Thursday, 8 February 2018

Device profile support

From version 0.6.16 onwards, MTF Mapper now supports device profiles embedded in input image files. If you normally feed MTF Mapper with raw camera files (via the GUI), then this new feature will not affect you in any way.

If you have been feeding MTF Mapper with JPEG files, or perhaps TIFF files produced by your preferred raw converter, then this new feature could have a meaningful impact on your results. You can jump ahead to the section on backwards compatibility if you want the low-down.

To explain what device profiles are, and why they affect MTF Mapper, I first have to explain what linear light is.

Linear light

At the sensor level we can assume that both CCD and CMOS sensors have a linear response, meaning that a linear increase in the amount of light falling on the sensor will produce a linear increase in the digital numbers (DNs) we read from the sensor. This is true up to the point where the sensor starts to saturate, where the response is likely to become noticeably non-linear.

The slanted-edge method at the heart of MTF Mapper expects that the image intensity values (DNs) are linear. If your intensity values are not linear, then the resulting SFR you produce using the slanted-edge method is incorrect.

Gamma and Tone Reproduction Curves

Rather than exploring the history of gamma correction in great detail, I'll try to summarize: Back in the day of Cathode Ray Tube (CRT) displays they found that a linear change in the signal (voltage) sent to the tube did not produce a linear change in the display brightness. If you were to produce a graph of the input signal vs brightness, you would obtain something that looks like this:
Figure 1: A non-linear display response
If you fast-forward to the digital era, you can see how this non-linearity in the brightness response can become rather tiresome if you want to display, say, a grayscale image. If you took a linear light image from a CCD sensor, which we assume produced linear values in the range 0 to 255, and put that in the display adaptor frame buffer, then your image would appear to be too dark. The solution was to pre-distort the image with the inverse of the non-linear response of the display, i.e., using this function:
Figure 2: The inverse of Figure 1
If you take a linear signal and apply the inverse curve of Figure 2, then take the result and apply the non-linear display response curve of Figure 1, you end up with a linear signal again. The process of pre-distorting the digital image intensity values to compensate for the non-linear display response is called gamma correction.

This scheme worked well enough when you knew what the approximate non-linear display response was: on PCs the curve could be approximated as f(x) = x2.2. Things became a lot more complicated when you wanted to display an image on different platforms, for example, early Macintosh systems were characterized by a gamma of 1.8, i.e., f(x) = x1.8.

The solution the platform interoperability problem was to attach some metadata to your image to clearly state whether the digital numbers were referring to linear light intensity values, or whether they were pre-distorted non-linear values chosen to produce a perceived linear brightness image on a display. So how do you specify what your actual image represents? Do you specify the properties of the non-linear pre-distortion you applied to produce the values found in the image file, or do you instead specify the properties of the display device for which you image has been corrected? It turns out that both strategies were followed, with the PNG specification choosing the former, and most of the other formats (including ICC profiles) choosing the latter.

To cut to the chase: One important component of a device profile is its Tone Reproduction Curve (TRC); Figure 1 can be considered to be a TRC of our hypothetical CRT display device. Depending on the metadata format, you can either provide a single gamma parameter (γ) to describe the TRC as f(x) = xγ, or you can provide a look-up table to describe the TRC.

Colour spaces

The other component of a device profile that potentially has an impact on how MTF Mapper operates is the definition of the colour space. The colour space matters because MTF Mapper transforms an RGB input image to a luminance image automatically. The main reason for this is that the slanted-edge method does not naturally apply to colour images; you have to choose to either apply it to each of the R, G and B channels separately, or you have to synthesize a single grayscale image from the colour channels. For MTF Mapper I chose the luminance (Y) component of the image, as represented in the CIE XYZ colour space, because this luminance component should correlate well with how our human vision system perceives detail.

So what is a colour space? To keep the explanation simple(r), I will just consider tristimulus colour spaces; in practice, those that describe a colour as a combination of three primary colours such as RGB (Red, Green, and Blue). Now consider the digital numbers associated with a given pixel in a linear 8-bit RGB colour space, e.g., (0, 255, 0) would represent a green pixel. Sounds straightforwards, right? The catch is that we have not defined what we mean by "green". Two common RGB colour spaces that we encounter are sRGB and Adobe RGB; they have slightly different TRCs, but here we focus on their colour spaces. The difference between sRGB and Adobe RGB is that they (literally) have different definitions of the colour "green": Our "green" pixel with linear RGB values (0, 255, 0) in the sRGB colour space would have the values (73, 255, 10) in the linear Adobe RGB colour space because the Adobe RGB colour space uses a different green primary compared to sRGB. Note that the actual colour we wanted has not changed, but the internal representation has changed.

The nub of the matter is that our image file may contain the value (0, 255, 0), but we only really know what colour that refers to once we know in which colour space we are working. I hope you can see the parallel to the TRC discussion above: the image file contains some numbers, but we really do have to know how to interpret these numbers if we want consistent results.

ICC profiles

A valid ICC profile always contains both the TRC information and the colour space information that MTF Mapper requires to produce a linear luminance grayscale image. In fact, the ICC profile contains the matrix that tells use how to transform linear RGB values into CIE XYZ values adapted for D50 illumination (that is very convenient if you do not want to get into chromatic adaptation).

So if you provide MTF Mapper with a TIFF, PNG* or JPEG file with an embedded ICC profile, you can be sure that the resulting synthesized grayscale image will be essentially identical regardless of which colour profile you saved your image in.
*MTF Mapper 0.6.17 and later.

JPEG/Exif files

If your JPEG file has no ICC profile, and no Exif metadata, then MTF Mapper will just assume that your image is encoded in the sRGB profile. Most cameras appear to at least add Exif metadata, but that only helps a little bit, since the Exif standard only really has a definitive way of indicating that the image is encoded in an sRGB profile. If your JPEG file is encoded in the Adobe RGB space (most DSLRs allow you to configure the JPEG output this way), then MTF Mapper will try to infer this from the clues in the Exif data. 

MTF Mapper will use the appropriate TRC (either sRGB, or Adobe RGB), and the appropriate D50-adapted RGB-to-XYZ matrix will be selected for the luminance conversion.

Backwards compatibility (or the lack thereof)

Unfortunately the addition of device profile support has encouraged me to change the way in which JPEG files are converted to grayscale luminance images. In MTF Mapper version 0.6.14 and earlier, the JPEG RGB-to-YCrCb conversion was used to obtain a luminance image; from version 0.6.16 onwards the device profile conversion is used. In practice, this means that older versions would use
Y = 0.299R + 0.587G + 0.114B
regardless of whether the JPEG file was encoded in sRGB or Adobe RGB, which is clearly incorrect in the case of Adobe RGB files (regardless of the TRC differences). A typical weighting for an sRGB profile in version 0.6.16 and later would be
Y = 0.223R + 0.717G + 0.061B.

The practical implication is that results derived from JPEG files will be different between versions <= 0.6.14 and 0.6.16 and later. Figure 3 illustrates this difference on a sample sRGB JPEG file. To make matters worse, the difference will be exacerbated by lenses with significant chromatic aberration because the relative weight of the RGB channels have changed.
Figure 3: SFR difference on the same edge of a JPEG image (Green is v0.6.14, Blue is v0.6.16)
In Figure 3 the difference is small, but noticeable. For example, when rounded to two decimal places this edge will display as an MTF50 of 0.19 c/p on version 0.6.16, but 0.20 c/p on version 0.6.14. I expect that there will be examples out there that will exhibit larger differences than what we see here, but I do not expect to see completely different SFR curves.

More importantly, MTF Mapper's behaviour regarding TIFF files has changed. In version 0.6.14 and earlier, all 8-bit input images were treated as if they were encoded in the sRGB profile; this probably produced the desired behaviour most of the time. If, however, a 16-bit TIFF file is used as input in version 0.6.14 and earlier, then MTF Mapper assumed the file contained linearly coded intensity values (i.e., gamma = 1.0). This behaviour worked fine if you used "dcraw -4 ..." to produce the TIFF (or .ppm) file, but would not work on 16-bit TIFF files produced by most raw converters or image editors. From version 0.6.16 onwards all TIFF files with embedded ICC profiles will work correctly, whether they are encoded in linear, sRGB, Adobe RGB or ProPhoto profiles. Figure 4 illustrates the difference on a 16-bit sRGB encoded TIFF file.
Figure 4: SFR difference on the same edge of a 16-bit sRGB TIFF image (Green is v0.6.14, Blue is v0.6.16)

In Figure 4 we see much larger differences between the SFR curves produced by versions 0.6.14 and 0.6.16; this larger difference is because 0.6.14 incorrectly interpreted the sRGB encoded (roughly gamma = 2.2) values as if they were linear.

One last important rule: MTF Mapper version 0.6.16 still interprets all other 16-bit input files without ICC profiles (PNG, PPM) as if they have a linear (gamma = 1.0) encoding.

Summary recommendations

Overall, you should now be able to obtain more consistent results with MTF Mapper now that it supports embedded device profiles. For best results, choose to embed an ICC profile if your raw converter or image editor supports it. Given a choice, I still recommend using raw camera files directly with the GUI, or doing the raw conversion using "dcraw -4 -T ..." to convert your raw files if you use the command-line interface.

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