Sum of absolute differences

The sum of absolute differences ( SAD abbreviation, of Engl. Sum of absolute differences) is a positive number that is created by taking the difference of two digital images. It serves as a measure of the difference between two images and finds application in the image processing and recognition section.

The SAD is obtained by the color values ​​of the images are summed pixel by pixel subtracted from each other and amount wise.

Mathematical Foundations

A picture is a picture of a two-dimensional set of definitions in a range of values ​​. The definition correspond to the amount of all the image points of the image and is therefore given by where b is the width and h is the height of the image in pixels. The range of values ​​corresponds to the color space of the image and is 7-bit color depth given by for an ordinary gray value model; If it is a color image, the range of values ​​is usually in three dimensions.

Where two images of the same size and the sum of the absolute differences defined by:

Where b is the width and h is the height of the images respectively.

The sum of the absolute difference is a positive semi-definite, thus always.

Implementation in computer science (monochrome images )

A digital image is represented in the computer science in general by the following data type:

Type picture {     int width;     int height;     int pixels [0 (width -1). ] [0 ( height -1). ]; } The algorithm is implemented for two images of the same size by the following pseudocode:

Long berechneSAD ( see Figure 1, Figure B2)   {      long SAD = 0;      For x = 0 to B1.Breite - 1 do         For y = 0 to B1.Hoehe - 1 do            SAD SAD = abs ( B2.Pixel [ x] [ y] - B1.Pixel [ x] [ y] )   } The algorithm refers to a complex of, where n is the number of pixels.

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