Spatial anti-aliasing

With anti-aliasing or anti- aliasing (AA) are in areas of digital signal processing, such as in recording or imaging, refers to techniques to reduce aliasing. Here, a low-pass filtering is applied to dampen the responsible for the aliasing high frequency components to the input signal.


In signal processing, aliasing occurs when digitizing analog signals: the original signal is sampled at regular intervals and restored during the subsequent reproduction by means of an analog low-pass filter. Thus it can be restored correctly, the original signal must be sampled at a rate according to the Nyquist-Shannon sampling theorem, which is more than twice as high as the maximum occurring in the signal frequency. Is the sampling damaged by too low a sampling rate, then the frequency components that were originally higher than half the sampling rate ( Nyquist frequency ), interpreted as a lower frequency, as occurs for this sub-sampling. This undesirable phenomenon is called aliasing.

The picture demonstrates the aliasing: The top graph shows the original signal whose frequency increases with time and is sampled at regular intervals. The reconstructed signal ( below) is the original signal only up to the Nyquist frequency correctly. After that, the original high frequencies are expressed in the reconstruction as an alias errors that manifest themselves in the wrong amplitudes and seemingly lower frequencies.

Electronic filtering

In the digital signal processing is the so-called Prefiltering to avoid aliasing standard. An analog low pass filter to the signal thereby applied before digitization. Wherein frequencies of the signal are attenuated above the Nyquist frequency. Such an electronic filter should be as steep edges, which can be achieved by consuming higher-order filters. However, parts of the signal are attenuated below the Nyquist frequency, and parts are not completely eliminated by the Nyquist frequency. The exact choice of the cutoff frequency is therefore a compromise between the maintenance of the desired signal and the elimination of the aliasing in the practice dar.

A simpler method is obtained if it is possible to oversample the input signal with a double or higher frequency. This creates a safety distance between the original spectrum and the alias spectrum, thus less stringent requirements are imposed on the filter. The requirements on the digital side to increase it.

Optical filtering

Without an anti- aliasing filter, an image can be degraded beyond repair, for example, by the following artifacts:

  • Clearly slanted object edges are not smooth ( straight ) course, but just a simple waveform ( in approaching a podium - type);
  • Thin, clear oblique lines ( for example, the rigging of a sailing ship away, hair in portraits) have these waves - podium - form on both sides of its edge, thus a seemingly regularly varying thickness; Depending on the sensor raw image - processing a reddish discoloration can occur alternately with a bluish discoloration additionally in the thicker sections because the visual aliasing takes place not in grayscale, but on the primary colors of a Bayer sensor mosaic.
  • Contrasts very fine structures are unnaturally increasing, as the transition between two colors, objects are no longer proportional to the pixel coverage of the two objects, but tend to be similar to the one or the other object. From this example follows: Artifacts that can be generated by the interpolation of the sensor the raw image supplied by Bayer, are greatly exaggerated (eg, irregular discoloration at edges );
  • The moiré artifacts at or only slightly oblique lines groups are strong.

This aliasing damage in the absence of an anti- aliasing filter are considered undesirable because of their

  • I.d.R. particularly disturbing observability intensity
  • Non- repairable in image processing
  • Visibility preserving these damages even when scaling to lower resolutions of display devices.
  • Obstruction of effectiveness and artifact poverty of image post-processing method in which the correct estimation of object edges (especially on - sub-pixel accuracy ) plays a role, including in algorithms for increasing resolution interpolation;
  • In algorithms which evaluate the statistical distribution of gradients (transitional contrasts ) on edges (eg for sharpening, or the sharpness of abstinence in denoising );
  • In algorithms for noise removal, which evaluate the frequencies of image detail ( for frequency-dependent differentiation of the noise of subject details ); Aliasing disturbs this since aliasing artifacts in high frequency regions, which also contributes a majority of sensor noise occur, so less noise can be correctly identified or defined as such;
  • ( easily eg tilted, black squares on a white background ) going out in algorithms for determining the sharpness and resolution of lenses, as used in common test images in conjunction with edge transition interpretive mathematical algorithms by a linear running edge-blending, thus from an intact anti- aliasing, go out.

Since ( algorithmically ) can not be restored adequately aliasing image damage calculation, in the digital image capture pre-filtering is realized by an optical anti -aliasing filter, which can only spatial frequencies that are roughly below the Nyquist frequency happen. It may involve several layers of a birefringent material such as quartz or lithium niobate, which divide an incident light beam into four parallel light beams and thus to different, adjacent light-sensitive cells.