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