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.
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.
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.
Famous quotes containing the words distance and/or transform:
“Small, black, as flies hanging in heat, the Boys,
Until the distance throws them forth, their hum
Bulges to thunder held by calf and thigh.”
—Thom Gunn (b. 1929)
“The lullaby is the spell whereby the mother attempts to transform herself back from an ogre to a saint.”
—James Fenton (b. 1949)