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An Evaluation Model of Level of Detail Consistency of Geographical Features on Digital Maps

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An Evaluation Model of Level of Detail Consistency of Geographical Features on Digital Maps International Journal of Geo-Information Article An Evaluation Model of Level of Detail Consistency of Geographical Features on Digital Maps Pengcheng Liu 1,2 and Jia Xiao 1,2,* 1 Hubei Province Key Laboratory for Geographical Process Analysis & Simulation, Central China Normal University, Wuhan 430079, China; [email protected] 2 College of Urban and Environmental Science, Central China Normal University, Wuhan 430079, China * Correspondence: [email protected]; Tel.: +86-157-0299-4209 Received: 29 May 2020; Accepted: 24 June 2020; Published: 26 June 2020 Abstract: This paper proposes a method to evaluate the level of detail (LoD) of geographic features on digital maps and assess their LoD consistency. First, the contour of the geometry of the geographic feature is sketched and the hierarchy of its graphical units is constructed. Using the quartile measurement method of statistical analysis, outliers of graphical units are eliminated and the average value of the graphical units below the bottom quartile is used as the statistical LoD parameter for a given data sample. By comparing the LoDs of homogeneous and heterogeneous features, we analyze the differences between the nominal scale and actual scale to evaluate the LoD consistency of features on a digital map. The validation of this method is demonstrated by experiments conducted on contour lines at a 1:5K scale and artificial building polygon data at scales of 1:2K and 1:5K. The results show that our proposed method can extract the scale of features on maps and evaluate their LoD consistency. Keywords: level of detail; graphical unit; geographical feature; digital map 1. Introduction Scale has always been a key study focus in various disciplines. In cartography, scale includes rich meanings. Several terms—semantic resolution, geometric precision, geometric resolution, and feature granularity—are all related to scale to some extent. In the field of geographic information science, the level of detail (LoD) adds another such term. It can be used in the analysis of any type of spatial data, especially that of geospatial vector data. It is obvious that the LoD of cartographic features is directly related to the map scale. Different categories of geographic features on a map should, theoretically, have the same level of detail. A small-scale topographical map is commonly generalized from a relatively large-scale map. However, cartographic generalization can easily cause inconsistency in different cartographic features’ LoDs due to the various generalization models. The consistency of LoD has become a research focus in recent years with the massive application of volunteered geographical information (VGI), e.g., VGI in OpenStreetMap [1–4]. VGI data come from a wide range of sources, e.g., coordinate data collected with the GPS devices, digital results that are vectorized from paper maps, interpretation results of remote sensing images, and so on [5–7]. It is difficult to ensure that the VGI data of various sources are at the same level of detail. Furthermore, the volunteers who provide the VGI data normally have different educational backgrounds and knowledge structures, which makes the inconsistency of LoD inevitable. Thus, the geographic features in the VGI data from different sources and providers generally demonstrate the inconsistent LoD, which reduces the data quality and might result in the misreading of Internet maps. Therefore, it is necessary to develop a unified metric to evaluate the LoD of the geographic features on the map. When we try to develop such a metric for web maps, it will face a lack of metadata as well as scale and resolution. ISPRS Int. J. Geo-Inf. 2020, 9, 410; doi:10.3390/ijgi9060410 www.mdpi.com/journal/ijgi ISPRS Int. J. Geo-Inf. 2020, 9, 410 2 of 16 ISPRS Int. J. Geo-Inf. 2020, 9, x FOR PEER REVIEW 2 of 16 Consistency evaluation of map LoD can be conducted at both the semantic and representational levels of a geometric graph. Touya et al. [8] divided building polygons in OpenStreetMap into four OpenStreetMap into four hierarchy levels (single building, street, city, and country) according to hierarchy levels (single building, street, city, and country) according to different LoD hierarchies different LoD hierarchies under different scales. As another example, considering features underrepresenting different forest scales. areas As and another single example, buildings, considering these features features bel representingong to different forest semantic areas and levels single: a buildings,forest area thesethat has features few vertices belong and to di overlapsfferent semantic several buildings levels: a forestshould area be considered that has few inconsistent vertices and at overlapsthe semantic several level buildings [9,10]. The should most bedirect considered method inconsistentof measuring at the the LoD semantic of a geometric level [9,10 element]. The most is to directcalculate method the shor of measuringtest distance the between LoD of a adjacent geometric points element belonging is to calculate to thethe feature. shortest For distance example, between Ai [11] adjacentmeasured points the LoD belonging of a point to the cluster feature. using For example,a point-oriented Ai [11] measuredDelaunay thetriangle. LoD of For a point a curve cluster or usingpolygon a point-oriented feature, the length Delaunay of the triangle. shortest For side a curveof the or feature polygon can feature, be used the as length the minimum of the shortest detail sideparameter of the featurefor cartographic can be used representation as the minimum [12 detail]. For parameter the sake forof cartographicclarity and representationreadability, curve [12]. Forsymbols the sake on a of map clarity have and a readability,minimum perceptible curve symbols width. on The a map larger have the a minimumscale, the perceptiblelarger the ground width. Thedistance larger to the which scale, the the line larger width the groundcorresponds. distance When to which the scale the line is less width than corresponds. a certain threshold When the value, scale isneighboring less than a parts certain of thresholdthe feature value, will aggregate. neighboring This parts means of the that feature the curve will aggregate.symbol width This of means curves that at theaggregation curve symbol can widthbe used of curves as a atparameter aggregation for can LoD be usedassessment as a parameter [12,13]. for This LoD assessmentmethod is [12called,13]. Thisincremental method iscurve called detail incremental detection. curve Another detail detection.method involves Another methodrasterizing involves curve rasterizing features curveusing featuresincremental using grid incremental widths. gridWhen widths. the grid When width the gridis greater width than is greater a threshold than a threshold value, the value, part the of partthe ofcurve the curvethat does that doesnot coalesce not coalesce at smaller at smaller grid grid widths widths appears appears to toaggregate. aggregate. The The grid grid size size which which is equal toto thethe threshold threshold value value is usedis used to define to define the LoD the ofLoD a curve of a [curve14]. Figure [14].1 Figure shows the1 shows LoD detection the LoD processesdetection processes employed employed by the aforementioned by the aforementioned methods. Inmethods. Figure1 Inb, Fig theure curve 1b, detailthe curve is clear detail when is clear the symbolwhen the width symbol is 1m; width however, is 1m; the however, symbol the aggregates symbol onceaggregates and twice once when and itstwice width when is 2 its m (Figurewidth is1c) 2 andm (Figure 3.5 m (Figure1c) and1 3.5d), m respectively. (Figure 1d), Figure respectively.1e–g show Figure the same1e-g show curve the rasterized same curve with rasterized di fferent with grid widths.different Results grid widths. obtained Results by the incrementobtained by grid the width increment method grid are consistentwidth method with those are consistent obtained by with the those obtained by the increment symbol width method. The LoD parameter of a feature can be increment symbol width method. The LoD parameter of a feature can be measured by the threshold measured by the threshold width (symbol width or grid width) where parts of the feature width (symbol width or grid width) where parts of the feature conglomerate together. conglomerate together. Figure 1. Detecting the LoD of a curve using the progressive increment method. (a) A curve with bends. Figure 1. Detecting the LoD of a curve using the progressive increment method. (a) A curve with (b–d) Curve representation when the symbol width is respectively 1m, 2m and 3.5m. (e–g) Rasterizing bends. (b–d) Curve representation when the symbol width is respectively 1m, 2m and 3.5m. (e–g) results of curves, respectively, at 1m, 2m and 3.5m. Rasterizing results of curves, respectively, at 1m, 2m and 3.5m. This paperpaper presents presents a methoda method that that uses uses computational computational geometry geometry to detect to the detect minimum the minimum graphical unitsgraphical of map units features of map and computesfeatures and LoD computes parameters LoD using parameters a mathematical using statistics a mathematical model. This statistics model estimatesmodel. This the model actual mapestimates scale and the itsactual deviation map fromscale map-nominal and its deviation scale andfrom evaluates map-nomi thenal level scale of detail and consistencyevaluates the of maplevel featureof detail representations. consistency of The map method feature obtains
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