Order Statistic Filter Class

Interface

Class Filt

Order-statistic filters are used for eliminating or reducing noise in images. Like other spatial filters, these filters assign to each pixel in an image a value based on the values of the pixels in the neighborhood or window surrounding (and including) the pixel. What characterizes order-statistic filters is that the replacement value is based on an ordering or ranking, from smallest to largest, of the values of the pixels in the window. The max filter assigns to each pixel the maximum value of the pixels in the window, the min filter the minimum value, the median filter the median value, and the midpoint filter the mean of the minimum and maximum values. The alpha-trimmed mean filter ignores the lowest and highest values of the pixels in the window, and finds the mean of the remaining values; the number of values ignored is determined by the trim value, with the trim/2 lowest and highest values ignored. In the limiting case of trim = 0, the filter becomes an averaging (mean) filter. In the other limiting case of M*N - 1, where M is the length of the window and N is the width of the window, the filter becomes a median filter.(Note that in this implementation the trim/2 value is truncated as an integer.)

Different order-statistic filters are suited for removing or reducing different kinds of noise. The median filter removes impulse or salt-and-pepper noise -- that is, small, scattered areas of low- and high-value pixels -- while preserving the edges of objects in the image. The min filter enhances areas of images with low-value pixels and removes salt noise. The max filter enhances areas of images with high-value pixels and removes pepper noise. The mid-point filter reduces noise that takes on a range of values, such as noise with a Gaussian or uniform distribution of values. The alpha-trimmed mean filter is useful where there are different kinds of noise, such as a combination of impulse and Gaussian noise.

The actual filtering of the image occurs in filt(). The selfunc parameter is the function that selects the values to be assigned to each pixel in the image by operating on the values of the pixels in the window after the values have been ordered. The particular function passed as an argument to filt() depends on the filter being applied. This is reflected in the naming scheme, with maxval() passed for the max filter, minval() passed for the min filter, and so on.

There are various ways to deal with the pixels on the border. In this implementation, the pixels are assigned the value of the nearest interior pixel. This is done in fillborder().

The selection functions (i.e. the *val() functions) are static so they can be passed as arguments to filt() with a much simpler syntax than if they were not static. fcmp() must be static so it can be passed as an argument to the qsort() function.

Authors

Steve Simon (April 2009)

Source Code

Source code is available when you agree to a GP Licence.

Not a member, then Register with CodeCogs. Already a Member, then Login.

Class Filt::alpha

Filt::alpha

This function replaces the pixels in an image with the mean of the values of the pixels in the filter window after removing the lowest and highest values; how many values to remove is specified by the user. Alpha-trimmed mean filters are useful for reducing the noise in an image where the noise is of different types, such as a combination of impulse and Gaussian noise.

out	output image
in	input image
nx	number of columns
ny	number of rows
trim	ignore trim/2 lowest and highest values when finding mean of pixel values in filter window

Returns

pointer to output image

Authors

Steve Simon (April 2009)

References

1. Gonzalez, R. and Woods, R. "Digital Image Processing," 3rd ed., pp. 156-157 and 325-330.

Class Filt::max

Filt::max

This function replaces the pixels in an image with the maximum value of the pixels in the filter window. Max filters enhance the parts of an image with high-value pixels and eliminate low-value impulse (or pepper) noise.

out	output image
in	input image
nx	number of columns
ny	number of rows

Returns

pointer to output image

Authors

Steve Simon (April 2009)

Class Filt::median

Filt::median

This function replaces the pixels in an image with the median value of the pixels in the filter window. Median filters are useful for eliminating impulse, or salt-and-pepper, noise.

out	output image
in	input image
nx	number of columns
ny	number of rows

Returns

pointer to output image

Authors

Steve Simon (April 2009)

Class Filt::midpoint

Filt::midpoint

This function replaces the pixels in an image with the midpoint of the pixels in the filter window -- that is, the mean of the lowest and highest values. Midpoint filters reduce noise in an image where the noise takes on a range of values, such as noise with a Gaussian or uniform distribution of values.

out	output image
in	input image
nx	number of columns
ny	number of rows

Returns

pointer to output image

Authors

Steve Simon (April 2009)

Class Filt::min

Filt::min

This function replaces the pixels in an image with the minimum value of the pixels in the filter window. Min filters enhance the parts of an image with low-value pixels and eliminate high-value impulse (or salt) noise.

out	output image
in	input image
nx	number of columns
ny	number of rows

Returns

pointer to output image

Authors

Steve Simon (April 2009)

Class Filt::alphaval

Filt::alphaval

w	Structure containing information about current filtering window.

Returns

The mean value of the pixels in the window ignoring the trim/2 lowest and highest.

Authors

Steve Simon (April 2009)

Class Filt::minval

Filt::minval

w	Information about the current filter window.

Returns

The minimum value of the pixels in the window.

Authors

Steve Simon (April 2009)

Class Filt::maxval

Filt::maxval

w	Information about the current filter window.

Returns

The maximum value of the pixels in the window.

Authors

Steve Simon (April 2009)

Class Filt::medval

Filt::medval

w	Information about the current filter window.

Returns

The median value of the pixels in the window.

Authors

Steve Simon (April 2009)

Class Filt::midval

Filt::midval

w	Information about the current filter window.

Returns

The midpoint of the values of the pixels in the window.

Authors

Steve Simon (April 2009)

Class Filt::filt

Filt::filt

This function assigns a value to each pixel in an image. The value assigned is based on the values of the pixels in a neighborhood or window surrounding, and including, the pixel. (Note that the pixels on the border of the image are a special case; see below.) The length of the sides of the filter window is given by the constant DIM.

To assign a value to a pixel, the values of the pixels in the window are first sorted. Then a function, the selfunc parameter, is applied to the array of sorted values to select the value to assign. How the value is selected -- that is, how the selection function operates on the array of sorted values -- depends on the type of filter being applied. Thus different filters can be applied by passing different functions as an argument. After all the interior pixels have been assigned a value, the pixels on the border are assigned values by calling the function fillborder().

out	output image
in	input image
nx	number of columns
ny	number or rows
pf	pointer to a function for selecting a value in the filter window
trim	specifies which pixel values to ignore (ignore the trim/2 lowest and highest)

Returns

output image

Authors

Steve Simon (April 2009)

Class Filt::fillborder

Filt::fillborder

img	image to operate on
nx	number of columns of image
ny	number of rows of image

Returns

image operated on

Authors

Steve Simon (April 2009)

Class Filt::fcmp

Filt::fcmp

p1	first floating point number to compare
p2	second floating point number to compare

Returns

result of comparison (-1 if p1 < p2, 0 if p1 == p2, 1 otherwise)

Authors

Steve Simon (April 2009)

References

1. Kernighan, B. and Pike, R. "The Practice of Programming." Section 2.3.