function L =watershed(varargin)

%WATERSHED Watershedtransform.

%   L = WATERSHED(A) computes a label matrixidentifying the watershed

%   regions of the input matrix A.  A can have any dimension.  The elements

%   of L are integer values greater than orequal to 0.  The elements

%   labeled 0 do not belong to a uniquewatershed region.  These are called

%   "watershed pixels."  The elements labeled 1 belong to the first

%   watershed region, the elements labeled 2belong to the second watershed

%   region, and so on.

L =WATERSHED(A) 计算一个标签矩阵, 用于识别输入矩阵A的汇水区域. A可以是任意维. L的元素均为大于等于0的整数值. 标签值为0的元素不属于任何一个汇水区域, 称它们为"分水岭". 标签值为1的元素属于第1个汇水区域, 标签值为2的元素属于第2个汇水区域, 以此类推.

%   By default, WATERSHED uses 8-connectedneighborhoods for 2-D inputs

%   and 26-connected neighborhoods for 3-Dinputs.  For higher

%   dimensions, WATERSHED uses the connectivitygiven by

%   CONNDEF(NDIMS(A),'maximal').

WATERSHED默认对2维输入数据采用8邻接, 对3维输入数据采用26邻接. 对于更高维数的输入, WATERSHED根据CONNDEF(NDIMS(A), 'maximal')的值来判定连通性.

%   L = WATERSHED(A,CONN) computes the watershedtransform using the

%   specified connectivity.  CONN may have the following scalar values:

%

%       4    two-dimensional four-connected neighborhood

%       8    two-dimensional eight-connected neighborhood

%       6    three-dimensional six-connected neighborhood

%       18   three-dimensional 18-connected neighborhood

%       26   three-dimensional 26-connected neighborhood

L =WATERSHED(A, CONN)根据指定的连通性判定规则计算分水岭变换. CONN可以有如下取值(标量)

4: 针对2维矩阵, 4邻接;

8: 针对2维矩阵, 8邻接;

6: 针对3维矩阵, 6邻接

18: 针对3维矩阵, 18邻接

26: 针对3维矩阵, 26邻接

%   Connectivity may be defined in a moregeneral way for any dimension by

%   using for CONN a 3-by-3-by- ... -by-3 matrixof 0s and 1s.  The 1-valued

%   elements define neighborhood locationsrelative to the center element of

%   CONN. If specified this way, CONN must be symmetric about its center.

连通性判定可以用一种更通用的方式指定, 即为CONN使用一个3X3X…X3矩阵, 每个元素的值只能为0或1. 值为1的元素定义相对于CONN的中心元素相邻位置(即值为1的元素视为与中心元素是邻接的). 如果采用这种方法, CONN必须满足中心对称.

%   Note

%   ----

%   The watershed transform algorithm used bythis function changed in

%   version 5.4 (R2007a) of the Image ProcessingToolbox.  The previous

%   algorithm occasionally produced labeledwatershed basins that were not

%   contiguous. If you need to obtain the same results as the previous

%   algorithm, use the function WATERSHED_OLD.

注:

自5.4版(R2007)图像处理工具箱以来, 该函数(R2015a)采用的分水岭变换算法已经改变了. 之前采用的算法偶尔会生成非毗邻的汇水盆地(?不一定翻译到位). 如果需要获取与之前算法同样的结果, 请调用WATERSHED_OLD.

%   Class Support

%   -------------

%   A can be a numeric or logical array of anydimension, and it must be

%   nonsparse. The output array L is an unsigned integer type.

类支持

A可以是任意维的数值或逻辑数组, 且必须是非稀疏的. 输出数组L的类型为无符号整型.

%   Example (2-D)

%   -------------

%   1. Make a binary image containing twooverlapping 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')

示例 (2维)

1. 制作一幅包含两个重叠圆形对象的二值图像

center1 = -10; %第一个圆的中心(-10, -10)

center2 =-center1;%第二个圆的中心(10, 10)

dist = sqrt(2*(2*center1)^2);%两圆心距离

radius = dist/2 * 1.4;%两圆心距离的0.7倍, 使得两个圆重叠

lims= [floor(center1-1.2*radius) ceil(center2+1.2*radius)];%[-3434]

[x,y] = meshgrid(lims(1):lims(2));%生成一个矩形网格, X: [-34, -34], Y: [-34, -34], x,y均为2维矩阵, 这两个矩阵可用于指定任何一个69X69矩阵的任何位置对应的直角坐标

bw1 = sqrt((x-center1).^2 + (y-center1).^2) <= radius;%产生第一个圆的二值图像

bw2 = sqrt((x-center2).^2 + (y-center2).^2) <= radius;%产生第二个圆的二值图像

bw = bw1 | bw2;%逻辑或, 两幅图像综合

figure,imshow(bw,'InitialMagnification','fit'), title('bw')