distance_transform — Compute the distance transformation of a region.
distance_transform computes for every point of the input
Region (or its complement, respectively) the
distance of the point to the border of the region. The parameter
Foreground determines whether the distances are calculated
for all points within the region (
'true') or for all points outside the region
Foreground = 'false'). The distance is computed
for every point of the output image
has the specified dimensions
The input region is always clipped to the extent of the output
image. If it is important that the distances within the entire
region should be computed, the region should be moved (see
move_region) so that it has only positive coordinates and
the width and height of the output image should be large enough to
contain the region. The extent of the input region can be obtained
Metric determines which metric is used for
the calculation of the distances. If
'city-block', the distance is calculated from the shortest
path from the point to the border of the region, where only
horizontal and vertical “movements” are allowed. They are
weighted with a weight of 1. If
'chessboard', the distance is calculated from the shortest
path to the border, where horizontal, vertical, and diagonal
“movements” are allowed. They are weighted with a weight of 1.
Metric = 'octagonal', a combination of these
approaches is used, which leads to diagonal paths receiving a higher
Metric = 'chamfer-3-4', horizontal and
vertical movements are weighted with a weight of 3, while diagonal
movements are weighted with a weight of 4. To normalize the
distances, the resulting distance image is divided by 3. Since this
normalization step takes some time, and one usually is interested in
the relative distances of the points, the normalization can be
'chamfer-3-4-unnormalized'. Finally, if
'euclidean', the computed distance is approximately
Region for which the distance to the border is computed.
Image containing the distance information.
Type of metric to be used for the distance transformation.
Default value: 'city-block'
List of values: 'chamfer-3-4', 'chamfer-3-4-unnormalized', 'chessboard', 'city-block', 'euclidean', 'octagonal'
Compute the distance for pixels inside ('true') or outside ('false') the input region.
Default value: 'true'
List of values: 'false', 'true'
Width of the output image.
Default value: 640
Suggested values: 160, 192, 320, 384, 640, 768
Typical range of values:
Height of the output image.
Default value: 480
Suggested values: 120, 144, 240, 288, 480, 576
Typical range of values:
* Step towards extracting the medial axis of a shape: gen_rectangle1 (Rectangle1, 0, 0, 200, 400) gen_rectangle1 (Rectangle2, 200, 0, 400, 200) union2 (Rectangle1, Rectangle2, Shape) distance_transform (Shape, DistanceImage, 'chessboard', 'true', 640, 480)
The runtime complexity is O(
distance_transform returns TRUE if all parameters are
P. Soille: “Morphological Image Analysis, Principles and
Applications”; Springer Verlag Berlin Heidelberg New York,
G. Borgefors: “Distance Transformations in Arbitrary Dimensions”; Computer Vision, Graphics, and Image Processing, Vol. 27, pages 321--345, 1984.
P.E. Danielsson: “Euclidean Distance Mapping”; Computer Graphics and Image Processing, Vol. 14, pages 227--248, 1980.