Median filter
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In image processing it is usually necessary to perform high degree of noise reduction in an image before performing higher-level processing steps, such as edge detection. The median filter is a non-linear digital filtering technique, often used to remove noise from images or other signals. The idea is to examine a sample of the input and decide if it is representative of the signal. This is performed using a window consisting of an odd number of samples. The values in the window are sorted into numerical order; the median value, the sample in the center of the window, is selected as the output. The oldest sample is discarded, a new sample acquired, and the calculation repeats.
Median filtering is a common step in image processing. It is particularly useful to reduce speckle noise and salt and pepper noise. Its edge-preserving nature makes it useful in cases where edge blurring is undesirable.
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[edit] Example
To demonstrate, the median filter will be applied to the following array with a window size of 3, repeating edge values:
x = [2 80 6 3]
y[1] = Median[2 2 80] = 2
y[2] = Median[2 80 6] = Median[2 6 80] = 6
y[3] = Median[80 6 3] = Median[3 6 80] = 6
y[4] = Median[6 3 3] = Median[3 3 6] = 3
so
y = [2 6 6 3]
where y is the median filtered output of x
[edit] Common problems
A common problem with all filters based on all adjacent pixels is how to process the edges of the image. As the filter nears the edges, a median filter may not preserve its odd number of samples criteria. It is also more complex to write a filter that includes a method to specifically deal with the edges. Common solutions to the problem are:
- Not processing edges, with or without a crop of the image edges afterwards.
- Fetching pixels from other places in the image. Typically the other horizontal edge on horizontal edges, and the other vertical edge on vertical edges are fetched.
- Making the filter process fewer pixels on the edges.
- Comparing the filtered sample to the original sample to determine if that sample is an outlier before replacing it with the filtered one.
[edit] Pseudo code
A simple median filter may look like this:
edgex := (window width / 2) rounded down
edgey := (window height / 2) rounded down
for x from edgex to image width - edgex:
for y from edgey to image height - edgey:
colorArray[window width][window height];
for fx from 0 to window width:
for fy from 0 to window height:
colorArray[fx][fy] := pixelvalue[x + fx - edgex][y + fy - edgey]
Sort colorArray[][];
pixelValue[x][y] := colorArray[window width / 2][window height / 2];
Notice that:
- This filter only processes one color channel.
- This filter takes a "Not processing edges" approach.
- "Window" refers to the pixel area we are processing for each pixel and "image" refers to our actual image.
- The algorithms described in External Links are much faster.
