Automatic Scree Representation for Topographic Maps

Scree – a mass of small stones covering a slope on a mountain – is extremely labour-intensive to reproduce on topographic maps when each stone is drawn separately. Th is is due to the large number of stones – typically several hundreds of stones per square centimetre in a scree fi eld. An automatic procedure to produce scree representations would therefore greatly simplify and accelerate the production of topographic maps of highmountain areas. Th is paper will present selected aspects of a project aiming at the development of a new algorithm for the automatic generation of scree representations approaching the quality of hand drawn representations. Swiss scree drawing 1. Th e offi cial maps of the Federal Offi ce of Topography swisstopo are famous for their immediate and descriptive representation of the third dimension in alpine areas (Fig. 1). Th ey use contour lines and spot heights that allow the mapreader to extract a numerical altitude for each location on the map — and display the terrain with a three-dimensional eff ect by the elaborate interplay of the following four elements: a shaded relief with an oblique illumination, a yellow illumination tone on bright sunlit slopes, a rock drawing with an oblique illumination, and a scree drawing emphasizing the underlying shaded relief. Th e shaded relief is drawn by hand with local adaptations of the direction of illumination to optimally convey the third dimension (Imhof, 1982; Jenny, 2001) and printed in a bright gray tone. To further emphasize the three-dimensional eff ect of the shading, a subtle yellow illumination tone is added on slopes oriented towards the source of illumination (Jenny and Hurni, 2006). In the area of cliff s and rock faces, sophisticated rock drawings illustrate the local type of rock with various combinations of hachures. Th is rock hachuring is again modulated with illumination, i.e. rock faces oriented towards the sun are rendered in a much brighter tone than faces oriented away from the sun (Imhof, 1982; Hurni et al., 2001). Th e scree drawing consists of tiny stones scattered in-between the other map features, and is mainly applied on high-mountain slopes, but also along fl at riverbanks to represent gravel and sandbanks. Th e stones forming a fi eld of scree vary in shape, density and size. Th e density and the size of stones on the map do not primarily refl ect the density of scree one encounters in situ. Th ey are rather adapted to optimally conveying the impression of an illuminated three-dimensional surface, i.e. when viewed from a distance, the individual stones become Enlarged sections of the swisstopo map Tödi (1193) 1:25,000 Fig. 1: Automatic Scree Representation for Topographic Maps 98 • Mountain Mapping and Visualisation 6th ICA Mountain Cartography Workshop indistinct and the eye perceives a continuously illuminated surface resulting from the combination of the shaded relief, the shaded scree and the shaded rock drawing. Another characteristic of scree representation is the arrangement of stones to indicate fall lines, which follow the line of the steepest slope. Scree drawing by error diff usion in Photoshop 2. Th e density of scree stones can be modulated with a Photoshop function that is applied on a shaded relief. First, a gradation curve is applied on the grayscale shading to increase its brightness (Fig. 2). Th e shading is barely visible in the resulting image. In a second step, the grayscale image is down-sampled to 254 dpi and then converted to a bitmap image (i.e. a binary image with only black and white colors, but no intermediate gray values). Th e image is rasterized at 185 dpi with the diff usion-dither option (Fig. 3). Th e resulting image shows blocky stones in a pseudo-random arrangement (Fig. 4), where each black pixel represents one scree stone. In a fi nal step, a mask is applied to remove stones outside of scree areas. Th e Federal Offi ce of Topography swisstopo invented this procedure (swisstopo, 2006), which was applied to a test sheet (Fig. 5) to evaluate an updated map design (Feldmann and Kreiter, 2006). Th e described technique is applied and does not require non-standard software. Another main advantage is that the density of scree stones can be easily adapted by adjusting the gradient curve. However, it has two major shortcomings: Th e stones are all square-shaped and all of the same size, which results in a very regular and unnatural appearance. Stones are not arranged in fall lines, i.e. the lines of steepest slope are not indicated by the stones. Pattern fi lling with an Illustrator plug-in 3. An alternative approach to the Photoshop technique presented above uses a plug-in for Adobe Illustrator (a vector graphics application). Th e plug-in was developed at the Institute of Cartography of ETH Zurich and is available for free at www.ika.ethz.ch/plugins/index.html (Werner and Hutzler, 2005 and 2006; Hutzler, 2007). It fi lls closed polygons with a pseudo-random pattern of user-defi nable symbols. We applied this plug-in to polygons defi ning the outlines of scree areas and used the scree symbols in Fig. 6. Th e plug-in takes obstacles into account, i.e. areas where no symbol should be placed can be defi ned by arbitrary lines or polygons. Th e plug-in then ensures that placed symbols don’t overlap these areas or are closer than a user-defi ned distance. When placing a symbol, the algorithm pseudorandomly picks one of the stones in Fig. 6. Th e probability for each stone to be picked can be adjusted by the user. (Note that the shape of the stones in Fig. 6 and applied in Fig. 8 are not generally recommendable for scree representations. Scree stones should have a more compact and convex shape.) Obstacle lines (blue in Fig. 8) are used to add a fl ow structure to the placed stones. Th is imitates the manual placement of scree stones, where stones are arranged along fall lines to indicate the line of steepest slope. Th e pattern-fi lling method with the Illustrator plug-in has the disadvantage that the density of scree stones is not modulated with the brightness of the shaded relief. Hence Each scree stone is represented by one pixel Fig. 4: Adjustment of the brightness of the shaded relief Fig. 2: Diff usion dither converts from a grayscale to a bitmap Fig. 3: image