# Linear Color: Applying the Forward Matrix

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.

# Color: Determining a Forward Matrix for Your Camera

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

(1)

Determining the nine coefficients of this matrix is the main subject of this article[1]. Continue reading Color: Determining a Forward Matrix for Your Camera

# Color: From Capture to Eye

How do we translate captured image information into a stimulus that will produce the appropriate perception of color?  It’s actually not that complicated[1].

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[2].  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:

# An Introduction to Color in Digital Cameras

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[1].

# Linearity in the Frequency Domain

For the purposes of ‘sharpness’ spatial resolution measurement in photography  cameras can be considered shift-invariant, linear systems.

Shift invariant means that the imaging system should respond exactly the same way no matter where light from the scene falls on the sensing medium .  We know that in a strict sense this is not true because for instance a pixel has a square area so it cannot have an isotropic response by definition.  However when using the slanted edge method of linear spatial resolution measurement  we can effectively make it shift invariant by careful preparation of the testing setup.  For example the edges should be slanted no more than this and no less than that. Continue reading Linearity in the Frequency Domain

# Information Theory for Photographers

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 and Equivalent Image Quality: Signal

One of the fairest ways to compare the performance of two cameras of different physical characteristics and specifications is to ask a simple question: which photograph would look better if the cameras were set up side by side, captured identical scene content and their output were then displayed and viewed at the same size?

Achieving this set up and answering the question is anything but intuitive because many of the variables involved, like depth of field and sensor size, are not those we are used to dealing with when taking photographs.  In this post I would like to attack this problem by first estimating the output signal of different cameras when set up to capture Equivalent images.

It’s a bit long so I will give you the punch line first:  digital cameras of the same generation set up equivalently will typically generate more or less the same signal in independently of format.  Ignoring noise, lenses and aspect ratio for a moment and assuming the same camera gain and number of pixels, they will produce identical raw files. Continue reading Equivalence and Equivalent Image Quality: Signal

# Why Raw Sharpness IQ Measurements Are Better

Why Raw?  The question is whether one is interested in measuring the objective, quantitative spatial resolution capabilities of the hardware or whether instead one would prefer to measure the arbitrary, qualitatively perceived sharpening prowess of (in-camera or in-computer) processing software as it turns the capture into a pleasing final image.  Either is of course fine.

My take on this is that the better the IQ captured the better the final image will be after post processing.  In other words I am typically more interested in measuring the spatial resolution information produced by the hardware comfortable in the knowledge that if I’ve got good quality data to start with its appearance will only be improved in post by the judicious use of software.  By IQ here I mean objective, reproducible, measurable physical quantities representing the quality of the information captured by the hardware, ideally in scientific units.

Can we do that off a file rendered by a raw converter or, heaven forbid, a Jpeg?  Not quite, especially if the objective is measuring IQ. Continue reading Why Raw Sharpness IQ Measurements Are Better

# How Sharp are my Camera and Lens?

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?

# I See Banding in the Sky. Is my Camera Faulty?

This is a recurring nightmare for a new photographer: they head out with their brand new state-of-the art digital camera, capture a set of images with a vast expanse of sky or smoothly changing background, come home, fire them up on their computer, play with a few sliders and … gasp! … there are visible bands (posterization, stairstepping, quantization) all over the smoothly changing gradient.  ‘Is my new camera broken?!’, they wonder in horror.

Relax, chances are very (very) good that the camera is fine.  I am going to show you in this post how to make sure that that is indeed the case and hone in on the real culprit(s). Continue reading I See Banding in the Sky. Is my Camera Faulty?