Spatial filters

In image processing, spatial filters are those from which an output pixel is computed from some neighbourhood (i.e. mask) (usually rectangular) surrounding the corresponding input pixel.

A characteristic of spatial filters is that, if the filter is to be applied strictly, the output image is smaller than the input image by an amount related to the mask size. Frequently this is not what is wanted; for example the user may want an output image that is the same size as the input image. In this case the problem is: what to do with the border regions? The problem is particularly acute if the filter mask size is significant compared with the data width. There are various options, used in the filter classes below, illustrated here using a constructor for an NxN averaging mask:

• By expanding the i/p image by N-1 pixels, the o/p image will end up the same size as the orignal i/p image. This raises the old question: what do we fill the new pixels in the i/p image with? Some common padding strategies are:
  • fill with black:

    IPLinearAverageC g(N,N,Original,PadBlack);

  • fill with nearest pixel from original i/p image:

    IPLinearAverageC g(N,N,Original,Repeat);

  • reflect the image about the border (complicated in the corner regions):

    IPLinearAverageC g(N,N,Original,Reflect);

  • filling with black suggests a further possibility: we can rescale the o/p in the border region so that the mean (for a linear filter) of the filter mask is preserved:

    IPLinearAverageC g(N,N,Original,PBRescale);

    In this case, a filter operating on an image of constant intensity would generate an o/p image of constant intensity.

• We can of course not expand, so that the o/p image is N-1 pixels smaller than the i/p image. This is unambiguous and simple:

  IPLinearAverageC g(N,N,Erode);

  Note that, if the "Erode" options is used, the following argument (if used) is ignored.

• There is also an option (maybe of limited use) to extend the i/p image by a further N-1 pixels, so that the o/p image in some sense contains all of the available information from the i/p image:

  IPLinearAverageC
  g(N,N,Expanded,PadBlack);

A separate problem is that of registering the output image with the input image. If the mask width N is odd, this is straightforward: the output pixel position is that of the input pixel under the centre of the mask. However, if N is even, there is no centre mask pixel, so that there is an effective ½ pixel shift. The direction of this shift can be controlled by the user (so that successive shifts can be cancelled if required). The default is to shift upwards and to the left. To shift the other way, the constructor might look like:

IPLinearAverageC g(N,N,Original,PBRescale,ShiftDR);

The options are documented in IPSpatFilterC, which is inherited by the filter classes. Note that not all of the possibilities are implemented for every filter. Also some arguments cause others to have no effect.

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