10.2. Principal Components Analysis
PCA is a mathematical technique which transforms the original image data, typically highly correlated, to a new set of uncorrelated variables called principal components.These new components are linear combinations of the original image bands and are derived in decreasing order of importance so that, for example, the first principal component accounts for as much as possible of the variation in the original data. Each principal component is called an eigenchannel. The benefits of the technique from a geological standpoint are principally that information not visible in false colour composite images can be highlighted in one of the resulting component images.
There is a high degree of correlation within the Peru images. As a result false colour composite images may not show the full range of information present in the image bands. A method of extracting subtle information within the image, such as Principal Components Analysis, will be of value in analysing this image.
Open a viewer window. Display a true colour composite image, i.e. band 1 assigned to the blue gun, band 2 to the green gun, band 3 to the red gun and a false colour composite (of channels 6,4,2). Produce a sketch map of the area.
To run the Principal Components Analysis program it is necessary to execute a program called Principal Components from the Raster tab,Resolution group and Spectral and Principal Components.
Figure 10.1 - : Prinpal Components window
Use all six input image channels and specify six 8-bit eigenchannel images to be produced (e.g. 1,2,3,4,5,6) in a file. You should also check the boxes for the Eigenvector matrix and Eigenvalues to be displayed in the session log as shown in figure 10.1.
The variance figures for each principal component are shown in the eigenvalue list. These indicate the amount of variation accounted for by each component within the feature space.You will notice that nearly 99% of the information within this feature space is found within the first two principal components (92.1% in channel 1, 6.5% in channel 2). However this does not necessarily mean that the remaining components do not contain any useful information.
Display each component as a greyscale image and examine each eigenchannel in turn. You will discover that one of the components indicates three distinct oval-shaped porphyry copper ore bodies. You may have noticed one of the ore bodies when looking at the true colour composite image, although rather less clearly defined. Add these features to your sketch map.
To determine the area of each of the ore bodies you will need to use the Measure facility from the Home tab,Information group. Define three polygons, one for each ore body. Select square kilometres as the measurement unit.
Figure 10.2 - : Result of Principle Component Analysis - Clockwise PC 1 (Gray Scale 1), PC 2 (Gray Scale 2), PC 3 (Gray Scale 3), PC 4 (Gray Scale 4) , PC 5 (Gray Scale 5) , PC 6 (Gray Scale 6)
The principal components themselves can be explained as follows:
- PC 1 - accounts for general changes in albedo, i.e. the reflectivity of surfaces. The component is derived from all the input bands
- PC 2 - depicts the areas of moisture and the line of the rivers. The component is derived principally from bands 1, 2 and 3 contrasted with band 5.
- PC 3 - picks out the areas of vegetation with the river valleys. The component is dominated by the signal from band 4, the near infrared band, contrasted with band 6.
- PC 4 - contrasts the granites with the vegetation. The component is dominated by band 3 contrasted with bands 1 and 5.
- PC 5 - picks out the porphyry copper ore bodies. The component is derived from band 6 and to a lesser extent band 4 contrasted with bands 5 and 3.
- PC 6 - accounts for the residual noise or redundant information within the scene
The three porphyry copper ore bodies seen in PC 5 have the following approximate areas:
|Ore body 1||4.5 km2|
|Ore body 2||1.3 km2|
|Ore body 3||1.4 km2|
where ore body 1 is at the top left of the image and ore body 3 at the bottom right. Ore body 1 is of a workable size, the other ore bodies are currently sub-economic.
As an additional task you may wish to attempt to derive a geological map using an unsupervised cluster analysis or supervised maximum likelihood classification. In this case it would be sensible to choose three or four of the principal component images. From the properties of the components above it would be best to choose components 5, 4, 2 and possibly 1. Note that this exercise shows another benefit of using Principal Components Analysis, namely the reduction of data without loss of information, prior to classification.