Surface normals analysis to visualise Stonehenge prehistoric rock carvings at high resolution

Introduction
Stonehenge is one of the most important prehistoric monuments in the world, but to this day roughly 23% of its above-ground stone surfaces have never been analysed by archaeologists (Abbott and Anderson-Whymark 2012, 12). These surfaces have been inaccessible to conventional surface scanners and photogrammetric techniques due to the dense coverage of lichen present on the stones (Field et al. 2015, 129). Preservation issues however prevent the removal of lichen. A recent 2011 survey of the stones found 71 new prehistoric axe-head carvings (Abbott and Anderson-Whymark 2012, 26), important for understanding the meanings of Stonehenge (Nash 2011, 847), on its bare surfaces. This highlights the possibility of further such carvings being obscured by lichen.
In this work, we create an algorithm to filter regions of a 3-D model of the stones of Stonehenge such that only regions likely to indicate carvings remain. This is a first step towards revealing carvings beneath lichen. Machine learning methodologies exist that can be trained on the filtered 3-D models to recognise objects (Qi et al. 2017; Socher and Huval 2012), and has been recently applied to rock art recognition (Gordienko et al. 2018; Mascardi et al. 2014; Zeppelzauer et al. 2016). These machine learning methodologies can then be applied to the lichen covered stone surfaces to identify the presence of carvings.
Our methodology presents an improvement on previous work by Abbott and Anderson-Whymark (2012) as we use surface normals and surface curvature which, with mathematical enhancement, can improve the appearance of shape and detail impossible to see under normal lighting conditions (Riris and Corteletti 2014). This, when combined with a machine learning approach to rock art recognition facilitates a more objective archaeological identification and interpretation of rock carvings, especially through distortion and noise due to lichen.

Methods
To reveal the shape and location of prehistoric carvings on the stone surfaces of Stonehenge, an algorithm was written in the programming language MATLAB. This algorithm compared the normal of a point, p_0, in 3-D space to the average of the normals of its closest neighbours. If the normal at p_0 differed in angle more than a set threshold to that of the average of its neighbours, then it would be highlighted, otherwise it would be discarded (Fig 1). The method of 3-D visualisation we employed was via a point cloud, i.e. a collection of 3-D points. However, before this methodology can be implemented on a point cloud, the point cloud required pre-processing similar to that by Fuad et al. (2018, 13)
To obtain data for testing the algorithm, 78 photographs were taken of a pair of axe-head and dagger carvings on stone 53. An example image is shown in Fig 2. These images were used to create 3-D reconstructions of the carvings. For this, we combined two structure from motion (SfM) software: COLMAP (Schonberger and Frahm 2016; Schönberger et al. 2016) and OpenMVS (Goldberg et al. 2011). COLMAP was used for feature extraction and matching, and for creating the sparse reconstruction. OpenMVS was used for mesh reconstruction.

Results
The best visualisation using our algorithm was achieved by comparing the normals of eight nearest neighbours and using an angle threshold of 14° (Fig 3A). Our algorithm clearly highlights the edges of the two prehistoric carvings. However, it also revealed much of the noise on the stone surface. This is the due to our algorithm, which only highlights regions of high curvature. Further refinement is required to create a measure that filters this noise. This could be achieved by removing shapes that are too small to be a carving or the automatic identification of carvings by performing fuzzy-based analysis to model the uncertainty in their outlines (Deufemia et al. 2014).
However, when combined with our use of SfM, these results still provide an immediately accessible methodology that remains accurate. Previous attempts by Abbott and Anderson-Whymark (2012) at visualising the carvings produced a cloudy image, where the boundaries of the carvings are diffuse and difficult to define. An example is their use of greyscale plane shading (Fig 3B). Our algorithm, in contrast, sharply defines the carving boundaries.
Other techniques used for identifying rock carvings often require the user to choose the direction of the light source, such as Polynomial Texture Mapping (Earl, Martinez, and Malzbender 2010), this reduces the repeatability of experiments and findings as whether a carving is identified may depend on how the 3-D object is lit (Lymer 2015, 161).

Conclusions
In this study we designed an algorithm that compared the surface normals of a SfM 3-D model of a region on stone 53 at Stonehenge to highlight prehistoric carvings. The analysis successfully revealed the presence and shape of a pair of axe-head and dagger carvings. Arguably, our visualisation of these carvings is an improvement on that by Abbott and Anderson-Whymark, who performed the most recent laser scan survey of Stonehenge. In their work, they used a greyscale plane shading technique. Although both methodologies were able to highlight areas of the stone surface indicative of carvings, ours gave a more well defined boundary to the carvings than their diffuse visualisation.
Our approach, with further refinement via noise reduction or use of fuzzy-based analysis for automatic carving identification, can be used to find much fainter, eroded carvings on the stones of Stonehenge. However, this methodology can be generalised to any stone surface to search for faint or eroded carvings. For archaeologists the implications of using this approach is an improvement in the objectivity of findings, and less reliance on techniques that, e.g., depend on virtual lighting conditions.
In future work, by treating the lichen on the stones of Stonehenge as noise, existing machine learning methodologies can be used to identify the presence of carvings beneath the lichen. This is possible using the same SfM surface reconstructions created in this study. With training on different 3-D datasets, this machine learning methodology can be generalised to search for any carvings hidden by lichen, such as those found on gravestones.

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