These consist of simple 3x3 or 5x5 matrix convolution filters.
These filters are applied by replacing each pixel intensity by a
weighted average of its neighbouring pixels. The weights that are
applied to the neighbouring pixel intensities are contained in a matrix
called the convolution matrix. In Pyxis, two convolution matrices
are applied sequentially to each pixel, these are referred to as the
primary and secondary matrices. The user can define custom 3x3 or
5x5 convolution matrices or use the provided predefined filter matrices
for the following convolution filters;
Low Pass: This filter
strongly weights the values in neighbouring pixels, so the effect is
similar to computing a local average. High frequency components
are attenuated by this filter.
High Pass: The high pass
filter uses negative weighting coefficients for the neighbouring
pixels, this effectively enhances regions of high intensity gradient in
the image so that finer details are emphasized.
Laplacian: This filter is
similar to the high-pass filter, however the sum of the weighting
coefficients is zero. This filter emphasizes contours in the
Sobel: This is a very strong
contour emphasizing filter.
Prewitt: Similar to Sobel
These are statistical filters that replace each
pixel value with either the minimal or maximal value from the set of
nearest neighbour pixels. Four sampling configurations for the
pixels can be selected by clicking on the desired sampling
configuration (shown on the right). A minimal filtering step is
referred to as "erosion" because it reduces the size of features in the
image. A maximal filtering operation is referred to as an
"expansion" because it has the opposite effect on features in the
image. Generally the minimal and maximal filters are not used
alone, but instead a maximal filtering step is followed by minimal
filtering step; the effect is to strongly attenuate very sharp spikes
in the image. The case of erosion followed by expansion is
referred to as "closing", whereas "opening" corresponds to the reverse
This is perhaps the most powerful filter for use in planetary image
processing. The idea is to create a strongly low-pass filtered
mask from the image that only contains the slow variations in the image
contrast and subtract it from the original image. The effect of
this operation is to very stongly enhance small contrast variations in
the image and attenuate less interesting low frequencies, as are due
for example to uneven illumination of the planet surface. In
Pyxis the unsharp mask can be created using either gaussian
cross-convolution or local averaging (the gaussian convolution is
generally preferred). Weighting factors for the mask and original
image must usually be adjusted to obtain optimum results for every
different case, although it is generally preferrable to use similar
settings when processing the individual colour channels of an object.
This convolution technique applies a gaussian profile weighting factor
first to the x-direction in the image, followed by the y-direction in
the image. Gaussian cross-convolution is a very quickly computed
smoothing filter; the extent of the smoothing is controlled by the
width of the applied gaussian profile.
Replaces the pixel value by the average over a given number of nearest
neighbour pixels. The pixel radius out to which pixels are
included in the average determines the amount of smoothing
This is probably the most powerful tool for removing large noise spikes
in the image. This is a statistical filter similar to the
minimal/maximal filters in that the pixels in the neighbourhood of the
pixel being processed are sampled and sorted in terms of
intensity. The median filter selects median intensity (the
intensity for which half the samples have greater intensity and half
the samples have lower intensity) in the sampled set of pixels.
The effect is to reject strong outlier low or high pixel intensities
while having a "relatively" small effect on the image details compared
to other smoothing techniques. The median filter is particularly
useful for removing cosmic ray spikes from images that have relatively
large stellar images on the CCD. The disadvantage of this
technique is that faint stars are often removed from the image.
Threshold and bias subtraction
Thresholding consists of constraining the pixel values to remain within
certain limits. Bias subtraction subtracts a fixed bias level
from the image.
Subtracting a model sky
It is often useful to subtract a planar gradient from the image to try
to remove sky effects that cannot be removed by flat fielding (for
example lunar glow in one corner of the image). The sky-model
tool estimates the slope of the sky background in the x and y
directions so that the planar component of the sky background can be
subtracted. Note that when the x-slope and y-slope are zero, this
simply corresponds to a fixed bias subtraction.
Fourier transform low or high pass
The Fourier transform (FT) filter converts the image to the spatial
frequency domain using a fast Fourier Transform algorithm. To do
this efficiently, the image is first converted to a square domain by
padding the edges of the image with the average value of the image
intensity. The FT returns the complex coefficients for each 2D
spatial frequency in the image up to Nyquist (1/2 the image
width). When the FT filter tool is invoked, the FT is
automatically computed and the FT of the image is displayed (actually,
what is displayed is the square modulus of the complex fourier
coefficients). The center of the FT image represents the lowest
spatial frequencies, whereas the edge represents the higher
frequencies. Clicking and dragging on the image causes a circle
of variable size to be drawn, centered on the image image center (i.e.
the frequency origin where, fx = 0 and fy = 0). This circle
represents the cutoff frequency to be used in the filtering.
Alternatively, the cutoff frequency may be entered manually in an edit
box below the image.
The cutoff is "apodized" or smoothed by using a gaussian edge profile
for the cutoff or "aperture function" - in this case a circular
aperture in frequency space. The purpose of the gradual cutoff is
to avoid "ringing" in the image effectively caused by the oscillatory
sin(x)/x response of the FT to a 2D intensity profile that is exactly 1
within a certain radius and 0 without. Note that the FT of a
Gaussian is another Gaussian, so that oscillations are suppressed by
Gaussian and other smoothly varying aperture functions. Once the
filtering parameters are selected, click "preview" to compute the
inverse FT of the modified image FT and thereby obtain the filtered
image. If excessive ringing is present (this appears as rings
around bright stars), increase the apodization width until the ringing
is suppressed to an acceptable level.