Fast spectral multiplication for real-time rendering

Simple item page
dc.contributor.authorWaddle, C Allen
dc.contributor.supervisorTzanetakis, George
dc.date.accessioned2018-05-02T14:51:14Z
dc.date.available2018-05-02T14:51:14Z
dc.date.copyright2018en_US
dc.date.issued2018-05-02
dc.degree.departmentDepartment of Computer Scienceen_US
dc.degree.levelDoctor of Philosophy Ph.D.en_US
dc.description.abstractIn computer graphics, the complex phenomenon of color appearance, involving the interaction of light, matter and the human visual system, is modeled by the multiplication of RGB triplets assigned to lights and materials. This efficient heuristic produces plausible images because the triplets assigned to materials usually function as color specifications. To predict color, spectral rendering is required, but the O(n) cost of computing reflections with n-dimensional point-sampled spectra is prohibitive for real-time rendering. Typical spectra are well approximated by m-dimensional linear models, where m << n, but computing reflections with this representation requires O(m^2) matrix-vector multiplication. A method by Drew and Finlayson [JOSA A 20, 7 (2003), 1181-1193], reduces this cost to O(m) by “sharpening” an n x m orthonormal basis with a linear transformation, so that the new basis vectors are approximately disjoint. If successful, this transformation allows approximated reflections to be computed as the products of coefficients of lights and materials. Finding the m x m change of basis matrix requires solving m eigenvector problems, each needing a choice of wavelengths in which to sharpen the corresponding basis vector. These choices, however, are themselves an optimization problem left unaddressed by the method's authors. Instead, we pose a single problem, expressing the total approximation error incurred across all wavelengths as the sum of dm^2 squares for some number d, where, depending on the inherent dimensionality of the rendered reflectance spectra, m <= d << n, a number that is independent of the number of approximated reflections. This problem may be solved in real time, or nearly, using standard nonlinear optimization algorithms. Results using a variety of reflectance spectra and three standard illuminants yield errors at or close to the best lower bound attained by projection onto the leading m characteristic vectors of the approximated reflections. Measured as CIEDE2000 color differences, a heuristic proxy for image difference, these errors can be made small enough to be likely imperceptible using values of 4 <= m <= 9. An examination of this problem reveals a hierarchy of simpler, more quickly solved subproblems whose solutions yield, in the typical case, increasingly inaccurate approximations. Analysis of this hierarchy explains why, in general, the lowest approximation error is not attained by simple spectral sharpening, the smallest of these subproblems, unless the spectral power distributions of all light sources in a scene are sufficiently close to constant functions. Using the methods described in this dissertation, spectra can be rendered in real time as the products of m-dimensional vectors of sharp basis coefficients at a cost that is, in a typical application, a negligible fraction above the cost of RGB rendering.en_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/9332
dc.languageEnglisheng
dc.language.isoenen_US
dc.rightsAvailable to the World Wide Weben_US
dc.subjectspectral renderingen_US
dc.subjectreal-time renderingen_US
dc.subjectnonlinear optimizationen_US
dc.subjectcomputer graphicsen_US
dc.subjectreflectance modelingen_US
dc.subjectapproximate joint diagonalizationen_US
dc.subjectfactor analysisen_US
dc.subjectpredictive renderingen_US
dc.titleFast spectral multiplication for real-time renderingen_US
dc.typeThesisen_US

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Waddle_C_Allen_PhD_2018.pdf
Size:
32.4 MB
Format:
Adobe Portable Document Format
Description:
dissertation
Download
License bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
license.txt
Size:
1.71 KB
Format:
Item-specific license agreed upon to submission
Description:
Download

Collections

Electronic Theses and Dissertations (ETD)
Theses (Computer Science)
 
University of Victoria Libraries

We acknowledge and respect the Lək̓ʷəŋən (Songhees and Esquimalt) Peoples on whose territory the university stands, and the Lək̓ʷəŋən and W̱SÁNEĆ Peoples whose historical relationships with the land continue to this day.