Tuesday, 6 January 2015

Forensics : Gaussian Analysis - Underexposure

Scope and Objective
In An Introduction to Gaussian Analysis (HERE) I outlined how most image quality parameters exhibit a Gaussian distribution around an optimum quality standard.  This presents an opportunity to look for 'Gaussian Signatures' left behind in digital images.  Here I am analysing Gaussian signatures for underexposure.  I am looking for evidence that would indicate if data (eg. subtle field marks) may have been lost due to underexposure in an image.  I am also looking to prove the opposite - in the absence of a Gaussian signature for underexposure is it reasonable to assume that there is no loss of detail due to underexposure clipping?

The Gaussian Signatures for Underexposure
Just like overexposure, underexposure works rather like an image brightening tool and has the effect of pushing the histogram to the left (for more on histograms see HERE).  However, unlike a brightening tool which stacks detail up on the side of the histogram, underexposure, like a conveyor belt, simply pushes tonal data off the edge of the histogram (clipping).

Once again, as with overexposure, progressive underexposure causes image fine details and colours to simply vanish.  Before detail vanishes it will get progressively darker and approaches pure black in colour (sRBG R=0, G=0, B=0).  This becomes a Gaussian signature for underexposure.

However probably a far more recognisable signature for underexposure is Image Noise.  Noise can obscure fine colour and detail long before these are clipped.  There are different types of image noise as neatly outlined HERE and HERE, but typically noise is expressed in terms of Luminance noise (fluctuations in the darkness of pixels) and Chroma noise (fluctuations in the hue and saturation of pixels)   Noise is quantified in terms of a signal to noise ratio (SNR).

ISO and Noise Reduction Software
ISO is a measure of the relative sensitivity of a photographic film or image sensor to light.  It is often considered part of the exposure triangle with shutter speed and aperture.  However, ISO in digital cameras is created by amplifying an image after the exposure is made, not during image exposure.  So, in reality ISO is distinct from exposure.  Modern digital cameras exhibit incredible ISO range.  This is due mainly to the sophistication of image amplification and noise reduction software.  As the name implies, the reduction or elimination of noise involves image manipulation, so it may have the effect of masking image detail.  So it would be advisable to pay attention to the ISO of an image.  A modern camera may not suffer quite as badly from underexposure but the trade-off could be that the image has has been over-processed by the camera instead.  That said, at lower ISOs, modern cameras far exceed and produce far more accurate results than their predecessors.  It is only at really high ISOs that we need to be more mindful of this problem.  Take for example the image below.  The Nikon Coolpix 4500 was a brilliant digiscoping camera in it's day but it's image quality is relatively poor compared with modern compact digital cameras.

Note how the level of noise is proportional to the darkness of the objects being photographed.  The darker head, neck and breast is very noisy because there is very little light from these areas, reaching the sensor.  There is slightly less noise on the dark grey mantle and less again in the paler grey portion of the bill, grey flank and on on the water.  Finally we see virtually no noise at all in the white areas of the bill and breast side.  So, provided a certain threshold of light reaches the sensor the noise problem is sorted.  It is also true to say that it is possible to have patches of underexposure, normal exposure and indeed overexposure, all within the same image.

Gamma or rather Gamma Correction is of particular relevance to this discussion.  The human visual system does not discriminate between increments of brightness in a linear fashion.  Our eyes are better able to distinguish between small changes in luminance within shadows and midtones in a scene.  In the highlights, or brighter areas of a scene our eyes can only distinguish between larger incremental changes in light intensity.  This attribute partly explains why human vision has such as broad dynamic range when compared to a camera.  Gamma correction is a correction made by an image processor to transform an image from a linear luminance distribution to one that matches the human visual system.  Display devices may also have their own additional gamma correction to cancel any non-linear properties they may have be it a CRT or LCD screen.  A consequence of this is that image detail can be lost within the highlights but an advantage is that there tends to be a greater range of tones preserved in the shadows and midtones.  Automatic camera exposure tends to compensate for this by tending towards underexposure rather than overexposure in an image.  As we can see from the example above however, excessive underexposure does nothing for an image.

Underexposure is a common image quality complaint, especially when we consider the challenging conditions under which many bird images are taken.  Whereas overexposed images can be analysed for clipping, image noise often tends to be a more significant issue than clipping within underexposed images - image detail and colour is often obscured by noise long before it is ever clipped.  It helps to get the know the typical noise signature of ones own camera and to pay attention to ISO ratings and the possible overuse of noise reduction software when analysing potentially underexposed images.  If an image is well exposed with little or no noise evident we have the best conditions possible for capturing accurate details and colours.  In contrast, when we have noisy, underexposed images we always need to consider that colours and fine details may have been obscured.

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