watershed

Watershed transform

Description

The watershed transform finds "catchment basins" or "watershed ridge lines" in an image by treating it as a surface where light pixels represent high elevations and dark pixels represent low elevations. The watershed transform can be used to segment contiguous regions of interest into distinct objects.

example

L = watershed(A) returns a label matrix L that identifies the watershed regions of the input matrix A.

L = watershed(A,conn) specifies the connectivity to be used in the watershed computation.

Examples

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Create a binary image containing two overlapping circular objects. Display the image.

center1 = -40;
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;
imshow(bw)
title('Binary Image with Overlapping Objects')

Calculate the distance transform of the complement of the binary image. The value of each pixel in the output image is the distance between that pixel and the nearest nonzero pixel of bw.

D = bwdist(~bw);
imshow(D,[])
title('Distance Transform of Binary Image')

Take the complement of the distance transformed image so that light pixels represent high elevations and dark pixels represent low elevations for the watershed transform.

D = -D;
imshow(D,[])
title('Complement of Distance Transform')

Calculate the watershed transform. Set pixels that are outside the ROI to 0.

L = watershed(D);
L(~bw) = 0;

Display the resulting label matrix as an RGB image.

rgb = label2rgb(L,'jet',[.5 .5 .5]);
imshow(rgb)
title('Watershed Transform')

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

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

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

D = -D;
D(~bw) = Inf;
L = watershed(D);
L(~bw) = 0;
figure
isosurface(x,y,z,L==1,0.5)
isosurface(x,y,z,L==2,0.5)
axis equal
title('Segmented objects')
xlabel x, ylabel y, zlabel z
xlim(lims), ylim(lims), zlim(lims)
view(3), camlight, lighting gouraud

Input Arguments

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Input image, specified as a numeric or logical array of any dimension.

Example: RGB = imread('pears.png'); I = rgb2gray(RGB);

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical

Pixel connectivity, specified as one of the values in this table. The default connectivity is 8 for 2-D images, and 26 for 3-D images.

Value

Meaning

Two-Dimensional Connectivities

4-connected

Pixels are connected if their edges touch. The neighborhood of a pixel are the adjacent pixels in the horizontal or vertical direction.

8-connected

Pixels are connected if their edges or corners touch. The neighborhood of a pixel are the adjacent pixels in the horizontal, vertical, or diagonal direction.

Three-Dimensional Connectivities

6-connected

Pixels are connected if their faces touch. The neighborhood of a pixel are the adjacent pixels in:

  • One of these directions: in, out, left, right, up, and down

18-connected

Pixels are connected if their faces or edges touch. The neighborhood of a pixel are the adjacent pixels in:

  • One of these directions: in, out, left, right, up, and down

  • A combination of two directions, such as right-down or in-up

26-connected

Pixels are connected if their faces, edges, or corners touch. The neighborhood of a pixel are the adjacent pixels in:

  • One of these directions: in, out, left, right, up, and down

  • A combination of two directions, such as right-down or in-up

  • A combination of three directions, such as in-right-up or in-left-down

For higher dimensions, watershed uses the default value conndef(ndims(A),'maximal').

Connectivity can also be defined in a more general way for any dimension by specifying a 3-by-3-by- ... -by-3 matrix of 0s and 1s. The 1-valued elements define neighborhood locations relative to the center element of conn. Note that conn must be symmetric about its center element. See Specifying Custom Connectivities for more information.

Note

If you specify a nondefault connectivity, pixels on the edge of the image might not be considered to be border pixels. For example, if conn = [0 0 0; 1 1 1; 0 0 0], elements on the first and last row are not considered to be border pixels because, according to that connectivity definition, they are not connected to the region outside the image.

Data Types: double | logical

Output Arguments

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Label matrix, specified as a numeric array of nonnegative integers. The elements labeled 0 do not belong to a unique watershed region. The elements labeled 1 belong to the first watershed region, the elements labeled 2 belong to the second watershed region, and so on.

Tips

  • The watershed transform algorithm used by this function changed in version 5.4 (R2007a) of the Image Processing Toolbox™ software. The previous algorithm occasionally produced labeled watershed basins that were not contiguous. If you need to obtain the same results as the previous algorithm, use the function watershed_old.

  • To prevent oversegmentation, remove shallow minima from the image by using the imhmin function before you use the watershed function.

Algorithms

watershed uses the Fernand Meyer algorithm [1].

References

[1] Meyer, Fernand, "Topographic distance and watershed lines,” Signal Processing , Vol. 38, July 1994, pp. 113-125.

Extended Capabilities

Introduced before R2006a