Unveiling the invisible: mathematical methods for restoring and interpreting illuminated manuscripts

Luca Calatroni,Paola Ricciardi,Rob Hocking,Carola-Bibiane Schönlieb,Simone Parisotto,Stella Panayotova,Marie D’Autume

doi:10.1186/s40494-018-0216-z

Abstract

The last 50 years have seen an impressive development of mathematical methods for the analysis and processing of digital images, mostly in the context of photography, biomedical imaging and various forms of engineering. The arts have been mostly overlooked in this process, apart from a few exceptional works in the last 10 years. With the rapid emergence of digitisation in the arts, however, the arts domain is becoming increasingly receptive to digital image processing methods and the importance of paying attention to this therefore increases. In this paper we discuss a range of mathematical methods for digital image restoration and digital visualisation for illuminated manuscripts. The latter provide an interesting opportunity for digital manipulation because they traditionally remain physically untouched. At the same time they also serve as an example for the possibilities mathematics and digital restoration offer as a generic and objective toolkit for the arts.

Highlights

The digital processing, analysis and archiving of databases and collections in the arts and humanities is becoming increasingly important
We consider automated and semi-automated models for digital image restoration based on partial differential equations, exemplar-based image inpainting and osmosis filtering, and their translation to the digital interpretation of illuminated manuscripts
We refer to mathematical image processing as the task of digital image restoration, that is the digital processing of a given image to correct for its visual imperfections

Summary

Introduction

The digital processing, analysis and archiving of databases and collections in the arts and humanities is becoming increasingly important This is because of a myriad of possibilities that digitisation opens up that go well beyond the organisation and manipulation of the actual physical objects, allowing, for instance, the creation of digital databases that are searchable with respect to several parameters (keywords), the digital processing and analysis of objects that are non-destructive to the original object, and the application of automated algorithms for sorting newly found objects into existing digital databases by classifying them into pre-defined groups in the database. We refer to mathematical image processing as the task of digital image restoration (or reconstruction), that is the digital processing of a given image to correct for its visual imperfections This is done with the main intention of producing a final result where imperfections have been corrected in a visually least distracting way. This is the case for several imaging tasks such as image denoising, deblurring and image inpainting

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