1. 4. Focal Analysis 4.1 Definition of focal analysis
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Advanced GIS
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4. Focal Analysis
4.1 Definition of focal analysis
4.2 Shape and size of neighborhood
4.3 Focal statistics
4.4 Point statistics
4.5 Line statistics

2. 4.1 Definition of focal analysis
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4.1 Definition of focal analysis
Focal analysis is also known as “neighborhood analysis” or
“per-neighborhood analysis”. The output is a function of the input cells in the specified neighborhood of each location.

3. 4.2 Shape and size of neighborhood
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4.2 Shape and size of neighborhood
Shapes
- Annulus (Ring)
- Circle
- Rectangle
- Wedge
Sizes: 2, 3, 4, 5, …
3 x 3 Square
(Default)
Circle: Radius = 2
Wedge: 45°, Radius = 3

4. 4.2 Shape and size of neighborhood (cont.)
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4.2 Shape and size of neighborhood (cont.)
Output cell center:
x = (w + 1)/2 = 2
y = (h + 1)/2 = 2
(Truncate to integer)
Output cell center:
x = (w + 1)/2 = 3
y = (h + 1)/2 = 3
Odd neighborhood size
Even neighborhood size
w – width of the neighborhood; h – height of the neighborhood.

5. ___________________________________________________________
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4.3 Focal statistics
ArcToolbox Spatial Analyst Tools Neighborhood  Focal Statistics
ArcToolbox Spatial Analyst Tools Neighborhood  Focal Statistics

6. 4.3 Focal statistics (cont.)
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4.3 Focal statistics (cont.)
Example 1: Raster data smoothing
Human Footprint Grid, South Ghana
(Data from CIESIN, Columbia University)
Smoothed Data
(mean)
Raw Data (color)
Raw Data (B/W)

7. 4.3 Focal statistics (cont.)
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4.3 Focal statistics (cont.)

8. 4.3 Focal statistics (cont.)
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4.3 Focal statistics (cont.)

9. 4.3 Focal statistics (cont.)
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4.3 Focal statistics (cont.)

10. ___________________________________________________________
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4.4 Point statistics
ArcToolbox Spatial Analyst Tools Neighborhood  Point Statistics

11. 4.4 Point statistics (cont.)
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4.4 Point statistics (cont.)
Example 2: Median rent of U.S. cities in 1990
Cities Shapefile
Point Statistics:
Mean of Median Rent
High $823
Low $148

12. 4.4 Point statistics (cont.)
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4.4 Point statistics (cont.)
Example 3: Median housing value of U.S. cities in 1990
Cities Shapefile
Point Statistics:
Mean of Median Rent
High $314,955
Low $27,400

13. 4.4 Point statistics (cont.)
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4.4 Point statistics (cont.)
Median Rent (1990)
High $823
Low $148
Median Value (1990)
Question: What are the
white areas in the output?
High $314,955
Low $27,400

14. 4.4 Point statistics (cont.)
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4.4 Point statistics (cont.)
Challenge Question 1:
Given a point shapefile for cities of the Contiguous United States,
create a new field in the shapefile attribute table, so that the values
in the field represent the number of cities within 100 km of each city.
(Answers will be provided after Module 7)
Dallas 34
Denton 28 …

15. 4.4 Point statistics (cont.)
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4.4 Point statistics (cont.)
Challenge Question 2: Density of TB cases
The left maps shows real TB cases in an area, and A, B, and C are
squares with equal size. It appears that C has the highest density
of TB cases, but point statistics in the squares show that A has the
highest density of TB cases (right). What would be the possible
reasons? A A B B C C

16. 4.4 Point statistics (cont.)
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4.4 Point statistics (cont.)
Example 4: Intensity of LiDAR points in a forest
The map shows 10 million LiDAR points for a 1 km by 1 km study area
(about 10 points per sq. meter) in the Soquel Demonstration State
Forest in California.
Objective: calculate average
intensity (return strength of the
laser pulses) in a 3 x 3 window
(cell size = 0.5 m). • • • • • • • • • • • • • • • • • • • • • • • •

17. 4.4 Point statistics (cont.)
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4.4 Point statistics (cont.)
Example 4: Intensity of LiDAR points in a forest (cont.)
Point statistics results:
Different intensity values from
ground objects, e.g. low intensity
from dense forests and asphalt
pavements, and high intensity
from open areas. • • • • • • • • • • • • • • • • • • • • • • • •

18. ___________________________________________________________
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4.5 Line statistics

19. 4.5 Line statistics (cont.)
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4.5 Line statistics (cont.)

20. Review 4.1 Definition of focal analysis
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Review
4.1 Definition of focal analysis
4.2 Shape and size of neighborhood
4.3 Focal statistics
4.4 Point statistics
4.5 Line statistics