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Principal component analysis is often used with remote sensing to decrease the dimensionality of multi-band imagery and to realign data with new axes to maximize variance in the imagery (Campbell and Wynne, 2011). Relief shaded maps using illumination from numerous aspect directions and inclinations from the horizon can also be input to principal component analysis (PCA), resulting in principal component maps that optimize variance and mimic relief shading. Using 15° increments of azimuth and inclination to vary illumination direction yields 121 relief shadings of the Churfirsten, Switzerland at 30 m. resolution, one of the sample elevation models available from http://shadedrelief.com/SampleElevationModels/ (Kennelly et al., 2021). PCA results in the three principal component images shown in Figure 1, accounting for more than 99% of the variance found in the 121 input relief shadings. While the first two principal component maps are similar to relief shading illuminated from near the horizon and separated by 90 degrees of azimuth, the third principal component map is similar to slope shading [ABSTRACT FROM AUTHOR]

The most often used and powerful terrain representation layers symbolize the orientation of the surface rather than its elevation. Techniques such as relief shading and slope-shading symbolize metrics of orientation, yet typically ingest elevation data to create those layers. Rather than processing elevation data to represent terrain, a shift in perspective to emphasize orientation data--surface normal vectors--can dramatically speed some analyses and opens the door to new techniques borrowed from the computer graphics field. Performance improvements are most apparent for multidirectional methods, making those techniques more available to cartographers with modest computing resources. Elevation is the dominant data model for terrain surfaces, and the de-facto input for widely available analytic cartography tools. It is the essential property driving hypsometric tinting or viewshed analyses. Yet the most widely used layers for terrain representation do not symbolize elevation, but rather orientation. These analyses depend on an interpretation of orientation from the elevation data. Each tool must do this on its own and may choose its own method for doing so. Complex techniques built upon relief shading or slope shading, such as Sky Model (Kennelly & Stewart, 2011) found in Esri's TerrainTools, perform this interpretation many times. This is duplicated work, and largely unnecessary. If adjacent tools interpret orientation differently, incongruencies introduce bias or noise to the analysis. An orientation-focused data model is available, widely used in other industries but under-used in GIS. This is a multiband raster dataset encoding surface normal vectors. Surface normal vectors completely capture pixel-by-pixel orientation independent of height and can be used directly in more modular and streamlined versions of the tools now common. This model separates elevation-to-orientation processing and executes only once, forming a persistent dataset to be fed to further analyses. The orientation calculations, because they are separate, can also be customized to the terrain type. When a tool such as Hillshade is unencumbered from this additional processing, it becomes more lightweight and executes faster, with less overhead. Multi-directional shading methodologies will benefit from improved performance in proportion to the number of lighting directions in the method. Sky Model runs the shading tool hundreds of times to accumulate a composite image (shown in Figure 1, compared with a traditional single-light shaded relief). An orientation-aware version runs several times faster than the widely available versions built atop conventional shading tools. Moving to a surface normal vector dataset permits us to implement proven techniques from the computer graphics field for novel cartographic effects. A version of displacement mapping has been used in GIS to raise patterns on a surface (Nighbert, 2002). This is a manipulation of the DEM. Bump-mapping produces a similar effect by operating on the surface normal vectors rather than the height data (Blinn, 1978). Bump-mapping, when employed with effective masking, is a useful technique to imprint textures onto the terrain that are themselves shaded properly. Critically, surface normal vector manipulations do not affect elevation analyses (hypsometric tints, shadows, etc). Patterns introduced to the relief shading, working alone or with other variables such as colour, are a means of differentiating distinct areas in the scene. Figure 2 illustrates the bump-mapping effect to create a textured shaded relief in which land use categories (forest and open water in this case) can be identified by colour, texture, or both. [ABSTRACT FROM AUTHOR]

Cartographers tout the merits of relief shading in giving terrain a three-dimensional appearance, while tending to ignore or discourage the use of shadowing for the shadow's tendency to obscure the underlying topographic details. It is possible, however, to discard relief shading and use only shadows from multiple light sources to create shadowing effects that have similar landform details and with the potential for a more dramatic three-dimensional effect when compared to relief shading. We present comparisons of a standard elevation model illuminated by a clear sky with a) relief shading, b) shadows, and c) relief shading plus shadows in Figure 1. We observe that adding relief shading to a shadowed rendering (Figure 1c) does not add much topographic detail to the shadow-based terrain representation (Figure1b). This may seem non-intuitive, as terrain is being represented not by the orientation of the land's surface with respect to a light source which is the basis of relief shading, but rather by the shadows cast by landforms that are aligned with the illumination direction. This result underscores the importance of illumination models that represent numerous point sources throughout the sky to simulate natural lighting conditions and result in soft shadows. Another important comparison between relief shading and representing terrain with shadows is that vertical exaggeration of the elevation model can produce more dramatic effects with the latter, as seen in the top row of Figure 2. This enhanced effect can be attributed to longer shadows with vertically exaggerated terrain. By contrast, vertical exaggeration of terrain for relief shading as seen in the bottom row of Figure 2 may make illuminated areas lighter and non-illuminated areas darker in grayness, but general patterns of lighter and darker areas remain the same while undergoing tonal modulations. These patterns are locked into place by the static nature of landform locations as opposed to the dynamic nature of their shadows' extents. [ABSTRACT FROM AUTHOR]

Standard Elevation Models We propose the use of standard elevation models to evaluate and compare the quality of various relief shading and other terrain rendering techniques. These datasets will cover various landforms, be available at no cost to the user, and be free of common data imperfections such as missing data values, resampling artifacts, and seams. Datasets will be available at multiple map scales over the same geographic area for multi-scale analysis. Utilizing a standard data model for testing and comparing methods is a common practice among many disciplines. Furthermore, the use of digital models to test rendering techniques based on qualitative visual production has been well established for decades. Following the generation of the first digital image in 1957, image processing and analysis required standard test images upon which methods could be tested and compared. During the 1960s and 1970s, many well-known standard test images emerged from this need for a comparative technique model. Today, institutions like the University of Southern California's Signal and Image Processing Institute maintain digital image databases for the primary purpose of supporting image processing and analysis research, including geographic imaging processes. Several well-known test models have also emerged from the world of three-dimensional image analysis. 3D test models like Newell's Utah teapot, for example, is a dataset created for testing computer generated rendering techniques like shading and textures (Lehman, 173-174). Although the Utah teapot differs slightly from its real life Melitta subject, it is derived from a real and recognizable object characterized by various topological features upon which rendering algorithms can be tested. Much like the free and open Utah teapot dataset, our spatial elevation test models are free of data imperfections for the purposes of surficial rendering methods testing. However, while the Utah teapot is a single model, ours is a series of test models at various geographic scales. While the need for standard digital test images began to emerge in computer graphics, the use of sensors mounted on airplanes and satellites to collect voluminous data began to thrive, producing new datasets that required novel processing and evaluation methods. High-resolution digital elevation models capturing detailed slope, elevation, and other topographic attributes, now offer earth scientists and cartographers powerful digital datasets for both understanding and rendering Earth's landscape. Among the branches of geo-science benefitting from high-resolution digital elevation models (DEM) was geomorphometry. Geomorphometry and relief shading techniques overlap in many aspects in that they are both areas of geographic rendering that make use of digital elevation models and other similar datasets for cartographic representation (Pike et al. 2009). Both branches of topographical representation pre-date computerized mapping, yet have been revolutionized with the growth of computer processing, thus routinizing their implementations (Pike 1999). However, since geomorphometric applications parameterize complex geomorphological influences for quantitative topographical analysis, many differences exist between geomorphometric models, such as predictive vegetation modeling and our proposed standard elevation models. Although our standard elevation models are created for testing mapping techniques, unlike geomorphometric models, ours are not for predicting or identifying landscape or geomorphological occurrences. Rather, the standard elevation models we propose are for the evaluation of cartographic rendering itself. Many studies to date have evaluated methods to render terrain for display for both two- and three-dimensional (2D and 3D) cartographic displays. In general, the evaluation involves comparing the new rendering with well-known and sometimes hand-rendered exemplars or typical terrain rendering techniques. Examples of the former include methods to reproduce historical Swiss-stlye rock drawings (Jenny et al., 2014), hand-drawn relief shading (Bell, 2018), and create plan oblique relief effects (Jenny and Patterson 2007), while examples of the latter include many examples that compare custom relief shading techniques with default hillshading techniques found in typical geographic information system (GIS) software (e.g. Huffman 2019, Marston and Jenny 2015, Kennelly and Stewart 2014, Tait 2002, Patterson 1997). Such studies typically involve searching for an appropriate and high quality DEM dataset, tasks that could be simplified with standard elevation models. Additionally, past research provides us with an opportunity to inventory the DEM data that was used previously in an effort to better understand the characteristics of the study areas that were selected. We will look at these past studies to determine attributes such as the geographic location, extent, and scale of previous models used to evaluate terrain representations. We will begin with reviews of relief shading and hypsometric tinting studies, and may expand our analysis to include other techniques such as 3D terrain mapping or other specialized techniques such as hachuring. While the idea of what a standard elevation model for relief shading is may evolve as the study progresses, we currently plan to focus on the following ideas in searching for candidates. As previously stated, the data should be free to distribute, of high quality, cover various landforms and be available at multiple scales. The standard elevation models should also cover areas that have been mapped frequently over time. Historical and contemporary geo-referenced terrain maps should be available for these areas to allow the user to easily compare new techniques to existing cartographic products. We hope that developers of new algorithms will use the standard elevation models to compare their results to previously existing methods and maps. [ABSTRACT FROM AUTHOR]