Grow labelled regions using grey-weighted distances
#include "dip_regions.h"
dip_Error GrowRegionsWeighted ( in, grey, mask, out, distance, pixelsize, chamfer, metric )
in: binary, integer
grey: interger, float (converted to dip_sfloat)
mask: dip_uint8
The regions in the input image in are grown according to a grey-weighted distance metric; the weights are given by grey. The optional mask image mask limits the growing. out contains the grown regions, and distance, if not 0, contains the grey-weighted distance of each pixel in mask to the nearest pixel in in. Non-isotropic sampling is supported through pixelsize, which can be set to 0 to assume isotropic sampling. chamfer selects the size of the chamfer metric: 3 or 5. Set chamfer to 0 to use a custom metric given by the image metric. This image should be odd in size, and each pixel gives the distance to the center pixel. The pixels set to 0 will not be considered as neighbors.
The chamfer metric used is the following for chamfer==3 (with ps0=pixelsize->array[0] and ps1=pixelsize->array[1]):
| sqrt(ps0*ps0+ps1*ps1) | ps1 | sqrt(ps0*ps0+ps1*ps1) |
| ps0 | 0 | ps0 |
| sqrt(ps0*ps0+ps1*ps1) | ps1 | sqrt(ps0*ps0+ps1*ps1) |
and the following for chamfer==5:
| 0 | sqrt(ps0*ps0+4*ps1*ps1) | 0 | sqrt(ps0*ps0+4*ps1*ps1) | 0 |
| sqrt(4*ps0*ps0+ps1*ps1) | sqrt(ps0*ps0+ps1*ps1) | ps1 | sqrt(ps0*ps0+ps1*ps1) | sqrt(4*ps0*ps0+ps1*ps1) |
| 0 | ps0 | 0 | ps0 | 0 |
| sqrt(4*ps0*ps0+ps1*ps1) | sqrt(ps0*ps0+ps1*ps1) | ps1 | sqrt(ps0*ps0+ps1*ps1) | sqrt(4*ps0*ps0+ps1*ps1) |
| 0 | sqrt(ps0*ps0+4*ps1*ps1) | 0 | sqrt(ps0*ps0+4*ps1*ps1) | 0 |
Setting chamfer to 0 and metric to an image with these values produces the same results as setting chamfer to 3 or 5.
The output image distance is comparable to the out image of GreyWeightedDistanceTransform, except that that function uses optimal chamfer distances whereas this one uses the (sub-optimal) true distance. In return, this function works on images of any dimensionality, allows for non-isotropic sampling, does not skip pixels close to the edge of the image, and can be used with a mask image to constrain the propagation. Note that the seed image in GreyWeightedDistanceTransform corresponds to the zero pixels of in for this function.
| Data type | Name | Description |
| dip_Image | in | Input binary or labelled image |
| dip_Image | grey | Input grey-value image |
| dip_Image | mask | Mask image |
| dip_Image | out | Output binary or labelled image |
| dip_Image | distance | Output distance image |
| dip_FloatArray | pixelsize | Pixel size |
| dip_int | chamfer | Chamfer distance |
| dip_Image | metric | Custom metric |
"3-D Texture characterized by Accessibility measurements, based on the grey weighted distance transform", K.C. Strasters, A.W.M. Smeulders, and H.T.M. van der Voort, BioImaging, vol 2, no. 1, 1994, p. 1-21.
"An efficient uniform cost algorithm applied to distance transforms", B.J.H. Verwer, P.W. Verbeek, and S.T. Dekker, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 4, 1989, 425-429.