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This chapter contains operators for filtering.
Filters are an important part of nearly every machine vision application.
can be used to smooth images,
to extract sub-pixel precise edges, and
to compute the fast Fourier transform of an image.
In the following, we will take a closer look at special cases: Using an image with a reduced domain as input for a filter, and problems caused by gray values outside of the image domain.
If a filter that is using a mask is applied to an image with a reduced domain, the result along the domain boundary might be surprising because gray values lying outside the boundary are used as input for the filter process. To understand this, you must consider the definition of domains in this context: For a filter, a domain defines for which input pixels output pixels must be calculated. But pixels outside the domain (which lie within the image matrix) might be used for processing.
Operators that have an image as output (most filter operators) only return results for pixels that were contained in the input domain.
For performance reasons, pixels that lie outside of the image domain become
'undefined'. These undefined pixels can differ from system to system, for
example if parallelization is activated or not. It is merely guaranteed
that the values are consistent if the program is executed repeatedly on
systems with the same configuration. In certain cases, these 'undefined'
pixels might lead to problems. Expanding the resulting image to the full
will lead to artifacts appearing outside of
the former image domain. Another cause of problems are undefined values
outside of the domain if two or more filters are applied consecutively as the
filters consider the undefined values close to the domain border as well.
This means that with every following filter the error increases, starting
from the border to the middle. In the following, four strategies for
solving those problems are presented.
Errors caused by undefined pixels can easily be prevented by, e.g., choosing
a domain that is considerably larger than the image part that is actually
needed and reducing the image domain (e.g., with the operators
) by half of the filter
width before applying the next filter. In doing so, those parts of the image
containing incorrect values are cut off and therefore will not increase the
error for the next filter operation.
Another option is to set the domain exactly to the size of the interesting
part within the image and then calling the operator
before applying a filter. This operator copies the
pixels inside of the border to the outside of the border
and therefore avoids errors caused by pixels that are undefined outside of
the domain. Subsequently, the domain can again be reduced to its original
size. This process should be repeated for every following filter operation.
Note, however, that this option increases the runtime significantly.
If runtime is not an issue, the operator
can be called
before applying the first filter to the image. That way, the whole image is
defined as domain and undefined pixels are avoided completely.
Another possibility of getting an image without undefined pixels is by
calling the operator
before applying a filter.
crops the image to the size of the
domain, which means that the domain then covers a complete smaller image.
Note, however, that for the cropped image the coordinate system has changed
in relation to the original image, which will influence all following
applications depending on the image coordinate system (e.g., calculating the
center of gravity).