Picture perfect

I first came to love mathematics not as an implement with which to do science, but for its beauty: mathematics and photography both have much in common with sculpture. Brief stints with the University of Texas at Austin and London's Courtauld Institute, and a spell of military photo-interpretation, confirmed my feeling that the boundaries are blurred between mathematical and visual imagery. Scientific computing was cumbersome in those days. Software for image analysis and enhancement is nowadays commonplace, and can be cobbled together relatively easily in generic mathematical packages.

Over the past year, a friend has been digitally restoring negatives from the 1944 Normandy invasion and from the American Civil War that had been damaged by heat or fungal growth. When Ray Girvan mentioned this topic, I was tempted to try experiments of my own. At Austin was Joseph Nicéphore Niépce's iconic pewter plate image View from the Window at Le Gras, taken c1826. Its shallow relief image, never easy to view, has suffered degradation by atmospheric pollutants. Some data sets from different views were available, generated by past studies, and for software I used what was available in Mathematica (first 5.1, later a 5.2 beta), without specialist additions.

Though comprising tonal bocks, a photographic image is perceived as luminance gradients and linear outlines mapped onto mental models. To attempt enhancement of the photographic image as such would set me up in hopelessly unequal competition with the Getty Conservation Institute. I was more interested in extracting informational templates mimicking what Niépce perceived on that day nearly two centuries ago. This could be done in one bite, but I took four and used a conventional graphics editing program to merge the results into a final image.

The first pass (with numerous trial runs, tuning the parameters along the way) extracted surface-effect density gradients over increasing radii, fitting smoothed curves to the result. Some data were considerably above the useful range of others, and these were identified in a second pass assigning a flat on/off bit. I expected outlines to be easier, but it wasn't so. Another set of gradient scans, this time over decreasing radii, theoretically identify sequences of adjacent catastrophic changes; in practice, fuzzy decisions have to be made. There are two different types of edge, which need to be traced separately: one continuous, the other with significantly less acutance.

Final output was colour differentiated: grey luminance fills, red high plateau bit; green outlines with hard edges solid. To my scientific self this was the most interesting but greys and slight edge blurring gave a truer psychoperceptual result.

I'm quite pleased with my amateur dabbling. The result more clearly portrays the informational content than reproductions of the original, or Kodak's gelatin and silver print copy of 1952. It is also satisfyingly close to Helmut Gernsheim's hand watercolour retouched copy.

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