Lecture 21: GIS Analytical Functionality (V) Topics 6. Statistical Analysis 6.1 Descriptive Statistics 6.2 Feature Extraction Readings on the topics Chapter 15 in Longley et al. (2005): pp. 342-362 Other readings Chapter 6 of Tomlin (1990): pp. 154- 165 (descriptive statistics) Chapter 11 of Campbell (1996): pp. 313-354 (Feature Extraction)

Outlines 6. Statistical Analysis: Statistical analysis is about globally characterising a group of numbers which are believed to be generated from a common process (random process). 6.1 Descriptive Statistics: Measures of characterizing a group of numbers The group of numbers must be defined first 6.1.1 Defining the group of numbers (values) in GIS Spatial extent (zones) There must be two layers involved: the base layer (zone layer, category layer) and the attribute layer (number layer) (Zone and Attribute Diagram) [15, 14,12,10,15,15,15,20,15,12,15,15,14,15,16,15]

6.1 Descriptive Statistics: (continued …) 6.1.2 Computing statistics: (1) Basic statistics: Mean: the average value of the group [15,14,12,10,15,15,15,20,15,12,15,15,14,15,16,15] 14.56 Median: the value at the middle of the group [10,12,12,14,14,15,15,15,15,15, 15,15, 15, 15,16,20] 15 Variance: the spread or variation of the numbers 4.53 Minimum: smallest [12] Maximum: the largest [20] (2) Histograms (frequency curve) and distribution How frequent each value appears in the group (Frequency Diagram)

6.1 Descriptive Statistics: (continued …) 6.1.2 Computing statistics: (continued …) (3) Cross-tabulation: (mainly for categorical data) How two groups of numbers based on different classifications (of different variables) are related? Example, how soil type is related to forest type? (Cross Tabulation Figure) (4) Correlation (ratio, interval data) Quantitatively determine how two variables are related. Money in mutual funds vs. income 6.1.3 Discussion: The zone does not have to be in existence, can be created from the attribute data layer through connected component analysis Compute the mean value of tree height of the largest tree patch under the raster representation.

6.2 Feature Extraction Identifying features using the information in remotely sensed images (UT Campus Image). There are two approaches to do this: signature-based and texture-based 6.2.1 Feature extraction based on signature (classification) (1) What is signature? A unique combination of reflectance values over a number of image bands for a feature. (The Signature Figure) (2) Classification a) identify signature b) classify pixels by comparing signature of the pixel and that of the class

6.2 Feature Extraction (continued …) 6.2.2 Feature extraction based on texture (segmentation) (1) What is texture? The variation of pixel values over a neighborhood of a pixel (The Texture Figure) (2) Segmentation grouping neighbouring pixels into classes based on the texture of the image in the neighbourhood 6.2.3 Discussion: Difference between image classification and image segmentation a) Signature vs. Texture b) aspatial vs. spatial

Questions: 1. What are the steps in computing statistics using GIS? 2. How would one compute the average tree height for the largest forest patch under the raster data model with only the tree height data layer (no zonal layer provided)? 3. What is a signature and what is a texture? 4. Describe the steps used in image classification. 5. How is image classification is different from image segmentation?