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.
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.
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.
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]