I was involved in a lot of similar work in the past but with stone decay on buildings. Here are some references on that work which you may find interesting (if a little old now):
Ball, J; Young, M E (2000) “Mapping The Decay & Weathering Of Stone: A Technique For The Assessment Of Large Numbers Of Buildings”,in Choi, S and Suh, M (Eds.) Proceedings of the New Millennium International Forum on Conservation and Cultural Property, 5-8 December 2000, Kongju National University, The Republic of Korea, pp. 134 - 147
Ball, J; Young, M E (2000) “A Simple Technique For Enhancing Rapid Field Assessment Of Stone Decay On Buildings”, in Fassina, V. (Ed.) 9th International Conference on Deterioration and Conservation of Stone, Proceedings, Venice, 19-24 June, Elsevier, vol. 2, pp. 13 - 21
Young, M E; Ball, J. and Laing, R (2000) “Quantification of the Decay of Building Sandstones”, In Conference Proceedings of Weathering 2000, Belfast, 26-30 June (paper may also be published in Journal of Earth Surface Processes & Landforms)
You can do this in a GIS if you set a suitable projection and coordinate system, which only have to be logical as far as your tombstone surface is concerned (i.e. obviously need no relationship to where the tombstone is). These days this would be my preferred option. however, back when I did this work, there were not so many of the amazing options for FOSS4G we have now and the research budget did not stretch to an ESRI licence. So I took an entirely different old-school approach using only Photoshop (GIMP will do) as follows (summarised):
- The photos were taken at high resolution and orthorectified to remove key-stoning and ensure accurate proportions across the surface (this is critical and may even apply to your tombstone depending on your camera setup, lenses etc.
- All non-stone elements of the building and photo (windows, doors, sky etc) were masked with a 'pure' colour (e.g. R=0,G=0,B=255 - anything will do that is not natural - like greenscreening in films), the free-select and paths tools in Photoshop and Gimp will help you do this accurately (and effectively come to the same thing as digitizing in a GIS).
- The decay was mapped on the photo - we were dealing with large buildings and the decay was best identified in the field but you have the advantage of dealing with a much smaller object and so your resolution can be effectively even higher and you can probably do the whole thing from the photo with field notes (which must include reference measurements of the tombstone).
- Each decay type was mapped to a different layer (again using the free select and paths tools to digitize the outlines. When each area was selected, it was filled with a block colour (now you can see why I'm stressing high-res images - our area calculations will be raster-based).
- You can now use your reference measurements to calculate the pixels to real-world units ratio. You can no calculate the surface area of the stone by subtracting the masked area using a histogram count (number of pixels) of your non-tombstone mask layer. In a similar way, you can now also calculate the % surface area for each stone-decay type by doing a histogram count on each digitized layer. (You can now see why using a single pure colour per layer for the mask and digitized decay layers is hugely important).
This method effectively turns Photoshop or GIMP into a simple raster GIS. However, when digitizing your areas make sure you deselect both antiailiasing and feather edges! The higher your resolution, the greater your accuracy within the usual limitations of the raster grid format.