Author Climbing in the Queyras, Summer 2013

Saturday, September 15, 2012


Fourier Finds Caesar:

A Study in the Physical Evidence of Roman Surveying and Land Usage Using Image Analysis and Periodic Functions


Landscapes are dynamic constructions, with each community and each generation imposing its own cognitive map on an anthropogenic world of interconnected morphology, arrangement, and coherent meaning.

--Kurt Anschuetz, An Archaeology of Landscapes


Finding the physical and epigraphical remains of Roman surveying and centuriation throughout the Roman world remains an area of research that currently engages only a few historians of cartography. In the past the practice of Roman surveying was studied by many important Roman historians like Theodore Mommsen and Max Weber[1]. There remain however, many difficult and unanswered questions about Roman cartography, and the lack of actual extant maps has made me begin to look elsewhere for information that might shed light on its origins and methods. My current research on this problem employs GIS and image analysis to historical aerial photography and remote sensing imagery. It is my hope that in the near future it will produce the first complete map of North African sites that shows both the extent and orientation of Roman mapping. Several authors, such as Rita Compatangelo [2], J.W.M. Peterson [3], D.J. Bescoby [4] have pioneered the use of various mathematical transforms in the analysis of remote sensing imagery for the purpose of finding new sites and orientations. I have started to apply these methods in combination with edge detection algorithms in order to calculate the extent of Roman surveyng and the various types of orientations associated with the physical remains of limites.

The physical remains of Roman centuriation take on a number of sizes and orientations, but are typically discovered through the outlines of the limites that seperated the various regions from one another. Limites or Limes (singular) can be defined as a man-made boundary or balk, that is uncultivated and wide enough to form a road or pathway, which divided centuriae or other land division units from one another. These can take many forms from simple paths all the way to larger structures like the main roads of the decumanus and kardo maximus that were centrally located in a surveyed region. The feature that makes these remains discoverable through the use of transformational techniques is the fact that they appear on the landscape as periodic phenomena. This simply means that the pattern of centuration repeats itself over areas of the landscape, showing up as linear freatures that appear in remote sensing imagery as periodic pattern of grids over fixed distances. One of the most useful ways to study periodic phenomenon, at least from a mathematical perspective, is through the use of Fourier Series and transforms [5]. These transforms model any periodic phenomenon that we might be ineterested in as a infintie series of cosine and sine functions of varying frequencies.


This sum can be expressed more conviently through the use of complex exponentials which are easier to work with algebraically. Using a discrete and algorithmic version of the Fourier transform, known as the fast Fourier transform (FFT), Peterson and Compatangelo, in truely ground breaking papers, showed that one could calculate the most common period found in a group of periodic linear features found on more modern maps. I say the most common period, because many of the linear features found on the landscape today are subdivisions of modern and medieval origin, and it is sometimes extremely difficult to determine the date of the features whose period the transforms are measuring. As an illustrative example, one can think of the linear features found in the landscape as a more complex superposition of the images in the figure shown below. In the figure we see that there are linear features that repeat themselves and that in each of the figures they have different periods of repetition. One of the figures also has a different orientation than the other two. What we see in the landscape is typically a combination of all of these in the same region and on the same remotely sensed image. Peterson used the FFT to generate periodograms that produced the most common harmonics in a series of regions dislaying linear features that he took from 19th Century Ordnance Survey Maps of Scole-Dickleburgh area in South Norfolk. What the periodogram does is allow one to pick out the frequency of the linear features and the larger harmonics. An simple example of this is shown in the figure below. The periodograms not only show the most common distances between the linear features found on the map or on the satellite image, but they also yield a series of harmonics that might have the physical meaning. Larger harmonics beyond the most common one may show subdivisions in the original survey or different grid patterns from the type one is looking for. Because we are not only interested in the distances between linear features in the landscape buy also in their orientation, we have employed a second technique known as a Radon transform. This technique has been used by Bescoby to detect Roman boundaries in aerial photographs in Albania. The strength of this method is that it allows for the calculation of the angle and hence the orientation of the series of linear features. When combined with the two-dimensional version of the Fourier transform, this allows a complete characterization of the grid formed by the limites of Roman surveying. The Radon transform can be expressed by the equation below and its operation can be seen in the graph shown in the figure. Finding the size and orientation of linear features in a landscape lets us compare what we have calculated with known patterns of centriation found in literary and epigraphical evidence, such as that found in the 5th or 6th century Corpus Argimensorum. According to Hyginus, one of the authors found in this compilation of Roman surveying texts, the typical layout for an area of surveyed land is shown below. The letters and numbers define the parcel of land and very often appear as eppigraphic inscriptions on surviving boundary stones. The main intersection shown in the figure is that of the kardo and decumanus maximus which are the beginning points of any Roman survey. A typical kardo or decumanus can be seen in the photograph below that I took in a heavily centuriated area around Carthage just north of Tunis. The distances that the Romans typically used and their various names are shown in the schematic, with a century measuring 2400 Roman feet or about 705 meters. Many of these grids would however have been further subdivided in a variety of schemes that are not easily dated using physical evidence. The research that I have been doing has concentrated its efforts on the non-coastal regions of North Africa, taking in parts of Tunisia, Algeria and Libya. Below are two satellite images of the areas around Dougga and El Jem in Tunisia both of which are the sites of important Roman towns and ruins.


In both of these photographs one can see a variety of linear features that may or may not be associated with Roman activity.



It would be interesting to know the extent to which the Romans actually produced maps of these areas considering their overall importance to the history of Roman colonization and occupation in the region. El Jem for example contains one of the best preserved Roman colesseums in all of Africa.

To apply these algorithms to remote sensgin imagery it was necessary to clean them up and enhance the linear features using edge detection algorithms. An example of this is shown in the figure below.



Once this is accomplished and the various transforms have been applied we can begin to compare the results with known grids based on our knowledge of Roman practice derived from the epigraphic and literary evidence.





Using ArcGIS I have generated maps with overlays showing the orientation and extent of the surveyed region under study. The map below shows a single division into centuriae around Enfida, Tunisia. The map below shows both a division into centuriae and into a second subdivison which probably dates from a later time. [1] There are many studies of Roman surveying. For a modern bibliography see Brian Campbell, The Writings of the Roman Land Surveyors, Society for the Promotion of Roman Studies, 2000.


[2] Rita Compatangelo, Un Cadastre De Peirre Le Salento Romain, Annales Litteraires de l'Universite de Besancon, 1989

[3] John Peterson, Fourier Analysis of Field Boundaries, in G. Lock and J. Moffet, CAA91: Computer Applications and Quantitative Methods in Archaeology 1991. BAR International Series s577. Oxford, 149-156.
[4] D.J. Bescoby, Detecting Roman land Boundaries in aerial photgraphs using Randon transforms, Journal of Archaeological Science (2006) 33, 735-743. See also, J. S. Bailly et'al "Agarian Landscapes linear features detection: application to artificial drainage networks" International Journal of Remote Sensing 29 (2008) 3489-3508 and E. Magli, et.al. Pattern Recognotion by means of the Radon transofrm and the continuous wavelet transform, Signal Processing 73 (9990 277-289.

[5] See any of the recommended books on Fourier Analysis on this blog or for a good introduction to the subject see L. Solymar, Lectures on Fourier Series, Oxford University Press, 1988.