Histograms and Scatter Plots

The purpose and value of histogram data plots have been discussed in Section 1. Here we will learn how to produce and display these and scatter plots as aids to understanding the statistical distribution of DN values in individual and paired bands.

1. For the moment we will work with the default image in the PIT window. Click on Windows, then drag over Open, then (in the small window to its right) click on Histogram, and then on Small View. Releasing the mouse button brings a small window up on the left called PIT - Histogram. Click on the Plot button, which drops a gray window with Source (highlight). Drag the mouse to the right into a window which has Thumbnail highlighted, then right again to a list of the bands that are active. Choose band 1 and release the mouse button. A histogram appears. Note the maximum and minimum DN values (the spread), the values where the first significant frequencies occur, and the peak values of the mono- or polymodal distribution; also the degree to which the distribution is gaussian or normal. This information is especially important when used by image processing programs that have several modes of contrast stretching.
2. PIT Histogram has an interesting feature. You can select a portion of the displayed histogram, which blocks out all the DN values in this range, and then display in the image that is up all the pixels that fall within that value range. This demarcates visually the spatial distribution of all such pixels.
3. To do this, take the histogram display window (assuming it is being shown), and placing the mouse cursor on its Title banner, drag the window away from the Thumbnail image to the open screen space to the right. Now, place the cursor somewhere within the actual histogram at whatever left DN point you wish to start the DN range. Drag the cursor rightward; as you do, that portion will fill in with color; continue until the area of the histogram containing the range you are going to display on the image has been highlighted (you can change color by clicking on Ranges, then checking the color desired). Raise (de-iconify) the Interpretation window (or open it if it had been closed). When that window is displayed, click on the button called Matching, then on Draw Boxes, followed by From Histogram. Watch as the color in the histogram starts to fill in image pixels falling in the chosen range, with this proceeding downward until the entire image is thus colored. All pixels within the range are now identified in their spatial positions. (Note, drag the PIT - Interpretation leftward until the image is near the left screen margin - this will allow you to see both image and histogram window fully. Even better - use 1280 x 1024 screen resolution and top schemes.)
4. To see pixel distributions for the other bands, first, remove the colored area on the histogram now open by clicking on the Delete button in color-bordered box in PIT - Histogram. Then, click and slide on Plot - Source - Interpret - Thumbnail - Band Listing (make choice). The histogram for the chosen band is displayed. But, the image in the PIT window is the default Thumbnail. You need to display the new band. From the PIT Window, choose View, then Display Image Control Window, and then from the dropdown window labeled Thumbnail Image Control, select (replace number or hit black triangle) the band desired. Once it is displayed, go through the histogram coloring and Match procedures as before.
5. Next, let us explore Scatter Diagrams. From the PIT window, click and drag through Windows - Open - Scatter - Small View, click and release. The PIT Scatter window drops into place. Click on Source, drag through Thumbnail to the right, and keep dragging rightward. You will see a window with a listing of Band 1 vs… through Band 7 vs… and by dragging further right a listing of the bands. To set up the scatter pairing do this: move cursor to first band of interest in the vs window; it will highlight in a whiter tone; then move cursor to last window on right and to the other band which will also highlight. Click on that and the Scatter Diagram will appear. Note that it consists of some geometric pattern in several shades of gray (the lighter the tone, the greater the number of pixels in the distribution). If the pattern is a narrow ellipse, with about a 45° angle, the two bands are strongly correlated; if the angle is less or greater than the same pixel point has two somewhat different DN values but there is still some correlation. If other than an ellipse occurs, this usually denotes a bimodal or polymodal distribution. Examination of the corresponding histograms helps in the interpretation of the type of pattern that emerges. To see Scatter Diagrams for other band pairs, simply repeat the process starting with Plot and ending with the desired pairing. To remove the diagram, click on Plot - Clear Plot.

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