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On chromatic and dichromatic sum equations

Yanpei Liu
1990 Discrete Mathematics  
This paper provides firstly an exposition on the theory of chromatic sums for rooted planar triangulations founded by W.T. Tutte.  ...  Further, a functional equation of the dichromatic sum functions for rooted nonseparable planar maps is also established by using the same decomposition lemmas as those in the chromatic case.  ...  Chromatic and dichromatic sum equationsIn order to determine what the functional equation satisfied by the chromatic sum function (1.1) for rooted nonseparable planar maps is, we have to partition Jc1  ... 
doi:10.1016/0012-365x(90)90372-o fatcat:wo2w6uefgja2pdelaw7slfxrau

Inheritance of color vision in a New World monkey (Saimiri sciureus)

G. H. Jacobs, J. Neitz
1987 Proceedings of the National Academy of Sciences of the United States of America  
This arrangement is discretely different from that found in Old World monkeys and humans.  ...  Squirrel monkeys (Saimiri sciureus) have a striking color-vision polymorphism; each animal has one of six different types of color vision.  ...  Krogh for help with the recording system and J. A. King for generously permitting us to test monkeys at the University of Arizona, Tucson.  ... 
doi:10.1073/pnas.84.8.2545 pmid:3470811 pmcid:PMC304691 fatcat:rhcpp2cxyfhdpgp4l3ipsw4lqq

Illumination Estimation Using a Multilinear Constraint on Dichromatic Planes

J. Toro, B. Funt
2005 Procedings of the British Machine Vision Conference 2005  
A new multilinear constraint on the color of the scene illuminant based on the dichromatic reflection model is proposed.  ...  The image region may cover an area of the scene encompassing several different materials and hence pixels from several different dichromatic planes.  ...  Multiplying out (3) , it is not difficult to verify that the equation can be written as the sum of n + 1 terms of the form d n 1 1 d n 2 2 (n 1 + n 2 = n) with associated coefficients depending on {  ... 
doi:10.5244/c.19.54 dblp:conf/bmvc/ToroF05 fatcat:hksvnqtptfcevbyehnp6chdgo4

Page 5263 of Mathematical Reviews Vol. , Issue 91J [page]

1991 Mathematical Reviews  
In this paper, the author gives some new chromatic in- dex critical graphs. Xiao Feng Guo (PRC-XINJ) 91j:05048 05C15 05C10 05C30 Liu, Yan Pei (PRC-ASBJ-AM) On chromatic and dichromatic sum equations.  ...  This paper contains two results concerning the theory of chromatic and dichromatic sums founded by W. T. Tutte.  ... 

Page 2454 of Mathematical Reviews Vol. , Issue 94e [page]

1994 Mathematical Reviews  
Summary: “This paper provides a functional equation satisfied by the dichromatic sum function of rooted outerplanar maps.  ...  By the equation, the dichromatic sum function can be found explicitly.” 94e:05112 05C15 Maffray, Frédéric (F-INPGAM-DS; Grenoble) Antitwins in partitionable graphs.  ... 

Generalized chromatic polynomials

David Joyce
1984 Discrete Mathematics  
There are several polynomials used in the study of combinatorics including Birkhoff's chromatic polynomial for graphs, Stardey's order polynomial for partially ordered sets, and Tutte's dichromatic polynomial  ...  We develop a common basis for these polynomials which depends on a sequence of standard reference objects in the category under consideration, the sequence being called a chromatic complex.  ...  See Tutte's article [10] for more information on the rank generating function and discussion of yet another dichromatic polynomial.  ... 
doi:10.1016/0012-365x(84)90034-7 fatcat:2l2vtis4dnervgi6bevwkgbx2e

Color-defective vision and computer graphics displays

G.W. Meyer, D.P. Greenberg
1988 IEEE Computer Graphics and Applications  
Thanks to the subjects for their time and patience in performing the color vision tests. The thoroughness with which one of the reviewers evaluated this article is also appreciated.  ...  Acknowledgments Jerry Hajjar and Bruce Bailey wrote the 3D finiteelement postprocessor used to produce Figure 16 , and TaoYang Han performed the analysis that is depicted.  ...  Since S, M, or 1, is zero, the color space of a dichromat collapses to one of the trichromat's coordinate planes, and the chromaticity diagram of a dichromat becomes one edge of the trichromat's unit plane  ... 
doi:10.1109/38.7759 fatcat:jhretgnzafafdnyf2d5ubboyai

Page 1216 of Mathematical Reviews Vol. 36, Issue 6 [page]

1968 Mathematical Reviews  
The dichromatic polynomials of the complete graphs are determined and a contribution is made to the theory of chromatic roots.”  ...  On dichromatic polynomials. J. Combinatorial Theory 2 (1967), 301-320.  ... 

Visual responses in the lateral geniculate nucleus of dichromatic and trichromatic marmosets (Callithrix jacchus)

T Yeh, BB Lee, J Kremers, JA Cowing, DM Hunt, PR Martin, JB Troy
1995 Journal of Neuroscience  
It was apparent from the analysis that rod and cone signals had to be summed rather than differenced.  ...  Responses of PC-cells from 543 (off cell) and 563 nm (on cell) dichromats on changing the relative phase of red and green modulated lights.  ... 
doi:10.1523/jneurosci.15-12-07892.1995 pmid:8613728 fatcat:wcy5gnqbrrfgpl7hbuy6v2hdyu

Standard response functions for protanopic and deuteranopic vision

D.B. Judd
1944 Journal of research of the National Bureau of Standards  
These three functions, therefore, serve to re13te the color matches made by dichromats to those made by normal trichromats, and so make conveniently accessible the color confusions of average dichromatic  ...  coordinate system to express these three functions in a form slIch that two of the three pairs 3.1S0 represent the color matches of the two recognized types of red-green-blind observer, the p rotanope and  ...  Since from their definitions the two coordinates sum to unity, only one of them is required to specify the dichromatic chromaticity of a stimulus. . 018 . 982 . 008 .992 450 Wa= Wa/(Wa+K) = Y /  ... 
doi:10.6028/jres.033.022 fatcat:i6zur4qq65gcznkhjx43h36bme

The contribution of structural-, psittacofulvin- and melanin-based colouration to sexual dichromatism in Australasian parrots

A. J. TAYSOM, D. STUART-FOX, G. C. CARDOSO
2010 Journal of Evolutionary Biology  
Structural blue colouration showed the largest and most consistent sexual dichromatism, both in area and perceptually relevant chromatic differences, indicating that it is often ornamental in parrots.  ...  This may depend on physiological costs, which depend on the mechanism of colour production (e.g. exogenously acquired colouration in passerine birds appears to be most sexually dichromatic).  ...  Again, structural blue was the only plumage type with chromatic contrast on average above 1 jnd and was significantly higher than dichromatism in psittacofulvin-and melanin-based colouration (Tukey tests  ... 
doi:10.1111/j.1420-9101.2010.02166.x pmid:21054624 fatcat:ltgeexogqrfrlom5op4eczcjou

Surface reflectance and normal estimation from photometric stereo

Qingxiong Yang, Narendra Ahuja
2012 Computer Vision and Image Understanding  
Using dichromatic reflection model, we introduce surface chromaticity as a matching invariant for photometric stereo, which serves as the foundation of the theory of this paper.  ...  An extremely simple and robust reflection components separation method is proposed based on the invariant.  ...  Method I c À I sum C c K c À C c : ð15Þ From (12) and (15) , I c À I sum C c ¼ ðK c À C c Þ P c2fr;g;bg q c Ll Áñ: ð16Þ According to the dichromatic reflection model, the surface chromaticity K c and  ... 
doi:10.1016/j.cviu.2012.03.001 fatcat:jnsupxhbbbdzfm6c6ilnhzwev4

Luminance noise and the rapid determination of discrimination ellipses in colour deficiency

B.C. Regan, J.P. Reffin, J.D. Mollon
1994 Vision Research  
As a population, dichromats had higher thresholds on the tritan axis of the test than did normals.  ...  A computer-controlled test of colour vision is described, in which luminance noise and masking contours are used to ensure that the subject's responses depend on chromatic signals.  ...  And when the luminance equation has been made, there still remains the fourth difficulty.  ... 
doi:10.1016/0042-6989(94)90203-8 pmid:8023437 fatcat:cg7ogv6alndqdhprjww2p7z7ui

Cone pigment variations in four genera of new world monkeys

Gerald H. Jacobs, Jess F. Deegan
2003 Vision Research  
The presence of a short-wavelength sensitive photopigment was established as well so these animals conform to the earlier pattern in predicting that all male monkeys are dichromats while, depending on  ...  Previous research revealed significant individual variations in opsin genes and cone photopigments in several species of platyrrhine (New World) monkeys and showed that these in turn can yield significant  ...  Sweet and L. Boldrick). G.L. Williams, J.A. Fenwick and K. Krogh helped with the data analysis and the recording equipment.  ... 
doi:10.1016/s0042-6989(02)00565-5 pmid:12535982 fatcat:n636vsnvkfgircbt3gvv56mjl4

Spectral tuning of dichromats to natural scenes

Chuan-Chin Chiao, Misha Vorobyev, Thomas W. Cronin, Daniel Osorio
2000 Vision Research  
Variations of the natural illuminants in forests have little or no effect on optimal spectral tuning, but variations of depth in coral reefs have moderate effects on the spectral placement of S and L cones  ...  The ratio of S and L cones typically found in dichromatic mammals reduces the discriminability of forest scenes; in contrast, the typical ratio of S and L cones in coral reef fishes achieves nearly the  ...  This material is based on research supported by NSF grants IBN-9413357 and IBN-9724028 (to TWC).  ... 
doi:10.1016/s0042-6989(00)00156-5 pmid:11008142 fatcat:7jcay5ade5h5tas3ihtxb6rgfm
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