# Sub-pixel resolution

Sub-pixel rendering of a circle

In digital image processing, sub-pixel resolution can be obtained in digital images containing well defined lines, points or edges that can be processed by an algorithm to reliably measure the position of the line, point or edge in the image with an accuracy exceeding the nominal pixel resolution of that image.

## Aliasing

While the end points of a straight line will fall on exactly within pixel,[clarification needed] other points on the line will not be as clearly defined unless the line is perfectly horizontal or vertical. These imperfections, known as aliasing, can be useful for gaining extra data from the image.

## Example

If for example, the image of a ship of length 50 metres (160 ft), viewed side-on, is 500 pixels long, the nominal resolution (pixel size) on the side of the ship facing the camera is 0.1 metres (3.9 in). 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 cm) with simple calibration procedures.[citation needed] 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.[1]

## Determining feasibility

Whether features in a digital image are sharp enough to achieve sub-pixel resolution can be quantified by measuring the 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.

## Footnotes

1. ^ "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).

## References

1. Shimizu, M.; Okutomi, M. (2003). "Significance and attributes of subpixel estimation on area-based matching". Systems and Computers in Japan 34 (12): 1–111. doi:10.1002/scj.10506. ISSN 1520-684X. edit
2. Nehab, D.; Rusinkiewiez, S.; Davis, J. (2005). "Improved sub-pixel stereo correspondences through symmetric refinement". Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1. pp. 557–563. doi:10.1109/ICCV.2005.119. ISBN 0-7695-2334-X. ISSN 1550-5499. edit
3. Psarakis, E. Z.; Evangelidis, G. D. (2005). "An enhanced correlation-based method for stereo correspondence with subpixel accuracy" (PDF). Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1. pp. 907–912. doi:10.1109/ICCV.2005.33. ISBN 0-7695-2334-X. ISSN 1550-5499. edit