Image Processing Reference
In-Depth Information
density and linearity, both of which can be summarized using standard nearest-
neighbor and linear-adjusted nearest-neighbor indices respectively. These indices
are then used to identify similar morphological configurations of various types of
residential and commercial land uses from second-order, classified satellite sensor
imagery. The ultimate objective is to build an automated image pattern recognition
system capable of identifying spatial point patterns, representing urban structural
morphologies, within image data.
The nearest-neighbor technique is designed to statistically calculate and sum-
marize spatial distributions (Pinder and Witherick
1973
). It compares the observed
average distance connecting neighboring points (
D
OBS
) and the expected distance
among neighbors in a random distribution (
D
RAN
). The statistic is an uncomplicated
ratio, where randomness is represented by parity; a clustering tendency has values
approaching 0; and perfect uniformity towards a theoretical value of 2.15. The
nearest-neighbor statistic
R
is expressed as,
D
(8.2)
R
=
OBS
D
RAN
where
D
OBS
is the total measured Euclidean distance between neighboring points
divided by the total number of points (
N
), and
D
RAN
is calculated as,
1
2/
D
=
NA
(8.3)
RAN
where (
N
/
A
) is the density of points within area
A
. One of the many strengths of the
nearest-neighbor statistic is the facility to compare spatial distributions on a con-
tinuous scale, especially when area (
A
) is constant.
Worked examples in Mesev (
2005
) and Mesev and McKenzie (
2005
) measured
six different residential neighborhoods from the city of Bristol in England (Table
8.2
and Fig.
8.4
). Four neighborhoods were successfully identified as having strong
Table 8.2
Density and nearest neighbor statistics with tests for signiicance of clustering and
dispersion
Type
N R LN LR
Residential-1 1479 0.466** 53 0.452
Residential-2 898 0.614** 20 0.503
Residential-3 365 0.942** 11 1.595
Residential-4 906 0.563** 38 0.538
Residential-5 640 0.585** 19 0.589
Residential-6 81 1.564** 14 0.995
Commerical-1 155 0.523** 23 0.509**
Commerical-2 637 1.297** 14 0.903
Commerical-3 18 0.627** 5 0.916
Commerical-4 321 1.289** 10 1.175
N
density (area constant);
R
nearest-neighbor;
LN
linear density(area constant);
LR
linear nearest-
neighbor
Test for statistical significance in clustering and dispersion using the standard normal deviate are
represented by *
p
values <0.05 and **
p
values <0.01
