Determining Rock Art Deterioration Through Time:

Automatic Change Detection with SfM

Structure from Motion (SfM) is a very useful tool for creating 3D models from unreferenced images. Since SfM can create highly detailed models from historic film and digital photographs, it is particularly helpful in examining changes in an object over time.  In this short post I'll show how data collected at a pictograph site in 2003 can be compared with more recent data to pinpoint areas of deterioration in a systematic way.

The pictograph we'll be looking at is located at 41CX2 and is part of a prehistoric site on the eastern edge of the Pecos River in West Texas. I like to use data collected from this site because there are no issues with making it publically available. I also go back to it because there are both older digital photographs of the site and much older historic photographs archived at the Texas Archaeological Research Laboratory (TARL). This provides a nice test bed of data to take advantage of.

In order to compare a set of historic photographs with modern ones, aligning the two image sets to each other is critical. This can be difficult because photographs contain all sorts of lens distortions and it is hard to reproduce the exact angle of a historic photograph with a modern camera. It may sound like a simple task to overlay one image on another in Photoshop but getting an exact alignment between two photographs taken at different times, is almost impossible. SfM can aid in the alignment process.  By analyzing the structure of the object in the photographs, SfM can remove virtually all distortion when a 3D model is created. Therefore, if you create one 3D model from historic photographs and another 3D model from more recent images, the two can almost perfectly aligned to each other. The easiest way to accomplish the alignment is by assigning the same coordinate system to each model and then converting those to a Digital Elevation Model (DEM).

2003 and 2011 SfM models aligned.

In this example, I have assigned the same arbitrary coordinate system to each model with the X and Y axis approximately in alignment with the natural surface of the rock. In other words, the Z, or elevation value, is greater the closer it is to the viewer and vice versa. With both models now in the same space and orientation, the Z values of the vertices can be sampled to create a DEM.  It is important to note the word "sample" here because each cell of the DEM is composed of a value derived from the average value of the vertices that fall within that cell. If cell sizes are not the same or have a different origin point, the DEM values can vary slightly for what appears to be the same location. In our example the 2003 3D model covers a slightly larger area than that collected in 2011. Due to this difference in area, the DEM cells are slightly offset. To help reduce this minor alignment problem, the 2003 model could be clipped to the same size as the 2011 data but for this project I left the models in their original state.

2003 DEM

2011 DEM

The result of subtracting the 2011 DEM from the 2003 DEM.
Areas of red have had the greatest change.

Having created the DEMs for the 2003 and 2011 models, each DEM was loaded into ArcGIS. To compare the changes between the DEMs over time, the 2011 data was subtracted from the 2003 data. This was done with the Spatial Analyst's Raster Calculator tool. The resulting DEM highlights those areas of significant change in red and the more stable areas in blue. As mentioned previously, the DEM cell values do not match exactly so there is minor variation visible across the model.  When the difference DEM is transposed against the pictograph images, areas of deterioration are obvious. While it is certainly possible to visually compare the photographs from different time periods and see that damage is taking place, this process allows for a systematic and quantifiable means of assessing that change.

2003 image imposed over differences map. 

2011 image imposed over differences map.  

Closeup of 2003 imagery and differences map.

Animation showing change from 2003 to 2011.

The implications for using this technique are exciting. Since SfM can work with historic film photographs, many older photographs of rock art panels can be analyzed and historic 3D models created. Furthermore, the process need not focus on pictographs; historic aerials can be converted to DEMs and geomorphological changes examined or the process could be applied to underwater photography to examine the morphological changes of coral reefs, etc. There are many possibilities.