Regionalization of multi-categorical landscapes using machine vision methods

Transcription

1 Regionalization of multi-categorical landscapes using machine vision methods Jacek Niesterowicz a, Tomasz F. Stepinski a a Space Informatics Lab, Department of Geography, University of Cincinnati, Cincinnati, USA, OH , USA Abstract We introduce a novel method for regionalization of multi-categorical landscape or land cover pattern based on the principle of machine vision rather than clustering of landscape metrics. Maps of land use/land cover (LULC), such as, for example, the NLCD 2006, show spatially varying pattern of LULC categories. Using a LULC map as an input our method discovers and maps different landscape types (LTs), each dominated by a characteristic LULC pattern that reflects varied influence of natural and anthropogenic factors. At the core of the method are the concepts of landscape signature and landscape dissimilarity adapted from the field of machine vision. A two-dimensional histogram of LULC categories and clump sizes is used as a landscape signature and the Jensen-Shannon measure is used as landscape dissimilarity. We have also adapted the machine vision technique of object-bases image analysis, consisting of segmentation and clustering, to find the set of LTs regions. Such technique maximizes spatial contiguity of the regions while also providing necessary level of generalization. The method is applied to the study area located in the northern part of the U.S. state of Georgia using the NLCD 2006 data. Local landscape is defined over a square, 3km 3km areal units; there are 8475 such units in the study area. Several different computational protocols for regionalization of these units are evaluated with the best protocol resulting in a discovery and delineation of fifteen LTs. The LTs are summarized from descriptive and quantitative perspective, their landscapes signatures are shown, and an example of each landscape is given. Delineated LTs agree well with perceptual patterns seen in the NLCD map. Non-urban LTs are arranged roughly in stripes running from SW to NE perpendicular to the regional gradient of elevation. Full resolution maps, the data, and our regionalization computer code are available at Keywords: regionalization, spatial pattern, landscape, land cover, NLCD Introduction 19 and Hoffman, 2004) The aim of regionalization (Chorley and Haggett, 1967; Johnston, 1968, 1970; Spence and Taylor, 1970; Haggett et al., 1977) is to aggregate a large number of geographical areal units into a much smaller number of spatially contiguous regions that group units having similar features. The goal of regionalization is to simplify and/or change the spatial representation of data into something that is more meaningful and easier to analyze. It has been applied to many diverse fields including demography (Openshaw and Rao, 1995; Benassi and Ferrara, 2010), political science (George et al., 1997), geomorphology (Chai et al., 2009), hydrology (Wiltshire, 1986; Peterson et al., 2011), climatology (Fovell and Fovell, 1993; Stooksbury and Michaels, 1991), biogeography (Proches, 2005; Patten and Smith- Patten, 2008; Kreft and Jetz, 2010), agricultural science (Lark, 1998; Hollander, 2012), and ecology (Hargrove Regionalization of LULC patterns Regionalization has been also applied to LULC (land use/land cover) patterns (Wickham and Norton, 1994) with particular focus on forest patterns (Long et al., 2010; Kupfer et al., 2012). A LULC pattern is a geometric of different LULC categories within a given areal unit. Such patterns have often functional significance (White, 2006) for landscape as they are associated with environmental conditions. Local LULC patterns (hereafter referred to as landscapes ) show great variability of composition and geometric form, but a limited number of semantically different landscape types (LTs) can be discerned from among this variance. The role of regionalization in the context of landscapes is to delineate boundaries between semantically different LTs. Technical challenges facing such task are as follows. (1) To select a scale of local landscape by setting the size Preprint submitted to Applied Geography September 29, 2013

2 of an areal unit. (2) How to describe a landscape in a quantitative fashion? (3) Given landscape description, how to calculate a degree of dissimilarity between two landscapes in a fashion that minimizes a discrepancy between calculated value of dissimilarity and the perceptual notion of dissimilarity. (4) Given a landscape description and corresponding similarity function, how to obtain a useful regionalization that delineates a study area into discernibly different patterns of land cover. Long et al. (2010) studied regionalization of binary (forest, non-forest) landscape patterns using the 25 m/pixel land cover dataset covering a forested land situated in British Columbia, Canada. They regionalized a 5.5 million ha area into the eight LTs characterized by different forest compositions and pattern configurations. Local landscapes were defined over 1 km 2 squared areal units that together partitioned the entire study area. Their character was encapsulated using five landscape metrics (for review of landscape metrics see Haines-Young and Chopping (1996)) and the Euclidean distance between 5-dimensional vectors of landscape metrics was used as a dissimilarity measure between a pair of landscapes. Regionalization was achieved by the means of clustering the vectors using an algorithm based on partitioning around medoids. The optimal number of clusters, and thus the number of forest LTs, was determined using the silhouette method (Rousseeuw, 1987). Kupfer et al. (2012) has also studied the regionalization of forest patterns using the 30 m/pixel National Land Cover Dataset 2001 (NLCD 2001). They regionalized the entire conterminous United States into the nine LTs. Local landscapes were defined over watersheds; 2109 eight-digit HUC (Hydrologic Unit Code) watersheds partitioned the entire United States. Local landscapes were characterized by five landscape metrics; note that selected metrics pertained not only to the pattern of forest category but also to interaction between forest category and other land cover categories. Euclidean distance between 5-dimensional vectors of landscape metrics was used as a dissimilarity measure between a pair of local landscapes. The novelty of their approach was to use a clustering technique, called RED- CAP (Guo, 2008), that is customized for regionalization purposes. REDCAP is a hierarchical clustering method that preserves spatial contiguity of clusters. The optimal number of clusters (nine), and thus the number of forest LTs, was determined using the so-called L-method (Salvador and Chan, 2004) New approach to regionalization of LULC patterns Methodologies used in the two studies described above, as well as methodologies used in other, similar studies, have a lot in common. (1) They describe local landscapes by means of vectors of landscape metrics. Landscape metrics may be well-suited for description of binary patterns (like the forest patterns) where only a small number of relative weights need to be set. However, they are not well-suited for description of multi-categorical patterns where a much larger number of metrics are needed without any guidance of how to set their weights. (2) They rely on Euclidean distance between vectors of metrics to measure dissimilarity between the patterns without any assessment on how such measurement corresponds to perceptual notion of dissimilarity. (3) Finally, they rely on clustering. Clustering, being a technique grouping objects on the basis of a nonspatial features, seems like an odd choice for regionalization procedure that suppose to yield spatially contiguous regions. This problem has been noted and addressed by using REDCAP (a clustering that enforces spatial contiguity) but not by using segmentation - the technique that seems like a natural choice to perform regionalization. In this paper we introduce a novel approach to regionalization of landscapes, one that departs significantly from existing methodologies. First, we are interested in regionalization of multi-categorical landscapes (as, for example, those stemming from the NLCD) rather than binary landscapes (as, for example, those consisting only of forest and non-forest categories). Second, our approach does not rely on landscape metrics for landscape quantification and it does not use Euclidean distance for comparison of different landscapes. Instead, inspired by the methods developed in the context of machine vision (Gevers and Smeulders, 2004; Datta et al., 2008; Lew et al., 2006), we use 2D, class/clump-size histograms as quantitative signatures of land cover patterns and we measure a dissimilarity between two landscapes using the so-called Jensen-Shannon divergence (Lin, 1991). In application to natural images, such a dissimilarity measure was shown to offer a good agreement with human visual perception in the side-by-side comparison with other measures (Rubner et al., 2001). Finally, we use a combination of segmentation and clustering to achieve an actual regionalization of landscapes. 2. Data and Methods Our study area is the 339 km 225 km region located in the state of Georgia and centered on 85.3W 2

3 N NLCD legend open water (11) ice/snow (12) developed open space (21) developed low intensity (22) developed med. intensity (23) developed high intensity (24) barren land (31) deciduous forest (41) evergreen forest (42) mixed forest (43) shrub/scrub (52) grassland (71) pasture/hay (81) cultivated crops (82) woody wetlands (90) emergent wetlands (95) km Figure 1: Land cover map (NLCD 2006) of the study area. Legend gives names and numerical codes of land cover categories. Inset shows the location of the study area within the United States and 33.5N (see Fig. 1). Note that, by coincidence, our study area is very similar to that previously considered by Wickham and Norton (1994). The land cover map of this area is provided by the NLCD 2006 in the form of the raster with pixels. The NLCD 2006 has 16 land cover categories of which most are present (with varied abundances) in the study area. Visual inspection of the study area reveals rich variation of local landscapes (Fig. 1). In addition to urban landscapes (that include the Atlanta metropolitan area) a variety of land cover patterns can be observed with the general direction of pattern change along the SE-NW axis. Our goal is to regionalize the landscape in the study area into several subregions characterized by distinct LTs using unsupervised machine learning process requiring minimum human judgment. Our methodology uses many techniques originally developed for querying the NLCD 2006 for locations having similar patterns (Jasiewicz and Stepinski, 2013; Stepinski et al., 2013). However, whereas the focus of previous work was on querying by example (see our web-based search application at the present focus is on regionalization. A local raster tile A is defined as a squareshaped section of the NLCD having the size of n n cells. A pattern of land cover categories within a tile forms a local landscape. In this paper we use tiles with n = 100, thus landscape is defined on the scale of 3 km. To cover the entire study area = 8475 tiles are arranged (without overlap) in a lattice of local landscapes Landscape signature Landscape signature is a compact mathematical description of a landscape. In previous works (Long et al., 2010; Kupfer et al., 2012) landscape signature was a vector of landscape metrics. Here a landscape signature is a 2D, land cover category/clump-size histogram constructed from the pixels in the tile. A clump is a contiguous group of same-category pixels. Segmentation of the NLCD into clumps is achieved using a connected components algorithm (Rosenfeld and Pfaltz, 1966; Netzel and Stepinski, 2013). A clump size is a number of pixels in a clump. We categorize clump sizes by assigning them to seven bins with ranges based on the powers of 5 (i.e. 1-4, 5-24, , , , ; >15625). In addition to its land cover category, each pixel inherits a clump-size category from the clump to which it belongs. The 2D histogram of tile s pixels (with respect to NLCD categories and clump-size

4 categories) is a signature of tile s landscape; it has 16 7 = 112 bins. Such a signature is invariant to rotation and translation. For more details on how the 2D histograms are constructed see Jasiewicz and Stepinski (2013) and Stepinski et al. (2013). Note that landscape signature can be calculated for a tile, segment, region, or any other section of the entire study area Dissimilarity between two landscapes Landscape dissimilarity is a function that assigns a numerical value of dissimilarity between any two landscapes on the basis of their respective signatures. In previous works (Long et al., 2010; Kupfer et al., 2012) landscape dissimilarity was the Euclidean distance between two vectors of landscape metrics. Here, because landscape signature is a histogram rather than a vector, a large selection of possible dissimilarity functions is available; for a comprehensive survey see Cha (2007). We use the Jensen-Shannon divergence (Lin, 1991) to calculate dissimilarity between two histograms because of its robustness and good performance in the side-byside comparison with other measures (Rubner et al., 2001). For two histograms A and B (representing two local landscapes) the Jensen-Shannon divergence (JSD) measures the deviation between the Shannon entropy (Shannon, 1948) of the mixture of the two histograms (A + B)/2 and the mean of their individual entropies, and is given by ( A + B ) JSD(A, B) = H 1 [H(A) + H(B)] (1) 2 2 where H(A) indicates a value of the Shannon entropy of the histogram A H(A) = 16 i=1 7 A i, j log 2 A i, j. (2) j=1 A i, j is a size of the bin in the 2D histogram - a fraction of pixels belonging to land cover class i and clump-size j. JSD is always defined, symmetric, bounded by 0 and 1, and equal to 0 only if A = B. For in depth explanation of how JSD assesses similarity between two histograms and why it constitutes a good measure of alikeness between two LULC patterns see Jasiewicz and Stepinski (2013) and Stepinski et al. (2013) Segmentation In machine vision, an image segmentation is the partition of an image into a meaningful set of regions that collectively cover the entire image. In our context segmentation is performed on a lattice of tiles instead of raster of image pixels. We have adopted a single pass region growing segmentation algorithm (Levine and Shaheen, 1981; Pitas, 2000) from image application to lattice of tiles application. Our algorithm has a single free parameter - the maximum dissimilarity threshold JSD th for allowing merging. The lattice is scanned starting from its upper-left corner. (1) A signature of a focus tile is compared (using Jensen-Shannon divergence) to signatures of adjacent, already existing but not necessary completed segments; the smallest value of JSD resulting from this comparison is denoted by JSD min1. (2) If JSD min1 < JSD th the focus tile is added to the segment corresponding to JSD min1 (3) If JSD min1 > JSD th the focus tile is compared to all not-adjacent already existing segments; the smallest value of JSD resulting from this comparison is denoted by JSD min2. (4) If JSD min2 < JSD th the focus tile is added to the not-adjacent segment corresponding to JSD min2, otherwise the focus tile becomes a seed of a new segment. Note that the algorithm is preferentially merging focus tiles with adjacent segments, but also allows for a merger of focus tile with a non-adjacent segment. This results in a smaller number of segments labels (for a given value of JSD th ), but it also makes possible, and even common, for a single segment label to be distributed between a number of spatially separated clumps Regionalization protocols The inputs to our regionalization algorithm are: a raster of land cover classes (a clip of the NLCD 2006) and a raster of clump sizes. The raster of clump sizes is categorized as described above. These two rasters are used to construct landscape signatures for all 8475 tiles constituting the study area. The lattice of tiles is processed by a combination of segmentation and clustering techniques to produce the final regionalization of the landscape in the study area. Every time the segmentation or clustering technique calls for computation of a distance we use the Jensen-Shannon divergence. Wherever clustering is called upon (either for tiles or segments of tiles) an agglomerative hierarchical clustering algorithm is used. The optimal number of clusters (>2) is determined using the silhouette method (Rousseeuw, 1987). Two types of linkage (criterion determining the distance between sets of tiles) were considered: average and Ward s minimum variance method (Ward, 1963). We have determined empirically that the Ward s linkage leads to a better regionalization results and have selected it as the linkage of choice for the results presented here. Note that the formal definition of Ward s method assumes that input units are vectors with 4

5 Euclidean distance as a dissimilarity measure. However, Ward s method can be implemented as an iterative procedure which does not require calculation of centroids and can be used with any dissimilarity measure including the Jensen-Shannon divergence. Three different computational protocols have been used to obtain regionalization of landscape in our study area. (1) Clustering of all tiles. This is a control protocol that relies only on clustering of all tiles and does not use segmentation at all. Visual inspection of the resultant map showing spatial distribution of ten (selected number of clusters) different LTs reveals a good agreement with perceptual patterns of land cover. However, the map suffers from noise - a large number of single tiles belonging to a different LT than its surroundings. This is expected as clustering does not enforce explicitly spatial contiguity. (2) Segmentation and clustering. Segmentation does enforce spatial contiguity, but its straightforward application to the tiles does not yield a useful regionalization. This is due to a large diversity of landscapes on the spatial scale we consider. Segmentation with a large value of JSD th (liberal agglomeration of neighboring tiles into contiguous segments) yields a small number of regions, but they are internally too diverse to constitute types of landscape. On the other hand, segmentation with a small value of JSD th (conservative agglomeration of tiles into contiguous segments) yields too many LTs. Our solution is to use a two-step approach inspired by the object-based image analysis (OBIA) (Blaschke, 2010; Hay and Castilla, 2008). In the first step the lattice of tiles is segmented conservatively (JSD th =0.2) yielding 345 internally uniform landscape objects. In the second step landscape objects are clustered into a small number of clusters constituting LTs. The resulting map of ten (selected number of clusters) LTs has minimum noise but does not differentiate between some patterns that are clearly perceived as different. We have traced this problem to the fact that segmentation of the lattice of tiles yields a lot of small (few tiles) segments in addition to relatively larger segments. The predominance of small segments distorts the subsequent clustering step because segments are agglomerated on the basis of their landscape signature alone and without considering their sizes. (3) Segmentation, clustering, and the nearest neighbors. This protocol is similar to the one discussed above, but only 109 segments 10 tiles are clustered. Subsequently, the remaining 236 small segments are assigned to the resultant clusters using the nearest neighbor algorithm. Small segments which don t have near neighbor are assigned to a new cluster. We judged this method, which yielded fifteen optimal LTs, as being most in agreement with visual perception Computer software and its performance The functions necessary to create the landscape signatures, to calculate the JSD, and to perform the segmentation were implemented as GRASS GIS (Neteler and Mitasova, 2007) extensions (requires GRASS v.7) and are written in ANSI C utilizing GRASS API. The suite of these extensions can be downloaded from Clumping of the NLCD 2006 data over the entire conterminous United States is available at With clumping available as an input data calculating all 8475 signatures (2D histograms) for our study area took 25 seconds using a PC with Intel Core7 processor running Linux. The performance of an algorithm calculating signatures scales linearly with the raster size if clumping data is available. For data for which clumping needs to be calculated we recommend using the fast connected components algorithm by Netzel and Stepinski (2013). The complexity of this algorithm depends on the character of the data; clumping the entire NLCD took 39 hours and resulted in labeling of 221,718,501 clumps. Once 2D histograms are calculated the segmentation of our study area took 2.2 seconds. The performance of the segmentation algorithm is similar to the performance of the clumping algorithm, it depends on the complexity of the underlying pattern. Functions necessary to calculate hierarchical clustering, the nearest neighbors classification, silhouette values, and the multi-dimensional scaling diagram (see section 4) are the part of R free software programming language and a software environment (Team, 2009). 3. Results Fig. 2 shows average silhouette values as functions of number of clusters. The purpose of this figure is to demonstrate an existence of optimal number of clusters and to show degree of separation between the clusters. The functions show the presence of maxima indicating existence of an optimal partitioning regardless of computing protocol. Silhouette values are highest for protocol (3) and lowest for protocol (2) confirming our visual assessment of degree of agreement between calculated regions and patterns perceived in the land cover map. For protocol (3) the highest value of silhouette ( 0.4) is attained for fourteen clusters. We use this partitioning, to which the nearest neighbor classification adds 5

6 average silhouette number of clusters A B C number of clusters average silhouette number of clusters Figure 2: Dependence of average silhouette value on the number of clusters. (A) Clustering only. (B) Clustering and segmentation. (C) Clustering, segmentation and the nearest neighbors. Landscape types legend 1 deciduous forest matrix 2 deciduous-evergreenpasture 3 evergreen-deciduousgrassland 4 evergreen- deciduous 5 evergreen forest matrix 6 deciduous-pastureevergreen 7 water 8 forest-water N 9 forest-wetlandgrassland 10 wetland-evergreencropland 11 wetland 12 forest-croplandgrassland 13 forest-croplandwetland 14 urban 15 downtown km Figure 3: The map of fifteen different landscape types within the study area obtained using the segmentation, clustering, and the nearest neighbor protocol. 6

7 Table 1: Description of landscape types ID Gridcode Description Percentages Code Area Cluster dev. Cluster diam. 1 1 deciduous forest matrix 64%-11% deciduous-evergreen-pasture 47%-20%-10% evergreen-deciduous-grassland 32%-30%-10% evergreen-deciduous 48%-20% evergreen forest matrix 62%-14% deciduous pasture evergreen 28%-26%-17% water 39%-22%-19% forest-water 25%-23%-23% forest-wetland-grassland 24%-19%-19%-14% wetland-evergreen-cropland 30%-20%-13% wetland 49%-15% forest-cropland-grassland 21%-18%-14%-14% forest-cropland-wetland 23%-22%-20% urban 24%-21%-16%-13% downtown 41%-27%-20% one more cluster for a total of fifteen, as our best result to be fully described here. The results of regionalization using all three protocols are available for download from as rasters in Geo- Tiff format. Fig. 3 shows the map of LTs within the study area as obtained using the segmentation, clustering, and the nearest neighbor computational protocol. The map has not been modified by any post-processing technique. Table 1 gives a description and the summary of identified LTs. The first column in the table gives the ID of the LT so it can be identified on the map. The second column gives a gridcode value to be used when inspecting a GeoTiff raster available for download. The third, fourth and fifth columns give short description of the LT, composition of its major land cover classes, and its code, respectively. We extended a nomenclature described in Wickham and Norton (1994). The land cover category that dominates (60% minimum) the LT is the matrix. Patch land cover components are those present but not dominant. The is a LT consisting of several patch components - a combination of land cover categories without any single category being dominant. We also define a feature - a pattern in which a single land cover category is abundant and concentrated in a single clump. LT code is a list of numerical labels (see legend to Fig. 1) corresponding to major land cover categories present in a given LT; bold font indicates matrix, bold-italic font indicate feature, and regular font indicates. The last three columns in Table 1 give the area of the LT in units of the number of tiles, cluster deviation, and cluster diameter, respectively. The last two quantities describe variance between segments constituting a given LT. Whereas segments, agglomerated using a small value of JSD th, are internally homogeneous with respect to their constituent tiles, LTs, agglomerated using a clustering technique without a notion of threshold, could be more diverse with respect to their constituent segments. This is a desirable feature as it allows for greater generalization of resultant regions. A medoid is defined as the segment in a cluster, such that its average dissimilarity to all the segments in the cluster is minimal. Medoid could be though of as the representative segment for a given LT. Cluster deviation is an average distance of all segments in a LT to its medoid. Cluster deviation measures level of diversity between segments in a given LT. For our LTs the cluster deviation varies from 0.17 (for LT #2) to 0.27 (for LTs #9 and #15). Note that LTs characterized by simple patterns, those described as matrix (#1 and #5), do not have necessarily the smallest deviations. Cluster diameter is defined as the largest dissimilarity between segments belonging to a given LT; large values indicate existence of outliers - segments having patterns significantly different from the majority of segments in the cluster. Overall, our LTs appear to have just the right amount of deviations, small enough to provide distinction between different LTs but large enough to allow for some level of generalization. This right balance is responsible for a good agreement between our map (Fig. 3) and visual perception of where the boundaries between different patterns of land cover categories should be (for in-depth comparison use the full resolution land cover map - a part of our download material). Fig. 4 shows landscape signatures of all fifteen LTs and Fig. 5 shows an example of a single tile from each LT. The signatures are collected from the entire spatial 7

8 1(1) 2(4) 3(6) 4(7) 5(9) 6(2) 7(5) 8(8) 9(14) 10(12) 11(13) 12(10) (11) 14(3) 15(15) Figure 4: Landscape signature of fifteen different landscape types identified by our segmentation, clustering, and the nearest neighbor protocol. Bins are colored to reflect color assignments of land cover categories they represent. Numbers indicate ID numbers of landscape types with gridcodes given in brackets. Lower-right corner panel shows multi-dimensional scaling diagram depicting relative similarities between landscape types. 8

9 1(1) 2(4) 3(6) 4(7) 5(9) 6(2) 7(5) 8(8) 9(14) 10(12) 11(13) 12(10) 13(11) 14(3) 15(15) Figure 5: Representative examples of tiles from each landscape type. Numbers indicate ID numbers of landscape types with gridcodes given in brackets. See Fig. 1 for land cover categories legend extent of respective LTs. Most LTs contain at least a trace amount of pixels from all land cover categories (except the ice/snow category), however, for clarity, only histogram bins containing minimum of 0.01% of LT s pixels are displayed. Tiles shown in Fig. 5 are selected from a medoid segment of each LT. As LTs are spatially diverse (see above) no single tile can represent the entire LT, so tiles shown in Fig. 5 may have local landscape signatures (not shown) that differ from corresponding LTs signatures shown in Fig. 4. The lower-right panel on Fig. 4 shows a multidimensional scaling (MDS) diagram constructed for LTs using the Sammon s algorithm (Sammon, 1969) This diagram illustrates relative similarities between the LTs; distances between labels on the diagram are proportional to dissimilarities between corresponding LTs. It is important to note that JSD does not take into account semantic similarities between land cover categories. LTs 1 to 5 are all dominated by forest and could be perceived by some as similar (especially as our maps use similar colors to depict different categories of forest). However, deciduous and evergreen forests are two independent land cover categories and the fact that both of them are forest is not taken into account by the JSD. Thus labels 1 to 5 on the MDS diagram are not clustered all together; instead they form an extended series on the diagram. The series starts with the deciduous matrix (LT=1), continues with LTs characterized by deciduous-evergreen s with progressively larger portions of evergreen forest, and ends with the evergreen matrix (LT=5). The logic behind such series can be best understood by examining signatures in Fig. 4 that clearly show the progression from LT=1 to LT=5. LTs 9 to 11 form another series of landscapes containing significant amount of wetland category but within progressively different patterns. In fact, LT=10 is more similar to LT=13 than to other LTs in the wetland series, and LT=9 is most similar to LT=12 than to other LTs in the wetland series. Finally, the downtown (LT=15) is dissimilar to all other LTs, even to the urban (LT=14). Overall, the fifteen LTs identified by our procedure represent well the different LULC patterns present in the study area. Depending on a particular need a coarser or finer regionalization may be needed, however, recall that other divisions will result in lower values of average silhouette and thus lead to less distinct landscape types. One can also further group the fifteen LTs man- 9

10 ually taking into account semantic similarities between them. For example, one possible manual grouping is into the following six regions: forest (LTs = 1,2,3,4,5), forest-pasture (LT=6), water (LTs = 7,8), wetlands (LTs = 9,10,11), cropland (LTs = 12,13), and urban (LTs = 14,15). 4. Discussion and future directions In this paper we offer a novel perspective on how to approach the regionalization of multi-categorical landscapes. The method is underpinned by principles of machine vision rather than more traditional principles stemming from ecological landscape analysis. The method grew from our desire to develop a suite of tools for robust and computationally efficient analysis of patterns in large categorical datasets (such as, for example, the NLCD). Whereas our earlier work (Jasiewicz and Stepinski, 2013; Stepinski et al., 2013) concentrated on supervised analysis (finding local landscapes similar to a given example), the present work focuses on an unsupervised analysis. Regionalization is an unsupervised analysis as its goal is to find hidden structure in unlabeled data of local landscapes. It can also be thought of as knowledge discovery process, as our methodology discovers types and spatial extents of landscapes that occur in the study area. Mapping landscape types has many potentially useful applications, some of them have been already outlined by Wickham and Norton (1994) and Long et al. (2010), but others are still waiting to be formulated. Traditionally, mapping LTs was done in the context of ecology for the benefit of a variety of management and conservation activities. However, another interesting research direction is to investigate controlling factors behind discovered LTs. These factors can be either of natural or anthropogenic origin. In our study area, many landscape types (LTs = 1,3,4,12,13) are arranged roughly in stripes running from SW to NE indicating natural controlling factors that change along the SE-NW axis. This is basically an axis of an elevation change in Georgia, which, in turn may be related to changes in topography, drainage density, and soils type. Controlling factors data are in the public domain including the landscape elements data available on our web site DataEye ( calculated using a geomorphons method (Jasiewicz and Stepinski, 2013b). Future research will identify which of these controlling factors correlates with the LTs. Note that some of these potential factors (for example, landform elements) are given in the form of multi-categorical rasters and the regions of their characteristic patterns can be found using a method described in this paper. Thus, for example, terrain types can be calculated from landform elements data in the same fashion as LTs are calculated from the NLCD. We hypothesize that at least some of the terrain types will correlate spatially with the LTs; future research will address this hypothesis. Urban planning is an another potential area of application for mapping LTs. Satellites such as Ikonos or QuickBird provide very high resolution (VHR) multispectral images. Methods of accurate classification of VHR images have being developed (for example see Bhaskaran et al. (2010); Myint et al. (2011); Pu et al. (2011)) resulting in increased availability of very high resolution LULC landscapes. Regionalization of such landscapes would yield LTs that can be used for classification of neighborhoods within cities. Similarly, LTs derived from VHR images of agricultural areas (Castillejo-Gonzalez et al., 2009) can be used to classify them into distinct agro-regions. Our methodology has a room to grow. In particular, future research will explore the possibility of incorporating semantic similarities between land cover categories. As we mentioned in section 3, the JSD does not take into account such semantic similarities, but some applications may benefit from semantic awareness. Ahlqvist (2008) has quantified semantic similarities between the NLCD categories. Utilizing his work and using the so-called Earth Mover s Distance (EMD) (Rubner et al., 2000) instead of the JSD to measure dissimilarity between the landscapes, the next version of our method would be able to perform a semantically aware regionalization of land cover patterns. Another research direction is to evaluate how different segmentation methods influence the content and spatial extent of resulting regions. In this paper we have only used the region growing segmentation method that constructs regions by means of agglomeration, but many more techniques exist including partitioning (rather than agglomerative) algorithms. Partitioning algorithms, such as, for example, the normalized cut algorithm (Shi and Malik, 2000) may be advantageous in applications to land cover patterns because, rather than focusing on local landscapes and their consistencies in the lattice, it aims at extracting the global impression of the entire study area. Acknowledgments. This work was supported in part by the National Science Foundation under Grant BCS , the Polish National Science Centre under grant DEC-2012/07/B/ST6/012206, and by the University of Cincinnati Space Exploration Institute.

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