DIGITAL IMAGE ANALYSIS

GOG 485-585

LAB 4

(Rev. 4/24/01)

See Last Page For Revisions

PRINCIPAL COMPONENTS ANALYSIS USING IDRISI 32 FOR WINDOWS 95/98

(Version I32.02)

The following image files are used for Lab 4:

From the :\idrisi32 tutorial\introductory ip\ folder:

· h87tm1.rst

· h87tm2.rst

· h87tm3.rst

· h87tm4.rst

· h87tm5.rst

· h87tm6.rst

· h87tm7.rst

PRINCIPAL COMPONENTS ANALYSIS ¹

A Principal Components Analysis (PCA) on a set of image bands produces a new set of images with components that are uncorrelated with each other and explain progressively less of the variance found in the original set of bands. This technique is used for data compression since the first two or three components explain 95 to 99 percent of the variance in the original set of bands. In cases like this, the components explaining less than a certain percent of the variance can be dropped. It is also useful in the analysis of time series data. Both unstandardized and standardized principal components analyses are offered. In the standardized case, the correlation matrix is used for input rather than the usual variance/covariance matrix.

After signing onto the computer, click the start button. Navigate to “Programs” and select “RUNIDRISI” from the program menu. Once the program has opened, click on the “Data Paths/Project Environment” icon in the tool bar. Set the main working folder to: (specify drive letter here):\idrisi32 tutorial\introductory ip\ which is the directory that holds the data for this lab. Click “OK”.

The data set from Howe Hill will be used for principal components analysis. Using the “Display” icon on the “Main Tool Bar”. Display the h87tm4 image with the “Grey Scale” palette and “autoscaling”. Open the remainder of the h87tm images (h87tm1-3 & 5-7) with the same selections. Minimize all the image windows with the exception of h87tm4. Maximize and examine the images as needed in order to answer the following questions.

Question # 1

a. Which band(s) appear similar to the TM 4 band? Explain how and why. (2 Points)

b. Explain the difference in Band 6. Be specific!

Minimize all the image windows and continue.

Click on “Analysis: in the “Main Drop Down Menu”. Navigate to the Image Processing \ Transformation menu and click on “PCA”. The “PCA – principle components analysis” window will be displayed. Select “Calculate covariances directly”. In the “Image bands to be used area”, click on the “up arrow” to change the “Number of files” to “7”. Notice that the number of boxes in the “Image Band Name” area increased to “7”. Click on the “…” button in the first box. A “pick” window will be displayed. Double click on h87tm1. Notice that h87tm1 now appears in the first box in the “Image Band Name” area. Repeat this procedure for the h87tm2-7 images. Change the “Number of components to be extracted” to “7”. Enter “h87” in the “Prefix for output files” box. Select “use unstandardized variables (variance/covariance matrix)”. Click “OK”. Notice that the status bar in the lower right hand corner reports the PCA processing progress. When the processing is complete the “Module Results” window will be displayed. Print out a copy of this table and examine the correlation matrix.

Question # 2

a. Do you find much correlation between bands? How much?

b. Which ones correlate with Band 1? Be specific as to the level of correlation!

c. Which ones correlate with Band 4? Be specific as to the level of correlation!

d. How does this compare with your answer to question 1 relative to TM Band 4?

e. Hand in the printout of the correlation matrix.

Examine the “Component” summary table. The “eigenvalues” express the amount of variance explained by each component and the “eigenvectors” are the transformation equations, summarized as the percent variance explained (% var.) at the top of each column.

Question # 3

a. How much variance (%) is explained by components 1, 2, and 3 separately?

b. How much variance is explained by components 1,2 and 3 together?

c. If only the first three components are kept, how much data about the total image is retained and how much data will you be discarding?

Examine “Loading” table. “Loadings” refer to the correlation between the components (columns) and the original bands (rows).

Question # 4

Describe the loadings and strength of each component. Be specific!

If you have a printout of this table, close the “Module Results”. Otherwise minimize the “Module Results” window and continue.

When the PCA was run on the h87tm1-7 images a new principal component image was created for each of the TM images, each with the prefix “h87cmp”. Click on the “Display” icon on the Main Tool Bar”. Click on the “…” button. Look through the image files and notice there are now seven new principal component images; h87cmp1-7 in the directory. Double click on the h87cmp1 image name and display it with the “Grey scale” palette and “autoscaling”. Repeat this procedure for the h87cmp2 and h87tm3 images.

Question # 5

a. Which component image, if any, looks similar to the TM4 image? Explain.

b. Does any Component look similar to the TM3 image? Explain.

c. How do your observations compare with your answers to Question 4?

Again, using the “Display” icon on the “Main Tool Bar”, display the h87cmp6 and h87cmp7 images with the “Grey scale” palette and “autoscaling”.

Question # 6

a. How well do these components compare with the original seven bands? Explain.

b. What do you think is contained in these components? Discuss the variance scores and their significance, if any.

c. Is one component more identifiable than the other? Explain.

Close all image windows and continue.

CONVERT ¹

CONVERT converts files between all possible combinations of Idrisi32 data and file types supported for image and vector files.

Click on “Reformat” on the “Main Drop Down Menu”. Click on “Convert”. The “CONVERT – idrisi data format conversion” window will be displayed. Select “Image” for the “File type”. Input h87cmp1 for the “Input file name”. Notice that the “Output file name” defaults to h87cmp1. Select “Byte” for the “Output date type”. Select “Binary” for the “Output file type”. Accept the other defaults. Click “OK”. Click “Yes” at the “Warning” window to overwrite the files. Repeat this procedure for the h87cmp2 and h87cmp3 images.

After completing the conversion for the 3 components use them to create a color composite image. Click on the “Create color composite” icon on the “Main Tool Bar”. Enter h87cmp3 for the “Blue image band”, h87cmp2 for the “Green image band” and h87cmp1 for the “Red image band”. Enter PCACOM for the “Output image”. Accept the other defaults. Click “OK”. The pcacom color composite image will be displayed. Examine the image.

Using the above procedure, create a color composite of the original TM image “TMORG”. Enter h87tm2 for the “Blue image band”, h87tm3 for the “Green image band” and h87tm4 for the “Red image band”. Enter TMORG for the “Output image”. Accept the other defaults. Click “OK”. The tmorg color composite image will be displayed. Examine the image. Compare the two images. It may be helpful to use the zoom and pan buttons in the “Composer” window for the comparison.

Question # 7

Comment on the appearance of the principal components colors and their association with land cover

types compared to the false color TM image.

Close all windows, exit Idrisi32 and follow the proper procedures to shut down the lab computer.

Footnotes:

1. Portions of this section were edited from the Idrisi I32.02 online help file and the Idrisi32 August 1999 Tutorial.

4/24/01 Revisions:

Added clarification language to questions 1a, 1b, 2a, 2b, 2c, 2d, 4, 5a, 5b, 6a, 6b, 6c.

GOG585LAB4.DOC