A Computational Study of the Internal Structure of Historical Papers: Leonardo da Vinci’s Notebooks

William Sethares, Abigail Slawik, Elisa Ou, Margaret Ellis, C. R. Johnson, Jr

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ABSTRACT

Leonardo da Vinci’s manuscripts present a puzzle for scholars who aim to recreate the pages’ original formats, sequence, and chronology. While the most practical way to capture two inner structural features (watermarks and chain lines) is via transmitted light, these traces of manufacture can be difficult to decipher when writing and other surface marks found on the surfaces of the sheet obscure them. Using diffuse specular (normal) light and transmitted light images of Leonardo’s Codex Leicester (Bill Gates Collection) and the Codex Arundel (British Library) as case studies, we describe a computational approach that minimizes surface marks and writing in order to facilitate the accurate matching of watermarks and chain lines. Using enhanced images of these structural features, it is possible to suggest moldmates (papers made from the same papermaking mold) in both Codices, providing evidence of origin, sequence, and date.

“Inside” a piece of “laid” (historical) paper

How historical paper was made:

Moldmates: papers produced from exact same mold

It can be difficult to decipher watermarks and chain lines in transmitted light due to interference from surface marks.

Maybe there is a way to use surface images to “subtract out” the markings on the two sides to reveal more of what is happening beneath the surface.
Key step is aligning everything so that the subtraction actually subtracts.

Manipulate[Image[m-xs a-ys b,ImageSize->800]//ImageAdjust,{xs,0,1},{ys,0,1},SaveDefinitions->True]

We’ve built a website where all the watermarks in Codex Leicester and Codex Arundel are described

Hyperlink["LeoCode", "https://leocode.org/"]

Sometimes we can (semi) automatically locate chain lines and then gather ratios to compare.

We manually locate/mark chain lines and then gather ratios to compare. For example, the top two match while the bottom one doesn’t

Row[{,}]

To Do :

Analyze more of Leonardo’s codices (Madrid Codex is next)

Apply to other historical writers/artists (a project with works by Rembrandt and another with works by Durer are underway)

Make the software for laid lines more accessible

Make the de-noising/surface removal process more accessible (underway, but trickier than it might seem)