Distance transform

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A distance transform, also known as distance map or distance field, is a derived representation of a digital image. The choice of the term depends on the point of view on the object in question: whether the initial image is transformed into another representation, or it is simply endowed with an additional map or field.

Distance fields can also be signed, in the case where it is important to distinguish whether the point is inside or outside of the shape.[1]

The map labels each pixel of the image with the distance to the nearest obstacle pixel. A most common type of obstacle pixel is a boundary pixel in a binary image. See the image for an example of a Chebyshev distance transform on a binary image.

A distance transformation

Usually the transform/map is qualified with the chosen metric. For example, one may speak of Manhattan distance transform, if the underlying metric is Manhattan distance. Common metrics are:

There are several algorithms to compute the distance transform for these different distance metrics, however the computation of the exact Euclidean distance transform (EEDT) needs special treatment if it is computed on the image grid.[2]

Applications are digital image processing (e.g., blurring effects, skeletonizing), motion planning in robotics, medical image analysis for prenatal genetic testing, and even pathfinding. [3] Uniformly-sampled signed distance fields have been used for GPU-accelerated font smoothing, for example by Valve researchers.[4]

Signed distance fields can also be used for (3D) solid modelling. Rendering on typical GPU hardware requires conversion to polygon meshes, e.g. by the marching cubes algorithm.[5]

See also[edit]


  1. ^ http://www.merl.com/publications/docs/TR2000-15.pdf
  2. ^ T.Strutz: The Distance Transform and its Computation. June, 2021, TECH/2021/06, arXiv:2106.03503v1, https://arxiv.org/abs/2106.03503
  3. ^ http://www.theoryofcomputing.org/articles/v008a019/v008a019.pdf
  4. ^ Green, Chris (2007). "Improved alpha-tested magnification for vector textures and special effects". ACM SIGGRAPH 2007 Courses on - SIGGRAPH '07. p. 9. CiteSeerX doi:10.1145/1281500.1281665. ISBN 9781450318235. S2CID 7479538. Missing or empty |title= (help)
  5. ^ https://www.youtube.com/watch?v=2MzSmdC49Ns
  6. ^ R. Kimmel, N. Kiryati, and A. M. Bruckstein. Distance maps and weighted distance transforms. Journal of Mathematical Imaging and Vision, Special Issue on Topology and Geometry in Computer Vision, 6:223-233,1996.

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