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mmgdist
Geodesic Distance Transform.

Synopsis

function y = mmgdist ( f , g , Bc , METRIC )

Input

f Image Binary image
g Image Binary image

Marker image
Bc Structuring Element

Default: 3x3 elementary cross

(metric for distance).
METRIC String

Default: NULL

'EUCLIDEAN' if specified.

Output

y Image

uint16 (distance image).

Description

mmgdist creates the geodesic distance image y of the binary image f relative to the binary image g. The value of y at the pixel x is the length of the smallest path between x and f. The distances available are based on the Euclidean metrics and on metrics generated by a neighbourhood graph, that is characterized by a connectivity rule defined by the structuring element Bc. The connectivity for defining the paths is consistent with the metrics adopted to measure their length. In the case of the Euclidean distance, the space is considered continuos and, in the other cases, the connectivity is the one defined by Bc.

Examples

f=mmbinary([...

 1,1,1,1,1,1;...

 1,1,1,0,0,1;...

 1,0,1,0,0,1;...

 1,0,1,1,0,0;...

 0,0,1,1,1,1;...

 0,0,0,1,1,1]);

Warning: converting image from double to int32

g=mmbinary([...

 0,0,0,0,0,0;...

 1,1,0,0,0,0;...

 0,0,0,0,0,0;...

 0,0,0,0,0,0;...

 0,0,0,0,0,0;...

 0,0,0,0,0,1]);

Warning: converting image from double to int32

y=mmgdist(f,g,mmsecross)

y =
      1      1      2      3      4      5
      0      0      1  65535  65535      6
      1  65535      2  65535  65535      7
      2  65535      3      4  65535  65535
  65535  65535      4      3      2      1
  65535  65535  65535      2      1      0

f=mmreadgray('maze_bw.tif');

g=mmintersec(f,0);

Warning: converting image from scalar to binary uint8

g=mmdraw(g,'FRECT:3,3,7,7:END');

y=mmgdist(f,g,mmsebox,'EUCLIDEAN');

mmshow(f,g);

mmdtshow(y,200);
f,g y,200

Equation

geodesic distance function using structuring element:

Algorithm

function y=mmgdist_equ(f,g,Bc)
  fneg = mmneg(f);
  gneg = mmneg(g);
  y = mmgray(gneg,'uint8',1);
  for i=1:255
     ero = mmcero(gneg,fneg,Bc,i);
     y = mmaddm(y,mmgray(ero,'uint8',1));
  end

Limitations

To generate useful Distance transforms, the structuring elements must be symmetric and with the origin included. The Euclidean Distance transform is rounded to the nearest integer, since it is represented in an unsigned integer image. You should use the mmsebox structuring element when computing the Euclidean Distance transform.

See also

mmdist Distance transform.
mmsecross Diamond structuring element and elementary 3x3 cross.
mmsebox Create a box structuring element.
mmfreedom Control automatic data type conversion.
mmcero Erode an image conditionally.
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Copyright (c) 1998-2008 by SDC Information Systems