1 Spatial Modelling of the Terrestrial Environment - Georeferencial

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202 Spatial Modelling of the Terrestrial Environment The multi-stage approach can be expressed more formally as a composition of two functions: I ◦ S = {(i ↦→ s) :i ∈ I, s ∈ S, ∃ f ∈ F([i ↦→ f ] ∧ [ f ↦→ s])} (1) where I is the set of multi-spectral responses in an image (i m,n = p m,n (λ 1 ,λ 2 ,...,λ w ), i ∈ I ), F is a set of first-order (i.e., land cover) themes (F = { f 1 , f 2 ,..., f x }), each of which exhibits a distinct spectral response and S is a set of second-order (i.e., land use) themes (S = {s 1 , s 2 ,...,s x }). Equation (1) states that there is a unique and unambiguous mapping from the image domain, I , for each geometric entity, i ∈ I , to a theme in the second-order thematic domain, S, that is itself a composition of two mappings: (i) from the image domain to the first-order thematic domain (∃ f ∈ F(i ↦→ f )) and (ii) from the firstorder to the second-order thematic domains (∃ f ∈ F( f ↦→ s)) (Barr and Barnsley, 1999). 1 The approach formalized in equation (1) has been employed in a number of studies seeking to derive information on urban land use from Landsat Thematic Mapper (TM) and SPOT-HRV XS images. These have typically made use of kernel-based (i.e., moving window) re-classification techniques to perform the second-stage mapping, that is, to infer land use from an analysis of either the frequency (Wharton, 1982a, 1982b; Treitz et al., 1992; Fung and Chan, 1994; Steinnocher, 1996; Steinnocher and Kressler, 1999) or the spatial pattern (Barnsley and Barr, 1992, 1996) of land-cover labels within an N × N pixel window. The assignment of the most appropriate land-use label to the central pixel in the window is variously achieved by using frequency-histogram clustering algorithms (Wharton, 1982a, 1982b), frequency-proportion rules (Fung and Chan, 1994; Steinnocher, 1996; Steinnocher and Kressler, 1999), statistical measures of frequency proportion (Treitz et al., 1992) or statistical measures of spatial pattern (Barnsley and Barr, 1992, 1999). Although each of these has produced encouraging results for specific case studies, with consistently higher levels of accuracy than traditional per-pixel classification techniques (Kontoes, 1999; Kontoes et al., 2000), the general utility of this approach has been questioned on a number of grounds. These include: (i) the smoothing effect of the moving window on region boundaries; (ii) the difficulty of selecting a single window size appropriate to the identification of all land-use categories; and (iii) issues relating to spatial scale and scale dependence (Forster, 1985; Toll, 1985; Barnsley and Barr, 1996; Donnay and Unwin, 2001; Donnay et al., 2001; Weber, 2001). In terms of the last point, spatial reclassification techniques were originally designed for application to images with a spatial resolution in the order of tens of metres (e.g. Landsat TM and SPOT-HRV). In these data, the pixels are approximately of the same size as many of the key spatial entities/objects in urban scenes (e.g. houses), so that their spatial disposition can sensibly be explored within a reasonably small N × N pixel window. Recently, however, new optical satellite sensors have been launched that acquire images at a spatial resolution of 1 − 4 m (McDonald, 1995; Fritz, 1996; Corbley, 1996; Aplin et al., 1997; Ridley et al., 1997; Barnsley, 1999). While these clearly have considerable potential for urban land-use mapping at spatial scales between 1:25 000 and 1:10 000 (Corbley, 1996; Ridley et al., 1997; Donnay et al., 2001), they are not well suited to the use of 1 Barr and Barnsley (1999) show formally that, for equation (1) to be valid, the sets F and S must be defined in terms of the cross. product of the possible members of the first-order and second-order themes (denoted by C and U, respectively) and the underlying set of geometrical entities (R ={r 1 , r 2 , r 3 ,...,r n }).
Characterizing Land Use in Urban Systems via Built-Form Connectivity Models 203 spatial reclassification procedures of the type outlined above. This is because the pixels are typically much smaller than the principal objects within the urban scene, such that a largemoving window is required to capture the relevant spatial patterns of buildings, roads and open spaces. Apart from increasing the required computation time, this has the unwanted effect of significantly smoothing/blurring the boundaries between land-use parcels. An alternative approach – one that is arguably much better suited to the new generation of high spatial resolution (
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Spatial Modelling of the Terrestria
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Copyright C○ 2004 John Wiley & So
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Contents List of Contributors Prefa
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Contributors Jonathan L. Bamber Sch
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List of Contributors xi George Perr
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xiv Preface in theory and applicati
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2 Spatial Modelling of the Terrestr
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Editorial: Spatial Modelling in Hyd
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Editorial: Spatial Modelling in Hyd
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2 Modelling Ice Sheet Dynamics with
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Modelling Ice Sheet Dynamics by Sat
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36 Spatial Modelling of the Terrest
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4 Using Coupled Land Surface and Mi
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Coupled Land Surface and Microwave
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100 Spatial Modelling of the Terres
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Editorial: Terrestrial Sediment and
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Editorial: Terrestrial Sediment and
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6 Remotely Sensed Topographic Data
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Remotely Sensed Topographic Data fo
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7 Modelling Wind Erosion and Dust E
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Modelling Wind Erosion and Dust Emi
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Page 158 and 159: Modelling Wind Erosion and Dust Emi
Page 164 and 165: 8 Near Real-Time Modelling of Regio
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Page 176 and 177: High Low TSM Concentration Figure 8
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Page 204 and 205: PART III SPATIAL MODELLING OF URBAN
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Page 232 and 233: 11 Modelling the Impact of Traffic
Page 234 and 235: Modelling the Impact of Traffic Emi
Page 248 and 249: PART IV CURRENT CHALLENGES AND FUTU
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268 Index Bi-spectral InfraRed Dete
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270 Index floodplain maps, UK 92 fl
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272 Index Long-Term Ecological Rese
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274 Index snow depth measurement ne
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276 Index urban land use in remotel
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1 Spatial Modelling of the Terrestrial Environment - Georeferencial

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