Correcting Barrel and Pin-cushion Distortion

Barrel Distortion	Original	Pin-cushion Distortion

It is very easy to correct Barrel and Pin-cushion distortion in photographic images using Photoshop, CorelPhoto, or any other image manipulation package with a suitable "Displace" function, provided you have the right "Displacement Map". The same map can be used to correct both Barrel and Pin Cushion distortion, but it in either case it must have the same aspect ratio (image width to height ratio) as the image being corrected. Although it is possible to crop a displacement map to the required aspect ratio this must be done with great care as you must crop the image symmetrically about its exact center. In any case you get slightly better results if you use a map designed for the required ratio.

Accordingly this page offers two displacement maps, with 4:3 and 3:2 aspect ratios respectively.

Most consumer digital cameras produce an image with an aspect ratio of 4:3, while most professional and so-called "prosumer" digital SLR's as well as 35mm film SLR's produce an image with a 3:2 ratio. These two ratios will therefore suffice for the majority of digital cameras.

Note that although you can crop a displacement map you must NEVER use "stretching" to change the aspect ratio.

How to use the displacement maps

Correcting Barrel Distortion

The procedure for correcting barrel distortion using Photoshop Elements is described here. The procedure using Photoshop or CorelPhoto is essentially the same.

• Copy the appropriate map (at the bottom of this Web page) to your hard disc
• For compactness the map is given in PNG (".png") format. Before the first time you use the map as a displacement map in Photoshop you must Load it and then save it as a ".psd" file, as for some reason Photoshop will only accept ".psd" files as displacement maps. Once you have done this you can delete the original file. This step may not be necessary using more forgiving image manipulation Packages
• Load the original image image you wish to correct into Photoshop (or whatever). You should always correct the original image, before changing the image size or performing any cropping or perspective distortion, etc.
  If necessary rotate the image (NOT the displacement map) so that it is in "Landscape" mode, so that its format agrees with that of the displacement map - you can rotate it back afterwards, ir required.
• Open the "Displace" filter. In Photoshop LE you will find it under Filters>Distort>Displacement Map. Set "Horizontal Scale" and "Vertical Scale" to (say) 10%. This value controls the degree of correction and both values must be set the same. Select "Stretch to fit" (mandatory) and either "Wrap around" or "Repeat" (I prefer the latter):
  
  
  
• Click "OK". A file dialog opens for you to select the displacement Map. Check that the map has the same aspect ratio as the image you are correcting.
• As soon as you click "Open" the correction is computed. If the degree of correction is not satisfactory, "Undo" the operation and repeat the correction using a different value for "Horizontal Scale" and "Vertical Scale", but remember they must both be the same.
• When you achieve a satisfactory result record the degree of correction required. This setting will be the same for all images of the same (pixel) size using the same lens at the same Zoom setting.
• You will need to crop the image slightly to remove spurious "repeated" pixels around the edges of the picture.

Correcting Pin-cushion Distortion

the procedure for correcting Pin-cushion Distortion is exactly the same as the procedure for correcting Barrel distortion, except that you must use negative values for "Horizontal Scale" and "Vertical Scale". Alternatively, you can simply rotate the displacement map by 180° before use.

How accurate is it?

It depends. Technically barrel distortion is a third order radial distortion - each straight line is distorted towards the axis at the ends and away from it at the middle (vice versa for pin-cushion). With care you can effectively remove all the third order distortion, leaving only fifth order distortion visible (away at 3 points, towards at 2). The amount of residual distortion is very small if you started with a good lens, but don't expect to correct the image from a fish-eye!

It is possible to create filters to correct 5th and higher order distortions (all radial distortions have odd order), but this is rarely necessary in practice.

The displacement maps

Copy (or drag) the displacement map below with the required aspect ratio to your hard disc. Both maps work well with normal images of any size – it is only necessary that the aspect ratio of the map you chose matches the aspect ratio of your image. Both maps have a horizontal resolution of 600 pixels: although it is easy to create displacement maps with higher resolution, there is no advantage in doing so when using normal 24 bit colour images, as the displacement values only change by at most 1 bit when moving from one pixel to the next.

Aspect ratio 4:3	Aspect ratio 3:2
f600450.png	f600400.png

Original 2006-03-18