Capturing Linear Images
01 July 2009
In a recent project, I had to capture and process linear images. In a linear
image, the value at every pixel is directly related to the number of photons
received at that location on the sensor. While most people do not have to worry
about linearity, and in fact, consumer cameras apply nonlinear response curves
to the captured data, scientists often derive relationships that assume
linearity. In this post, I describe several methods for achieving linear images
and describe a few pitfalls that I encountered while attempting to capture
linear images.
Most semi-professional and professional cameras allow the images to be stored in
a RAW format. This format encodes the sensor data before the in-camera
processing that is used to produce more familiar image formats, such as JPEG.
The RAW format has been called the digital equivalent of the negative and the
format allows a user to adjust parameters to produce a final image in the same
way that professional photographers would adjust their images using darkroom
techniques.
The RAW format is a linear image, but it is not the easiest format to work with
since it is specific to a camera manufacturer. In order to analyze RAW images in
mathematical software such as MATLAB, you must convert them to a more
common format. But depending on how you do the conversion, you may end up with
images that are not linear. For those who need linearity, I have documented
several workflows that preserve it. I also describe my methodology for checking
linearity.
Data capture
For all tests, I used a Munsell Neutral Value Scale, matte edition. The scale is
a fan deck with 31 patches of various shades of gray, shown on the left below.
Note that I am assuming that the lighting across the scale is uniform and that
the individual cards in the scale are lying flat. To analyze images of the
scale, I made a mask in Photoshop to sample a 64 x 64 section of
each patch. The mask is shown on the right below.
The Munsell scale has a reflectance percentage printed below each of the 31
patches. These values are:
| Patch | Reflectance | Patch | Reflectance | Patch | Reflectance |
|---|---|---|---|---|---|
| 1 | 3.1 | 12 | 17.6 | 23 | 50.7 |
| 2 | 3.8 | 13 | 19.8 | 24 | 54.8 |
| 3 | 4.6 | 14 | 22.1 | 25 | 59.1 |
| 4 | 5.5 | 15 | 24.6 | 26 | 63.6 |
| 5 | 6.6 | 16 | 27.2 | 27 | 68.4 |
| 6 | 7.7 | 17 | 30.0 | 28 | 73.4 |
| 7 | 9.0 | 18 | 33.0 | 29 | 78.7 |
| 8 | 10.4 | 19 | 36.2 | 30 | 84.2 |
| 9 | 12.0 | 20 | 39.5 | 31 | 90.0 |
| 10 | 13.7 | 21 | 43.1 | ||
| 11 | 15.6 | 22 | 46.8 |
I created the mask so that it would be simple to map the intensity value in the
mask to the reflectance value printed on the Munsell scale: the value of each
patch was 8 times the patch index. Therefore, I could divide the value in the
mask by 8 and use the result as an index into the reflectance table above. Note
that I configured Photoshop to use a linear colorspace when making the mask so
that the numerical values in the PNG file (as read in MATLAB) would be the same
values I specified in Photoshop (and not gamma-mapped in any way). The tutorial
I used to create a linear colorspace can be found
here.
Photoshop Camera RAW
Photoshop is able to load and process RAW images using the Camera RAW plugin
released in 2003. I loaded my RAW image (a Nikon NEF file) and saved it as a
16-bit PNG. I then loaded the image in MATLAB plotted the intensities at the
patches in the mask versus the known reflectances. The plot below shows that the
data stored in the PNG file is not linear, even though I used a linear tone
curve in the Camera RAW dialog and set all sliders in the Basic panel to 0. The
black dashed lines show the best linear fit to the data in each channel.
The problem was that the colorspace was set to sRGB in the Camera RAW workflow
(accessed by clicking the link at the bottom of the Camera RAW dialog). One
option is to change the image to 32 bits (Image→Mode→32 Bits/Channel) and save
as a 32-bit file type, such as OpenEXR. Another option is to convert the image
to a linear colorspace (Edit→Convert to Profile…), created according
to the instructions mentioned above, and then save the image as a PNG. When the
settings are correct, the plot of intensities versus reflectances should be
close to linear, as shown below.
dcraw
For those who do not own Photoshop, there is a free conversion utility known as
dcraw. I was able to convert the RAW
file to a linear image using the following options:
dcraw -v -4 -H 0 -W -w -q 3 file.nef
where file.nef is a Nikon RAW file. I also checked that these
options would yield linear images for Canon CRW files. The definitions of the
options can be found in the dcraw documentation, or in related tutorials, such
as this tutorial.
Photoshop Merge to HDR
One final method for capturing linear images is to photograph the scene at
several different exposures and merge the images into a high dynamic range (HDR)
image using Photoshop. This option is also useful if the scene luminance exceeds
the dynamic range of your camera (both dark blacks and bright highlights).
In Photoshop, the Merge to HDR option is available under File→Automate and you
select several files to be merged into a single image. I found that the 32-bit
HDR image could be saved as a 32-bit image and the resulting image was linear
when loaded in MATLAB.
Conclusions
If linearity is important to your project, I suggest verifying the linearity of
your entire workflow using the approach I described here. With several different
tools and file formats in the workflow, it is possible a gamma is being applied
at some point without you realizing it. For example in Photoshop, a pitfall
to be aware of is how colorspace settings can affect common image
operations. In the default colorspace, I found that operations such as grayscale
conversion (Image→Mode→Grayscale) and copy-paste (without explicitly setting
the colorspace) would affect the linearity of the image. For these reasons, I
suggest testing your entire workflow for linearity.