Matlab的标记分⽔岭分割算法
1 综述
Separating touching objects in an image is one of the more difficult image processing operations. The watershed transform is often applied to this problem. The watershed transform finds "catchment basins"(集⽔盆) and "watershed ridge lines"(⼭脊线) in an image by treating it as a surface where light pixels are high and dark pixels are low.
如果图像中的⽬标物体是连接在⼀起的，则分割起来会更困难，分⽔岭分割算法经常⽤于处理这类问题，通常会取得⽐较好的效果。分⽔岭分割算法把图像看成⼀幅“地形图”，其中亮度⽐较强的区域像素值较⼤，⽽⽐较暗的区域像素值较⼩，通过寻找“汇⽔盆地”和“分⽔岭界限”，对图像进⾏分割。
Segmentation using the watershed transform works better if you can identify, or "mark," foreground objects and background locations. Marker-controlled watershed gmentation follows this basic procedure:
直接应⽤分⽔岭分割算法的效果往往并不好，如果在图像中对前景对象和背景对象进⾏标注区别，再应⽤分⽔岭算法会取得较好的分割效果。基于标记控制的分⽔岭分割⽅法有以下基本步骤：
1. Compute a gmentation function. This is an image who dark regions are the objects you are trying to gment.
1.计算分割函数。图像中较暗的区域是要分割的对象。
2. Compute foreground markers. The are connected blobs of pixels within each of the objects.
2.计算前景标志。这些是每个对象内部连接的斑点像素。
3. Compute background markers. The are pixels that are not part of any object.
3.计算背景标志。这些是不属于任何对象的像素。
4. Modify the gmentation function so that it only has minima at the foreground and background marker locations.
4.修改分割函数，使其仅在前景和后景标记位置有极⼩值。
5. Compute the watershed transform of the modified gmentation function.
5.对修改后的分割函数做分⽔岭变换计算。
U by Matlab Image Processing Toolbox
使⽤MATLAB图像处理⼯具箱
注：期间⽤到了很多图像处理⼯具箱的函数，例如fspecial、imfilter、watershed、label2rgb、imopen、imclo、imreconstruct、imcomplement、imregionalmax、bwareaopen、graythresh和imimpomin函数等。
2 步骤
Step 1: Read in the Color Image and Convert it to Grayscale小金刚
第⼀步：读⼊彩⾊图像，将其转化成灰度图像
clc; clear all; clo all;
rgb = imread('pears.png');
if ndims(rgb) == 3
I = rgb2gray(rgb);
el
I = rgb;
end
figure('units', 'normalized', 'position', [0 0 1 1]);
subplot(1, 2, 1); imshow(rgb); title('原图');
subplot(1, 2, 2); imshow(I); title('灰度图');
Step 2: U the Gradient Magnitude as the Segmentation Function
第2步：将梯度幅值作为分割函数
U the Sobel edge masks, imfilter, and some simple arithmetic to compute the gradient magnitude. The gradient is high at the borders of the objects and low (mostly) inside the objects.
使⽤Sobel边缘算⼦对图像进⾏⽔平和垂直⽅向的滤波，然后求取模值，sobel算⼦滤波后的图像在边界处会显⽰⽐较⼤的值，在没有边界处的值会很⼩。
hy = fspecial('sobel');
hx = hy';
毒的组词
Iy = imfilter(double(I), hy, 'replicate');
Ix = imfilter(double(I), hx, 'replicate');
gradmag = sqrt(Ix.^2 + Iy.^2);
figure('units', 'normalized', 'position', [0 0 1 1]);
subplot(1, 2, 1); imshow(I,[]), title('灰度图像')
subplot(1, 2, 2); imshow(gradmag,[]), title('梯度幅值图像')
Can you gment the image by using the watershed transform directly on the gradient magnitude?
可否直接对梯度幅值图像使⽤分⽔岭算法？
L = watershed(gradmag);
教师朗诵稿Lrgb = label2rgb(L);
figure('units', 'normalized', 'position', [0 0 1 1]);
subplot(1, 2, 1); imshow(gradmag,[]), title('梯度幅值图像')
subplot(1, 2, 2); imshow(Lrgb); title('梯度幅值做分⽔岭变换')
No. Without additional preprocessing such as the marker computations below, using the watershed transform directly often results in "overgmentation."
直接使⽤梯度模值图像进⾏分⽔岭算法得到的结果往往会存在过度分割的现象。因此通常需要分别对前景对象和背景对象进⾏标记，以获得更好的分割效果。
Step 3: Mark the Foreground Objects
第3步：标记前景对象
A variety of procedures could be applied here to find the foreground markers, which must be connected blobs of pixels inside each of the foreground objects. In this example you'll u morpholo
gical techniques called "opening-by-reconstruction" and "closing-by-reconstruction" to "clean" up the image. The operations will create flat maxima inside each object that can be located using imregionalmax.
有多种⽅法可以应⽤在这⾥来获得前景标记，这些标记必须是前景对象内部的连接斑点像素。这个例⼦中，将使⽤形态学技术“基于开的重建”和“基于闭的重建”来清理图像。这些操作将会在每个对象内部创建单位极⼤值，使得可以使⽤imregionalmax来定位。
开运算和闭运算：先腐蚀后膨胀称为开；先膨胀后腐蚀称为闭。开和闭这两种运算可以除去⽐结构元素⼩的特定图像细节，同时保证不产⽣全局⼏何失真。开运算可以把⽐结构元素⼩的突刺滤掉，切断细长搭接⽽起到分离作⽤；闭运算可以把⽐结构元素⼩的缺⼝或孔填充上，搭接短的间隔⽽起到连接作⽤。
Opening is an erosion followed by a dilation, while opening-by-reconstruction is an erosion followed by a morphological reconstruction. Let's compare the two. First, compute the opening using imopen.
开操作是腐蚀后膨胀，基于开的重建（基于重建的开操作）是腐蚀后进⾏形态学重建。下⾯⽐较这两种⽅式。⾸先，⽤imopen做开操作。
= strel('disk', 20);
Io = imopen(I, );
figure('units', 'normalized', 'position', [0 0 1 1]);
subplot(1, 2, 1); imshow(I, []); title('灰度图像');
subplot(1, 2, 2); imshow(Io), title('图像开操作')
Next compute the opening-by-reconstruction using imerode and imreconstruct.
接下来，通过腐蚀后重建来做基于开的重建计算。
Ie = imerode(I, );
Iobr = imreconstruct(Ie, I);
figure('units', 'normalized', 'position', [0 0 1 1]);
subplot(1, 2, 1); imshow(I, []); title('灰度图像');
subplot(1, 2, 2); imshow(Iobr, []), title('基于开的重建图像')
Following the opening with a closing can remove the dark spots and stem marks. Compare a regular morphological closing with a closing-by-reconstruction. First try imclo:
开操作后，接着进⾏闭操作，可以移除较暗的斑点和枝⼲标记。对⽐常规的形态学闭操作和基于闭的重建操作。⾸先，使⽤imclo：
Ioc = imclo(Io, );
Ic = imclo(I, );
figure('units', 'normalized', 'position', [0 0 1 1]);
subplot(2, 2, 1); imshow(I, []); title('灰度图像');
subplot(2, 2, 2); imshow(Io, []); title('开操作图像');
subplot(2, 2, 3); imshow(Ic, []); title('闭操作图像');
subplot(2, 2, 4); imshow(Ioc, []), title('开闭操作');
Now u imdilate followed by imreconstruct. Notice you must complement the image inputs and outp
ut of imreconstruct. IM2 = imcomplement(IM) computes the complement(补集) of the image IM. IM can be a binary, intensity, or RGB image. IM2 has the same class and size as IM.
现在使⽤imdilate，然后使⽤imreconstruct。注意必须对输⼊图像求补，对imreconstruct输出图像求补。IM2 = imcomplement(IM)计算图像IM的补集。IM可以是⼆值图像，或者RGB图像。IM2与IM有着相同的数据类型和⼤⼩。
Iobrd = imdilate(Iobr, );
Iobrcbr = imreconstruct(imcomplement(Iobrd), imcomplement(Iobr));
Iobrcbr = imcomplement(Iobrcbr);
figure('units', 'normalized', 'position', [0 0 1 1]);
subplot(2, 2, 1); imshow(I, []); title('灰度图像');
subplot(2, 2, 2); imshow(Ioc, []); title('开闭操作');
subplot(2, 2, 3); imshow(Iobr, []); title('基于开的重建图像');
subplot(2, 2, 4); imshow(Iobrcbr, []), title('基于闭的重建图像');
As you can e by comparing Iobrcbr with Ioc, reconstruction-bad opening and closing are more effective than standard opening and closing at removing small blemishes without affecting the overall shapes of the objects. Calculate the regional maxima of Iobrcbr to obtain good foreground markers.
通过⽐较Iobrcbr和loc可以看到，在移除⼩污点同时不影响对象全局形状的应⽤下，基于重建的开闭操作要⽐标准的开闭重建更加有效。计算Iobrcbr的局部极⼤来得到更好的前景标记。
fgm = imregionalmax(Iobrcbr);
figure('units', 'normalized', 'position', [0 0 1 1]);
subplot(1, 3, 1); imshow(I, []); title('灰度图像');
subplot(1, 3, 2); imshow(Iobrcbr, []); title('基于重建的开闭操作');
subplot(1, 3, 3); imshow(fgm, []); title('局部极⼤图像');
To help interpret the result, superimpo(叠加) the foreground marker image on the original image.
为了帮助理解这个结果，叠加前景标记到原图上。
It1 = rgb(:, :, 1);
事情发展顺序
It2 = rgb(:, :, 2);
It3 = rgb(:, :, 3);
It1(fgm) = 255; It2(fgm) = 0; It3(fgm) = 0;
I2 = cat(3, It1, It2, It3);
figure('units', 'normalized', 'position', [0 0 1 1]);
subplot(2, 2, 1); imshow(rgb, []); title('原图像');
subplot(2, 2, 2); imshow(Iobrcbr, []); title('基于重建的开闭操作');
小木桥subplot(2, 2, 3); imshow(fgm, []); title('局部极⼤图像');
subplot(2, 2, 4); imshow(I2); title('局部极⼤叠加到原图像');
鳄鱼养殖
Notice that some of the mostly-occluded and shadowed objects are not marked, which means that the objects will not be gmented properly in the end result. Also, the foreground markers in some objects go right up to the objects' edge. That means you should clean the edges of the marker blobs and then shrink them a bit. You can do this by a closing followed by an erosion.
注意到⼤多闭塞处和阴影对象没有被标记，这就意味着这些对象在结果中将不会得到合理的分割。⽽且，⼀些对象的前景标记会⼀直到对象的边缘。这就意味着应该清理标记斑点的边缘，然后收缩它们。可以通过闭操作和腐蚀操作来完成。
2 = strel(ones(5,5));
fgm2 = imclo(fgm, 2);
fgm3 = imerode(fgm2, 2);
figure('units', 'normalized', 'position', [0 0 1 1]);
subplot(2, 2, 1); imshow(Iobrcbr, []); title('基于重建的开闭操作');
subplot(2, 2, 2); imshow(fgm, []); title('局部极⼤图像');
subplot(2, 2, 3); imshow(fgm2, []); title('闭操作');
subplot(2, 2, 4); imshow(fgm3, []); title('腐蚀操作');
This procedure tends to leave some stray isolated pixels that must be removed. You can do this using bwareaopen, which removes all blobs that have fewer than a certain number of pixels. BW2 = bwareaopen(BW,P) removes from a binary image all connected components
(objects) that have fewer than P pixels, producing another binary image, BW2.
这个过程将会留下⼀些偏离的孤⽴像素，应该移除它们。可以使⽤bwareaopen，⽤来移除少于特定像素个数的斑点。BW2 = bwareaopen(BW,P)从⼆值图像中移除所以少于P像素值的连通块，得到另外的⼆值图像BW2。
fgm4 = bwareaopen(fgm3, 20);
It1 = rgb(:, :, 1);
It2 = rgb(:, :, 2);
It3 = rgb(:, :, 3);
It1(fgm4) = 255; It2(fgm4) = 0; It3(fgm4) = 0;
I3 = cat(3, It1, It2, It3);
figure('units', 'normalized', 'position', [0 0 1 1]);
subplot(2, 2, 1); imshow(I2, []); title('局部极⼤叠加到原图像');
subplot(2, 2, 2); imshow(fgm3, []); title('闭腐蚀操作');
subplot(2, 2, 3); imshow(fgm4, []); title('去除⼩斑点操作');
subplot(2, 2, 4); imshow(I3, []); title('修改局部极⼤叠加到原图像');
Step 4: Compute Background Markers
Now you need to mark the background. In the cleaned-up image, Iobrcbr, the dark pixels belong to the background, so you could start with a thresholding operation.
第4步：计算背景标记
现在，需要标记背景。在清理后的图像Iobrcbr中，暗像素属于背景，所以可以从阈值操作开始。
bw = im2bw(Iobrcbr, graythresh(Iobrcbr));
figure('units', 'normalized', 'position', [0 0 1 1]);
subplot(1, 2, 1); imshow(Iobrcbr, []); title('基于重建的开闭操作');
subplot(1, 2, 2); imshow(bw, []); title('阈值分割');
The background pixels are in black, but ideally we don't want the background markers to be too clo to the edges of the objects we are trying to gment. We'll "thin" the background by computing the "skeleton by influence zones", or SKIZ, of the foreground of bw. This can be done by computing the watershed transform of the distance transform of bw, and then looking for the watershed ridge lines (DL == 0) of the result. D = bwdist(BW) computes the Euclidean distance transform of the binary image BW. For each pixel in BW, the distance transform assigns a number that is the distance between that pixel and the nearest nonzero pixel of BW. bwdist us the Euclidean distance metric by default. BW can have any dimension. D is the same size as BW.
背景像素在⿊⾊区域，但是理想情形下，不必要求背景标记太接近于要分割的对象边缘。通过计算“⾻架影响范围”来“细化”背景，或者SKIZ，bw的前景。这个可以通过计算bw的距离变换的分⽔岭变换来
实现，然后寻找结果的分⽔岭脊线（DL==0）。D = bwdist(BW)计算⼆值图像BW的欧⼏⾥得矩阵。对BW的每⼀个像素，距离变换指定像素和最近的BW⾮零像素的距离。bwdist默认使⽤欧⼏⾥得距离公式。BW可以由任意维数，D与BW有同样的⼤⼩。
D = bwdist(bw);
DL = watershed(D);
bgm = DL == 0;
figure('units', 'normalized', 'position', [0 0 1 1]);
牵牛花的作文subplot(2, 2, 1); imshow(Iobrcbr, []); title('基于重建的开闭操作');
subplot(2, 2, 2); imshow(bw, []); title('阈值分割');
subplot(2, 2, 3); imshow(label2rgb(DL), []); title('分⽔岭变换⽰意图');
>孕妇能吃虾吗
