Band Ratioing - Lecture Material - Completely Remote Sensing tutorial, GPS, and GIS -
Band Ratioing

Another image manipulation technique is ratioing. For each pixel, we divide the DN value of any one band by the value of another band. This quotient yields a new set of numbers that may range from zero (0/1) to 255 (255/1) but the majority are fractional (decimal) values between 0 and typically 2 - 3 (e.g., 82/51 = 1.6078...; 114/177 = 0.6440...). We can rescale these by stretching to provide a gray-tone image of each Band X/Y ratio, in which each can fill out 16 or 256 levels, depending on the computer display limits.

One effect of ratioing is to eliminate dark shadows, because these have values near zero in all bands, which tends to produce a "truer" picture of hilly topography in the sense that the shaded areas are now expressed in tones similar to the sunlight sides. To illustrate this, suppose that an inclined surface of some material facing the Sun has a brightness value of 70 in one band (A) and 50 (B) in another. For the same material in shadow on a slope away from the Sun, the BV values may be 35 and 25 for A and B respectively. A divided by B in the Sun-facing case is 24; for the shadow case A/B = 1.4. So, in the ratio image, both front and back slope areas would have the same value. The problem, of course, is that for another material, with BVs of 51 (sunlit) and 37 (shadow), the A/B would also B 1.4, so that material is not differentiated from the first.

Still, while class-related tonal contrasts may smooth out, certain ratios can point to certain tonal anomalies that are diagnostic of special conditions. This first ratio image (in Wyoming), made from an MSS Band 5/MSS Band 4 data set, exemplifies this. A red surface would give a high DN value in Band 5 (MSS red band) and a low number in Band 4 (little green light), so that the ratio would be a large number that would produce a light tone in an image. In the image below, the bright tonal patch just below the center is an iron-rich anomaly (reddish on the ground) over a small oil field that has leaked petroleum which leached out iron oxide to form a tell-tale stain (the linear white pattern in the middle right is a red-colored geologic outcrop):

A Band 5/Band 4 ratio image of an area in the Wind River Basin of Wyoming

For a Landsat MSS data set, a total of six ratios (Bands 4/5. 4/6, 4/7, 5/6, 5/7, 6/7) and six reciprocals (5/4, 6/4....7/6) are possible. Three pairs of ratio images can be co-registered (aligned) and projected as color composites. In individual ratio images and in these composites, certain ground features tend to be highlighted, based on unusual or anomalous ratio values. For example, an ore deposit may be weathered or altered so that a diagnostic surface staining, called gossan, develops. This stain consists of hydrated iron oxide (rust) that is normally yellow-brown. In Band 3, this material reflects strongly in the red but it is apt to be dark in Band 4. The ratio quotient values for this situation tend, therefore, to exceed 2-3, giving rise to a bright spot pattern in a 5/4 image.

IDRISI generates ratio images through a module called OVERLAY. These may need to be rescaled and converted to byte format for display. However, the new images are difficult to combine in composites. We show just one ratio image made by dividing Band 1 DN values into Band 4 DNs, to illustrate a characteristic product.

Ratio image of the Morro Bay scene made by dividing Band 1 into Band 4; light tones relate to actively growing vegetation.

In this unstretched version, most of the image is moderately dark without much variation in gray levels. This implies similarities in DN values for equivalent pixels in the two bands. However, the tonally bright (high DNs) golf course fairways at (s) contrast sharply with their surroundings. Fields also stand out in this way. The grassy area at (v) has well-defined boundaries and is ligher toned.

(Note: the above ratio 1/4 image was produced on a DOS version of IDRISI. The writer (NMS) tried to create new ratio images on IDRISIW, the Windows version, with no luck. But excellent examples of ratio images, and ratio color composites, developed on the IDIMS system at NASA Goddard while the writer was still there, are shown on page 5-3.) To preview this, look at a TM Band 3/Band 1 ratio image of a mineralized area in southwestern Utah, and then a color composite made from 1/7 = blue; 4/2 = green; 3/1 = red.

Ratio image 3/1 showing an area in southwest Utah near Milford. Much of the interior of this scene is made up of altered volcanic rocks, with iron oxides showing up as light tones.

The lightest tones coincide with iron enriched surface material (reds and yellows in the field).

Color composite of the Utah scene made from ratios 1/7 = blue; 4/2 = green; 3/1 = red. Yellows, oranges, and reds associate with iron-rich alteration.

The yellows and reds in this composite denote areas of rock alteration and mineralization.