Re: fine art reproduction questions
Re: fine art reproduction questions
- Subject: Re: fine art reproduction questions
- From: Robin Myers <email@hidden>
- Date: Fri, 7 May 2010 14:07:59 -0700
A very interesting description of a complex topic.
To me, the issue is not that HP may have a complex method of creating an ICC profile, but that alternative methods are being attempted and put forward for people to use. Standardization creates common interchange of information, but it can stifle creativity. I look forward to seeing other solutions to the color matching problem.
Robin Myers
On May 7, 2010, at 12:20 PM, Klaus Karcher wrote:
>>> Ben Goren wrote:
>>>> Any chance there's more information on the process somewhere?
>>>> Perhaps, say, enough for somebody to figure out a way of doing
>>>> the same basic thing manually?
>
>> Robin Myers wrote:
>>> HP has been very quiet with details of the process.
>
> I don't know much about the internals of the HP Artist solution as well, but let me try to conclude what's inside the "black HP box" from the inputs and outputs (A patent research might reveal more details as well, but I'm too lazy to do it).
>
> The inputs are:
>
> - the /spectral/ properties of the light source
> - the /spectral/ properties of the camera or scanner
> - the camera response (RGB image)
> - spectral data of at least 50 arbitrary measuring points of the original
>
> The "magic" part is that there has to be no relation between the measured spectra and their RGB values: you don't have to tell the software the /location/ of the measuring points and I suppose the software also does not try to locate corresponding RGB values. So at first sight the additional information is just a bunch of spectra /without/ corresponding device values.
>
> The output is an ordinary RGB image with an ordinary (image specific) ICC profile, i.e. device values and a "dictionary" or mathematical relation that permits to translate the device values into /colorimetric/ values.
>
> So the question is: how can one use this bunch of unrelated spectra to improve the colorimetric prediction accuracy of a spectrally characterized system?
>
> Before one can answer this question, one needs to understand what does it mean to have a spectrally characterized system. One way to regard spectral data is to treat every measured band as separate dimension. If we measure spectral data e.g. from 380 through 750nm in 10nm intervals, we can mark every measured spectrum as one vector in an 38-dimensional space. We can treat the R,G and B sensor of our camera (or scanner or colorimeter) as set of 3 vectors in this high-dimensional space and the sensitivities of the human (standard) observer as another set of vectors. The set of all possible device values of our camera spans a 3-dimensional subspace of our high-dimensional space and the set of sensations of the Standard Observer spans another subspace.
>
> If there exists a relation that maps (transforms) every possible device value into exactly one corresponding sensation (and hence also vice versa), our Camera is said to fulfill the Luther Condition and we are off the hook: We can use this transformation to translate the camera responses into human sensations. We've got a perfect camera as we can bring it to "see" exactly the same as we see.
>
> Unfortunately such a camera does not exist in real life.
>
> Let's get back to our high dimensional space: I already mentioned that the device values of an input device or the sensations of an observer can be regarded as lower-dimensional subspaces of our hyperspace. If we take an arbitrary spectrum (i.e. vector) our device response can be regarded as the /projection/ of this vector onto the devices subspace. As the dimensionality of our subspace is lower than the dimensionality of our spectral space, the projection is not invertible: Though we can map every spectrum to /one/ device value, there is an infinite number of spectral vectors that map to exactly the /same/ RGB vector. All this spectral vectors are metamers for this device (or observer) as they evoke exactly the same device response (or sensation) and there is no chance to find out which of the countless possible spectra caused a certain camera response.
>
> A good example for a projection onto a lower dimensional subspace might be a shadow theater: what we see is the projection of an three dimensional scene onto a two dimensional projection screen. We loose the information of the third dimension and when we see the shadow of an object we can only guess what's really behind the screen. Is the object that casts this shadow a real person or is it just a cardboard character? How tall is the object? How far is it away from our projection screen? What's its volume? In fact we can imagine an /infinite/ number of possible objects that project exactly the same shadow. This infinite set of possible objects /has to/ share some common properties (as all of them cast the same shadow onto our screen), but we are not able to define exactly what's behind the screen from the limited information we have.
>
> If we had a second screen (e.g a slightly curved screen at a different location), this screen might show different shadows for two objects we can't distinguish on our first screen (e.g the real person and the cardboard character), but there are also objects that look the same on the /second/ screen but are indistinguishable on the first. In other words: there is no unambiguous mapping between the shadows on our two screens as long as our information is limited to (two-dimensional) projections.
>
> Back to the spectral space: the projection of spectra onto a device's or observer's subspace is ambiguous. The set of spectra that causes the same device response (the metamer set) can be regarded as a cloud of points in spectral space. Every "metamer cloud" has an infinite number of points, but fortunately metamer sets have two nice properties: If the spread of our spectral space is finite, the clouds are always closed and convex. Ok, maybe one needs a certain affinity to mathematics to feel properties like closeness and convexity as nice ;-) but at least this properties are practical as on can e.g. border and locate such sets, calculate their volumes and intersections with others and so on. Another nice propertiy of these metamer clouds is: The more we can narrow down the set of /plausible/ input spectra, the smaller the metamer clouds will get.
>
> Another way of thinking about these clouds and spaces is: we are always loosing information if we project onto lower-dimensional subspaces. The more dimensions we loose, the more grave is the ambiguity we get. If there were a way to reduce the dimensionality of our input space, it would be easier to keep the projection "more unequivocal".
>
> The key to reduce the dimensionality as "gently" as possible is to "sort" the dimensions by importance and to leave of only less important dimensions. The mathematical method to transform data into "sorted" dimensions is called Principal Component Analysis (PCA) and I guess that HP uses exactly this method in the Artist solution: I suppose they use the bunch of measured spectra to derive a set of important basis functions. The basis functions are intended to explain typical spectral features of the original as good as possible and one can use this basis functions to refine the prediction model. There is still a huge loss of information, but if the basis functions are properly defined, the model is able to make a more "educated guess" abut the eligible spectra and hence tristimulus values that might have caused a certain device value: The relevant regions of the metameric sets can be narrowed down.
>
> But there are still remaining discrepancies between our perception and the device values. I.e. there are still situations where two spectra can result in the same device values but different perceptions or vice versa. No ICC profile can ever resolve these remaining discrepancies.
>
> And there's an additional catch: the selection of "important" basis functions tries to minimize /spectral/ errors. But to minimize a spectral error does not necessarily mean to minimize a cororimetric error as the correlation between spectral an colorimetric errors is anything but simple: tiny spectral errors can result in huge Delta E's and very dissimilar spectra can evoke nearly indistinguishable color sensations.
>
> The HP Artist solution is certainly suitable to improve the colorimetric accuracy of a camera or scanner, but it's not the magic answer to all problems. There might be less complex solutions with comparable or even better performance.
>
> Klaus Karcher
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