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6.2.4.8 Filtering (smoothing) operators ¶

Image filtering is commonly used for smoothing: every pixel value in the output image is created by applying a certain statistic to the pixels in its vicinity.

filter-mean

Apply mean filtering (or moving average) on the input dataset. During mean filtering, each pixel (data element) is replaced by the mean value of all its surrounding pixels (excluding blank values). The number of surrounding pixels in each dimension (to calculate the mean) is determined through the earlier operands that have been pushed onto the stack prior to the input dataset. The number of necessary operands is determined by the dimensions of the input dataset (first popped operand). The order of the dimensions on the command-line is the order in FITS format. Here is one example:

$ astarithmetic 5 4 image.fits filter-mean

In this example, each pixel is replaced by the mean of a 5 by 4 box around it. The box is 5 pixels along the first FITS dimension (horizontal when viewed in ds9) and 4 pixels along the second FITS dimension (vertical).

Each pixel will be placed in the center of the box that the mean is calculated on. If the given width along a dimension is even, then the center is assumed to be between the pixels (not in the center of a pixel). When the pixel is close to the edge, the pixels of the box that fall outside the image are ignored. Therefore, on the edge, less points will be used in calculating the mean.

The final effect of mean filtering is to smooth the input image, it is essentially a convolution with a kernel that has identical values for all its pixels (is flat), see Convolution process.

Note that blank pixels will also be affected by this operator: if there are any non-blank elements in the box surrounding a blank pixel, in the filtered image, it will have the mean of the non-blank elements, therefore it will not be blank any more. If blank elements are important for your analysis, you can use the isblank operator with the where operator to set them back to blank after filtering.

For example in the command below, we are first filtering the image, then setting its original blank elements back to blank in the output of filtering (all within one Arithmetic command). Note how we are using the set- operator to give names to the temporary outputs of steps and simplify the code (see Operand storage in memory or a file).

$ astarithmetic image.fits -h1        set-in \
                5 4 in filter-mean    set-filtered \
                filtered in isblank nan where \
                --output=out.fits

filter-median

Apply median filtering on the input dataset. This is very similar to filter-mean, except that instead of the mean value of the box pixels, the median value is used to replace a pixel value. For more on how to use this operator, please see filter-mean.

The median is less susceptible to outliers compared to the mean. As a result, after median filtering, the pixel values will be more discontinuous than mean filtering.

filter-sigclip-mean

Apply a \(\sigma\)-clipped mean filtering onto the input dataset. This is very similar to filter-mean, except that all outliers (identified by the \(\sigma\)-clipping algorithm) have been removed, see Sigma clipping for more on the basics of this algorithm. As described there, two extra input parameters are necessary for \(\sigma\)-clipping: the multiple of \(\sigma\) and the termination criteria. filter-sigclip-mean therefore needs to pop two other operands from the stack after the dimensions of the box.

For example, the line below uses the same box size as the example of filter-mean. However, all elements in the box that are iteratively beyond \(3\sigma\) of the distribution’s median are removed from the final calculation of the mean until the change in \(\sigma\) is less than \(0.2\).

$ astarithmetic 3 0.2 5 4 image.fits filter-sigclip-mean

The median (which needs a sorted dataset) is necessary for \(\sigma\)-clipping, therefore filter-sigclip-mean can be significantly slower than filter-mean. However, if there are strong outliers in the dataset that you want to ignore (for example, emission lines on a spectrum when finding the continuum), this is a much better solution. Note that \(\sigma\)-clipping is easily biased by outliers, so filter-madclip-mean is more robust.

filter-sigclip-median

Apply a \(\sigma\)-clipped median filtering onto the input dataset. This operator and its necessary operands are almost identical to filter-sigclip-mean, except that after \(\sigma\)-clipping, the median value (which is less affected by outliers than the mean) is added back to the stack. Note that \(\sigma\)-clipping is easily biased by outliers, so filter-madclip-median is more robust.

filter-madclip-mean

Apply a MAD-clipped mean filtering onto the input dataset. MAD stands for Median Absolute Deviation, this is much more robust to outliers than the \(\sigma\)-clipping. This operator is called in a similar way to filter-madclip-mean, for example in the command below, we use \(4\times\)MAD clipping with a termination criteria of 0.01 on an image:

$ astarithmetic 4 0.01 5 5 image.fits filter-madclip-mean

filter-madclip-median

Apply a MAD-clipped median filtering onto the input dataset; see the description of filter-madclip-mean for more.