DEM visualisation techniques: Multi-scale integral invariants

Earlier this year, I was impressed by Hubert Mara‘s presentation at the CAA workshop in Berlin. He had used a method called multi-scale integral invariants (MSII) to extract the incised charcaters from cuneiform tablets and inscription from old tombstones. This was surely be something that could be useful for visualisaing LIDAR-based DEMs: back in the office, I implemented it as an additinal algorithm in LiVT.

Now, how does it work? To begin with, it is a multi-scale approach (hence the name). The algorithm places multiple spheres of different diameters on each pixel in the DEM and computes how much of the volume of the spheres is above/below the DEM surface. As a result, you get a number of values (volume fractions above surface) for each DEM pixel. These sets of n values are interpreted as n-dimensional vectors.

By computing the distance of these n-dimensional vectors from a reference vector, the data can be reduced to a raster map containing a single value for each pixel. Low values (low vector distance) indicate high similarity with the reference vector and vice versa. Using an appropriate greyscale histogram stretch, this raster map can be displayed as an image. The reference vector can, for example, be determined by extracting the vector values for a specific relief feature or a point within a cuneiform character or simply by chosing the origin of the n-dimensional coordinate system (i.e. zero).

MSII visualisation (distance from origin, 8 scales starting with radius=2 and scale-to-scale factor 1.414) of the same area as in the post about local dominance  LIDAR data (c) LGL/LAD.

MSII visualisation (distance from origin, 8 scales starting with radius=2 and scale-to-scale factor 1.414; greyscale histogram stretch 1.35…1.55) of the same area as in the post about local dominance. LIDAR data (c) LGL/LAD.

References

Mara, H., Krömker, S., Jakob, S., Breuckmann, B., 2010. GigaMesh and Gilgamesh – 3D Multiscale Integral Invariant Cuneiform Character Extraction, in: A. Artusi, M. Joly-Parvex, G. Lucet, A. Ribes u. D. Pitzalis (Hg.), The 11th International Symposium on Virtual Reality, Archaeology and Cultural Heritage VAST (Paris, France, 2010), 131–138.