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closest_point_transform — Compute the closest-point transformation of a region.
closest_point_transform(Region : Distances, ClosestPoints : Metric, Foreground, ClosestPointMode, Width, Height : )
closest_point_transform computes for every pixel of the input region Region (or its complement, respectively) the distance to the closest pixel outside the region (i.e., to the pixel on the outside border of the region) and returns this information in Distances. In addition to the distance, the corresponding closest pixel is returned in ClosestPoints.
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 pixel of the output images Distances and ClosestPoints. The size of the images is specified by 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.
The parameter ClosestPointMode determines how the closest points are stored. For ClosestPointMode = 'absolute', absolute coordinates are stored in ClosestPoints. For ClosestPointMode = 'relative', the offset to the coordinate of the respective pixel is stored in ClosestPoints.
It should be noted that the closest points are usually not unique, i.e., for each pixel in the image Distances, there usually exist several points on the outer border of the region that have the respective distance to that pixel. For example, all points on the skeleton of the region in the chosen metric have the same distance to at least two distinct points on the outer border of the region. closest_point_transform returns one of these points that is determined by the implementation of the algorithm. In particular, invariances with respect to rotation or mirroring of the region should not be expected.
Furthermore, it should be noted that for Foreground = 'true', point coordinates that lie outside the image defined by Width and Height are returned if the input region Region touches the border of this image, since in this case the outside border of the region lies one pixel outside of the image. If the returned coordinates should be used for a direct access to an image, a suitable border treatment must be implemented.
Region for which the distance to the border is computed.
Image containing the distance information.
Image containing the coordinates of the closest points.
Type of metric to be used for the closest-point 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'
Mode in which the coordinates of the closest points are returned.
Default value: 'absolute'
List of values: 'absolute', 'relative'
Width of the output images.
Default value: 640
Suggested values: 160, 192, 320, 384, 640, 768
Typical range of values: 1 ≤ Width
Height of the output images.
Default value: 480
Suggested values: 120, 144, 240, 288, 480, 576
Typical range of values: 1 ≤ Height
The runtime complexity is O(Width*Height).
closest_point_transform returns 2 (H_MSG_TRUE) if all parameters are correct.
threshold, dyn_threshold, regiongrowing
threshold, vector_field_to_real
Y. Ge, C.R. Maurer, Jr., J.M. Fitzpatrick: “Surface-based 3-D image
registration using the Iterative Closest Point algorithm with a
closest point transform”; in: “Medical Imaging 1996: Image
Processing”, M.H. Loew, K.M. Hanson, Editors, Proc. SPIE 2710,
pages 358--367, 1996.
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
| Operators |