Forensics : Gaussian Analysis - Overexposure

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 the Gaussian signature for overexposure.  I am looking for evidence that would indicate if data (eg. subtle field marks) may have been lost due to overexposure in an image.  I am also looking to prove the opposite - in the absence of a Gaussian signature for overexposure is it reasonable to assume that there is no loss of detail due to overexposure clipping?

The Gaussian Signature for Overexposure

Overexposure works rather like an image brightening tool and has the effect of pushing the histogram to the right (for more on histograms see HERE).  However, unlike a brightening tool which stacks detail up on the right hand side of the histogram, overexposure, like a conveyor belt, simply pushes tonal data off the edge of the histogram (clipping).  Progressive overexposure causes image fine details and colours to simply vanish.  Before detail vanishes it will get progressively paler and approaches pure white in colour (sRBG R=255, G=255, B=255).  This becomes the Gaussian signature for overexposure.

In the experiment above I have highlighted the Gaussian signature of overexposure in blue.  Before our target vanishes it is consumed by sRGB white.  I equate the signature to an Amoeba devouring a food item, or a flood submerging objects throughout an environment.  There are two useful conclusions.

(1) It is always worth checking images for blown highlights (generally anything above level 250 might be considered a blown highlight).  Blown highlights indicate overexposure and may indicate masked detail.  Bare in mind though that detail will not clip evenly in all channels.  Blue and Red channels may be clipped (level 255) but Green may still harbour a ghost impression of the detail (level <255).

(2) Having identified blown highlights it is worth analysing the distribution of sRGB pure white.  This is the proper clipping line (all channels at level 255).  The presence of sRGB white indicates clipping - image detail has been lost beyond this point.  The absence of sRGB white should indicate that clipping has NOT taken place in the image, so the remnants of fine detail and colour should be present, if somewhat masked and hard to discern.  Refer to postings HERE and HERE for tips on how to recover hidden image data from RAW and JPEG images respectively.

The Plan

Here is my proposed recipe for analysing the Gaussian Signature of Overexposure.

Step 1 Careful Review of the Images

Once again it helps to carefully review all the images first.  Look for lighting and exposure patterns and document.

Step 2 Analyse clipping

HERE I outlined how image histograms can be used to analyse clipping.  I recommend the Adobe Elements Levels tool.  By selecting the white dropper tool in Levels and by pressing the Alt key while the dropper is over the image the tool will automatically highlight the clipped areas of the image.  Individual colour channels can even be selected for individual scrutiny.  Very handy!

Requirements: Adobe Elements

Step 3 Replacing sRGB white with a tracer

Here I recommend using the Color Quantizer tool (freeware available online) to replace sRGB white pixels with a colour tracer.  This is done by first postarizing the image to 4096 colours.  Next arrange the colours by luminosity in ascending order.  Finally right click on the top left hand colour (which should be sRGB white) and replace this with a vivid colour to act as a tracer.  Finally re save the image as a new file.  The tracer colour in the new image highlights fully blown highlights.  

Requirements: Color Quantizer tool (freeware).

Analysis

If it is suspected that detail in an area of the image has been completely lost due to clipping that area of the image should appear completely 'submerged' by the tracer colour.  On the other hand if the area is not submerged it should indicate that clipping has not occurred in that area of the image.

Step 4 Document

Once again, in order for others to be able to verify the results it is important to document all steps.