Image Processing Toolbox User's Guide

watershed

Find image watershed regions

Syntax

• L = watershed(A)
  L = watershed(A,CONN)
  

Description

L = watershed(A) computes a label matrix identifying the watershed regions of the input matrix A, which can have any dimension. The elements of L are integer values greater than or equal to 0. The elements labeled 0 do not belong to a unique watershed region. These are called watershed pixels. The elements labeled 1 belong to the first watershed region, the elements labeled 2 belong to the second watershed region, and so on.

By default, watershed uses 8-connected neighborhoods for 2-D inputs and 26-connected neighborhoods for 3-D inputs. For higher dimensions, watershed uses the connectivity given by conndef(ndims(A),'maximal').

L = watershed(A,CONN) specifies the connectivity to be used in the watershed computation. CONN can have any of the following scalar values.

Value	Meaning
Two-dimensional connectivities
4	4-connected neighborhood
8	8-connected neighborhood
Three-dimensional connectivities
6	6-connected neighborhood
18	18-connected neighborhood
26	26-connected neighborhood

Connectivity can be defined in a more general way for any dimension by using for CONN a 3-by-3-by- ...-by-3 matrix of 0's and 1's. The 1-valued elements define neighborhood locations relative to the center element of CONN. Note that CONN must be symmetric about its center element.

Class Support

A can be a numeric or logical array of any dimension, and it must be nonsparse. The output array L is of class double.

Example

2-D Example

1. Make a binary image containing two overlapping circular objects.

• center1 = -10;
  center2 = -center1;
  dist = sqrt(2*(2*center1)^2);
  radius = dist/2 * 1.4;
  lims = [floor(center1-1.2*radius) ceil(center2+1.2*radius)];
  [x,y] = meshgrid(lims(1):lims(2));
  bw1 = sqrt((x-center1).^2 + (y-center1).^2) <= radius;
  bw2 = sqrt((x-center2).^2 + (y-center2).^2) <= radius;
  bw = bw1 | bw2;
  figure, imshow(bw,'InitialMagnification','fit'), title('bw')
  

2. Compute the distance transform of the complement of the binary image.

• D = bwdist(~bw);
  figure, imshow(D,[],'InitialMagnification','fit')
  title('Distance transform of ~bw')
  

3. Complement the distance transform, and force pixels that don't belong to the objects to be at -Inf.

• D = -D;
  D(~bw) = -Inf;
  

4. Compute the watershed transform and display it as an indexed image.

• L = watershed(D);
  rgb = label2rgb(L,'jet',[.5 .5 .5]);
  figure, imshow(rgb,'InitialMagnification','fit')
  title('Watershed transform of D')
  

3-D Example

1. Make a 3-D binary image containing two overlapping spheres.

• center1 = -10;
  center2 = -center1;
  dist = sqrt(3*(2*center1)^2);
  radius = dist/2 * 1.4;
  lims = [floor(center1-1.2*radius) ceil(center2+1.2*radius)];
  [x,y,z] = meshgrid(lims(1):lims(2));
  bw1 = sqrt((x-center1).^2 + (y-center1).^2 + ...
       (z-center1).^2) <= radius;
  bw2 = sqrt((x-center2).^2 + (y-center2).^2 + ...
       (z-center2).^2) <= radius;
  bw = bw1 | bw2;
  figure, isosurface(x,y,z,bw,0.5), axis equal, title('BW')
  xlabel x, ylabel y, zlabel z
  xlim(lims), ylim(lims), zlim(lims)
  view(3), camlight, lighting gouraud
  

2. Compute the distance transform.

• D = bwdist(~bw);
  figure, isosurface(x,y,z,D,radius/2), axis equal
  title('Isosurface of distance transform')
  xlabel x, ylabel y, zlabel z
  xlim(lims), ylim(lims), zlim(lims)
  view(3), camlight, lighting gouraud
  

3. Complement the distance transform, force nonobject pixels to be -Inf, and then compute the watershed transform.

• D = -D;
  D(~bw) = -Inf;
  L = watershed(D);
  figure, isosurface(x,y,z,L==2,0.5), axis equal
  title('Segmented object')
  xlabel x, ylabel y, zlabel z
  xlim(lims), ylim(lims), zlim(lims)
  view(3), camlight, lighting gouraud
  figure, isosurface(x,y,z,L==3,0.5), axis equal
  title('Segmented object')
  xlabel x, ylabel y, zlabel z
  xlim(lims), ylim(lims), zlim(lims)
  view(3), camlight, lighting gouraud
  

Algorithm

watershed uses a variation of the Vincent and Soille algorithm [1]. For details of the variation, see toolbox/images/images/private/watershed_vs.h.

See Also

bwlabel, bwlabeln, bwdist, regionprops

Reference

[1]  Vincent, Luc, and Pierre Soille, "Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations," IEEE Transactions of Pattern Analysis and Machine Intelligence, Vol. 13, No. 6, June 1991, pp. 583-598.

warp

whitepoint

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