List of Sections ↓

Filters are an important part of nearly every machine vision application. They can, for instance, be used to smooth images (e.g., mean_imagemean_imageMeanImageMeanImageMeanImagemean_image), extract sub-pixel precise edges (e.g., edges_sub_pixedges_sub_pixEdgesSubPixEdgesSubPixEdgesSubPixedges_sub_pix) or process the frequency domain of images (e.g., fft_imagefft_imageFftImageFftImageFftImagefft_image).

Usually, filter operations are applied using filter masks, which are moved across the input image pixelwise. For each pixel a new value is calculated based on its neighborhood. The neighborhood is determined by shape and size of the filter mask (see the scheme below).

image/svg+xml image/svg+xml 200 200 200 200 200 96 96 96 40 image/svg+xml 200 96 200 200 96 96 96 40 40 image/svg+xml
(1) (2) (3) (4)
(1) Image with a filter mask of size 3x3 pixels (orange). (2) For the computation of the new pixel value of the pixel located at the center point of the mask all the pixel values within the mask are taken into account. (3) The mask is moved across the image pixel by pixel. (4) In this case a median filter (see median_rectmedian_rectMedianRectMedianRectMedianRectmedian_rect) is used for the computation of the resulting image.

You can tell from the working principle of filter masks, the treatment of pixels along the image or domain border requires special attention, as part of the filter mask exceeds the domain. In the following sections some consequential issues will be discussed.

Applying Filter Masks on Reduced Image Domains

If a filter that is using a mask is applied on 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 (see scheme below).

image/svg+xml image/svg+xml image/svg+xml image/svg+xml
(1) (2) (3) (4)
(1) Image with a region (yellow) to which the image domain shall be reduced to. (2) The image domain is reduced to the chosen region using reduce_domainreduce_domainReduceDomainReduceDomainReduceDomainreduce_domain. (3) For the computation of a new value for the pixel in the center of the mask all the pixel values within the mask are taken into account. For pixels along the domain border this also includes pixels from outside the domain. (4) Result image after the application of a median filter (see median_rectmedian_rectMedianRectMedianRectMedianRectmedian_rect).

To understand this, the definition of domains in this context must be considered: 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 nevertheless.

Problems Caused by Gray Values Outside of the Input Image Domain

Another point to notice is the handling of pixels outside the input image domain. The parameter 'init_new_image'"init_new_image""init_new_image""init_new_image""init_new_image""init_new_image" of set_systemset_systemSetSystemSetSystemSetSystemset_system determines how those pixels are treated. If the pixels are initialized with 0, consecutive runs will yield identical results. Otherwise, those pixels remain undefined. While this enhances the program runtime, 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 domain with full_domainfull_domainFullDomainFullDomainFullDomainfull_domain will lead to artifacts appearing outside of the former image domain.

Problems Caused when Applying Filters Consecutively

When two or more filters are applied consecutively on the same domain, the undefined or unexpected values (as described in the paragraphs above) have a higher impact on the result image. This is because 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.

Artifacts at the domain border after applying two consecutive filters.
  1. Errors caused by undefined pixels can easily be prevented by, e.g., choosing a dilated domain (see Morphology / Gray Values) according to the filter mask. If multiple filters are applied consecutively, the image domain can be dilated in advance, considering the filter sizes to be used. For instance, when using a cascade of rectangular filters of arbitrary dimensions, the width and length dimension of the dilation mask can be calculated considering the individual filter mask dimensions and the number of filter operations :


    After the filters were applied, the image domain can be reduced to its original size (e.g., with reduce_domainreduce_domainReduceDomainReduceDomainReduceDomainreduce_domain).

  2. Another option is to set the domain exactly to the size of the interesting part within the image and then calling the operator expand_domain_grayexpand_domain_grayExpandDomainGrayExpandDomainGrayExpandDomainGrayexpand_domain_gray 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.

    The result of expand_domain_grayexpand_domain_grayExpandDomainGrayExpandDomainGrayExpandDomainGrayexpand_domain_gray looks as if the boundary is copied multiple times and added at the outside.
  3. If runtime is not an issue, the operator full_domainfull_domainFullDomainFullDomainFullDomainfull_domain 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.

  4. Another possibility of getting an image without undefined pixels is by calling the operator crop_domaincrop_domainCropDomainCropDomainCropDomaincrop_domain before applying a filter. The operator crop_domaincrop_domainCropDomainCropDomainCropDomaincrop_domain 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).

List of Sections