 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 james.hamiel@doj.ca.gov

2. 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.

3. 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.

4. 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.

5. [1] The Biquadratic:

6. 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.

7. The known light vectors are used to find a least squares fit to the linear system seen below:

8. 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/

9. 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

10. Examples • 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.

11. Specular Enhancement One light source normal to the surface vs. Specular Enhancement

12. Seeds

13. Depth of Field

14. PTM Design

15. PTM Dome