IMAGE_DENOISE
Remove Noise from an Image

IMAGE_DENOISE is a C library which uses the median filter to try to remove noise from an image.

A gray scale image can be represented using a 2D array of nonnegative integers over some range 0 to GMAX. The value 0 indicates black, and GMAX white. Intermediate values represent shades of gray in a natural way. Note, however, that the eye has a nonlinear response to intensity, so that the value GMAX/2 will not be perceived as halfway between 0 and GMAX. That is a separate issue.

A color image can be represented using a set of three 2D arrays, which can be thought of as R, G, and B, and which represent the intensity of the red, green and blue signals that combine to form the color image. A common maximum value is assumed, RGBMAX.

The ASCII PGM and PPM formats are a convenient, if somewhat inefficient, way to store such images. These ASCII formats are easy to read and write from a program.

In the example considered here, a good image is damaged by the addition of "salt and pepper" noise; that is, a scattering of individual pixels have been randomly reset to the lowest or highest possible values. In a gray scale picture, such noise looks as though salt and pepper were added to the picture.

It turns out that the median filter can clear up most of the noise, but not all of it. Because the noise values are extreme (0 or 255), it is not unlikely for a 2x2 block of noisy values to occur. Such a block will not be filtered out by the NEWS median filter!

Since an image is fairly "smooth", each good pixel should actually be fairly close to the values of good pixels nearby, while this will not be true for the salt and pepper pixels. So one way to make the noise go away, at the cost of some minor blurring, is to replace each pixel by the median value of itself and its neighbors.

There are sophisticated programs for applying the filters to a noisy image, with the user allowed to specify the shape of a rectangular neighborhood about each pixel. However, in this example, we go through some of the lower level details "by hand", applying simple versions of the median filter, in which each pixel is replaced by the median of nearby values.

By the way, my example programs need to read ASCII image files, either in PGM or PPM format. One way to create them is with the IMAGEMAGICK convert program:

        convert balloons.png -compress none balloons.ppm
      

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

IMAGE_DENOISE is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

IMAGE_COMPONENTS, a C library which seeks the connected "nonzero" or "nonblack" components or "segments" of an image or integer vector, array or 3D block.

IMAGE_DENOISE_OPENMP, a C library which applies simple filtering techniques to remove noise from an image, carrying out the operation in parallel using OpenMP.

IMAGE_EDGE, a C library which demonstrates a simple procedure for edge detection in images.

PGMA_IO, a C library which handles the ASCII Portable Gray Map (PGM) format.

• image_denoise.c, the source code.
• image_denoise.h, the include file.

Examples and Tests:

• image_denoise_test.c, a sample calling program.
• image_denoise_test.txt, the output file.

BALLOONS is an RGB image of a couple with balloons, to which salt and pepper noise has been added.

• balloons_noisy.ascii.pgm, the ASCII PGM file of glassware, with added noise.
• balloons_noisy.png, a PNG version.
• balloons_median_news.ascii.ppm, the ASCII PPM file of balloons, after the noise has been filtered using the median NEWS filter.
• balloons_median_news.png, a PNG version.
• balloons_median_news2.ascii.ppm, after application 2 of MEDIAN NEWS.
• balloons_median_news2.png, a PNG version.
• balloons_median_news3.ascii.ppm, after application 3 of MEDIAN NEWS.
• balloons_median_news3.png, a PNG version.
• balloons_median_news4.ascii.ppm, after application 4 of MEDIAN NEWS. Notice that most of the remaining defects are 2x2 blocks of equal noise value, which cannot be filtered.
• balloons_median_news4.png, a PNG version.

GLASSWARE is a grayscale image of glassware, to which salt and pepper noise has been added.

• glassware_noisy.ascii.pgm, the ASCII PGM file of glassware, with added noise.
• glassware_noisy.png, a PNG version.
• glassware_mean_news.ascii.pgm, the ASCII PGM file of glassware, after the noise has been filtered using the mean NEWS filter.
• glassware_mean_news.png, a PNG version.
• glassware_median_news.ascii.pgm, the ASCII PGM file of glassware, after the noise has been filtered using the median NEWS filter.
• glassware_median_news.png, a PNG version.

List of Routines:

• GRAY_MEAN_NEWS uses a mean NEWS filter on a gray scale image to remove noise.
• GRAY_MEDIAN_NEWS uses a median NEWS filter on a gray scale image to remove noise.
• I4MAT_COPY copies one I4MAT to another.
• I4VEC_FRAC searches for the K-th smallest entry in an I4VEC.
• I4VEC_mean_i4 returns the integer mean of an I4VEC.
• I4VEC_MEDIAN returns the median of an unsorted I4VEC.
• PGMA_READ_DATA reads the data in an ASCII PGM file.
• PGMA_READ_HEADER reads the header of an ASCII PGM file.
• PGMA_WRITE writes the header and data for an ASCII PGM file.
• PGMA_WRITE_DATA writes the data for an ASCII PGM file.
• PGMA_WRITE_HEADER writes the header of an ASCII PGM file.
• PPMA_READ_DATA reads the data in an ASCII portable pixel map file.
• PPMA_READ_HEADER reads the header of an ASCII portable pixel map file.
• PPMA_WRITE writes the header and data for an ASCII portable pixel map file.
• PPMA_WRITE_DATA writes the data for an ASCII portable pixel map file.
• PPMA_WRITE_HEADER writes the header of an ASCII portable pixel map file.
• RGB_MEDIAN_NEWS uses a median NEWS filter on RGB data to remove noise.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C source codes.