Now that we know how to create a 3×3 linear matrix to convert white balanced and demosaiced raw data into connection space – and where to obtain the 3×3 linear matrix to then convert it to a standard output color space like sRGB – we can take a closer look at the matrices and apply them to a real world capture chosen for its wide range of chromaticities.
We understand from the previous article that rendering color during raw conversion essentially means mapping raw data represented by RGB triplets into a standard color space via a Profile Connection Space in a two step process
The process I will use first white balances and demosaics the raw data, which at that stage we will refer to as , followed by converting it to Profile Connection Space through linear transformation by an unknown ‘Forward Matrix’ (as DNG calls it) of the form
Determining the nine coefficients of this matrix is the main subject of this article. Continue reading Color: Determining a Forward Matrix for Your Camera
How do we translate captured image information into a stimulus that will produce the appropriate perception of color? It’s actually not that complicated.
Recall from the introductory article that a photon absorbed by a cone type (, or ) in the fovea produces the same stimulus to the brain regardless of its wavelength. Take the example of the eye of an observer which focuses on the retina the image of a uniform object with a spectral photon distribution of 1000 photons/nm in the 400 to 720nm wavelength range and no photons outside of it.
Because the system is linear, cones in the foveola will weigh the incoming photons by their relative sensitivity (probability) functions and add the result up to produce a stimulus proportional to the area under the curves. For instance a cone will see about 321,000 photons arrive and produce a relative stimulus of about 94,700, the weighted area under the curve:
This article will set the stage for a discussion on how pleasing color is produced during raw conversion. The easiest way to understand how a camera captures and processes ‘color’ is to start with an example of how the human visual system does it.
An Example: Green
Light from the sun strikes leaves on a tree. The foliage of the tree absorbs some of the light and reflects the rest diffusely towards the eye of a human observer. The eye focuses the image of the foliage onto the retina at its back. Near the center of the retina there is a small circular area called the foveola which is dense with light receptors of well defined spectral sensitivities called cones. Information from the cones is pre-processed by neurons and carried by nerve fibers via the optic nerve to the brain where, after some additional psychovisual processing, we recognize the color of the foliage as green.
Ever since Einstein we’ve been able to say that humans ‘see’ because information about the scene is carried to the eyes by photons reflected by it. So when we talk about Information in photography we are referring to information about the energy and distribution of photons arriving from the scene. The more complete this information, the better we ‘see’. No photons = no information = no see; few photons = little information = see poorly = poor IQ; more photons = more information = see better = better IQ.
Sensors in digital cameras work similarly, their output ideally being the energy and location of every photon incident on them during Exposure. That’s the full information ideally required to recreate an exact image of the original scene for the human visual system, no more and no less. In practice however we lose some of this information along the way during sensing, so we need to settle for approximate location and energy – in the form of photoelectron counts by pixels of finite area, often correlated to a color filter array.
Equivalence – as we’ve discussed one of the fairest ways to compare the performance of two cameras of different physical formats, characteristics and specifications – essentially boils down to two simple realizations for digital photographers:
- metrics need to be expressed in units of picture height (or diagonal where the aspect ratio is significantly different) in order to easily compare performance with images displayed at the same size; and
- focal length changes proportionally to sensor size in order to capture identical scene content on a given sensor, all other things being equal.
The first realization should be intuitive (future post). The second one is the subject of this post: I will deal with it through a couple of geometrical diagrams.
You want to measure how sharp your camera/lens combination is to make sure it lives up to its specs. Or perhaps you’d like to compare how well one lens captures spatial resolution compared to another you own. Or perhaps again you are in the market for new equipment and would like to know what could be expected from the shortlist. Or an old faithful is not looking right and you’d like to check it out. So you decide to do some testing. Where to start? Continue reading How Sharp are my Camera and Lens?