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Polynomial Texture Mapping (PTM)

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Polynomial Texture Maps (PTMs) are a simple representation for images of functions instead of just images of color values. In an conventional image, each pixel contains static red, green, blue values. In a PTM, each pixel contains a simple function that specifies the red, green, blue, values of that pixel as a function of two independent parameters, lu and lv.

Typically, PTMs are used for displaying the appearance of an object under varying lighting direction, and lu,lv specify the direction of a point light source. However, other applications are possible, such as controlling focus of a scene. PTMs can be used as light-dependent texture maps for 3D rendering, but typically are just viewed as ‘adjustable images’.

PTMs are typically produced with a digital camera by photographing an object multiple times with lighting direction varying between images. Even a low-end digital camera provides enough resolution to produce good PTMs, and almost any light source can be used such as a light bulb, LED or flash.

Tools for viewing PTMs are downloadable below, as are tools for constructing your own PTMs from images. Given a stack of images of an object under varying lighting direction, one has collected samples of the object’s reflectance function at each pixel. Independently for each pixel, the PTMfitter fits a low order polynomial to those samples to produce a PTM. The PTMviewer simply evaluates this polynomial in real time independently for each pixel to produce an image.

This can be done at real-time rates on even low-end computers because of the simplicity of the polynomial, allowing interactive control of lighting direction. In addition, once the reflectance functions are represented in this manner, they can be transformed to make the surface detail existing on the object more apparent. We call this method reflectance transformation, and an example on a 3000 year old cuneiform tablet is shown above.

» Paper: appears in Siggraph 2001 proceedings (4.9 MB)
» Slides presented at Siggraph 2001 (2.45 MB)
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Paper: correction
Java based Interactive Relighting (demos)
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Interactive Relighting Page
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Relighting the Antikythera Mechanism
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Smithsonian Institutes page with >400 interactive examples
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Cultural Heritage Imaging's PTM / RTI links
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CHI’s blog describing many recent archeological applications
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University of Southampton Archaeological Computing Research Group PTM demo Page
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Downloads of PTMviewer, PTMfitter, Sample PTMs, etc.
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Making PTMs
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Download PTM Builder
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Reflectance Imaging
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Reflectance Transformation
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Antikythera Mechanism download page
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Applications in Paleontology                                                                                                          » New: Google Tech Talk                                                                                                                 » New: EconomistArticle                                                                                                                   » New: Scientific American Article
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"Reading Ancient Inscriptions in Virtual Light," USC's West Semitic Research Project
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Tom Malzbender
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Dan Gelb

 

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