This blog post is part of a series on the conference “Artificial Intelligence in Archives and Collections” held on December 12-13, 2024, at the Herder Institute in Marburg and presents perspectives on the coference contribution by Yury Korolev, University of Bath – written by Marco Colombo.
Recent advancements in artificial intelligence and mathematical techniques are transforming the way we approach cultural heritage preservation. These technologies provide new ways to analyze and interpret digital data, particularly in the realm of historical documents and artifacts. By applying mathematical models to imaging data, researchers can uncover hidden details, restore ancient manuscripts, and better understand the history behind archaeological findings.
In the world of cultural heritage preservation, technology plays an increasingly vital role in uncovering and understanding historical artifacts. One of the most promising advancements in this field is mathematical imaging, which has revolutionized the way we analyze historical documents. This article delves into how spectral decomposition aids in processing images for cultural heritage applications, with a focus on analyzing handmade medieval paper. This topic was treated by Assistant Professor Yury Korolev in his oral presentation at the conference.
The Power of Spectral Decomposition in Image Processing
At its core, spectral decomposition involves breaking down an image or signal into simpler components that can be interpreted and manipulated independently. A well-known example is the Fourier transformation, which decomposes a signal into sine and cosine waves of different frequencies. This method has long been used in audio processing, where equalizers modify frequencies to emphasize or dampen specific sounds.
Applying this principle to image processing allows researchers to filter images by modifying their spectral components. Similar to how equalizers can adjust bass or treble in music, spectral decomposition enables the enhancement or suppression of specific image features, revealing details otherwise hidden in noise and distortions.

Challenges in Fourier-Based Image Processing
Traditional Fourier-based filtering presents certain challenges when applied to images. One primary issue is the handling of edges and sharp transitions within an image. The Fourier transform favors smooth variations and struggles with the abrupt changes often found in historical documents, where distinguishing between textual content, illustrations, and background textures is crucial for accurate analysis.
Additionally, artifacts such as noise and dirt often share high-frequency components with vital image details, making it difficult to distinguish between essential and extraneous elements. This limitation necessitates alternative approaches that can better separate meaningful structures from irrelevant noise.
Total Variation Spectral Decomposition: A More Effective Approach
A promising solution to these challenges is total variation (TV) spectral decomposition [1, 2, 3]. Unlike Fourier methods, TV decomposition is particularly effective in processing images with sharp edges and high contrast variations, such as handwritten medieval manuscripts. This approach decomposes images based on the scale and contrast of details, allowing for a more meaningful separation of image elements.
Using TV spectral decomposition, an image is analyzed at different levels of detail, isolating high-contrast features such as text and marks while preserving background textures like paper grain and chain lines. The ability to filter images in this way is invaluable for historians and archivists, as it allows them to extract key structural elements from historical documents with remarkable precision.

Applications in Medieval Paper Analysis
One particularly compelling application of TV spectral decomposition is in the study of handmade medieval paper. This type of paper was created using molds made of metal wires, which left distinctive imprints known as chain lines (vertical lines) and laid lines (horizontal lines). Additionally, many papers featured watermarks that identified their origin, providing crucial insights into historical trade networks and manuscript provenance.
By applying spectral decomposition techniques, researchers can:
- Digitally remove overlying text and stains from historical documents to better reveal the mold imprints.
- Enhance faint chain lines and laid lines, allowing for accurate identification of the paper’s origin.
- Segment different elements of an image to isolate and analyze individual components more effectively.
This methodology has been successfully employed on manuscripts from the Cambridge University Library, enabling historians to trace the origins and movements of medieval texts with better accuracy.
Beyond Cultural Heritage: Broader Implications
The benefits of TV spectral decomposition extend beyond historical paper analysis. This approach has demonstrated its effectiveness in several other imaging applications, including:
- Image Denoising: Removing unwanted noise from photographs, particularly in low-light conditions.
- Image Segmentation: Identifying and categorizing different elements within an image, useful in medical imaging and microscopy.
- Image Fusion: Combining multiple imaging modalities to create a more comprehensive representation of an object, especially in medical diagnostics.
Moreover, machine learning is being integrated into these spectral decomposition processes, significantly improving computational efficiency. Researchers are developing AI-driven models to automate and optimize these transformations, making them more accessible and scalable for various imaging needs.

Future Prospects and Challenges
While TV spectral decomposition has proven to be a powerful tool, it is not without its challenges. One notable limitation is its preference for detecting rounded or disk-like structures, which may not always align with the features of certain historical documents. Future research is focused on refining these methods to accommodate a wider variety of structural elements, making them even more effective for cultural heritage applications.
Additionally, computational efficiency remains a concern. Unlike standard Fourier filtering, TV-based decomposition requires solving complex optimization problems, making it computationally intensive. However, ongoing advancements in machine learning and algorithmic optimization are expected to mitigate these challenges, paving the way for faster and more efficient implementations.
Conclusion
Spectral decomposition, particularly through total variation methods, represents a powerful technique for cultural heritage applications. By enabling clearer and more detailed analysis of historical documents, this technology offers invaluable insights into the past while preserving artifacts for future generations. As AI and machine learning continue to enhance these techniques, the potential for further breakthroughs in digital humanities and archival science remains immense.
With continued research and innovation, spectral decomposition will undoubtedly play a crucial role in unlocking the hidden secrets of our cultural heritage, bridging the gap between history and technology.
References
[1] Gilboa, G., 2014. A total variation spectral framework for scale and texture analysis. SIAM journal on Imaging Sciences, 7(4), pp. 1937-1961.
[2] Grossmann, T.G., Schönlieb, C.B. and Da Rold, O., 2023. Extracting chain lines and laid lines from digital images of medieval paper using spectral total variation decomposition. Heritage Science, 11(1), p. 180.
[3] Grossmann, T.G., Dittmer, S., Korolev, Y. and Schönlieb, C.B., 2022. Unsupervised learning of the total variation flow. arXiv:2206.04406.
Marco Colombo is a PhD student in the Materials Analysis Group at the Darmstadt Technical University. He was a participant at the conference in Marburg and was particularly interested in Yury Korolev’s work, so he decided to write down his impression and perspectives on his presentation.
The original title of Yury Korolev‘s presentation at the conference was “Image filtering based on total variation spectral decompositions: an overview of the method and an application in medieval paper analysis”. For further information on the conference see the programme.
Title picture: Book of Hours — a prayer book written in Medieval Latin (c. 15th century).
All pictures: symbolic images, public domain via Wikimedia, see also here.
OpenEdition schlägt Ihnen vor, diesen Beitrag wie folgt zu zitieren:
Lab 1.3 Digitale Heuristik und Historik (2. Juni 2025). Unlocking the Past with AI: Spectral Decomposition for Image Processing in Cultural Heritage. Value of the Past. Abgerufen am 10. November 2025 von https://doi.org/10.58079/141my
