Distance transform

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 importan to distinguish whether the point is inside or outside of the shape.

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 chessboard 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:

• Euclidean distance
• Taxicab geometry, also known as City block distance or Manhattan distance.
• Chessboard distance

Applications are digital image processing (e.g., blurring effects, skeletonizing), motion planning in robotics, and even pathfinding.

See also

• Signed distance function

External links

• Fast distance transform in C++ by Felzenszwalb and Huttenlocher
• Distance Transform tutorials in CVonline
• Survey of fast exact Euclidean distance transform algorithms
• Using distance mapping for AI
• Distance Transforms by Henry Kwong and Dynamic Step Distance Transforms by Richard Scott, The Wolfram Demonstrations Project.
• Morphological DistanceTransform function in Mathematica
• Morphological InverseDistanceTransform function in Mathematica