| Operators |
distance_transform — Compute the distance transformation of a region.
distance_transform(Region : DistanceImage : Metric, Foreground, Width, Height : )
distance_transform computes for every point of the input region 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 (Foreground = 'true') or for all points outside the region (Foreground = 'false'). The distance is computed for every point of the output image DistanceImage, which has the specified dimensions Width and Height. 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 with smallest_rectangle1.
The parameter Metric determines which metric is used for the calculation of the distances. If Metric = '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 Metric = '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 Metric = 'octagonal', a combination of these approaches is used, which leads to diagonal paths receiving a higher weight. If 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 suppressed with Metric = 'chamfer-3-4-unnormalized'. Finally, if Metric = 'euclidean', the computed distance is approximately Euclidean.
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: 1 ≤ Width
Height of the output image.
Default value: 480
Suggested values: 120, 144, 240, 288, 480, 576
Typical range of values: 1 ≤ Height
* 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(Width*Height).
distance_transform returns 2 (H_MSG_TRUE) if all parameters are correct.
threshold, dyn_threshold, regiongrowing
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.
Foundation
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