Homer restored: Virtual reconstruction of Papyrus Bodmer 1

Documents from Antiquity rarely reach us in a complete state. Therefore, one of the tasks of archaeologists and historians is to propose hypotheses for reconstructing the original state of the objects they study. The Papyrus Bodmer 1 is an exceptional piece: it preserves a part of a land register written in Middle Egypt (Panopolis) around 215 AD that is 31 cm high and 5.70m long while it could have been up to 11m long when it was complete [3]. At an unknown moment after 215 AD, a scribe cut this roll into two and copied on the back Book 5 and 6 of Homer's Iliad. For yet unexplained reasons, he chose a different number of verses per column between the two books (29 to 31 in Book 5, 38 to 40 in Book 6). For this work, we chose to focus on one column of Book 5 (see Figure 1). Images of the other parts and information on the papyrus are available on the online catalog of the Bodmer foundation¹.

The left papyrus is partially destroyed, parts of the papyrus and the text are missing. The reconstruction of the papyrus on the right is complete, no pieces of the papyrus are missing, and the text is fully readable.

One of the interests of this long and rather well-preserved papyrus is to offer evidence of how a unique document (the land register) of major historical value was reused to bear a key piece of ancient literature (the Iliad). The semi-cursive handwriting of the Iliad part is more challenging than calligraphic scripts where all letters are detached, but is also more comparable with dated specimens. It thus forms an ideal case study for computational restoration assisting current research in ancient History.

Image reconstruction methods have become increasingly powerful in recent years, thanks in particular to advances in the field of deep learning. As far as the restoration of old documents is concerned, work in the field of automatic image processing focuses mainly on improving the overall quality of documents, by removing blur, increasing the definition of the document or retrieving a deleted text [7]. Very recently, some work has also focused on assembling fragments for the reconstruction of old documents. In 2022, a PhD thesis [18] focused on the pairing of papyrus fragments using Siamese networks. Another work from 2020 [15] deals with the reconstruction of a papyrus using its fragments. This one proposes a solution using a graph neural network to create a graph representing the reconstruction of the papyrus by linking each fragment to its neighbors.

Despite these advances, the reconstruction of damaged ancient documents with known text but missing fragments has, to our knowledge, not been studied much. There is currently no machine learning solution for this task. Moreover, in the case of papyri, there are little data to train a model.

The main contributions of the paper are summarized as follows:

1. We propose a novel method for reconstructing heavily degraded papyri by restoring the original text with knowledge of it,
   
2. We show that it is possible to use GANs or more handcraft inpainting methods to restore heavily degraded papyri.
   

In the following section, we cover the related works about inpainting of image and documents. In section 3, we explain the proposed methods to complete the missing parts of one column of the Papyrus Bodmer 1. Then, in section 4, we present our experiments, and finally, we show and discuss different results in section 5.

Inpainting is the process of filling in the missing parts of an image. It can be done physically as an artwork by a conservator-restorer, or digitally, as a computer vision task, using various techniques.

Among the first digital inpainting techniques proposed are Efros et al. [4] and Bertalmio et al. [1]. The first proposed a method which consists in extending an image made of a regular pattern, by synthesizing the texture. This method uses statistical information on the image patterns, modeled by a Markov random field model. A pixel is synthesized at a time, according to its neighboring pixels, by finding in the image a neighborhood of similar pixels. The second used diffusion process (Laplacian) to propagate pixels surrounding the area to inpaint.

Deep learning techniques have allowed for semantically meaningful inpainting [17, 25]. Many model architectures have been used to perform this task.

Liu et al. proposed in [12] an encoder-decoder based convolutional neural network (CNN) method to inpaint images with missing parts of various shapes and sizes.

A method of inpainting on historical documents to restore irregular holes using a U-Net [20] and Partial Convolution [11] is proposed in [8]. The U-Net generates a mask of the irregular holes from the historical degraded document. Partial convolution is used to inpaint the holes using the generated mask and the document image.

Autoencoders are neural networks that learn two functions: encode the input and decode to recreate the input from the code generated just before. Some inpainting methods have been developed using an autoencoder [5, 29].

Generative Adversarial Networks (GAN) [6] are neural networks that generate data by making two networks confront each other. The first network, called the “generator”, attempts to generate the most realistic data possible, in order to make the second network, the “discriminator”, believe that the generated data are real data. The discriminator is trained with real data, and must detect whether a sample is real or generated by the generator. Several GAN-based methods were developed for inpainting [2, 13, 22, 28].

Kim et al. focused in [9] on using a Super-resolution GAN to inpaint the fold lines of old documents. The fold lines to be inpainted are manually marked. The method used does not aim to reconstruct heavily degraded documents, as inpainting is applied on very small areas of the documents.

DeepFillv2 is presented in [26]. DeepFillv2 is a GAN-based architecture used to inpaint images with free-form mask and guidance. The generator is composed of two networks, the first generates a “coarse” inpainted version of the masked image. The second takes as input the “coarse” inpainted image and the masked image to produce a more detailed inpainted image. The generator uses Gated Convolution and a contextual attention block.

Transformers models [24] are deep learning models based on attention mechanisms. Inpainting models based on transformers are able to inpaint large missing parts of images and output semantically plausible results [10, 27].

Diffusion models are probabilistic machine learning models, using Markov chains. Very recently, different methods based on diffusion models for inpainting, denoising, image generation, and image resolution enhancement have appeared. The method proposed by Saharia et al. [21] is based on a conditional diffusion model, which allows coloring of images, increasing the quality of images, or inpainting. It is able to restore complex structures in missing areas of the images. Lugmayr et al. [14] proposed a denoising diffusion probabilistic model to inpaint images with a free-form mask.

While some methods presented above, especially neural network-based ones, can sometimes reconstruct the missing text of an image, none of them preserves the semantics of that text. They are therefore unsuitable for the text reconstruction of a heavily degraded document.

The text of the Iliad, the papyrus to be reconstructed, and its annotations are used to reconstruct the papyrus text. A first method to reconstruct the background of the papyrus uses a strip of papyrus and the papyrus with the reconstructed text for a traditional inpainting task and provides a first reconstruction. The second method uses the GAN deepfillv2, trained with images of the complete papyrus, to reconstruct the papyrus background.

In this section, we detail our two phases methodology to reconstruct the papyrus. The first phase aims to reconstruct the text of the papyrus, which is no longer present due to damage. In order to do this, since we otherwise know the text of the Iliad, we have used the preserved characters on the papyrus and pasted them at possible locations on the image to obtain a readable text. The second phase aims to reconstruct the papyrus background (the papyrus paper) in order to obtain a realistic reconstruction.

3.1 Text reconstruction

In the first phase, we aim at reconstructing the missing parts of the Iliad in order to recreate the full original text.

3.1.1 Data processing. The image of one column of the papyrus, a text file containing its transcription, and the annotations of the visible characters are used as input. The text file indicates which parts of the text are visible and which are missing on the image of the papyrus. The annotations are in COCO format (in a JSON file) exported from the Research Environment for Ancient Documents (READ)² interface and can be seen online³.

A character patch dictionary is created using the annotation file provided by the papyrologists (this file describes the position, the associated Greek letter and the state quality of the visible characters, from BT1 for complete to BT3 for not recognizable anymore). For each character present in the annotation file, a patch, associated with its Greek letter, is extracted. Only the characters with the best quality (tagged BT1) and not exceeding a width of 50 pixels are extracted. Thanks to these two conditions, we avoid characters that would hardly be readable or too wide to fit in the reconstruction. The dictionary allows us to have several patches for a letter, and thus to vary the patch used. Several reconstructions with randomly selected characters were tested.

The papyrus background is removed during extraction so that only the character ink remains (see Figure 3). This step is done with a basic method, only the darkest pixels (corresponding to the ink) are selected, defined as having a value lower than the average pixel of the patch.

The original image of the character contains the background of the papyrus on the image. The image of the character after extraction of the character does not contain the papyrus background.

3.1.2 Character placement. Once all the character patches have been extracted and the text file has been read, the characters can be placed in their probable locations.

For each area where characters are missing, the characters that should be present are determined, and corresponding patches for each of them are randomly drawn from the character patch dictionary.

To take advantage of all the available space in each zone, the characters are placed so that there is an equal amount of space between each character patch from the same row. If it is not possible to have any space between the patches (the total width of the patches is greater than the space available), then the patches will overlap slightly. Only pixels with minimum values are kept on the overlapping areas so that the characters are visible despite the overlap.

A part of the papyrus column at this phase with only the reconstructed text is shown in Figure 4. Some noise comes from the darkest papyrus fibers and illustrate the issue of ink fragmentation on papyri as seen during the DIBCO competition at ICDAR 2019 [19], where binarizing papyri images proved difficult.

Part of the Papyrus Bodmer 1 column with text already present and characters that have been pasted in to reconstitute the original text.

The evaluation of the results was done in a subjective visual way and with the help of the experts’ opinion, as we do not have as Ground Truth the original papyrus to compare our result to.

The two complete reconstructions, a reconstruction of the text and the original image of the Papyrus Bodmer 1 column, can be found at the link in the following footnote ⁵.

5.1 Subjective visual analysis

Inpainting results with the reconstructed text are shown on Figure 6 and Figure 1 (the full column).

The reconstruction results obtained on real data (Figure 6) show that the colors of the papyrus are decently synthesized, but the texture aspect of the papyrus is missing. The fibers of the papyrus are not reconstructed. Furthermore, the general color of the papyrus is reconstructed, but it is easy to see on the bottom image at epoch 430 that the color tone doesn't quite match the rest of the patch. A slight dark edge at the tear is also visible, due to compression artifacts of the papyrus column image, causing the papyrus to not be clearly separated from the black background.

In each line, a different image is tested for inpainting with deepfillv2. In each column, it is a different step of the training. The first column corresponds to the input and the second one to the mask.

Figure 7 compares the same section of the papyrus in the two reconstructions. The top one corresponds to the reconstruction using the traditional inpainting method (copying the strip). With this technique, the texture of the document is perfectly recovered, but a repetitive pattern can be observed and there is no continuity in the fibers between reconstructed and original parts. The bottom reconstruction is the one using GAN. The textures of the papyrus are largely missing in the reconstructed parts and patterns are repeated very strongly on the upper right part. As in the other reconstruction, the continuity of the fibers is not kept.

In both reconstructions, the text is correctly reconstructed and readable.

Two part of final reconstructions using differents methods.

5.2 Analysis by papyrology experts

Both proposed methods to reconstruct a full column of Iliad allow specialists and lay audience picturing how the original papyrus could have looked like. In a detailed view, papyrologists and careful observers cannot mistaken it for a genuine piece due to the still visible transitions between the reconstructed parts and the original ones as well as the erratic aspect of the reconstructed text that has not fully managed to mimic a cursive script (see Figure 8). At the column level, however, it provides a convincing general impression and ground for future discussions among specialists, for instance on the motivation to choose a given number of verses per column. The most convincing restoration of the background is the traditional inpainting because it preserves the vertical pattern of the fibers. This is possible because a) it is written on the side where the fibers are vertical (on the other side of the roll, the fibers are horizontal, thus along and not across the writing) and b) it has a large, well-preserved lower margin to take a coherent strip from. We can thus speculate that this solution would be less successful and more time consuming if extended to the almost 6-meter long roll, and maybe not applicable on a text written along the fibers.

A piece of the reconstruction to which the original part of the document is darkened to see the boundary.

In this paper, we proposed a complete method to reconstruct a column of papyrus with both its written text and background starting from the preserved parts of the original. The choices made to restore the text (random selection of individual letters to avoid repetition, ink segmentation method) and the two approaches tested for the backgrounds yielded convincing results at the page (column) level, already useful for discussions among specialists and educational information of a lay audience.

A future advance for this method would be a better generation of the background by including the texture of the papyrus. Since no relation is attested between the background and the text, if the final goal is a hypothetical reconstruction of a complete roll, we could choose in the future to segment all the written text and paste it on a homogeneous papyrus background that would not be the original. Another direction would be to generate characters as proposed in [23] to avoid reusing those already present in the document. We would also need to better take into account the cursive aspects of the handwriting (esp. ligatures) to more correctly predict the precise size of the reconstruction. Last, a metric could be developed to evaluate the result of a papyrus reconstruction without knowing the original document. The study of Papyrus Bodmer 1 is planned to continue in the future towards a complete simulation of the original state of both sides of this fascinating manuscript that will, for ethical reasons, include a clear distinction between preserved and restored parts. This new form of experimental papyrology will contribute to better understanding practical aspects of ancient books in general.