1 . the region of interest ( roi ) was selected as inside of one half of radius at a circle fitted to the margin of the iris . corneal reflection of exposure light was included from roi . the original red - blue - green ( rgb ) color image is transformed to optical density ( i ). i  ( x , y ) = 255 - [ 0 . 299 0 . 587 0 . 114 ] · ( r  ( x , y ) g  ( x , y ) b  ( x , y ) ) ( 1 ) most iris color changes were visible to the observer , but the color imaging system provides a means to quantify these changes and make them observer - independent . the rgb values captured by an imaging device depend on the illumination , eye - camera - geometry , corneal surface reflectance and iris pigment color properties . as a result , even a homogeneous colored pigment may be recorded to a broad spectrum of rgb values . to detect color change of iris , it is required to reduce the artificial effects of illumination and scene geometry . the human perception of color is luminance , hue and saturation . luminance is achromatic and describes the brightness of the scene . hue represents the dominant wavelength and saturation represents the amount of white light mixed with the pure color . to compute perceptual color components of hue , saturation and luminance , the c - y color model is computed from rgb color space as : ( y ( r  -  y ) ( b  -  y ) ) = ( 0 . 299 0 . 587 0 . 114 0 . 701 - 0 . 587 - 0 . 114 - 0 . 299 - 0 . 587 0 . 886 )  ( r g b ) , ( 2 ) where r , g , and b are the red , green and blue components of the original rgb image . the c - y coordinates are converted into the polar coordinates of hue and saturation and h = tan - 1  ( ( b  -  y ) ( r  -  y ) ) , ( 3 ) s = v  ( r  -  y ) 2 + ( b  -  y ) 2 ( 4 ) where the saturation s is the length of the vector from the origin to the specific color , and the hue h is the angle between the ( r - y ) axis and the saturation vector . i ( x , y )=( i 1 ( x , y ), i 2 ( x , y ), i 3 ( x , y )) t of a small surface p is i i · ( x , y ) = ∫ λ   ( ∑ l ≤ j ≤ n  ( n · n j ) ; l j  ( λ ) )  s  ( x , y , λ )  f i  ( λ )   λ , ( 5 ) where ƒ i ( x ) is the wavelength response of the i &# 39 ; th sensor class , l j ( λ ) is spectral distribution of illumination and n 1 , n 2 , n n are corresponding direction vectors . ƒ 1 ( λ ), ƒ 2 ( λ ), and ƒ 3 ( λ ) correspond to the red , green and blue sensing elements . another image of p obtained using the same viewing geometry but with a new illumination environment is new color image i ′ ( x , y )=( i ′ 1 ( x , y ), i ′ 2 ( x , y ), i ′ 3 ( x , y )) t is described by i ′  ( x , y ) = ∫ λ   ( ∑ l ≤ j ≤ n  ( n · n j ′ ) ; l j ′  ( λ ) )  s  ( x , y , λ )  f   i  ( λ )   λ , ( 6 ) where the surface is illuminated by n ′ sources with direction n ′ 1 , n ′ 2 . . . , n ′ n , and spectral distributions 1 1 ( x ), 1 2 ( λ ), . . . , 1 n ( λ ). let m 1 , m 2 , and m 3 be the diagonal elements of m p and it can be estimated from i ′ ( x , y ) and i ( x , y ) using m i = e  ( i i ′  ( x , y ) i i  ( x , y ) ) , ( 8 ) where e denotes the spatial average over the patch p . the correction matrix m p for illumination environments are estimated images of controlled surface area such as a color scale bar ( which can be placed near to iris ) or eye lids where least color changes expected due to medication . if eye - camera geometry is held reasonably consistent , this correction reduces artifact caused by exposure level . a color image that is identical to ( 4 ) is obtained if the set of n sources is replaced by a composite source with spectral distribution l c  ( λ ) = ∑ 1 ≤ j ≤ n  ( n · n j ) ;  l j  ( λ ) ( 9 ) color changes d of a small surface p over time a and b with arbitrary spectral reflectance functions . where i a  ( x , y ) = ∫ λ  l a  ( λ )   s a  ( x , y , λ )   f a  ( λ )    λ , ( 11 ) i b  ( x , y ) = ∫ λ  l b  ( λ )   s b  ( x , y , λ )   f b  ( λ )    λ ( 12 ) to quantitate iris color change is to measure changes of spectral reflectance functions s a ( x , y , λ ) and s b ( x , y , λ ) of iris . illumination environments are estimated using eq ( 6 ) and the wavelength response of sensor ( camera , film , film development , film scanner ) is controlled . these environmental and sensor response difference over time may introduce artifact and reduce the sensitivity and reproducibility to quantitate iris color change . to overcome these problems , color ratio which is comparing spectral reflectance of different color of iris is used . from e q ( 5 ) it is possible to estimate a color ratio r between color image i i ( x , y ) and i i ′ ( x , y ) r ii ′ ( x , y )= i i ( x , y ) / i i ′ ( x , y ) ( 13 ) where i i  ( x , y ) = ∫ λ  l i  ( λ )   s i  ( x , y , λ )   f i  ( λ )    λ ( 14 ) i i ′ ( i i ′  ( x , y ) = ∫ λ  l i ′  ( λ )   s i ′  ( x , y , λ )   f i ′  ( λ )    λ ( 15 ) then eq ( 12 ) is r ii ′  ( x , y ) = ∫ λ  s i  ( x , y , λ )   λ ∫ λ  s i ′  ( x , y , λ )   λ ( 16 ) therefore , color ratio r is the ratio between spectral reflectance of different color and is independent from change in illumination environment and wavelength response of the sensor . 5 . iris color is separated from background by thresholding density and stretching density range of iris color . image enhancement is done as y  ( i , j ) = c · x  ( i , j ) - a b - a ( 17 ) where x in an optical density image whose histogram values are limited in the interval [ a , b ], smoothing background by threshold ( ts ): z  ( i , j ) = { y  ( i , j ) , y  ( i , j ) & lt ; ts c , y  ( i , j ) ≤ ts ( 18 ) 6 . enhancement of iris color . the most iris color changes occur at the site of dark color compared to their surroundings . the receptive field algorithm uses a difference of a gaussian on - center off - surround receptive field ( rf ) by enhancing matching local image structures and suppressing the rest . rf  ( x , y ) = b · { α · exp  ( - ( x 2 + y 2 ) 2  p 1 2 ) - j · exp  ( - ( x 2 + y 2 ) 2  p 2 2 ) } ( 19 ) where b , a , p 1 , p 2 and j are constants , x and y are image coordinates . 7 . segmentation of iris color from background is done applying a squashing function by transforming both sets closer to the extreme values by adjusting the squashing function parameters ; ( scale , offset , & amp ; include ) as : where i k and sqk depict the image array and the squashing function ( sqk ) at the k - iteration while , sq  ( i k ) = scale _ 1 + exp  [ - include _ · ( i k - offset _ ) ] ( 21 ) the histogram vector of i k is smooted by defining the threshold value t : t = min mode ( hist ( i )□[ a 0 , . . . , a 0 . 3 · scale − 1 ]) ( 22 ) where hist ( i ) returns the histogram of i , a 0 , . . . , a 0 . 3 · scale − 1 =| 0 . 3 scale | − 1 define the moving average filter coefficients , and min mode returns the minimum between two maxima . t is used to segment the original image into background and iris pigmentation . 8 . a binary mask is used to characterize segmented iris color . segmented iris color from background is divided into a binary mask using multiple thresholds and their gravity centers are computed as the local maxima of the image pixel densities . the image is divided into binary masks ( sp ) sp , p = 1 , …   l , using   multiple   threshold   tp   sp  ( i , j ) = { 1 , t p - 1 ≤ y  ( i , j ) & lt ; tp o , elsewhere  ( 23 ) 9 . to detect iris color changes , image extraction is made using spatial gray - level dependence matrices . this algorithm is based on the estimation of the second order conditioned probability density p ( i , j : d , θ ), in which probability that two different pixels are on the direction ( angle θ ) and distance ( d ) will have values i and j , respectively . the features used in this algorithm are sum   entropy = - ∑ i = 2 2  n  p x + y  ( i )  log  { p x + y  ( i ) , } ( 24 ) angular   second   moment = ∑ i  ∑ j  { p  ( i , j ) } 2 ( 25 ) inverse   difference   moment = ∑ i  ∑ j  1 1 + ( i - j ) 2  p  ( i , j ) ( 26 ) and   contrast =  ∑ i = 1 ng - 1  n 2  { ∑ i = 1 ng  ∑ i = 1 ng  p  ( i , j ) }   i - j  = k ( 27 ) where ng is number of gray levels , μ x and ∂ x are the mean and standard deviation of the row sums of the matrix p ( i , j ), and μ y & amp ; ∂ y are corresponding statistics of the column sums , with p x − y and p x + y given by : p x - y  ( k ) =  ∑ i = 1 ng  ∑ j = 1 ng  p  ( i , j ) ,  k = 0 , 1 , …   ng - 1   i - j  = k ( 28 ) p x + y  ( k ) =  ∑ i = 1 ng  ∑ j = 1 ng  p  ( i , j ) ,  k = 2 , 31 , …   2  ng   i - j  = k ( 29 ) each measurement is evaluated for d = 1 , 2 , 3 and ?= 0 °, 45 °, 90 °, 135 ° three initial studies were done . the first two studies were carried out on normal subjects at baseline and over time . for these studies , color slides of the iris were analyzed using the red - green - blue spectrum or white light . the first study , for normal subjects , was to determine at baseline the exposure which gave the best reproducibility of the measurements of area and density of iris color using white light . subjects had three slit lamp photographs taken for each of three different exposures , low , medium and high . the reproducibility , calculated as percent coefficient of variation (% cv ), was then determined for each exposure . as a % cv , the lowest values were with high exposure levels for yellow - brown and green - brown iris and with the medium levels of exposure for the blue - grey iris . subsequently , these levels of exposures were used for follow - up visits . the range of mean percent coefficient of variation of yellow - brown and green - brown iris for the area of pigment was 4 . 17 to 5 . 83 % and for density of color was 1 . 79 to 2 . 3 %. for the blue - grey brown iris , the range of mean percent coefficient of variation for area of pigment was 4 . 04 to 4 . 86 % and for density of pigment was 2 . 67 to 2 . 73 %. the second study also determined the reproducibility on two follow - up visits of the same normal subjects in the first study with photographs taken at the exposure determined at baseline to give the best reproducibility . furthermore , the second study determined any difference between mean values for area and density of iris color between baseline and the follow - up visits . the subjects were requested to return for follow - up photographs . the mean difference in time interval between the baseline and the first follow - up visit was 6 . 5 ± 1 . 7 months . the time interval between the first and second follow - up visit was 3 . 6 ± 0 . 8 months for a total follow - up of a mean of 10 . 1 months . the percent difference was determined between the first follow - up visit and baseline and the second follow - up visit and baseline . the percent difference ( as absolute values ) was calculated as follow - up visit minus baseline / baseline × 100 . the range of percent difference for all three irides was from 1 . 2 to 6 . 3 %. the third study used the red / blue method and compared this method to the white light method for measuring density of iris photographs on the eyes of twenty - three glaucoma patients treated with xalatan eye drops for 36 months . iris photographs were taken at baseline , 1 month , 4 , 8 , 12 , 16 , 20 , 24 , 28 , 32 and 36 months . the reproducibility of the red / blue methods with the methods used in study 1 and 2 were compared for duplicate measurements . the reproducibility appears similar for all methods except the selected area of the red / blue method which had a somewhat larger mean value . compared to the white light method , the means are larger for the red / blue method as well as the standard deviation of the means indicating a greater spread of the data over time for the red / blue method . this suggests a greater sensitivity of the red / blue method in detecting changes in iris color over time for patients treated with xalatan eye drops . also there was a good correlation of the slopes of the measurements over time obtained with the red / blue total method with other measurements using methods to evaluate the change in color of iris photographs . furthermore , the red / blue total method was used for iris measurements of normal eyes over time taken from iris photographs for the second study with a first follow - up visit at 6 . 5 ± 1 . 7 months and a second follow - up visit at 3 . 6 ± 0 . 8 months following the first follow - up visit . the total follow - up was a mean of 10 . 1 months . the measurements show no significant change over time indicating that with the red / blue as well as the white light methods , normal irides appear stable over time . three studies were done . the first two studies were carried out on normal subjects at baseline and over time . the third study was an analysis of iris photographs of patients with glaucoma treated with xalatan eye drops over 36 months . as previously indicated , the first study , for normal subjects , was to determine at baseline the exposure which gave the best reproducibility of the measurement of area and density of iris color using white light . thirty subjects were chosen who had no evidence of ocular disease and were using no ocular medications . the irides of the subjects were categorized by color , green - brown ( n = 10 ), blue - grey brown ( n = 10 ) and yellow - brown ( n = 10 ). a zeiss slit lamp camera was used to take the color photographs of the iris . for the baseline study , three photographs were taken of the iris for each of three different exposures , low , medium and high . using white light for area and density , analysis of the reproducibility of the measurements by selecting the smallest percent coefficient of variation of the baseline data provided the optimum exposure for follow - up visits . only this exposure was used and three photographs were made at the chosen exposure level at each of two follow - up visits . the second study also determined the reproducibility on two follow - up visits of the same subjects in the first study with photographs taken at the exposure determined at baseline to give the best reproducibility . furthermore , the second study determined any difference between mean values for area and density of iris color between baseline and the follow - up visits . the first follow - up visit was 6 . 5 ± 1 . 7 months after baseline . the second follow - up visit was 3 . 6 ± 0 . 8 months after the first follow - up visit . for the second study , most of the baseline photographs were remeasured . the third study used the red / blue method for measuring density of iris photographs on glaucoma patients treated with xalatan eye drops for 36 months . for the third study , one eye of twenty - two glaucoma patients and both eyes of one glaucoma patient had iris photographs taken at baseline , 0 , 1 , 4 , 8 , 12 , 16 , 20 , 24 and 28 , 32 and 36 months . iris photographs , masked for time and duplicate , were measured using the white light and red / blue methods . this method was then compared to the white light method for density and area which was used in the first two studies . in the initial studies of measuring iris color from colored photographs , a modified method to the one proposed was used . each slide was digitized using a nikon film scanner ( ls - 1000 , nikon - usa ). the original red - green - blue ( rgb ) color image is transformed to optical density ( i ) i  ( x , y ) = 255 - [ 0 . 299   0 . 587   0 . 114 ] · ( r  ( x , y ) g  ( x , y ) b  ( x , y ) ) image analysis programs were designed to determine the region of interest ( roi ). since most dark color of the iris was near the pupil , the roi was selected as being inside one half of the radius of circle fitted to the peripheral margin of the iris with the area of corneal reflection excluded . the roi was digitized and iris color is separated from background by thresholding density and stretching density range of iris color . image enhancement is done as y  ( i , j ) = c · x  ( i , j ) - a b - a where x in an optical density image whose histogram values are limited in the interval [ a , b ], where a ≦ o , b ≦ c , image y is product of image enhancement . smoothing background by threshold ( ts ): z  ( i , j ) = { y  ( i , j ) , y  ( i , j ) & lt ; ts c , y  ( i , j ) ≤ ts a binary mask was applied to characterized iris color using multiple thresholds and their gravity centers are computed as the local maxima of the image pixel densities . sp , p = 1 , . . . l , using multiple threshold tp sp  ( i , j ) = { 1 , t p - 1 ≤ y  ( i , j ) & lt ; tp o , elsewhere  as a result the roi was divided into three density levels ( 1 ) dark 0 to 25 th percentile , ( 2 ) light 75 th to 100 percentile , and ( 3 ) background 25 th to 75 th percentile . for the first two studies , the segmented area was converted from the number of pixels to square millimeters using the millimeter scale photographed together with the iris image . differences of iris color over time for position , area and density distribution on each segmentation were divided into a number of regions ( clusters ). a directional difference with low frequency distribution was filtered out as artifact , and well focused high density difference located in the colored area of iris was defined as class region . to reduce the effect of deviation of roi on each visit , mean density for each segmented area was normalized using the ratio to the mean density of roi . the area for each segmented area was also normalized using the ratio to the area of roi . similarly , the averaged density for each segmented area was normalized using the ratio to the average density of roi . each slide was measured at least once to obtain three measurements for each iris . standard deviation was calculated for reproducibility and the percent coefficient of variation (% cv ) was determined as the standard deviation / mean × 100 and used as the index of reproducibility . for the third study , the red / blue method was used or the density measurements of the total region of interest as well as a selected area based on 0 to 25 th percentile of the density curve for the region of interest . non - parametric tests were used for analyses mainly the wilcoxon rank sum test , the kruskal - wallis and the mann - whitney u tests . slopes over time were determined by a least regression line and spearman correlations determined the significance of the trend over time . tables 1 , 2 and 3 provide the percent coefficient of variations for the three different exposures categorized by iris color at baseline ( fig1 to 6 ). in fig2 the region of interest ( roi ) is the circular area surrounding the pupil excluding areas of light reflection . the light color ( lc ) area ( 75 th to 100 th percentile density level ) is 26 . 3 % of the roi area and the light color density is 115 % of the roi density . the dark color ( dc ) area ( 0 to 25 th percentile density level ) is 24 % of the roi area and the dark color density is 78 % of the roi density . in fig4 the region of interest ( roi ) is the circular area surrounding the pupil excluding areas of light reflection . the light color ( lc ) area ( 75 th to 100 th percentile density level ) is 26 . 4 % of the roi area and the light color density is 125 % of the roi density . the dark color ( dc ) area ( 0 to 25 th percentile density level ) is 23 . 8 % of the roi area and the dark color density is 82 % of the roi density . in fig6 the region of interest ( roi ) is the circular area surrounding the pupil excluding areas of light reflection . the light color ( lc ) area ( 75 th to 100 th percentile density level ) is 27 . 7 % of the roi area and the light color density is 137 % of the roi density . the dark color ( dc ) area ( 0 to 25 th percentile density level ) is 24 . 4 % of the roi area and the dark color density is 61 % of the roi density . as a % cv , the lowest values were with high exposure levels for yellow - brown and green - brown iris and with the medium levels of exposure for the blue - grey iris . subsequently , these levels of exposures were used for follow - up visits . the range of mean percent coefficient of variation of yellow - brown and green - brown iris for the area of pigment was 4 . 17 to 5 . 83 % and for density of color was 1 . 79 to 2 . 3 %. for the blue - grey brown iris , the range of mean percent coefficient of variation for area of pigment was 4 . 04 to 4 . 86 % and for density of pigment was 2 . 67 to 2 . 73 %. some significant differences were noted between the various exposures for each iris color . the coefficients of variation for the region of interest were significantly different for the blue - gray brown iris between the high and medium exposures ( p = 0 . 0211 wilcoxon rank sum test ) ( table 2 ). the coefficients of variation for the dark segment density were significantly different ( p = 0 . 0113 ) between the medium and low exposures for the yellow - brown iris ( table 3 ). the coefficients of variation for the region of interest were significantly different for the area of color and the density of color for the low to high exposures ( p = 0 . 0172 and p = 0 . 0257 ) ( table 3 ). the subjects were requested to return for follow - up photographs . the mean difference in time interval between the baseline and the first follow - up visit was 6 . 5 ± 1 . 7 months . the time interval between the first and second follow - up visit was 3 . 6 ± 0 . 8 months . tables 4 , 5 and 6 provide the percent coefficient of variation for the baseline with the two follow - up visits at the exposure chosen for each eye , the range of mean percent coefficient of variation for all three irides was from 1 . 0 to 4 . 1 %. kruskall - wallis analysis showed no significant differences between the baseline , first and second follow - up visits except for a significant difference for the light segment area ( p = 0 . 257 ) and for the light segment of density ( p = 0 . 0246 ) for the yellow - brown iris ( table 6 ). mann - whitney u analyses showed significant differences for the light segment area between the first follow - up visit and baseline ( p = 0 . 0191 ) and between the second follow - up visit and baseline ( p = 0 . 0211 ). similarly , for the light segment of density , there was only a significant difference between the first follow - up visit and the baseline ( p = 0 . 0065 ). tables 7 , 8 and 9 show the percent difference between the first follow - up visit and baseline and the second follow - up visit and baseline . the percent difference ( as absolute values ) was calculated as follow - up visit minus baseline / baseline × 100 . the range of percent difference for all three irides was from 1 . 2 to 6 . 3 %. table 10 compares the reproducibility of the red / blue methods with the methods used in study 1 and 2 for duplicate measurements . the reproducibility appears similar for all methods except the selected area of the red / blue method which has a somewhat larger mean value . table 11 shows the means and the standard deviations of the mean for all the measurements of the twenty - three eyes by the red / blue method . compared to the white light method , the means are larger for the red / blue method as well as the standard deviation of the means indicating a greater spread of the data over time for the red / blue method . this suggests a greater sensitivity of the red / blue method in detecting changes in iris color over time . the photographs in this study were also visually evaluated for increased iris color or pigmentation over time . eleven of the 23 eyes showed an increase while 12 showed no change . the slope of the iris color measurements over time was determined by a least regression line . the significance of the slope over time was determined by a spearman correlation . in addition , the difference of the average of the final two measurements minus the initial two measurements was calculated . also trends of the direction of the iris measurements over time was evaluated by visual inspection of the plots ( fig7 to 11 ). table 12 shows that associated with a positive significant or non - significant slope was an increase in darkening of the iris over time , a positive difference of final minus initial measurements and an increasing trend . associated with a negative significant or borderline significant slope was no change in darkening of the iris on visual inspection , a negative difference of final minus initial measurements and a decreasing trend . these results indicate that there is a good correlation of the slopes of the measurements over time of the red / blue total method with other methods to evaluate the change in color of iris photographs . fig1 shows the data obtained on using the red / blue total method for iris measurements of normal eyes over time taken from iris photographs for the second study with a first follow - up visit at 6 . 5 ± 1 . 7 months and a second follow - up visit at 3 . 6 ± 0 . 8 months following the first follow - up visit . the total follow - up was a mean of 10 . 1 months . the measurements show no change over time indicating that with this method , red / blue as well as the white light method , normal irides appear stable over time .