The directional illumination used in shaded relief visualisation can never show all relief details in an optimal way. Combining several shaded relief images computed for different illumination directions (e.g. by creating RGB colour composites or by applying Principal Component Analysis) can help, but the resulting images can be difficult to read.
Shaded relief image (illumination azimuth 315°, elevation 60°, no vertical exaggeration) of part of the Iron Age oppidum Heidengraben, Baden-Württemberg. LIDAR data (c) LGL/LAD.
Because the optimal illumination for the recongnition of topographic detail depends to a large part on topographic position (mainly on slope and aspect), one option to improve relief feature visibility is to locally adapt illumination directions. Exaggerated Relief as proposed by Rusinkiewicz et al. (2006) is an algorithm that implements this idea. It’s not a simple process; it took me quite a while to fully understand how it works. Exaggerated Relief as described here is not to be confused with vertical exaggeration in creating shaded relief images.
It uses the same principle that underlies shaded relief illumination: pixel brightness is proportional to the cosine of the angle between the incoming light beam and the surface normal. But instead of using one global illumination direction for the whole DEM, illumination elevation is locally adjusted in a way that the light always strikes the surface at a shallow angle. Of course, doing this requires knowlwedge of surface slope and aspect; these parameters are computed for a smoothed (low-pass filtered) version of the same DEM. (To be precise, instead of smoothing the DEM, a surface normal map computed from the DEM is smoothed. This does not make a difference for the resulting images, but it makes computations easier.)
The resulting image for such a locally adapted illumination strongly emphasises local relief details, but it does not convey a visual impression of the overall topography. Therefore, the same computations are repeated at several scales: Another image for locally adapted illumination is calculated from the smoothed DEM, using a further, more strongly smoothed version of the same DEM to compute surface slope and aspect for locally adapting illumination elevation.
This process is repeated several times, smoothing the DEM surface normal map step by step and locally adjusting illumination elevation. Thereby, a series of images is created which each emphasise relief detail at a certain scale: the entire process is a multi-scale approach.
Pixel brightness for each of the resulting images is then multiplied by a constant exaggeration factor and limited (clamped) to a fixed range of values (-1…1). Finally, all images and one shaded relief image without local illumination adjustment (“base coat”) are combined to a single image by computing a weigthed average. To control how strongly the different images (i.e. the level of relief detail) influence the combined image, the weighting factor for each image is computed as a power of the standard deviation of the size of the Gaussian low pass filter which was used to smooth the DEM surface normal map and normalised so as to make the sum of weighting factoprs for all scales 1.
Several parameters can be adjusted to control the resulting image: global illumination direction (azimuth and elevation), minimum smoothing radius, number of scales, scale-to-scale incremental factor, exaggeration factor and weight exponent. To facilitate computation, a surface normal map (SNM) is computed from the DEM in a first processing step. Because all further computations are based on this SNM, other sources for SNMs (e.g. Polynomial Texture Mapping, PTM) can be used to compute Exaggerated Relief images.
Because Exaggerated Relief is based on the same fundamental principle of directional illumination, the resulting images are visually similar to shaded relief images. With appropriate settings, however, Exaggerated Relief conveys much more relief details largely irrespective of topographic position: subtle relief features are visible both in flat areas and on steep slopes, and there are almost no homogeneous white or black areas.
Exaggerated Relief visualisation of the same area (number of scales: 8, scale -to-scale factor: 1.414, exaggeration factor: 8, weight exponent: -0.5, global illumination azimuth: 315°, elevation: 45°). LIDAR data (c) LGL/LAD.
Exaggerated Relief visualisation of the same area (number of scales: 8, scale -to-scale factor: 1.414, exaggeration factor: 8, weight exponent: 0.0, global illumination azimuth: 315°, elevation: 45°). LIDAR data (c) LGL/LAD.
Exaggerated Relief visualisation of the same area (number of scales: 8, scale -to-scale factor: 1.414, exaggeration factor: 8, weight exponent: 0.5, global illumination azimuth: 315°, elevation: 45°). LIDAR data (c) LGL/LAD.
Does this mean that Exaggerated Relief is a perfect visualisation technique and that we don’t need any other technique? Not quite. One important issue is computation time. Because Exaggerated Relief is a relatively complicated algorithm working at multiple sucessive scales, computation times are high (increasing in particular with the number of scales).
Another problematic issue are visual artefacts resulting from the algorithm: depending on the settings (increasingly with a stronger influence of high-frequency relief details, i.e. a lower weight exponent), apparent banks are present along terrain edges. Interpretation of Exaggerated Relief images requires careful consideration of such artefacts and comparison with other visualisation techniques to avoid misinterpretations.
Rusinkiewicz, S., Burns, M., DeCarlo, D., 2006. Exaggerated Shading for depicting shape and detail. ACM Transactions on Graphics (Proceedings SIGGRAPH) 25(3), 1199–1205. [article link]