Filtering

Filtering consists in applying a transformation (called a filtre) to all or to part of a digital image by applying an operator. There are the following types of filters:

• Low-pass filters, which consist in attenuating image components with a high frequency (dark pixels). This type of filtering is usually used to attenuate the image noise; this is why it is usually called smoothing. The average filters are a type of low-pass filters whose principle is to take the averages of the values of neighbouring pixels. The result of this filter is a fuzzier image.
• High-pass filters, contrary to low-pass filters, these attenuate the low frequency image components and in particular, make it possible to accentuate details and contrast, this is why the term "sharpening filter" is sometimes used.
• • Band-pass filters allow the difference between the original image and that obtained by applying a low-pass filter to be obtained.
• Directional filters apply a transformation according to a given direction.

What is a filter?

A filter is a mathematical transformation (called a convolution product) which allows the value of a pixel to be modified according to the values of neighbouring pixels, with coefficients, for each pixel of the region to which it is applied.

The filter is represented by a table (matrix), which is characterized by its dimensions and its coefficients, whose centre corresponds to the pixel concerned. The table coefficients determine the properties of the filter. The following is an example of a 3 X 3 filter:

Thus, the product of the image matrix, which is usually very large because it represents the initial image (pixel table), by the filter yields a matrix corresponding to the processed image.

The concept of noise

Noise characterizes signal parasites or interference, i.e. the parts of the signal that have been locally deformed. Thus, the noise of an image indicates image pixels whose intensity is very different from those of nearby pixels.

The noise can be due to various causes:

• To the environment during acquisition
• To the quality of the sensor
• To the sampling quality

Smoothing

OThe filtering operation aimed at eliminating the noise from an image is called “smoothing” (or anti-noise filter).

The specific smoothing operation that consists in overcoming the staircase effect produced by pixels on the edge of a geometrical shape is called anti-aliasing.

Sharpening

Sharpening is the opposite of smoothing; it is an operation aimed at accentuating the differences between nearby pixels.

Thus, the sharpening can make it possible to highlight the borders between homogeneous regions of the image and it is then called contour extraction (or contouring).

Dithering

Dithering (or halftoning) is a technique that consists in alternating geometrical patterns using little colour, called “halftones”, in order to simulate a more elaborate colour.

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