3.%20Shape%20analysis%20(2D)

1
Lecture 26 Spatial Indices and Landscape
Measures II
Topics
3. Shape analysis (2D) 4. Heterogeneity
References
- Baker, W. and Y. Cai, 1992. The r.le programs
for multiscale analysis of landscape structure
using the GRASS geographical information system.
Landscape Ecology, Vol. 7, No. 4, pp. 291-302. -
Turner, M.G. and R.H. Gardner, 1991.
Quantitative Methods in Landscape Ecology,
Springer-Verlag, New York.
2
Outlines
3. Shape Analysis 3.1 Perimeter and Area-Based
Measures a) Perimeter/area S P
/ A where P is the perimeter and A is
the area of the patch Problem same
shape with different size results in difference
S b) Correct perimeter/area
S is 1 for a circle and S is infinity for a line
3
3.2 Linear Dimension and Area-Based Measures
The idea compare the patch with the
smallest circle that
circumscribes the patch (a) Related
circumscribing circle
Where D is the length of the longest axis and A
is the area of the area of the patch
RCC ranges from 1 for a circle to 0 for a line
4
3.2 Linear Dimension and Area-Based Measures
(continued ) (b) Compactness ratio
CR ranges from 1 for a circle to 0 for a line
5
4. Heterogeneity Measuring variety within
an area 4.1 Diversity Measures (1)
Richness The number of different
types of attributes in a sampling area
(2) Shannon Index (Entropy)
Dominance or evenness
Where n is the number of
attributes in the sampling area pi is
the fraction (percentage) of the sampling area
occupied by attribute i.
Ranges from 0 to 1
6
4.2 Texture Analysis Quantify the
adjacency of similar attributes within a region
1) Contagion Quantify the
degree of clumping
where Pij is the percentage of
times that attribute i is
adjacent to attribute j. when C 2ln(n)
means maximum clumping,
meaning the sample area is occupied by
one attribute while C 0
means that the landscape is dissected
into many small patches.
7
4.2 Texture Analysis (continued ) 2)
Angular second moment quantifying the
homogeneity of the landscape (in terms
of number of ways patches are connected
with each other)
where Pij is the percentage of times
that attribute i is adjacent
to attribute j. larger values indicate more
homogeneity (large patches).
8
4.2 Texture Analysis (continued ) 3)
Contrast Amount of local variation
present in the landscape
The larger the value the more the contrast
9
4.3 Edginess (Juxtaposition) A measure of
edginess surrounding a center pixel
Where wij is the relative quality given
to the edges between attributes i and j
q is the ranking of adjacency 2 for
horizontal or vertical connection 1 for
diagonal connection
10
Questions
1. What is the problem with the simple perimeter
to area ratio? How does the corrected perimeter
to area ration fix the problem? 2. What is the
difference between RCC and corrected perimeter to
area ratio? How to interpret RCC? 3. What is the
difference between CR and RCC? 4. How would one
interpret Shannon Index (entropy) value in the
context of measuring diversity? 5. Explain the
difference between Contagion and Angular second
moment in terms of what each of them measure. 6.
In defining edginess, how would one define the
weight associated with each edge?