Analytic solution for separating spectra into illumination and surface reflectance components
Bibliographic record
Abstract
The measured light spectrum is the result of an illuminant interacting with a surface. The illuminant spectral power distribution multiplies the surface spectral reflectance function to form a color signal--the light spectrum that gives rise to our perception. Disambiguation of the two factors, illuminant and surface, is difficult without prior knowledge. Previously [IEEE Trans. Pattern Anal. Mach. Intell.12, 966 (1990); J. Opt. Soc. Am. A21, 1825 (2004)], one approach to this problem applied a finite-dimensional basis function model to recover the separate illuminant and surface reflectance components that make up the color signal, using principal component bases for lights and for reflectances. We introduce the idea of making use of finite-dimensional models of logarithms of spectra for this problem. Recognizing that multiplications turn into additions in such a formulation, we can replace the original iterative method with a direct, analytic algorithm with no iteration, resulting in a speedup of several orders of magnitude. Moreover, in the new, logarithm-based approach, it is straightforward to further design new basis functions, for both illuminant and reflectance simultaneously, such that the initial basis function coefficients derived from the input color signal are optimally mapped onto separate coefficients that produce spectra that more closely approximate the illuminant and the surface reflectance for any given dimensionality. This is accomplished by using an extra bias correction step that maps the analytically determined basis function coefficients onto the optimal coefficient set, separately for lights and surfaces, for the training set. The analytic equation plus the bias correction is then used for unknown input color signals.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".