View source for Sub-pixel resolution

[[File:SubpixelCircleint.png|thumb|right|Sub-pixel rendering of a circle]]

In [[Digital image processing|digital image processing]], '''sub-pixel resolution''' can be obtained in images constructed from sources with information exceeding the nominal [[Image resolution|pixel resolution]] of said images. 

==Aliasing==
{{main|Aliasing}}

[[File:Aliasing a.png|thumb|200px|Left: An aliased image of the letter ''A'' in Times New Roman. Right: An ''anti-aliased'' image. (''See also'': [[Font rasterization|Font rasterization]])]]

When an object with a certain resolution is represented on a display with lower resolution, the imperfections due to the loss of information are known as [[Aliasing|aliasing]].
This can happen with geometric objects, [[Vector graphics|vector graphics]], [[Computer font#Outline fonts|vector fonts]] or [[3D computer graphics|3D graphics]].
The most common kind of visual aliasing is when a smooth object such as a line appears jagged because the pixels are large enough to be easily distinguished by the naked eye.
These effects can be reduced by anti-aliasing techniques, e.g. adjusting the colour or transparency of a pixel according to how much of it is covered by the object (sub-pixel rendering).

==Example==
For example, if the image of a ship of length {{convert|50|m}}, viewed side-on, is 500&nbsp;pixels long, the nominal resolution (pixel size) on the side of the ship facing the camera is {{convert|0.1|m}}. Now sub-pixel resolution of well resolved features can measure ship movements which are an order of magnitude (10×) smaller. Movement is specifically mentioned here because measuring absolute positions requires an accurate lens model and known reference points within the image to achieve sub-pixel position accuracy. Small movements can however be measured (down to 1&nbsp;cm) with simple calibration procedures.{{Citation needed|date=January 2010}} Specific fit functions often suffer specific bias with respect to image pixel boundaries. Users should therefore take care to avoid these "pixel locking" (or "peak locking") effects.<ref>"[https://arxiv.org/abs/1104.3776 Accurate particle position measurement from images]". Y. Feng, J. Goree, and Bin Liu, ''Review of Scientific Instruments'', Vol. 78, 053704 (2007); also selected for ''Virtual Journal of Biological Physics Research'', Vol. 13, (2007).</ref>

==Determining feasibility==
Whether features in a digital image are sharp enough to achieve sub-pixel resolution can be quantified by measuring the [[Physics:Point spread function|point spread function]] (PSF) of an isolated point in the image. If the image does not contain isolated points, similar methods can be applied to edges in the image. It is also important when attempting sub-pixel resolution to keep image noise to a minimum. This, in the case of a stationary scene, can be measured from a time series of images. Appropriate pixel averaging, through both time (for stationary images) and space (for uniform regions of the image) is often used to prepare the image for sub-pixel resolution measurements.
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Relation between image PSF and achievable sub-pixel resolution.
Relation between image noise and achievable sub-pixel resolution.
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==Footnotes==
{{Reflist}}

==References==
{{refbegin}}
#{{cite journal| last1 = Shimizu | first1 = M.| last2 = Okutomi | first2 = M.| doi = 10.1002/scj.10506| title = Significance and attributes of subpixel estimation on area-based matching| journal = Systems and Computers in Japan| volume = 34| issue = 12| pages = 1–111| year = 2003| s2cid = 41202105| issn = 1520-684X}}
#{{cite book| last1 = Nehab | first1 = D.| last2 = Rusinkiewiez | first2 = S.| last3 = Davis | first3 = J.| doi = 10.1109/ICCV.2005.119| chapter = Improved sub-pixel stereo correspondences through symmetric refinement| title = Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1| pages = 557–563| year = 2005| issn = 1550-5499| isbn = 0-7695-2334-X| s2cid = 14172959}}
#{{cite book| last1 = Psarakis | first1 = E. Z.| last2 = Evangelidis | first2 = G. D.| doi = 10.1109/ICCV.2005.33| chapter = An enhanced correlation-based method for stereo correspondence with subpixel accuracy| title = Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1| url = http://xanthippi.ceid.upatras.gr/people/evangelidis/george_files/ICCV_2005.pdf| pages = 907–912| year = 2005| issn = 1550-5499| isbn = 0-7695-2334-X| s2cid = 2723727}}
{{refend}}

{{DEFAULTSORT:Sub-Pixel Resolution}}
[[Category:Image processing]]

{{Sourceattribution|Sub-pixel resolution}}