1. Lecture 26: Spatial Indices and Landscape Measures II
Topics:
3. Shape analysis (2D)
4. Heterogeneity
References:
- Baker, W. and Y. Cai, The r.le programs for multiscale analysis of landscape structure using the GRASS geographical information system. Landscape Ecology, Vol. 7, No. 4, pp
- Turner, M.G. and R.H. Gardner, 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 = 2*ln(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?