DEM visualisation techniques: Openness

Several DEM visualisation techniques are based on some sort of simulated terrain illumination: Shaded Relief simulates directional illumination from a point light source, Sky-View Factor simulates diffuse illumination from a homogeneously bright hemisphere.

Openness is a visualisation technique which is similar to Sky-View Factor. However, contrary to considering a homogeneously bright hemisphere centered above each pixel, the computation of Openness considers a full sphere centered on each pixel. The Openness algorithm looks at a surrounding area with a specified radius and assesses whether or not there are terrain points which would obstruct illumination from that direction. In practice this is achieved by finding (along each radial line) the smallest angle between terrain points and the zenith angle. These angles are then aggregated for n radial lines (usually 8 or 16) by computing their average. As a result, higher/lower Openness values are assigned to more/less exposed terrain points.

Charcoal burning platforms in the southern Black Forest. Positive Openness visualisation.

Charcoal burning platforms in the southern Black Forest. Positive Openness visualisation.

When you think about this principle for a while you might wonder what would happen if you calculated Openness as the average of the smallest nadir angles (instead of zenith angles). And yes, this can be used as a visualisation technique as well. To distinguish between the two approaches, the one based on zenith angles is called Positive Openness while the one based on nadir angles is called Negative Openness. Negative Openness has high/low values for strongly/weakly incised terrain points.

It is worth noting that Negative Openness is not simply Positive Openness with a ‘-‘ sign but is based on a different computation resulting in different values for the same point. Negative Openness calculated as described above has a positive range of values. However, to make the resulting visualisations more intuitively readable, Negative Openness values calculated by LiVT are multiplied with -1. As a result, positive terrain features are characterised by higher values of both Positive and Negative Openness then negative terrain features. Positive and Negative Openness visualisations can be combinedby computing a (weighted) average of th respective greyscale images.

Charcoal burning platforms in the southern Black Forest. Negative Openness visualisation.

Charcoal burning platforms in the southern Black Forest. Negative Openness visualisation.

Charcoal burning platforms in the southern Black Forest. Grayscale average of Positive and Negative Openness.

Charcoal burning platforms in the southern Black Forest. Grayscale average of Positive and Negative Openness.

Openness visualisations can be vey useful for interpreting lidar-based DEMs as they clearly show small-scale relief features. At first sight, they appear somewhat similar to Sky-View Factor visualisations; however, the visual impression of the overall landscape forms is lost. An advantage is that small-scale features are visulised equally well on flat terrain and on slopes.

References

Yokoyama, R., Shirasawa, M., Pike R.J., 2002. Visualizing topography by openness: a new application of image processing to digital elevation models. Photogrammetric Engineering & Remote Sensing 68(3), 257-265.

Doneus, M., 2013. Openness as visualization technique for interpretative mapping of airborne lidar derived digital terrain models. Remote Sensing 5(12), 6427-6442. [open access]

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.