1Color Vision Oct 20, ‘07Source to Detector Light Source--spectrum Path to illuminated object Reflection from object--reflectivity Path to Cornea Focusing to two-dimensional spatialmap of object on retinasource spectrumreflectivityarriving spectrumSource to DetectorWhat arrives on retina 1? Light is Electromagnetic Wave EM waves have speed, frequency,wavelength c = f λ E and B are transverse to direction Time variation of each recreates theother advanced forward in location Passage of oscillating E shakeselectrons found along the pathWhat arrives on retina 2? Light interacts in discrete energybundles, known as quanta, or photons The energy in one photon is determinedby the frequency of the wave E = hf,where h is Planck’s ConstantVisible Light Speed 3 x 108 meters/s (very fast) Wavelengths ~ 400-700 nanometers (violet tored) Frequencies so high that electrons are aboutthe only thing able to shake that fast (tocreate the light in the first place) Photon energies ~ 2 to 3 electron Volts (nicesize for instigating chemical reactions)2What Happens at Retina 1? Photons absorbed by pigments in sensingcells (rods or cones) cause associated nervesto fire Rods are mainly useful in vision at very lowlight levels--role in color vision (whichrequires bright light) is small Three types of cones with different pigmentsensitivity functions (short S, middle M, andlong L wavelength sensitive versions)Incoming spectrumsensitivityfiring ratesensitivityfiring ratesensitivityfiring rateblue redCone Sensitivity FunctionsCone Sensitivities00.10.20.30.40.50.60.70.80.91400 450 500 550 600 650 700wavelength (nanometers)respo nseLMS Short, Medium,and Long λ Med and Longvery similar(recentevolutionarydistinction) Red-Green colorblindness missingone of L, MMonkey Story > 50 Myr ago: “Old World” apes only, 2 receptors only (S, ML) ~35 Myr ago: Some OWA migrated to “New World”--theirdescendants remain today, 2 receptors only Next: LM receptor on X chromosome of OWA duplicates andone copy mutates slightly--> three receptors on some OWAs(S,M,L) Three receptor version propagates through OWA population,likely with significant advantage (as brain had to change to useit). (e.g. finding red berries in green foliage). Humans arose from OWAs. To this day, 7% of males (havingonly one X chromosome) still have only one LM receptor type.Most females with two X chromosomes manage to avoid thecorresponding R-G color blindness.3Cross Talk in the Eye The [firing rates of the three types of cones, at eachposition on the retina] is NOT the information passed on tothe brain for assembling and interpreting the image (orsequence of images). A lot of processing occurs in the eye, combining signalsfrom different cone types and different locations, hard-wired processing, for identifying objects (via theiredges and colors), measuring their motion, etc. Red-Green color discrimination improved by recording(weighted) difference between L and M cone responses. Complementary colors provide clues to combinations--color opposites. (After-images.)A Little fuzzy here Top picture shows thethree responses usedfor a standard observerin color adding andmatching The second shows (myapprox) combinations ofL, M, and S that arevery similar I could not find a gooddiscussion of goingfrom L,M,S to R,G,B,(actually called x,y,z)Linear Com binations of L, M, S00.20.40.60.811.21.41.61.82300 400 500 600 700 800wavelength (nanome ters)respons e1.9L-1.4M+.4S0.8L+.25M1.8*SRGBThe St andard Observer00.20.40.60.811.21.41.61.82300 400 500 600 700 800wavelength (nanome ters)respons eredgreen blueRGBAside on Edges Edges (in brightness orcolor) are easily foundby combining thebrightness at eachlocation with thenegative of the averagebrightness (of the sameor a different colorchannel) in a slightlylarger area. This form may also beuseful in patternrecognitionfilterintensitysignalTrichromatic Model of ColorSensation Three channels,loosely R, G, B Sum of three gives ameasure of totalintensity of light Fractions of total inany two channelsdeterminedperceived colorLinear Combinations of L, M, S00.20.40.60.811.21.41.61.82300 400 500 600 700 800wavelen gth (nanometers )respo nse1.9L-1.4M+.4S0.8L+.25M1.8*SRGBRelative responses toindividual wavelengths oflight (monochromatic)Fraction-Fraction Diagram f(green) vs. f(red) Line of no blue All combinations of incidentlight produce responseinside horseshoe (like centerof mass) “White” has equal responsesin each channel Locus of purples Complementary colors faceeach other across whiteThe Horseshoe (Chromaticity) Diagram00.20.40.60.810 0.2 0.4 0.6 0.8 1fraction (red)fraction (green)400500600700525475575550YROGBVWExample: 3 Incident Spectra Bluish, Even, andRedish distributions oflight arriving on cones “perceived color” isdetermined by locationin horseshoe Intense color nearboundary, pale nearwhite spotThree lig ht source spectra and the Combo Chan nel Sensi tivity Function s00.511.522.53300 400 500 600 700 800wavelength (nanome ters)respons e1.9L-1.4M+.4S0.8L+.25M1.8*Sblueish lighteven lightreddish lightThe Horseshoe ( Chromaticity) Diagram00.20.40.60.810 0.2 0.4 0.6 0.8 1fraction (red)fraction (green)monochromebluishevenreddish400500600700525475575550YROGBVW4Color VersionProblems w Trichromatic Model Another dimension--what are brown,olive, and other colors not found in therainbow? How is it that we can correctly identifythe colors of objects in a scene whenthe color of the illuminating light variesenormously? (color constancy)Three DimensionalityCompare to Surroundings Brown is dimorange with abright surroundColor Constancy Scene includes a mixture of objects withdifferent intrinsic “colors” and brightnesses. Color of illuminating source changesblue end red endreflectivityExample 3 retinal receptor channels (R, G, B) 3 objects with different reflectivities,peaking in red, green, blue 1 white object 3 light sources (used one at a time),one blueish, one greenish (or evenish),one redish5Example CharacteristicsAssumed Illuminations00.20.40.60.811.2400 450 500 550 600 650 700wavelength (nanometers)bluishevenredishAssumed Object Reflectivities00.20.40.60.811.2400 450 500 550 600 650 700wavelength (nanometers)475550625Linear Com binations of L, M, S00.20.40.60.811.21.41.61.82300
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