) not 
ative 
An 
Tiers 
BD) 
ible. 
1 the 
ually 
c on 
Kim 
0 the 
| the 
ough 
rban 
it of 
nsity 
)«2 
nore 
294), 
gher 
le to 
ithin 
; not 
crete 
terns 
d is 
9). 
zhest 
y in 
nsity 
nsity 
| the 
jared 
e of 
sical 
vich, 
itish 
z00d 
a to 
nent. 
nore 
yet 
sible 
Is of 
and 
nage 
the 
t has 
sing 
data, 
| as 
the 
ntial 
attenuates with distance, can be modeled by responsive fractal 
geometry and fractal-based density functions. 
It is hoped that research into links between remote sensing, 
GIS, and spatial analysis will continue and more applications 
will be developed. The urban application in this paper has 
produced valuable insights into the manner in which residential 
development can be measured and modeled. In particular the 
increased amount of detail now possible, and the effect of 
development constraints on density profiles. It has produced 
results which may be used for urban monitoring management, 
as well as for prescribing planning decisions. 
REFERENCES 
Barnsley, M.J., Sadler, G.J. and Shepherd, J.W., 1989. 
Integrating remotely sensed images and digital map data in the 
context of urban planning. Proc. of 5th Annual Conference of 
the Remote Sensing Society University of Bristol, UK 
(Nottingham Remote Sensing Society) pp. 25-32. 
Batty, M. and Kim, K.S., 1992. Form follows function: 
reformulating urban population density functions. Urban 
Studies, 29, 1043-1070. 
Batty, M. and Xie, Y., 1994. Modelling inside GIS: part 1. 
Model structures, exploratory spatial data analysis and 
aggregation. International Journal of Geographical Information 
Systems, 8(3), pp. 291-307. 
De Cola, L.. 1989. Fractal analysis of a classified Landsat 
scene. Photogrammetric Engineering and Remote Sensing 55, 
pp. 601-610. 
Forster, B.C., 1985. An examination of some problems and 
solutions in monitoring urban areas from satellite platforms. 
International Journal of Remote Sensing, 6, pp. 139-151. 
Fotheringham, A.S., Batty, M. and Longley, P.A., 1989. 
Diffusion-limited aggregation and the fractal nature of urban 
growth. Papers of the Regional Science Association, 67, pp. 55- 
69. 
Frankhauser, P., 1994. La Fractalite des Structures, Urbaines. 
Collection Villes, Anthropos, Paris, France. 
Lo, C.P., 1986. Applied Remote Sensing. Longman, Harlow 
and London, UK. 
Longley, P.A. and Mesev, T.V., 1996. The use of diverse RS- 
GIS sources to measure and model urban morphology. 
Geographical Systems, (in press). 
Martin, D.J. and Bracken, L, 1991. Techniques for modelling 
population-related raster databases. Environment and Planning 
A, 23, pp. 1069-1075. 
Maselli, F., Conese, C., Petkov, L. and Resti, R., 1992. 
Inclusion of prior probabilities derived from a nonparametric 
process into the maximum-likelihood classifier. 
Photogrammetric Engineering and Remote Sensing, 58, pp. 
201-207. 
Mather, P.M., 1985. A computationally-efficient maximum 
likelihood classifier employing prior probabilities for remotely- 
sensed data. International Journal of Remote Sensing 6, pp. 
369-376. 
Mesev, T.V., 1995. Urban Land Use Modelling From Classified 
Satellite Imagery. Unpublished PhD thesis, British Library 
Catalogue, pp 279. 
Mesev, T.V., Gorte, B. and Longley, P.A., 1996. Modified 
maximum-likelihood classifications and their application to 
urban remote sensing. In: Remote Sensing and Urban Analysis, 
J.-P. Donnay and M.J. Barnsley (editors), Chapter 3, 
(forthcoming). 
Mesev, T.V., Batty, M., Longley, P.A. and Xie, Y., 1995. 
Morphology from imagery: detecting and measuring the density 
of urban land use. Environment and Planning A, 27, pp. 759- 
780. 
Mesev, T.V., Longley, P.A. and Batty, M., 1996. RS/GIS and 
the morphology of urban settlements. In: Spatial Analysis: 
Modelling in a GIS Environment, P. Longley and M. Batty 
(editors), Chapter 7. (forthcoming). 
Strahler, A.H., 1980. The use of prior probabilities in maximum 
likelihood classification of remotely-sensed data. Remote 
Sensing of Environment, 10, pp. 135-163. 
Thomas, LL., Benning, V.M. and Ching, N.P, 1987. 
Classification of Remotely-Sensed Images, IOP, Bristol, UK. 
Zielinski, K., 1979. Experimental analysis of eleven models of 
population density. Environment and Planning A, 11, pp. 629- 
641. 
Table 1. Classification results using equal and unequal prior probabilities 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996 
Dwelling Type Census Equal Priors Unequal Priors 
census tracts Area 96 Pixels Area 96 Error Pixels Area % Error 
Detached 37 364 42.40 12 486 38.75 -3.65 . 13 910 43.17 +0.77 
Semi-Detached 26 675 30.27 10311 32.00 +1.75 9 161 28.43 -1.84 
Terraced 21 088 23.93 8 030 24.92 +0.99 7 440 23.09 -0.84 
Apartments 2 987 3.39 1395 4.33 +0.94 1 712 5.31 +1.92 
Totals 88 114 100.00 32222 100.00 7.33 32223 100.00 5.37 
*total error in absolute terms 
Table 2. Fractal dimensions from linear regression 
Dwelling Type Fractal Dimension (D) r-squared (cumulative) r-squared (density) 
Detached 1.423 0.953 0.770 
Semi-Detached 1.408 0.954 0.787 
Terraced 1.661 0.919 0.320 
Apartments 1.176 0.950 0.903 
561