Negative to Positive CFS-244 April 19, 2004

Transcription

1 egative to ositive CFS-244 April 19, ersonal ote This report has a lot of algebra and basi physis of photography in it, but it is not "roket siene." evertheless, it is quite triky to wade through and we have not seen this material treated in a similar way elsewhere. We have seen a great deal of basially inorret material on the topi, both on the web and in print. For a simple example, what hotoshop alls "Invert," that is, Image Adjust Invert, sounds like it should onvert a negative to a positive, and the result looks like that may be happening, but that proess - whih also appears in other imaging programs and sanner software to an unknown extent - is far removed from what atually needs to be done to orretly onvert a sanned negative image to a positive. It is not neessarily easy to tell from results whether sanner software is based on the priniples in this report beause it is possible to approximate what we present here by "profiling," that is, by having a test ase for whih the results are known and adjusting a series of arbitrary orretion fators to make the results math. With a basi priniples approah, the equations have physial meaning rather than being arbitrary urve fit forms and thus are more likely to respond better to variations in proessing, manufature, and storage. If any reader is aware of this material being published and available elsewhere, we would appreiate knowing about it so we an ompare notes. lease ontat us through our web site. This doument is viewable only. We believe this will be adequate for people who do not intend to study it. lease ontat us through our web site if you need a printable version. We are aware that the no-print an be defeated, but again we ask that you ontat us instead. We really need to know if and how people are finding these douments useful, and this seems one of the few ways we have to enourage feedbak. In this doument we make frequent referenes to the ompanion douments CFS-242, Film Gamma Versus Video Gamma and CFS-243 Maintaining Color Integrity in Digital hotography. Refer to those douments, available on our web site, for the further explanation of the symbols, equations, and onepts used here. Muh of the material and its treatment in this doument is original with us and this doument is Copyright 2004 by C F Systems If you plan to use our original material in any published form, please ontat us at for terms and onditions.

2 CFS egative, ositive, and the S-Curve In CFS-242, Film Gamma Versus Video Gamma, we dealt with the S-urve, used to desribe traditional or silver-based images, expressing the sensitivity of film to light. This S-urve relationship is physially measured for eah type of film under speifi proessing: d max d d min E ref log E Figure 1 S-Curve for a egative hotographi Film Where the straight line portion of the "S" has the equation: d log 10 (E /E Ref ) Here d is the photographi density, with d 0 meaning transparent film and as d beomes larger, transpareny dereases (the film beomes darker). E is the light exposure the film reeives, measured in andela-se/m 2 or similar units. is the slope of the straight-line portion of the S-urve. E ref is the exposure for whih d 0 when the straight-line portion is extrapolated through the log E axis. hotographi density is the base 10 logarithm of an intensity ratio. In this ase, it is the ratio between the intensity of the light impinging on a the negative to the light passing through a the negative. That is: Imax d log 10 I Suh intensity ratios turn up very often in digital photography and are usually the inverse of the one above, whene they beome normalized, onfined between 0 and 1 in value. 2

3 CFS We use the notation I/I max as a shorthand for suh normalized intensity ratios, and thus d log 10 ( ). In CFS-242, Film Gamma Versus Video Gamma, we also showed that a positive silverbased image has a similar form to the negative, but with the "S" mirror reversed, and with the straight-line portion having the equation: d log 10 (E/E ref ) We showed that this is true whether the positive image is produed by reversal proessing, suh as is done for slides, or is printed as a positive from a negative. Traing the ath from egative through to ositive The proess under investigation involves produing a positive image from a sene by first reating a negative film image. There will be separate exposures for the positive and negative images and we use E S as the exposure to the sene for the negative and E as the exposure to the illuminated negative to produe the positive: d log 10 (E S /E ref ) d log 10 (E /E ref ) To find what exposure the positive media will get from light passing through the negative media, we apply the definition of density for the negative and use the notation for the normalized intensity ratio: d log 10 (I max /I ) log 10 (I /I max ) log 10 ( ) The exposure to produe this density will be proportional to the sene intensity applied for an exposure time t S through a f-aperture: E S /E ref k S, so that d log 10 (k S ) The k is a single onstant fator relating sene intensity ratios to negative densities. One an think of k as being determined by taking a light meter reading of the sene. Make k larger and the negative of the sene will be darkened, with k smaller, the negative will be thin. In any ase, we will be seleting some speifi S SR that we want to result in some speifi density in the negative, d d R, or equivalently R so: d R log 10 (k SR ) log 10 (k ) + log 10 ( SR ) log 10 ( R ) log 10 (k SR ) log 10 ( k) + log 10 ( SR ) So, sine d log 10 (k S ) log 10 ( ) log 10 ( S ) log 10 (k) log 10 ( S ) + log 10 ( R ) + log 10 ( SR ) 3

4 CFS or R SR R S SR S The exposure for the positive will be this intensity applied for an exposure time t through a f-aperture so that E /E ref k where k aounts for both the exposure time and f-aperture applied to the light passing through the negative: d log 10 (k ) as before, we meter an exposure whih will math a speifi density in the positive d R, or equivalently R, to a speifi intensity ratio in the negative (whih may be different than R ): d R log 10 (K ) log 10 (k ) + log 10 ( ) log 10 ( R ) log 10 (K ) log 10 (k ) + log 10 ( ) or log 10 ( ) log 10 ( ) log 10 (K) log 10 ( ) + log 10 ( R ) + log 10 ( ) R R The Connetion between Exposure arameters The base requirement is that the intensity ratios of the positive image math the intensity ratios of the sene, that is, S : so that R SR R S SR R R S First, it is obvious that to have S requires mathed gammas, that is, 1, so that SR R R S 4

5 CFS R and further that 1 SR R Thus, if we wish the positive image to math the sene, S, we must have mathed gammas and also require that the exposure of the negative and the positive be related: or R SR R SR R R umerial Examples of the Sene to egative to ositive Trae The CIE L* "lightness" funtion is designed to mimi the behavior of human vision (as explained in CFS-243, Maintaining Color Integrity in Digital hotography) and runs from L* 0, pure blak, to L* 100, the brightest disernable area in a sene. Eah inrement of 1 in L* approximates a barely visible step in a gray sale from blak to white. Eah value of L* orresponds to an intensity ratio Y/Y n, through a somewhat ompliated formula. Y/Y n orresponds to our S. In Tables 1 and 2 below we use the L* sale to trae the resolution of a sene S, as a positive image,, going through an intermediate negative,. In this way the rows in the table are visually evenly spaed along a gray sale, making it easier to understand what is happening. In preparing Table 1 we hose our exposure so that SR 1 and d R d max, that is, the maximum density d max ours at the maximum intensity ratio in the soure. While that appears mathematially sensible and is useful for illustration, note that one does not normally tie exposure to the brightest highlights in real situations. The requirement for the positive is R If we expose the positive using SR 1, and use 1, then R R. We have used R R whih a density range of about 2.95, going from 1 to 100 on the L* sale. SR R 5

6 CFS Table 1 From Sene through egative to ositive For 1 and R R L S * S [Y/Y n ] S d L * d [Y/Y n ] L * It an immediately be seen that L S * L * and S for the entire table, meaning that the positive image is a math for the sene, whih is our base requirement. Closer inspetion shows some surprising results. On the negative,, the entire range of intensities from 0.25 to 1, that is the part of the negative that is about middle gray in the negative (for middle gray, 0.18 and L* 50) through lear, orresponds to only the very darkest grays in the original sene (and in the positive image). In the negative image the very darkest areas, mostly well below middle gray in the negative, are responsible for most of the tones in the final positive image, while all the lighter parts of the negative, from lear through middle gray, form just the first 4 darkest steps out of the 100 steps in the gray sale in the positive image. 6

7 CFS The Connetion between egative and ositive is Extreme ositive Intensity Ratio versus egative Intensity Ratio For 1 and R R The graph above shows how extreme this relationship really is. The urve barely breaks away from the axes even near the (0, 0) point in the lower left orner. Most of the intensity ratios in the positive image are represented by just the lowest intensity ratios in the negative, and vie versa. It should be noted that what hotoshop alls "Invert," that is, Image Adjust Invert, orresponds to the diagonal dashed line in the above graph, far removed from the atual inversion of a negative to a positive. Another way of desribing the hotoshop Invert is that it subtrats the negative image from a totally white image. The belief that this subtration will atually invert a (film) negative image to an aurate positive is fairly widespread, whether the funtion is in hotoshop or in other image editing or sanner software. In photographi media, however, it is not intensity ratios, 's, whih are additive, but densities, d log 10, that are additive. See Mathematial roof of hotographi Gamma Equation for ositives in CFS-242, Film Gamma Versus Video Gamma - or just think of the way that olor ompensation filters are added by density. egatives are just omplex filters, in whih the olor of the filter hanges for eah "pixel." Adding and subtrating densities is the equivalent of multiplying and dividing intensity ratios. A umerial Example with on-unity Gammas Table 2 shows the same trae for a mathed gamma where both 0.5 and 2. (To be mathed, 1). Again we require that R SR R If we expose again using SR 1, this time 2, and so and 2 R R. We again have used R whih orresponds to going from 1 to 100 on the L* sale, whih is what we wish for the positive image. 7

8 CFS Table 2 represents a thinner negative, that is, one with a lower d max. If we allowed the negative to be exposed to the same d max as it was in Table 1, it would be possible to make a full-range positive image from a portion of the density range of the negative. There would still be (mathematially) an exat orrespondene between the sene intensity ratios and the positive image intensity ratios, at least for the range of ratios overed by the positive image. Table 2 From Sene through egative to ositive For 0.5, 2 and R , R L S * S [Y/Y n ] S d L * d [Y/Y n ] L * ositive Intensity Ratio versus egative Intensity Ratio For 0.5, 2 and R , R

9 CFS The graph shows that the relationship between orresponding positive and negative intensity ratios is still very extreme. The pratie of using a low-gamma negative has been widely used in manufaturing olor negative films. Film (like most media) is largely limited by its d max. When negative film is made with a low gamma (low ontrast), the same d max apability allows it to aurately represent a muh wider range of sene intensity ratios, so that it has muh wider exposure latitude. When the negative is printed on media with a mathed gamma (higher ontrast), intensity ratios from the sene will be orretly represented, but of ourse the positive print will represent only the range of intensity ratios that falls within its d max apability. A thin "underexposed" negative will print well but so will a dark "overexposed" negative. The quote marks are intended to mean that the negatives appear to be under- or over-exposed but are within the expanded latitude of the olor negative film and so not atually under- or over-exposed. Before we an effetively deal with real world inversion of negative to positive, we must first deal with the muh maligned "orange mask." The Infamous Orange Mask To judge from advie given on the web, it is widely believed that the problems in dealing with olor negatives are due mostly to the olor mask, the pronouned orange, blue, or other olor ast seen on most types of olor negative. In atuality, the mask is equivalent to a uniform olored filter sandwihed with a negative olor image that is more aurate than ould be obtained otherwise and more aurate than any positive olor film. All that is neessary to ompletely orret for the mask is to add a filter of omplimentary olor to the mask. Why the Orange Mask? The olored dye moleules used to form images in olor film are hemially ombined with "oupler" moleules so that the ombined moleule is olorless and transparent. When the film is developed, light exposed grains of silver halide are onverted to silver metal to form the image. Coupled dye moleules adjaent to the sites where silver grains are formed break apart, releasing the dye moleule in its olored form, and the dye moleules form the olored image. In olor film the dyes are normally: magenta, whih passes red and blue light freely but bloks green light; yan, whih passes green light and blue light freely but bloks red; and yellow, whih passes red light and green light freely but bloks blue. The problem is that very few types of dyes an be made to work hemially as required to form the oupled ompounds that properly break apart during film development. Consequently, the atual dyes that are used are not at all perfet. For instane, the magenta dye typially bloks some of the blue light it is supposed to pass freely, and the yan typially bloks some of the blue and green light that it is supposed to pass freely. 9

10 CFS A lever way of improving the dye ation was introdued very early in olor negative history. Instead of ombining the dye moleules with oupler moleules that made them olorless, the dye was ombined with a oupler hosen so that the ompound had exatly the same light absorption as the unwanted absorption of the dye moleule. So, the magenta dye would be ombined with a oupler produing a yellow-olored ompound so it would absorb some blue light just like the imperfet magenta dye, and the yan dye would be ombined with a oupler produing a pinkish ompound that would absorb some blue and green light, just like the imperfet yan dye. The pinkish and yellow olors together formed the orange mask. If during film development some silver halide was redued to silver, ausing a nearby magenta dye moleule to break loose of its oupler, that meant the yellow oupled dye moleule had been broken and the yellow was gone. So, throughout the image, either a magenta dye moleule would be present or the yellow oupled dye moleule remained. Either way, the same amount of blue light would be absorbed, so the effet is like plaing a yellow filter over a lear but more perfet negative. The same ation with the yan dye plaes a pinkish filter over the whole image. So, the entire mask effet is a filter that an be anelled by adding a filter omplimentary to the mask olor - and brightening the image to ompensate for the darkening from the resulting "neutral density" filter. Dealing with the Orange Mask This is how "diffiult" it is to deal with the infamous "orange mask" in hotoshop. San in a olor negative, using "raw" (linear) mode, 16 bits/hannel, and preferably as a positive, or "slide." The reason for this latter is that most sanners really will deliver a raw linear san for a slide, but many will attempt their own "orange mask" orretion on what they deliver as a "raw linear" san of a negative. Arrange the negative so that some of the orange mask that is between frames shows at the edge of the san - between frames rather than at the film edge to avoid possible film edge effets. The following shows the hotoshop Levels histograms for the Red, Green, and Blue hannels for a olor negative with quite a bit of edge showing: In eah ase, the smaller lump at the right of the histogram represents the orange mask. Sine this mask is the result of plaing a (fairly) uniform orange filter over the image, all that needs to be done is to make the mask "lear" or white. 10

11 CFS In the above illustration, at left is the hotoshop Levels showing RGB, and below the dialog box a small portion of the olor negative image an be seen, with the orange mask at the edge. To orret the orange filter, we lik the highlight button, the rightmost eyedropper 1. Clik on the orange mask and get a reasonably stable setting. The mask will be mostly white, and the orretion for the "orange mask" is ompleted. This is true whether the orange mask really is orange, or if it is bluish, reddish, or some other olor, as is the ase for some varieties of olor negative. Very easily done. The problems in dealing with olor negatives lie elsewhere. Inidentally, the "spiny" histogram on the right is due to the fat that hotoshop uses 8-Bits/Channel values for intermediate histogram alulation even when the image is 16-Bits/Channel. The histogram of the image is smooth when viewed after atual onversion, as shown below. The result of removing the mask is shown below: 1 To use the highlight eyedropper properly, be ertain this button is set to pure white, (R,G,B) (255,255,255), whih is the default value. This may be heked in the dialog box obtained by doubleliking the highlight button. Also, prior to alling the Levels tool, be ertain that the eyedropper seletion tool is set to sample a 5x5 area rather than 3x3 or single point. This an be done by liking the eyedropper in the "Tools" box and setting the "Sample Size:" The exat method varies with the version of hotoshop. Finally, prior to alling up the Levels tool it is wise to zoom in, selet a portion of the edge and apply a gaussian filter to it, enough to make it fairly uniform (typially 5 pixels or so), then deselet. Be sure the seleted area is well within the uniform edge mask so that non-mask areas do not get blurred into the sample. Sample from this more thoroughly mixed area when orreting for the mask. With very grainy negatives this blurring beomes more neessary. 11

12 CFS We have ropped off the now lear mask before taking the Levels histograms - it would have shown up as a half-lump at the very right of eah histogram. ote that there is very little on the right hand side of the histograms. This is exatly what should be expeted. Earlier we learned that the lighter areas of the negative, to the extent of the rightmost 3/4ths, represent just the very darkest shadows of the positive image, the first four steps of gray in a 100 step uniform sale. ote, however, that this usually long tail is "gathered up" by the inverse relationship and olletively is very important to shadow detail. One problem we have noted with some sanner software we have worked with is that it seems to work on the theory that if there is very little in the negative histogram, it should be trimmed, so some sanners will return an image with the following histograms as a "linear raw" negative! All we an say is that suh sans will lak shadow detail, are not "raw," and may not be linear. Without knowing preisely what has been done, the user is left with an image that is impossible to aurately onvert to a positive image. The best one an do with suh a san is to guess. Real World Film egative Inversion To better understand the properties of the negative-positive film system, reonsider the basi equation: R For atual appliations there is no need to separate out R and, so this an be redued to: K 12

13 CFS This inverse relationship has a very interesting property relative to the ation of filters. Suppose we have a negative whih has a histogram like the following: There appears to be nothing on the right hand side of this histogram, so let us move over the right hand Highlights slider until it meets the data. As we have learned previously, the Highlights slider is equivalent to a filter and/or a hange in overall illumination and merely multiplies all the 's by a onstant fator. Moving that slider is exatly what happened above to the individual olor hannels to remove the orange mask filter. Thus, the ation of moving the highlights slider is exatly the same as hanging K in the above equation. ow onsider the situation where we are looking at the histogram of a positive image, intending to move the highlights slider to apply a filter and/or a hange in overall illumination. This will multiply all the 's by a onstant fator. So again the ation of moving the highlights slider is to hange the K in the above equation. Whether we are working with the negative or the positive image, the ation of moving the highlights slider is to hange K, so filters an be applied to either the positive or the negative as is onvenient for the required numerial operations. ow we are equipped to experiment with a real photographi negative in hotoshop. The image for this experiment should ontain a gray sale and the same gray sale should be available for diret omparison. For the purpose of illustration, we used a very old test negative whih inluded the image of a Kodak test booklet whih we still have: We sanned the negative as a slide in raw mode using a Minolta Dimage San Multi RO film sanner and removed the orange mask as desribed above. We then used the hotoshop Curves tool to adjust the negative to math the positive. This was done using a visual omparison with the gray sale in the original book and also numerially against a positive san of the book produed by a Hewlett akard Sanjet 4670 flatbed sanner. The two methods produed very similar orretion urves and the omparison with the sanned image is shown below: 13

14 CFS This urve was determined using a C omputer whih has an operating display gamma of 2.2. That is, what is stored as the omputer image is "gamma adjusted" * K where The real p [ gamma gives a urve that looks like: * ] 1. Correting the above urve for this This urve an be losely mathed with 2.0 and K Table 3 below represents this real negative to positive inversion in the same format that we used above, going from sene to negative to positive. 14

15 CFS Table 3 From Sene through egative to ositive For 0.5, 2 and K L S * S [Y/Y n ] S d L * d [Y/Y n ] L * There is one area in whih Table 3 differs from the previous theoretial tables. Full representation of the deepest shadows in the sene requires negative densities that are less than zero, or 's that are greater than one. These are impossible requirements and thus this negative theoretially an not represent the deepest shadow detail - it is underexposed ositive Intensity Ratio versus egative Intensity Ratio For 0.5, 2 and K

16 CFS These tests above were done measuring and judging a gray sale in general. It is possible, of ourse, to do the same thing to the individual primaries, red, green, and blue, finding a separate value of and K for eah. In fat, there sometimes is an intentional manufaturing differene in the 's for eah olor. This an be measured if there are gray sale images for the partiular film type, and it an be visually estimated if several negatives of the film type are available for test, and it is found that, for example, the shadows run too blue in all of them while the highlights run too yellow. The K values will naturally tend to differ for the three olors, as the relative adjustment of the K's is the adjustment of overall olor balane. The Limits on K The above example shows that there are limits on the value of K. When K is outside these limits the negative image is either under- or overexposed and the resulting positive image will lak either shadow or highlight detail. These limits depend upon d max, the maximum density range expressible in the positive image, and d max, the maximum density range of whih the negative material is apable. The operating relationship is: K To represent the omplete density range of the positive image, at one limit the minimum expressible min 10 dpmax will orrespond to a density in the negative of zero, or 1. Thus: K max min 10 d max At the other extreme, the positive density of zero, or 1, must our at or above a negative density min 10 dnmax, so: K min 1 K min p min p pd min 10 max So for full range overage 10 pd min min max p K 10 d max ote that if 1 and d max d max there is only one value of K that works to give full range overage. ormally > 1, and enough greater than one that even though typially d max > d max, there remains a substantial range of values over whih K an range and still 16

17 CFS give full dynami range overage. For example, with 2, if we assume that d max d max 3, the approximate range represented by the CIE L* "lightness" funtion the mimis the behavior of the human eye, we find that the range is: whih is a substantial range of values K For some additional perspetive on this, the K for both Table 1 and Table 2 was , the high end of the range. In those tables the assumed d max was 2.95, just slightly shy of the 3 assumed in the above paragraph. Digital Limitations on K The negative to positive onversion involves taking a power, taking an inverse of that, and then taking that result to a power. While suh operations are trivial and quite preise on the double preision floating point digital arithmeti ommonly used on omputers, these same operations are problematial when using fixed point arithmeti of fairly low preision, as is ommonly the ase in working with digital images. Some problems remain even if the atual alulations are done preisely and the low preision fixed point is used only for image storage. The omplete transformation between negative and positive images is: * K where, the "gamma adjustment," is usually 0.45 for Cs and 0.56 for Mas. When working with negatives, the 's are typially stored in 16-bit unsigned integers, thus limited to integer values between 0 and ( 65535), where the integer is understood to be divided by to obtain. Eventually, the 's are usually onverted to 8-bit integers, limited to values between 0 and ( 255) where the integer is understood to be divided by 255 to obtain. Two different problems an our, for values near * 1 and for values near * 0. For the purposes here we will define j as the integer part of First, near * 1 (j * 65535) the possible values thin out. That is, two suessive integer values j and j + 1 will produe widely spaed values j * and j * m. To produe an image without visible "stair steps" in its tonal range, it is desirable that m 256 so that in the 8-bit version of *, all values 0 to 255 will be possible. To determine this, start with * K 17

18 CFS * p K The problem will our where * 1: 1 K p K 1 Find the rate of hange in * with respet to : d d * 1 p K substitute the value of where * 1, and the absolute value of that derivative must be less than 256; that is, 1 step in for must lead to no more than 1 step in 255 in * (whih is 256 steps in in *): 256 > 1 p + p K K 256 > K p < K 1 p 1 p K > 256 p For the values used above, 2 and 0.45, this gives K > , so that there might be stair-stepping in the highlights for a onversion toward the lower end of the range of K we gave for 2 example above. This situation should be rare, but might our for a very heavy negative. There appears to be no generalized remedy when it does our (beyond dithering, whih should be a last resort). Shadow Treatment, Low * The seond problem ours near * 0 (j * 0), where high values of annot possibly produe the lowest values of *. * K 18

19 CFS The highest possible value of is 1, so * min K Obviously, that annot be zero and to have j* min 1 (or * min 1/65535) would require that for the example K (1/65535) , whih is way out of the pratial range. For pratial purposes, as above, it would be desirable to have j* min 257 (or * min 1/255). Then K (1/255) , whih is still so low that it exludes most of the pratial range for the example ase. In fat, we find that at the upper end of the range in the example ase K whih leads to * min 11/255, so that there an be no detail in the deep shadows represented by the first 10 ounts in the range of an 8-bit image with a onversion K that large. In our underexposed test ase, we found that K , whih leads to * min 30/255, even worse. This an present a serious problem, sometimes making it impossible to get deep shadows from a negative. It should be pointed out in passing that most of this problem is due to * the "gamma orretion," that is,. In CFS-243, Maintaining Color Integrity in Digital hotography we mentioned that the "Levels" gamma orretion in hotoshop is inorret for gammas around the value of 0.45 (or 2.2 in hotoshop onvention), and we believe this error is really intended to be a makeshift orretion for the problem we are dealing with here. While there is no ompletely aurate solution to this problem when it ours, there is a pratial work-around. For the work-around, we will adjust instead of * in order to lessen the distortion of the olors in the shadows. This olor distortion effet is explained fully in CFS-243. We an adjust so that the minimum will be zero: * adj 1 min min ote that to use this form we must use min instead of * min in order to properly math. Thus if we hoose to take min where 1, then min K. In pratial terms, it often makes more sense to find from histogram data the max as the largest value for whih there is a signifiant ount of pixels. (Alternatively, above whih the ount of pixels is small enough to be ignored.) In doing this, it is well to remember that in this lightest area of the negative, a long range of brightnesses will represent just a short range of brightnesses in the darkest shadows of the positive, so a long span of nearly empty histogram ells is important to the shadow quality of the result. In any event, the relationship then beomes: min K max 19

20 CFS The key to the suess of this operation is to perform all the intermediate alulations in full double preision floating point arithmeti on the omputer and never store an intermediate integer value of j. That is, to perform the alulation as: * adj K K K 1 max max ote that in terms of omputer operations, one K,,, and max are known, a table orresponding to all possible values of an be formed and filled with the double preision omputed values of * adj, so that the atual onversion of an image file an be done using the resulting lookup table. Alternatively, an adjustment an be made that may be more aurate in terms of olor integrity (although preliminary testing suggests that the hanges in olor would be essentially invisible in most ases). First, for the largest omponent, "m" of R, G, B, (that is, the smallest q where "q" is the olor index) alulate: K K m m max adj K 1 m max ote that this is not gamma adjusted. Then, also alulate the unorreted values for eah omponent: q K q ote that although substitution tables are no longer possible, a set of four tables of double preision alulated values an be reated and used. So, for the predominant primary m, and for olor q, use: * q adj This alulation preserves the ratios between the olor omponents as they should be in the linear positive image, and thus is more aurate but slower to alulate. The entire alulation should be kept in double preision floating point until * for the final image is stored. q m 20

21 CFS Highlight Treatment, Low On most of the versus urves we have shown, at low, there is a onsiderable gap between the urve and the axis even when it reahes 1. It appears like this gap might represent onsiderable loss in highlight detail, but that is mostly an illusion. This area of the urve is where the negative is at its greatest density, and that will normally not be full-sale of the sanner. Thus no pixels will have intensities for the lowest values, and the "missing" values will not be a problem at all. The best approah is to find min from histogram data, the lowest for whih there is a signifiant pixel ount. The value of K an then be set to that 1 at this. K min This is the best starting value of K, and the minimum value whih will retain all the shadow detail. Final Summary The infamous "orange mask" that is so often blamed as the main soure of diffiulty in dealing with film negatives is atually very easily handled. The relationship between the positive and negative images is an inverse one: * K Here is the "gamma adjustment" that is typially applied to images stored in Cs, and the star notation means that the positive image * has been gamma adjusted. The real problem in dealing with negatives is in determining and K. should be nearly the same for all properly proessed olor negatives of a partiular film type, although may be different for eah of the three primary olors. It an be visually estimated by examining test images of a negative inverted to a positive, partiularly if several tests are made and ompared, but is more aurately estimated by omparison of an inverted image to a known final image. The orret estimation of is important to image olor integrity, sine this should be "mathed" to the of the negative to get the olors orret. The K regulates the overall lightness/darkness of the image. The best estimation or seletion of K varies from negative to negative, even of the same negative type. Color negatives typially are designed with < 1, whih gives them wider exposure latitude, and K is a measure of exposure. A starting value for K is K min, and there are numerous onstraints, adjustments, and alulation methods for K that arise from physial and numerial onsiderations. 21

22 CFS Sine olor negatives have a wide latitude, it will sometimes be that ase that final positive images are best made as omposites of two images derived using different K values. An example would be a landsape in whih the sky is bright enough to lak detail. The seond image would be darker, showing the sky detail. This is similar to the traditional photographi tehnique of "burning in" the sky working with a olor negative and an enlarger. Muh more detail is potentially available than would be available from digitally burning in the image from a single K onversion. For best results, separate values of should be obtained for eah of red, blue, and green, for a partiular film type, estimated from gray sale images if possible. Differing gammas for the separate olors an be visually estimated if several negatives of the film type are available for test, and it is found that, for example, the shadows run too blue in all of them while the highlights run too yellow. The K values for the three primaries will naturally tend to differ for the three olors, as the relative adjustment of the K's is the adjustment of olor balane. The method of onversion of negative to positive that is desribed here, inluding the use of the orret gammas, is neessary to preserve the olor integrity of the original negative (see CFS-243, Maintaining Color Integrity in Digital hotography for further elaboration of this problem). The result may have a tonal sale that needs improvement; often it will be too dark. A "urves" adjustment in 16-Bits/Channel mode ould ompress the highlights without losing detail. Sine at this point the olors should be orret or at worst out of olor balane in a way that an be adjusted by a olor orretion filter, the best method is to onvert the image to CIE Lab olor and adjust the Lightness urve in that mode to plae the tonal values where they are wanted. The image an then be onverted bak to RGB for further adjustment, inluding final olor balane. 22