Arithmetic Operations


See how to execute an Arithmetic Operation in SPRING.


For operations between bands, in image processing, the Spring offers the options addition, subtraction, division (or ratio among bands) and the multiplication of one band by a constant (linear enhancing).

In these operations it is used one or two bands from the same geographical area previously georeferenced. The "pixel" by "pixel" operation is performed, through a defined mathematical rule, having as a result a band representing the original band combination.

These operations allow the data compression, reducing the number of bands, causing lost of original information. The operations result can pass the 0-255 interval. These results are automatically normalized, saturating the values below 0, and above 255, into 0 and 255 respectively, causing lost of spectral information.

These operations may require a gain factor (multiplicative) or "off-set" (additive), to enhance the image contrast quality. The definition of these values depend on the user ability, in the operation definition and the spectral characteristics of the used bands.

In general, it is used the addition operation to enhance similarity between bands or different images and, the subtraction, the multiplication and the division, to enhance spectral differences.

Image Subtraction

The image or band subtraction is used to enhance spectral differences . This operation is a linear relation.

Knowing the spectral behavior curves of the interest target and the spectral interval of the sensors bands, it is possible to define what bands will be used to enhance the spectral differences through the bands subtraction.

Examples of the bands subtraction application:

  • identification of different types of vegetal cover;
  • identification of minerals formed by iron oxide;
  • detection of the pattern change cover, such as soil usage, urban expansion, deforesting.

When, in the image, the histogram average and standard deviation to be subtracted do not coincide, it is suggested the average and standard deviation equalization, before the subtraction, through a contrast increase adequate to both images. In case this procedure is not executed, the subtraction result between the images will not correspond to the real difference between them.

Adding Images

Adding images or bands of the same image is a linear operation. This operation can be used to get the arithmetic average between images, minimizing the noise presence. To get the images average it is required to adopt as a gain value 1/n, where n is the number of bands used in the operation. The addition can still be used to an image integration resulting of different processing.

Multiplication

It is a linear operation which consists in the multiplication of a constant by the gray levels in a band.

It is used in the implementation of transformations that one wants to perform in the image.

Division or ratio between bands

The image division operation consists in a non-linear operation. It is used to enhance the spectral differences of a pair of bands, characterizing certain aspects of the spectral signature curve of some targets.

This operation is limited in bands that present noise, because these will be enhanced. The presence of the atmospheric spreading, selective in relation to the spectral bands, interfere in the bands ratio, resulting in gray level values that do not represent the reflectance difference among targets. Another limiting factor is the presence of distinct objects in the original bands that present similar spectral characteristics, but with different intensity. In the ratio resulting image between bands these objects will not be distinct.

The ratio operation between bands can:

  • remove gain effects from the spatial or temporal variations, when it happens in bands of the same image;
  • reduce variations of the image radiance, from topographic effect, declivity and aspect;
  • increase radiance differences between soil and vegetation.

To remove the effect of a gain factor, such as illumination effect, consider, for instance, that the radiance of one pixel is 1, the illumination factor is "a", and that the sensor detected answer is the product of these two factors. Remove the illumination effect dividing each "pixel" in a band (1) by the corresponding "pixel" in another band (2). In this way, if R is the independent result of the illumination factor, then:

  • R1,2 = a.L1/a.L2 = L1/L2

The reduction of the illumination effect also eliminates the topographic shadowing effect.

To increase the contrast between soil and vegetation, the ratio between bands related to red and next infrared can be used , getting the vegetation indexes (NDVI).

The C = G * ((A-B)/(A + B)) + O, option in SPRING, when applied to:

  • A = next infrared band
  • B = red band

constitutes the normalized difference vegetation index (NDVI), that besides increasing the spectral contrast between vegetation and soil, has the illumination effects, surface declivity and "aiming" geometry partially compensated by the index.

 

See also:

Other Image Processing techniques.
How to execute an Arithmetic Operation.