distance_transformdistance_transformDistanceTransformDistanceTransform (Operator)


distance_transformdistance_transformDistanceTransformDistanceTransform — Compute the distance transformation of a region.


distance_transform(Region : DistanceImage : Metric, Foreground, Width, Height : )

Herror distance_transform(const Hobject Region, Hobject* DistanceImage, const char* Metric, const char* Foreground, const Hlong Width, const Hlong Height)

Herror T_distance_transform(const Hobject Region, Hobject* DistanceImage, const Htuple Metric, const Htuple Foreground, const Htuple Width, const Htuple Height)

void DistanceTransform(const HObject& Region, HObject* DistanceImage, const HTuple& Metric, const HTuple& Foreground, const HTuple& Width, const HTuple& Height)

HImage HRegion::DistanceTransform(const HString& Metric, const HString& Foreground, Hlong Width, Hlong Height) const

HImage HRegion::DistanceTransform(const char* Metric, const char* Foreground, Hlong Width, Hlong Height) const

HImage HRegion::DistanceTransform(const wchar_t* Metric, const wchar_t* Foreground, Hlong Width, Hlong Height) const   (Windows only)

static void HOperatorSet.DistanceTransform(HObject region, out HObject distanceImage, HTuple metric, HTuple foreground, HTuple width, HTuple height)

HImage HRegion.DistanceTransform(string metric, string foreground, int width, int height)


distance_transformdistance_transformDistanceTransformDistanceTransformDistanceTransform computes for every point of the input region RegionRegionRegionRegionregion (or its complement, respectively) the distance of the point to the border of the region. The parameter ForegroundForegroundForegroundForegroundforeground determines whether the distances are calculated for all points within the region (ForegroundForegroundForegroundForegroundforeground = 'true'"true""true""true""true") or for all points outside the region (ForegroundForegroundForegroundForegroundforeground = 'false'"false""false""false""false"). The distance is computed for every point of the output image DistanceImageDistanceImageDistanceImageDistanceImagedistanceImage, which has the specified dimensions WidthWidthWidthWidthwidth and HeightHeightHeightHeightheight. 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_regionmove_regionMoveRegionMoveRegionMoveRegion) 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 with smallest_rectangle1smallest_rectangle1SmallestRectangle1SmallestRectangle1SmallestRectangle1.

The parameter MetricMetricMetricMetricmetric determines which metric is used for the calculation of the distances. If MetricMetricMetricMetricmetric = 'city-block'"city-block""city-block""city-block""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 MetricMetricMetricMetricmetric = 'chessboard'"chessboard""chessboard""chessboard""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. If MetricMetricMetricMetricmetric = 'octagonal'"octagonal""octagonal""octagonal""octagonal", a combination of these approaches is used, which leads to diagonal paths receiving a higher weight. If MetricMetricMetricMetricmetric = 'chamfer-3-4'"chamfer-3-4""chamfer-3-4""chamfer-3-4""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 suppressed with MetricMetricMetricMetricmetric = 'chamfer-3-4-unnormalized'"chamfer-3-4-unnormalized""chamfer-3-4-unnormalized""chamfer-3-4-unnormalized""chamfer-3-4-unnormalized". Finally, if MetricMetricMetricMetricmetric = 'euclidean'"euclidean""euclidean""euclidean""euclidean", the computed distance is approximately Euclidean.

Execution Information


RegionRegionRegionRegionregion (input_object)  region(-array) objectHRegionHRegionHobject

Region for which the distance to the border is computed.

DistanceImageDistanceImageDistanceImageDistanceImagedistanceImage (output_object)  image objectHImageHImageHobject * (int4)

Image containing the distance information.

MetricMetricMetricMetricmetric (input_control)  string HTupleHTupleHtuple (string) (string) (HString) (char*)

Type of metric to be used for the distance transformation.

Default value: 'city-block' "city-block" "city-block" "city-block" "city-block"

List of values: 'chamfer-3-4'"chamfer-3-4""chamfer-3-4""chamfer-3-4""chamfer-3-4", 'chamfer-3-4-unnormalized'"chamfer-3-4-unnormalized""chamfer-3-4-unnormalized""chamfer-3-4-unnormalized""chamfer-3-4-unnormalized", 'chessboard'"chessboard""chessboard""chessboard""chessboard", 'city-block'"city-block""city-block""city-block""city-block", 'euclidean'"euclidean""euclidean""euclidean""euclidean", 'octagonal'"octagonal""octagonal""octagonal""octagonal"

ForegroundForegroundForegroundForegroundforeground (input_control)  string HTupleHTupleHtuple (string) (string) (HString) (char*)

Compute the distance for pixels inside ('true'"true""true""true""true") or outside ('false'"false""false""false""false") the input region.

Default value: 'true' "true" "true" "true" "true"

List of values: 'false'"false""false""false""false", 'true'"true""true""true""true"

WidthWidthWidthWidthwidth (input_control)  extent.x HTupleHTupleHtuple (integer) (int / long) (Hlong) (Hlong)

Width of the output image.

Default value: 640

Suggested values: 160, 192, 320, 384, 640, 768

Typical range of values: 1 ≤ Width Width Width Width width

HeightHeightHeightHeightheight (input_control)  extent.y HTupleHTupleHtuple (integer) (int / long) (Hlong) (Hlong)

Height of the output image.

Default value: 480

Suggested values: 120, 144, 240, 288, 480, 576

Typical range of values: 1 ≤ Height Height Height Height height

Example (HDevelop)

* 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(WidthWidthWidthWidthwidth*HeightHeightHeightHeightheight).


distance_transformdistance_transformDistanceTransformDistanceTransformDistanceTransform returns 2 (H_MSG_TRUE) if all parameters are correct.

Possible Predecessors

thresholdthresholdThresholdThresholdThreshold, dyn_thresholddyn_thresholdDynThresholdDynThresholdDynThreshold, regiongrowingregiongrowingRegiongrowingRegiongrowingRegiongrowing

Possible Successors




See also



P. Soille: “Morphological Image Analysis, Principles and Applications”; Springer Verlag Berlin Heidelberg New York, 1999.
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.