Decorrelation of L- and M-cone signals
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JOSA COMMUNICATIONS Communications are short papers. Appropriate material for this section includes reports of incidental research results, comments on papers previously published, and short descriptions of theoretical and experimental techniques. Communications are handled much the same as regular papers. Proofs are provided. Decorrelation of L- and M-cone signals Qasim Zaidi College of Optometry, State University of New York, 100 East 24th Street, New York, New York 10010 Received May 27, 1997; accepted July 21, 1997; revised manuscript received July 28, 1997 For a large sample of broadband lights reflected from natural and man-made objects, the correlation between L- and M-cone absorptions was found to be 0.99. The correlation between L 1 M and L 2 M signals was 0.21. The early recombination of cone signals in the visual system thus leads to a substantial decorrelation [Proc. R. Soc. London Ser. B 220, 89 (1983)]. © 1997 Optical Society of America [S0740-3232(97)01812-7] Key words: Cone signals, opponent-color signals, decorrelation. 1. CONE AND POSTRECEPTORAL CORRELATIONS FOR BROADBAND LIGHTS Psychophysical and physiological estimates have shown that there is considerable overlap between human L- and M-cone absorption spectra, 1,2 thus predicting a substan- tial correlation between L- and M-cone signals from ob- jects in a visual scene. For monochromatic lights the Pearson correlation coefficient between L- and M-cone ab- sorptions is 0.86. Buchsbaum and Gottschalk 3 noted from simple engineering principles that it would be inef- ficient to transmit two separate highly correlated signals from the retina to the cortex. They showed that when cone signals from monochromatic lights are optimally decorrelated by use of a transform based on the eigenvec- tors of the variance – covariance matrix, the transformed linear combinations bear a resemblance to the luminance and opponent-color mechanisms of color theory. The lights normally incident on the retina, such as those reflected from objects, have broadband spectra, and it is possible that the correlation between L- and M-cone absorptions for these lights can be even higher than for monochromatic lights. The main purpose of this Com- munication is to present the unexpectedly high magni- tude of this correlation. The 170 spectra of natural and man-made objects measured by Vrhel et al. 4 were taken as the sample of objects. The Smith– Pokorny 1 estimates were used for L- and M-cone absorption spectra, and ab- sorptions for each cone type were calculated for each ob- ject illuminated by a unit amount of equal-energy light (the L and M spectra were normalized to equal area). In Fig. 1 (top), each point represents the M-cone absorption from an object plotted versus the L-cone absorption. The correlation between these signals is 0.99 and is shown clearly in the figure. (The average pairwise correlation between the reflectance spectra of the 170 objects is 0.5341.) It is obvious that it would be desirable to deco- rrelate L- and M-cone signals from objects at a very early stage in the visual stream. In Fig. 1 (bottom) are plotted the L 1 M signals from these objects versus the L 2 M signals. The points are now spread over the graph, and the correlation between the signals is only 0.21. The decorrelation is robust within a range of reasonable rela- tive weights of L and M signals in the combinations. One other point should be noted about Fig. 1 (bottom). Fig. 1. Top, M-cone absorptions from 170 objects in equal- energy light plotted versus L cone absorptions; bottom, L 1 M signals from the same objects plotted versus L 2 M signals. 0740-3232/97/123430-02$10.00 © 1997 Optical Society of America
Transcript of Decorrelation of L- and M-cone signals
JOSA COMMUNICATIONSCommunications are short papers. Appropriate material for this section includes reports of incidental research results,comments on papers previously published, and short descriptions of theoretical and experimental techniques.Communications are handled much the same as regular papers. Proofs are provided.
Decorrelation of L- and M-cone signals
Qasim Zaidi
College of Optometry, State University of New York, 100 East 24th Street, New York, New York 10010
Received May 27, 1997; accepted July 21, 1997; revised manuscript received July 28, 1997
For a large sample of broadband lights reflected from natural and man-made objects, the correlation betweenL- and M-cone absorptions was found to be 0.99. The correlation between L 1 M and L 2 M signals was 0.21.The early recombination of cone signals in the visual system thus leads to a substantial decorrelation [Proc. R.Soc. London Ser. B 220, 89 (1983)]. © 1997 Optical Society of America [S0740-3232(97)01812-7]
Key words: Cone signals, opponent-color signals, decorrelation.
1. CONE AND POSTRECEPTORALCORRELATIONS FOR BROADBAND LIGHTSPsychophysical and physiological estimates have shownthat there is considerable overlap between human L- andM-cone absorption spectra,1,2 thus predicting a substan-tial correlation between L- and M-cone signals from ob-jects in a visual scene. For monochromatic lights thePearson correlation coefficient between L- and M-cone ab-sorptions is 0.86. Buchsbaum and Gottschalk3 notedfrom simple engineering principles that it would be inef-ficient to transmit two separate highly correlated signalsfrom the retina to the cortex. They showed that whencone signals from monochromatic lights are optimallydecorrelated by use of a transform based on the eigenvec-tors of the variance–covariance matrix, the transformedlinear combinations bear a resemblance to the luminanceand opponent-color mechanisms of color theory.
The lights normally incident on the retina, such asthose reflected from objects, have broadband spectra, andit is possible that the correlation between L- and M-coneabsorptions for these lights can be even higher than formonochromatic lights. The main purpose of this Com-munication is to present the unexpectedly high magni-tude of this correlation. The 170 spectra of natural andman-made objects measured by Vrhel et al.4 were takenas the sample of objects. The Smith–Pokorny1 estimateswere used for L- and M-cone absorption spectra, and ab-sorptions for each cone type were calculated for each ob-ject illuminated by a unit amount of equal-energy light(the L and M spectra were normalized to equal area). InFig. 1 (top), each point represents the M-cone absorptionfrom an object plotted versus the L-cone absorption. Thecorrelation between these signals is 0.99 and is shownclearly in the figure. (The average pairwise correlationbetween the reflectance spectra of the 170 objects is0.5341.) It is obvious that it would be desirable to deco-rrelate L- and M-cone signals from objects at a very earlystage in the visual stream. In Fig. 1 (bottom) are plottedthe L 1 M signals from these objects versus the L 2 M
0740-3232/97/123430-02$10.00 ©
signals. The points are now spread over the graph, andthe correlation between the signals is only 0.21. Thedecorrelation is robust within a range of reasonable rela-tive weights of L and M signals in the combinations.
One other point should be noted about Fig. 1 (bottom).
Fig. 1. Top, M-cone absorptions from 170 objects in equal-energy light plotted versus L cone absorptions; bottom, L 1 Msignals from the same objects plotted versus L 2 M signals.
1997 Optical Society of America
JOSA Communications Vol. 14, No. 12 /December 1997 /J. Opt. Soc. Am. A 3431
Because of the high correlation between L and M signals,the range of L 2 M is an order of magnitude smaller thanthe range of L 1 M. For most scenes the spatially an-tagonistic center-surround structure of the receptivefields of postreceptoral neurons serves to bring the rangesof the two classes of signals closer in magnitude.Whereas local L 2 M signals are transmitted to the cor-tex by the parvostream, both the parvostream and themagnostream convey only the L 1 M spatial-contrast sig-nal, i.e., the difference between the center and the sur-round L 1 M signals.5 Since local spatial variations inL 1 M signal are generally small, the range of the con-trast signals is generally of the same order as the range ofthe color-opponent signals.
ACKNOWLEDGMENTThis research was supported by National Eye Institutegrant EY07556 to Q. Zaidi.
REFERENCES1. V. C. Smith and J. Pokorny, ‘‘Spectral sensitivity of the
foveal cone photopigments between 400 and 700 nm,’’Vision Res. 15, 161–171 (1975).
2. J. L. Schnapf, T. W. Kraft, and D. A. Baylor, ‘‘Spectral sen-sitivity of human cone photoreceptors,’’ Nature (London)325, 439–441 (1987).
3. G. Buchsbaum and A. Gottschalk, ‘‘Trichromacy, opponentcolours coding and optimum colour information transmis-sion in the retina,’’ Proc. R. Soc. London Ser. B 220, 89–113(1983).
4. M. Vrhel, R. Gershon, and L. S. Iwan, ‘‘Measurement andanalysis of object reflectance spectra,’’ Color Res. Appl. 19,4–9 (1994).
5. A. M. Derrington, J. Krauskopf, and P. Lennie, ‘‘Chromaticmechanisms in lateral geniculate nucleus of macaque,’’ J.Physiol. 357, 241–265 (1984).
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