Investigating the possibility of using fewer training samples
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Qu, Yuanyuan
Gooran, Sasan
The goal of the present work is to reduce the number of the training samples used in our color prediction model based on CIEXYZ using an Effective Coverage Map while keeping satisfying prediction. A general approach is proposed in this paper to choose the best reference combination for the training samples. The approach is based on the dot gain behavior of each primary ink, which is characterized by three curves using CIEXYZ tri-stimulus values. The proposed approach is built in our model to predict the color values for the color prints using two different devices, i.e. a laser printer and an inkjet printer. For the laser printer the number of the training samples is reduced from 125 to 64 while still giving quite good result. The approach also shows that for the test laser printer it is possible to further cut this number to 53 with a satisfying result. For the inkjet printer the number of training samples for our model is reduced from 125 to 79 or 64, both giving satisfying results.
 Thank you. Thank you for your introduction. My name is Yuan Yuan-chui. The co-author of this presentation is my supervisor, Sun Sun Goran. Unfortunately, he cannot come this time. I'm going to present our work about using fewer training samples in the color prediction model. Before I start, please allow me to briefly remind you what a color prediction model does. It is like a black box for any kind of print device. It lends the combined property of the ink, paper, print, enumeration, half toning, and so on, and to predict the printed color according to any given reference ink compilation. The full title of this, as well as the main work of this presentation is investigating the possibility of using fewer training samples in the color prediction model based on CIE XYZ venues using an effective coverage map while keeping satisfying prediction results. As you see, the highlighted phrases are the keywords of this work, as well as the outline in my presentation. Before I go to introduce the proposal we used to reduce the number of the training samples, it is necessary to introduce the color prediction model based on the XYZ venues that we used, as well as the effective coverage map used in this work. About the color prediction model, the most famous and almost simplest model is Mordewis model. My colleague Daniel has already introduced this model very well, but I want to add that pay attention that in Mordewis model it assumes that the inks and all the materials should be ideal, which means, for example, the spectrum of the yarn should be exactly as the solid yarn line showed in this figure, but in reality the materials are never ideal, and we know that during the printing the dot gain exists all the time. Assume we have a color patch with only 30% yarn, and according to the Mordewis model, the calculates vector reflectance is the right one. We can say that it is far away from the ring one, which is the real measured data. Consider the dot gain, roughly we increase the fractional coverage of the yarn step by step to 0.6. We can say by each changing the curve gets closer to the measured one, but level overlap. You and Nielsen's research on the ink penetration and the late scattering showed that the relationship between the spectrum of the color patch and the spectrum of the ink and the paper, they are nonlinear and it can be described using this power function. The N pyramid is the N factor. By optimization, we find the closest curve to the measured one as the radical. This is roughly the optical dot gain and the physical dot gain. But in our opinion, actually during the measurements of the color patch, there is having both optical dot gain and physical dot gain included in the data. For example, if we print 11 seagull patch with their reference coverage ranging from 0 to 1, we measure the XYZ venues and use the Mordewis model, we can calculate three different effective coverage for each sample for each amount of seagull. We can say clearly that we plot the three groups of data in this figure. This red one is based on CIEX venues with this venue and the green one is based on Y venue, blue one is based on Z venue. This green curve is an optimized curve. We can say clearly that they are quite different from each other. So it might be not completely correct to use single dot curve for each ink. Therefore, we think about using all of those three curves instead of single dot gain curve. Actually, this proposal works well especially for print colors involving only one ink. More details and results refer to the reference list on the bottom. Actually, according to the experiments, we find that the dot gain behavior of each ink actually changed without any rules when the ink superposition happens. For example, if we have 30% seagull actually printed on paper, actually the dot gain behavior of this amount of seagull is different from that when it is printed together with magenta or yellow or both. In this situation, the effective coverage map was proposed. Imagine that there is a coordinate system whose three axis refer to the three primary inks, seagull, magenta, and yellow. If we apply 0, 25, 50, 75, and 100% as the reference coverage for the three primary inks, then we can get 125 points located especially even in this coordinate system. The map is created by filling with each point with effective coverage of the three primary inks based on CA XYZ venues respectively. Like this simple point, it contains full yellow and seagull. Obviously, it's effective coverage for seagull and yellow equal to zero no matter which data you use but zero for magenta. As soon as all of these points are filled with those venues, suitable venues for each one, given any reference coverage, we can calculate the effective coverage of the involved ink by interpellation, cubic interpellation. Then, Damichur's equations are used to calculate the effective fractional coverage for each primary and secondary colors. Then, we use the extended Damichur equation to calculate the XYZ venues of the color patch. About how to create this effective coverage map, it is introduced in the coming volume of the general of image science and technology. But a brief introduction is given here. We start with the situation when the color patch contains only two inks. For example, cyan and magenta, we call it effective coverage grade. Because the calculation based on X venue, Y venue and Z venue are similar, so here we only use the X venue to illustrate. We can say in this grade that the points marked by the blue star and the step one, actually, they are color patch involving only one ink. So their effective coverage can be easily calculated using this equation. As soon as they are filled, those blue points, which marked by step two, then they can be filled using the venues come from their neighbors. The purpose of this is that neighbors have close effective coverage for the same ink they are taking with. As soon as those points are filled, we can go to those points marked by step three and step four. About the color patch involves three inks, actually, we calculate using those three effective coverage grade. You can see we can get three groups of possible effective coverage venues. By matching and optimization, finally, we can fill all the points in the map with effective coverage venues for three primary inks based on CIE XYZ venues, respectively. As I mentioned before, if we use this theory of venues to be the reference coverage for CIE and magenta yellow respectively, then we need 125 samples to build this map. So we think about, can we reduce the number of the training samples while keeping satisfying prediction? Actually, choosing the training samples is a kind of work, is a same work to choose the combination of, combination of reference coverage of these three inks. So we start, we begin with trying to, yeah, we start with trying to kick out or change few venues in this area. For example, take Siam, for example, again, we prepare nine Siam patches, their reference coverage is like this one, like this area. And we can, we close their dot gain curves based on CIE XYZ venues, respectively. Here, we use the three, sorry, we use the two print devices. One is laser printer with A4 uncoated paper, and the other one is inkjet printer with photo quality paper. We can say that for the laser printer, the dot gain of Siam, all the three curves is symmetrical, but for the inkjet printer, the peaks look moved left a little bit. So how about use this area for Siam instead of this one and for laser printer? And how about use this one instead of that one for inkjet printer? So we did the same proceeding for Magenta and Yellow respectively. And we almost go through all the possible theories for Siam, Magenta and Yellow respectively and make sure the elements in this area less than four elements, sorry, less than five elements. Then according to the performance of the prediction of single ink printing, we find the suggested reference coverage for Siam, Magenta and Yellow. For example, for laser printer for Siam, the suggested reference coverage is this one and for Magenta is that one, for Yellow is that one, and for inkjet printer, we also get three suggested reference coverage for Siam, Magenta and Yellow respectively. Using our model and apply the suggested reference coverage, we calculate the prediction results and list them on the first column in this table. Compare with the results that we got when using previously reference coverage, we can say they are not bad actually, both for laser printer and inkjet printer. We also tried other interesting reference combination. For example, we use this one for Magenta instead of the suggested one. We still got good results, it's okay. But for inkjet printer, if you notice that actually the choice of the reference coverage for Magenta affected the prediction of Magenta quite much. We tried to use this one instead of that one and you can see the results goes worse. So here we come to the conclusion. For the laser printer, the number of samples was reduced from 125 to 64, we are still getting quite good results. It is possible to cut this number further to 53 with satisfying results. For the inkjet print, it is reduced from 125 to 17 like or 64, both giving satisfying results. Our approach would be useful for building an automatic computer to plate calibration system in printing workflow. So thank you for your attention. Thank you very much. Any questions? Thank you for this presentation. Very interesting work. I was asking, I didn't really understand if you make spectral measurements or if it's enough to do XYZ measurements. I'd love to use only say XYZ values. Okay, so that's a very strong point because you can make kind of sensors from which you compute XYZ and that makes the whole thing much simpler. Maybe this should be stressed in your presentation. That's a big progress. Thank you very much. Any more questions? No? Well, thank you very much. Thank you. Thank you.
 Thank you. Thank you for your introduction. My name is Yuan Yuan-chui. The co-author of  this presentation is my supervisor, Sun Sun Goran. Unfortunately, he cannot come this  time. I'm going to present our work about using fewer training samples in the color  prediction model. Before I start, please allow me to briefly remind you what a color prediction  model does. It is like a black box for any kind of print device. It lends the combined  property of the ink, paper, print, enumeration, half toning, and so on, and to predict the  printed color according to any given reference ink compilation.  The full title of this, as well as the main work of this presentation is investigating  the possibility of using fewer training samples in the color prediction model based on CIE  XYZ venues using an effective coverage map while keeping satisfying prediction results.  As you see, the highlighted phrases are the keywords of this work, as well as the outline  in my presentation. Before I go to introduce the proposal we used to reduce the number  of the training samples, it is necessary to introduce the color prediction model based  on the XYZ venues that we used, as well as the effective coverage map used in this work.  About the color prediction model, the most famous and almost simplest model is Mordewis  model. My colleague Daniel has already introduced this model very well, but I want to add that  pay attention that in Mordewis model it assumes that the inks and all the materials should  be ideal, which means, for example, the spectrum of the yarn should be exactly as the solid  yarn line showed in this figure, but in reality the materials are never ideal, and we know  that during the printing the dot gain exists all the time.  Assume we have a color patch with only 30% yarn, and according to the Mordewis model,  the calculates vector reflectance is the right one. We can say that it is far away from the  ring one, which is the real measured data. Consider the dot gain, roughly we increase  the fractional coverage of the yarn step by step to 0.6. We can say by each changing the  curve gets closer to the measured one, but level overlap.  You and Nielsen's research on the ink penetration and the late scattering showed that the relationship  between the spectrum of the color patch and the spectrum of the ink and the paper, they  are nonlinear and it can be described using this power function. The N pyramid is the  N factor. By optimization, we find the closest curve to the measured one as the radical.  This is roughly the optical dot gain and the physical dot gain.  But in our opinion, actually during the measurements of the color patch, there is having both optical  dot gain and physical dot gain included in the data. For example, if we print 11 seagull  patch with their reference coverage ranging from 0 to 1, we measure the XYZ venues and  use the Mordewis model, we can calculate three different effective coverage for each  sample for each amount of seagull. We can say clearly that we plot the three groups  of data in this figure. This red one is based on CIEX venues with this venue and the green  one is based on Y venue, blue one is based on Z venue. This green curve is an optimized  curve. We can say clearly that they are quite different from each other. So it might be  not completely correct to use single dot curve for each ink. Therefore, we think about  using all of those three curves instead of single dot gain curve. Actually, this proposal  works well especially for print colors involving only one ink. More details and results refer  to the reference list on the bottom. Actually, according to the experiments, we find that  the dot gain behavior of each ink actually changed without any rules when the ink superposition  happens. For example, if we have 30% seagull actually printed on paper, actually the dot  gain behavior of this amount of seagull is different from that when it is printed together  with magenta or yellow or both. In this situation, the effective coverage map was proposed.  Imagine that there is a coordinate system whose three axis refer to the three primary  inks, seagull, magenta, and yellow. If we apply 0, 25, 50, 75, and 100% as the reference  coverage for the three primary inks, then we can get 125 points located especially even  in this coordinate system. The map is created by filling with each point with effective  coverage of the three primary inks based on CA XYZ venues respectively. Like this simple  point, it contains full yellow and seagull. Obviously, it's effective coverage for seagull  and yellow equal to zero no matter which data you use but zero for magenta. As soon as all  of these points are filled with those venues, suitable venues for each one, given any reference  coverage, we can calculate the effective coverage of the involved ink by interpellation, cubic  interpellation. Then, Damichur's equations are used to calculate the effective fractional  coverage for each primary and secondary colors. Then, we use the extended Damichur equation  to calculate the XYZ venues of the color patch. About how to create this effective  coverage map, it is introduced in the coming volume of the general of image science and  technology. But a brief introduction is given here. We start with the situation when the  color patch contains only two inks. For example, cyan and magenta, we call it effective coverage  grade. Because the calculation based on X venue, Y venue and Z venue are similar, so  here we only use the X venue to illustrate. We can say in this grade that the points marked  by the blue star and the step one, actually, they are color patch involving only one ink.  So their effective coverage can be easily calculated using this equation. As soon as  they are filled, those blue points, which marked by step two, then they can be filled  using the venues come from their neighbors. The purpose of this is that neighbors have  close effective coverage for the same ink they are taking with. As soon as those points  are filled, we can go to those points marked by step three and step four. About the color  patch involves three inks, actually, we calculate using those three effective coverage grade.  You can see we can get three groups of possible effective coverage venues. By matching and  optimization, finally, we can fill all the points in the map with effective coverage  venues for three primary inks based on CIE XYZ venues, respectively. As I mentioned before,  if we use this theory of venues to be the reference coverage for CIE and magenta yellow  respectively, then we need 125 samples to build this map. So we think about, can we  reduce the number of the training samples while keeping satisfying prediction? Actually,  choosing the training samples is a kind of work, is a same work to choose the combination  of, combination of reference coverage of these three inks. So we start, we begin with trying  to, yeah, we start with trying to kick out or change few venues in this area. For example,  take Siam, for example, again, we prepare nine Siam patches, their reference coverage  is like this one, like this area. And we can, we close their dot gain curves based on CIE  XYZ venues, respectively. Here, we use the three, sorry, we use the two print devices.  One is laser printer with A4 uncoated paper, and the other one is inkjet printer with photo  quality paper. We can say that for the laser printer, the dot gain of Siam, all the three  curves is symmetrical, but for the inkjet printer, the peaks look moved left a little  bit. So how about use this area for Siam instead of this one and for laser printer? And how  about use this one instead of that one for inkjet printer? So we did the same proceeding  for Magenta and Yellow respectively. And we almost go through all the possible theories  for Siam, Magenta and Yellow respectively and make sure the elements in this area less  than four elements, sorry, less than five elements. Then according to the performance  of the prediction of single ink printing, we find the suggested reference coverage for  Siam, Magenta and Yellow. For example, for laser printer for Siam, the suggested reference  coverage is this one and for Magenta is that one, for Yellow is that one, and for inkjet  printer, we also get three suggested reference coverage for Siam, Magenta and Yellow respectively.  Using our model and apply the suggested reference coverage, we calculate the prediction results  and list them on the first column in this table. Compare with the results that we got  when using previously reference coverage, we can say they are not bad actually, both  for laser printer and inkjet printer. We also tried other interesting reference combination.  For example, we use this one for Magenta instead of the suggested one. We still got good results,  it's okay. But for inkjet printer, if you notice that actually the choice of the reference  coverage for Magenta affected the prediction of Magenta quite much. We tried to use this  one instead of that one and you can see the results goes worse. So here we come to the  conclusion. For the laser printer, the number of samples was reduced from 125 to 64, we are  still getting quite good results. It is possible to cut this number further to 53 with satisfying  results. For the inkjet print, it is reduced from 125 to 17 like or 64, both giving satisfying  results. Our approach would be useful for building an automatic computer to plate calibration  system in printing workflow. So thank you for your attention.  Thank you very much. Any questions?  Thank you for this presentation. Very interesting work. I was asking, I didn't really understand  if you make spectral measurements or if it's enough to do XYZ measurements. I'd love to  use only say XYZ values. Okay, so that's a very strong point because  you can make kind of sensors from which you compute XYZ and that makes the whole thing  much simpler. Maybe this should be stressed in your presentation. That's a big progress.  Thank you very much. Any more questions? No? Well, thank you very much.  Thank you.  Thank you.
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