Neighborhood (image processing)
In digital image processing , a neighborhood describes a small, defined image region around a pixel . Many image processing operations look at the pixels within a neighborhood in order to compute a new color or gray value for their center . With the four-neighborhood (also D-neighborhood ) and the eight-neighborhood there are two basic neighborhood concepts.
Neighborhood of four
Each pixel P of an image has four neighbors D , horizontal and vertical . These direct neighbors are characterized by the fact that they each have a pixel edge in common with P. They are called D-neighbors or 4-neighbors .
If one takes the coordinates of P with , then the coordinates of the four D neighbors are through
given. Each D neighbor is exactly one unit away from P.
The set that contains the point P and its neighbors D is called a four-neighborhood. A neighborhood of four therefore consists of five points (see adjacent figure). It is usually referred to as.
See also: Von Neumann neighborhood
Eighth neighborhood
Besides the four D-neighbors of each pixel has P an image four diagonal neighbors N . These have only one corner in common with P and are defined by the coordinates
given. The distance of the neighbor N of P is determined by the used metric. If, for example, the Euclidean metric is used as a basis, the distance is , while it is 2 for the Manhattan metric .
The set that contains the point P and its neighbors D and N is called a neighborhood of eight. A figure eight neighborhood therefore consists of nine points (see adjacent figure). It is often referred to as or simply or .
See also: Moore Neighborhood
application
In many operations in digital image processing, new color or gray values are calculated for the pixels on the basis of neighborhoods around the pixels of an image. This is primarily the case with neighborhood operators , such as precedence operators or morphological operators . Neighborhood definitions are also used in other areas, e.g. B. in some segmentation methods required.
If a neighborhood is used in image processing and no explicit reference is made to the use of a neighborhood of four or another in the specific application, a neighborhood of eight is generally used.
The size and shape of a neighborhood always depends on the application. For many operators, a square shape with usual. Deviating from this, a neighborhood can also be defined, for example, according to the Manhattan metric with a maximum distance of 2 from the center point P (see adjacent figure). Round or even completely asymmetrical neighborhoods are also conceivable.
The pixel in the middle of a neighborhood does not necessarily have to be the center point P of the neighborhood, which, however, occurs rather rarely. To avoid confusion, the center point P is also referred to as an anchor in cases where it deviates from the mathematical center point .
Edge problem
In the practical application of neighborhood operators, the edge problem inevitably arises: How is the case handled when a pixel is so close to the edge of an image that the neighborhood “protrudes” over the image (see figure on the right)?
Four different approaches are conceivable:
- The edge pixels are not considered. The disadvantage here is that the result image is then slightly smaller (at a -Nachbarschaft with odd n to pixels on each side). If several neighborhood operators are applied one after the other, the image shrinks with each application.
- If the mask protrudes beyond the edge of the image, it is reduced accordingly by the "protruding" areas.
- The required pixels outside the image are extrapolated according to the closest pixels . The disadvantage here is that extrapolation errors can continue into the interior of the image when several neighborhood operators are used one after the other.
- The picture continues periodically. This method can only be used if there is at least an approximate periodicity of the image.
literature
- Bernd Jähne : Digital image processing. 6th, revised and expanded edition. Springer-Verlag, Berlin 2005, ISBN 3-540-24999-0
- Rafael C. Gonzalez, Richard E. Woods: Digital Image Processing. 2nd Edition. Prentice Hall, 2001, ISBN 0-201-18075-8 (English)