A list,

Mathematical morphology operations can be divided into binary morphology and gray morphology. Gray morphology is expanded from binary morphology. There are two basic operations of mathematical morphology, namely corrosion and expansion, and corrosion and expansion combine to form open and closed operations. Open operation is first corrosion and then expansion, closed operation is first expansion and then corrosion.

1 binary morphology

Roughly speaking, corrosion can “shrink” the target area, essentially shrinking the image’s boundaries, and can be used to eliminate small, meaningless objects. The formula is expressed as:



The formula says with structure corrosion. A, B need to be aware of is the need to define A B origin, [and the moving process of B are consistent with the process of convolution kernels mobile, with convolution kernels and image overlap again after calculation as 】 when B origin to image A translation like yuan (x, y), if B (x, y), fully contained in the image A overlapping area, (That is, all the corresponding image values of A at the position of element 1 in B are also 1) then the pixel (x,y) corresponding to the output image is assigned A value of 1, otherwise 0 is assigned.

Let’s look at a demo.



B moves on A in sequence (the same as the convolution kernel moves on the image, and then performs morphological operation on the coverage domain of B). When the coverage region of A is [1,1;1,1] or [1,0;1,1], (that is, ‘1’ in B is A subset of the coverage region), the position of the corresponding output image will be 1.

2 expansion

Roughly speaking, expansion “enlarges” the range of the target area, merging background points in contact with the target area into the target object, making the target boundary expand outwards. It can be used to fill some holes in the target area and eliminate the small particle noise contained in the target area.



In this formula, A is expanded by structure B, and the origin of structural element B is shifted to the position of image pixel (x,y). If the intersection of B and A at image pixel (x,y) is not empty (that is, at least one image value of A corresponding to the position of element 1 in B is 1), then the pixel (x,y) corresponding to the output image is assigned the value of 1; otherwise, it is assigned the value of 0.

Demo picture:



3 summary

In other words, no matter corrosion or expansion, structural element B is shifted on the image like convolution operation. The origin of structural element B is equivalent to the core center of the convolution kernel, and the result is also stored on the element at the corresponding position of the core center. However, corrosion means that B is completely contained in the area covered by it, and there is an intersection between B and the area covered by it during expansion.

Before telling the gray value morphology, we make A convention that the area of image A covered by structural element B is denoted as P (take Part meaning).

5. Corrosion of gray scale morphology

So corrosion in grayscale morphology is an operation similar to convolution. The small rectangle formed by subtracting structural element B from P can be assigned to the position of the corresponding origin by taking the minimum value.

Let’s look at an example to deepen our understanding of grayscale morphology.

Suppose we have the following image A and structural element B:



The process of gray morphological corrosion is as follows:



We specifically show the output result of the first element of the output image, that is, the position of 4 corresponding to the origin. The values of the other elements of the output image are also obtained in this way. We’ll see that the region that B first covers is the subtracted matrix, and then we take min in the difference matrix to be the value of the origin.



Expansion of grayscale morphology

According to the above description of corrosion, expansion is described in the same way. Expansion in grayscale morphology is an operation similar to convolution. P is added to B, and then the maximum value in this region is assigned to the position corresponding to the origin of structural element B.





Here is also the origin of the value of the first element of the output image.



The maximum value of the sum of the above matrices is 6, so assign 6 to the position corresponding to the origin of the structural element.

6 Summary Above introduced the concept of gray morphology, here to say their use. Compared with the original image, the corrosion results in smaller pixels than before, so it is suitable for removing peak noise. As a result of gray expansion, each pixel becomes larger than the previous one, so it is suitable for removing the trough noise.

Ii. Source code

%% % Eye-based fatigue detection % Practice reporting requirements: %1, use the mobile phone camera to shoot the face part; %2, using algorithms to take out part of the eyes; %3Do relevant feature extraction; %4Formulate rules for detecting drowsiness fatigue; %5, verify the correctness of rules. % Completed: Tang Men % Completed Time:2021.5clc; clear all; %% read image Img='test.jpg'; % Enter the path of the image Origin=imread(Img); Face_area = FaceRecogition(Origin); figure('name'.'Face recognition map'); imshow(Face_area); %% Gray= rGB2Gray (Face_area); BW=im2bw(Gray,60/255);  
figure('name'.'Binary plot'); imshow(BW); Eye_area=EyeRecogition(BW); figure('name'.'Eye map'); imshow(Eye_area); %% OpenPercentage = OpenRecogition(Eye_area); endCopy the code

3. Operation results



Fourth, note

Version: 2014 a