Antialiasing (signal processing)
With anti-aliasing or anti-aliasing ( AA ) are used in fields of digital signal processing , such as the recording or image capture techniques to reduce aliasing , respectively. Low-pass filtering is applied to the input signal in order to attenuate the high frequency components responsible for the aliasing effect.
background
In signal processing, aliasing effects occur when digitizing analog signals: The original signal is sampled at regular time intervals and then restored using an analog low-pass filter when it is reproduced later . According to the Nyquist-Shannon sampling theorem, in order for it to be correctly restored, the original signal must be sampled at a rate that is more than twice as high as the highest frequency in the signal. If the sampling theorem is violated by a sampling rate that is too low, frequency components that were originally higher than half the sampling rate ( Nyquist frequency ) are interpreted as lower frequencies, since undersampling takes place for them. This undesirable phenomenon is called the aliasing effect.
The picture on the left demonstrates the aliasing effect: The upper graph shows the original signal, the frequency of which increases over time and which is sampled at regular intervals. The reconstructed signal (below) reproduces the original signal correctly only up to the Nyquist frequency. The high original frequencies are then expressed in the reconstruction as aliasing errors that are expressed in incorrect amplitudes and apparently lower frequencies.
Electronic filtering
In digital signal processing, so-called prefiltering to avoid aliasing is standard. An analog low-pass filter is applied to the signal before it is digitized . This attenuates frequencies of the signal above the Nyquist frequency. Such an electronic filter should be as steep as possible, which can be achieved by using complex higher-order filters. However, parts of the signal below the Nyquist frequency are inevitably attenuated and parts above the Nyquist frequency are not completely eliminated. The exact choice of the cut-off frequency therefore represents a compromise in practice between maintaining the useful signal and eliminating the aliasing effect.
A simpler method is when it is possible to oversample the input signal at twice or more frequency . This creates a safety margin between the original spectrum and the alias spectrum, which means that fewer requirements can be placed on the filter. The requirements on the digital side are increased for this.
Optical filtering
Without an anti-aliasing filter, an image can be irreparably degraded due to the following artifacts, for example:
- clearly sloping object edges do not have a smooth (straight) course, but a slight wave shape (approximating a staircase pattern);
- thin, clearly oblique lines (for example the rope of a distant sailing ship, hair in portraits) have this wave-stepped shape on both sides of their edge, thus an apparently regularly fluctuating thickness; Depending on the processing of the raw sensor image, a reddish discoloration alternating with a bluish discoloration can occur in the thicker sections, since the optical aliasing does not take place on gray levels , but on the basic colors of a Bayer sensor mosaic.
- Contrasts of very fine structures are unnaturally exaggerated because the transition colors between two objects are no longer proportional to the pixel coverage by the two objects, but tend to be similar to one or the other object. It follows, for example:
- Artifacts that can be generated by interpolating the raw image provided by the Bayer sensor are greatly exaggerated (for example, irregular discoloration on edges);
- The moiré artifacts in groups of lines that are not or only slightly inclined are very pronounced.
This aliasing damage in the absence of an anti-aliasing filter is considered undesirable because of them
- i. d. Usually particularly disturbing perceptibility intensity
- Non-repairability in image processing
- Maintaining the visibility of this damage even when scaling to lower resolutions of image display devices.
- Impairment of the effectiveness and lack of artifacts of image post-processing processes in which the correct estimation of object edges (especially on sub-pixel accuracy) plays a role, including
- in algorithms for resolution-increasing interpolation;
- in algorithms that evaluate the statistical distribution of gradients (transition contrasts) on edges (e.g. for sharpening, or for refraining from sharpness in the case of noise reduction);
- in algorithms for noise removal that evaluate the frequencies of image details (for frequency-dependent delimitation of the noise from subject details); This interferes with aliasing, since aliasing artifacts occur in the high frequency ranges in which main components of the sensor noise also occur, so that less noise can be correctly identified or delimited as such;
- in algorithms for determining the sharpness or resolution of lenses, since the usual test images used (e.g. very slightly tilted, black squares on a white background) in conjunction with edge transition interpreting mathematical algorithms assume a linearly flowing edge transition, thus from an intact anti-aliasing.
Since aliasing image damage cannot be adequately restored mathematically (algorithmically), pre-filtering is implemented in digital image acquisition using an optical anti-aliasing filter that only allows spatial frequencies that are roughly below the Nyquist frequency to pass. This can 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 into different light-sensitive cells lying next to one another.
literature
- Gabriele D'Antona, Alessandro Ferrero: Digital Signal Processing for Measurement Systems: Theory and Applications, pp. 115-126. Springer, New York 2006, ISBN 0-387-24966-4
- Rainer Scheithauer: Signals and Systems, pp. 270–276. Teubner, Stuttgart 2005, ISBN 3-519-16425-6
- Thomas Sandmann: Aliasing , in: Prof. Dr. Dr. Horst Hischer, Mathematics Lessons and New Media , Verlag Franzbecker, 2002, ISBN 3-88120-353-2
Web links
Individual evidence
- ↑ Adrian Davies, Phil Fennessy: Digital Imaging for Photographers, 30. Focal Press, Oxford 2001, ISBN 0-240-51590-0