CN114943744A - Edge detection method based on local Otsu thresholding - Google Patents

Abstract

The invention discloses an edge detection method based on local Otsu thresholding, which comprises the steps of uniformly partitioning an original image to obtain four regions with the same area; then, calculating the threshold value of each block of area by adopting an Otsu algorithm to obtain four threshold values; then, carrying out thresholding treatment on respective regions by utilizing each threshold value to obtain a binary image; and finally, carrying out edge detection on the binary image by using an edge detection operator to obtain an edge image. The method of the invention improves the edge detection quality, can effectively filter noise, reserve key edges, and can obtain single-pixel closed edge lines with good continuity, thereby providing good foundation for feature extraction, target identification and the like.

Description

An edge detection method based on local Otsu thresholding

technical field

The invention relates to an edge detection method based on local Otsu thresholding, and belongs to the technical field of edge detection.

Background technique

The generalized digital image processing technology is divided into three levels from low level to high level. The first is image processing in a narrow sense. Both the input and output are a complete image, and only specific details are enhanced on the basis of the original image, or the quality of the image is improved to provide a basis for subsequent processing. The second is image analysis, which only analyzes and processes a part of the image. Usually, the important information of the image is contained in this part of the area. Therefore, it is necessary to extract as much key information as possible and reduce the surrounding areas. Impact. The last is image recognition and understanding, which is based on image analysis.

Image edge detection belongs to the level of image analysis. When processing most of the images in practical applications, we often do not need to pay attention to the entire image, and usually use some features to ignore the part we don't pay attention to, that is, the background area, and only focus on the feature area, that is, the foreground. area. Edge detection is one of the key steps to extract image features in digital image processing. This is similar to human vision: when an unknown object appears in the range of human sight, it is usually judged by the outline of the unknown object. The contour can be formed by connecting a plurality of edge segments, so in digital image processing, the image recognition can be made easy by successfully detecting the edge of the image, and the information to be processed in the subsequent digital image processing can be simplified. The results of edge detection are usually applied to higher-level image processing techniques, such as feature recognition, image recognition, and image compression, for further analysis and understanding.

From the perspective of the optimization process of edge detection algorithms, the difficulty of edge detection has always been that it is necessary to correctly detect valid edges to ensure the accuracy of the results and the integrity of details, and to ensure that the detection response is preferably a single pixel. wide to minimize the effect of noise. However, if you want to minimize missed edge detection, it will inevitably be affected by noise, resulting in too wide edge lines and even false edges, making it difficult to distinguish true and false edges, but if you want to minimize the impact of noise, then It is difficult to ensure that the details of the image are not lost. Therefore, in practical situations, these two requirements are usually contradictory, especially when the image is complex, it is difficult to obtain a better edge with only a simple edge detection algorithm.

Based on this difficulty, edge detection operators often require a preprocessing step before they are used. In this preprocessing step, we strive to reduce all noise in the image without losing the edge information of the image. Through the study of edge detection operators, it is not difficult to find that the concept of threshold runs through. The selected threshold is mostly the judgment condition of edge points, which can well balance the contradiction between effective edge and noise. If the threshold is properly selected, the noise in the image can be reduced very effectively, but if the threshold is not selected properly, it is easy to cause a large area of loss of image details. But how to choose a suitable threshold is also a difficulty.

Using the threshold value automatically calculated by the algorithm in advance to threshold the image as a preprocessing step of edge detection can effectively avoid the problem of low efficiency caused by artificial selection of the threshold value. The maximum between-class variance (Otsu) method is one of the most classic thresholding algorithms. It can calculate the optimal threshold by itself, and because it has the characteristics of strong practicability and simple calculation compared with other threshold algorithms, it has been widely used.

However, when there are multiple targets in the image, uneven illumination, etc., a single threshold obviously cannot meet the needs of subsequent edge detection. The disadvantage of the maximum inter-class variance method is that it is realized by traversing the image and obtaining the threshold based on the inter-class variance and the intra-class variance, and usually only produces an optimal threshold.

SUMMARY OF THE INVENTION

In order to solve the above problems, the present invention provides an edge detection method algorithm based on local Otsu thresholding.

The edge detection method based on local Otsu thresholding, the specific steps are as follows:

S1, the input image can be a grayscale image or a color image. Divide the input image into four regions according to the size of the area;

S2, the Otsu (maximum inter-class variance method) algorithm is used to calculate the threshold of each area, and four thresholds are obtained.

S3, using each threshold to perform thresholding processing on the respective regions to obtain a binary image;

S4, finally use an edge detection operator to perform edge detection on the binary image to obtain an edge image.

Further, the steps of the Otsu algorithm in S2 are as follows:

(1) Set the _gray value of the image to G={0, 1, .

(2) Use P _i to represent the probability of the occurrence of a pixel whose gray value is i in the image, then we have

(3) Select a threshold t, and divide the pixels in the image into two categories and C1, C0 is composed of all pixels in the image whose gray value is between [0, t], and C1 is composed of the gray value in the image. All pixels between [t+1, 255] are composed;

(4) Calculate the probability P ₀ and P ₁ of the two types of pixel point sets appearing, P ₁ =1-P ₀ ;

(5) Calculate the average gray value μ ₀ and μ ₁ of the two types of pixels and the average gray value μ of the entire image:

(6) Calculate the between-class variance of C0 and C1:

σ ² =P ₀ (μ-μ ₀ ) ² +P ₁ (μ-μ ₁ ) ² =P ₀ P ₁ (μ ₀ -μ ₁ ) ² (14)

(7) Traverse the gray value of the image, set each gray value as a threshold, and then calculate the inter-class variance, so that the threshold with the maximum inter-class variance is the optimal threshold.

Further, the thresholding process in S3 is specifically as follows

Let the original image be f(x, y) and the thresholded image be g(x, y), then

Further, the edge detection operators in S4 are specifically the Sobel operator and the Canny operator.

Further Sobel operator is specifically

The Sobel operator strengthens the weights of the pixels in the four areas of the center pixel, and weights the gray values of the upper, lower, left and right areas of the pixel to be processed to reach the extreme value at the edge, highlighting the edge information of the image to detect the edge, Its expression is:

in

G _x =[f(x+1,y-1)+2f(x+1,y)+f(x+1,y+1)]-[f(x-1,y-1)+2f( x-1, y)+f(x-1, y+1)] (16)

G _y =[f(x-1, y+1)+2f(x, y+1)+f(x+1, y+1)]-[f(x-1, y-1)+2f( x, y-1)+f(x+1, y-1)] (17)

The two templates are:

The above two templates represent the horizontal and vertical gradients of the image, respectively.

The Canny operator is further divided into the following four steps:

(1) First, use the first derivative of the two-dimensional Gaussian function to smooth the image.

Let the two-dimensional Gaussian function be:

where σ is the variance parameter of the Gaussian function. Like the previous application of the LOG operator in edge detection, the size of the variance parameter also directly affects the smoothness of the image, so it is also necessary to appropriately select the variance parameter according to the actual situation.

(2) Then, calculate the gradient size and gradient direction of all pixels in the image. Let the first-order directional derivative of the Gaussian function in a certain direction:

为梯度矢量。Among them, n is the direction vector;

is the gradient vector.

的基础上，图像的边缘强度可以用平滑后的图像在待测像素点梯度的幅值来表示：The Canny operator is built in two dimensions

On the basis of , the edge strength of the image can be represented by the magnitude of the gradient of the smoothed image at the pixel to be measured:

The direction of the edge is expressed as:

(3) Apply "non-maximum suppression" to the magnitude of the gradient. Since the global gradient in the image cannot determine the edge, it is necessary to traverse the entire image. If the gray value of a pixel is not the largest compared with the gray values of the two pixels before and after its gradient direction, then set the pixel value to It is 0, that is, the local maxima points in the image gradient are retained, and other non-local maxima are set to zero to obtain refined edges. The gradient direction of the pixel should be quantified according to 8-connectivity. If the gradient direction of the central pixel points to the direction of the C area, the adjacent pixels that need to be compared when performing local non-maximum suppression are the upper left and lower right. two pixels.

(4) "Hysteresis thresholding" of gradients and edge connections. The so-called "hysteresis thresholding" is to take two thresholds for the gradient, one strong threshold Th ₁ and one weak threshold Th ₂ , and the two thresholds satisfy Th ₁ =0.4·Th ₂ . Any pixel with a gradient magnitude smaller than the weak threshold is definitely not considered an edge point. Since the weak threshold is low, more edge information can be retained; all pixels with a gradient magnitude greater than the strong threshold are determined. considered as an edge point. At this time, because the value of the strong threshold is high, although most of the noise is removed, some edge information is also lost, so that the image with missing edge points cannot form a complete outline. At this time, the pixels whose gradient amplitude is between the two can be judged as edge points by examining their 8-connectivity with other edge points. If the gradient magnitude of a pixel point is greater than the weak threshold and less than the strong threshold, and there is a connected relationship with another edge point, the pixel can be regarded as an edge point; but a pixel that is not connected to any edge point cannot be identified as for pixel points. This makes it possible to connect missing edge points to form contours.

Using the edge detected by the Canny operator can reduce the edge interruption phenomenon in template detection, which is conducive to obtaining more complete edges, high positioning accuracy, and large signal-to-noise ratio. Some weak edges in the image background can also be detected. .

Compared with the prior art, the present invention adopts the above technical scheme, and has the following technical effects: the present invention firstly performs uniform partitioning on the original image; then adopts the Otsu algorithm to calculate the threshold value of each area; Finally, the edge detection operator is used to detect the edge of the binary image. Through the method of the invention, the quality of edge detection is improved, noise can be effectively filtered out, key edges can be retained, and a single-pixel closed edge line with good continuity can be obtained. Base.

Description of drawings

1 is a flowchart of an edge detection method based on local Otsu thresholding of the present invention;

Figure 2 Calculates the global threshold (left) and calculates the local threshold (right);

Figure 3 Global thresholding (left) and local thresholding (right);

Figure 4 uses Sobel operator (left) and Canny operator (right) to detect the original image results;

Figure 5 uses the Sobel operator (left) and the Canny operator (right) to detect the results of the global thresholded image;

Fig. 6 adopts Sobel operator (left) and Canny operator (right) to detect the result of local thresholding image;

Figure 7 uses Canny operator to detect the original image results (left) and local map (right);

Figure 8. Detection results (left) and local maps (right) of local thresholded images using Canny operator.

Detailed ways

The present invention and its beneficial technical effects will be described in detail below with reference to the accompanying drawings and various specific embodiments.

As shown in Figure 1, the edge detection method based on local Otsu thresholding of the present invention includes:

The first step is to acquire an image, and divide the image into four regions according to the size of the area. The image can be a color image or a grayscale image. A grayscale image is actually the process of making the R, G, and B components of a color image equal in value. For example, use the rgb2gray function that comes with MATLAB to process the obtained color image to obtain a grayscale image. Other well-known methods can also be used to realize the grayscale of the image, which will not be illustrated here. As shown in Figure 2, the image is equally divided into four regions according to the size of the area.

In the second step, the local threshold is calculated using the Otsu algorithm. In order to compare the effect of the local Otsu calculation threshold, the left picture in Figure 4 shows the global threshold calculated by the global Otsu algorithm. It can be seen that the global threshold is 170, while the local thresholds for partition calculation are 177, 166, 172, 146, respectively. The lower right region has a significantly lower local threshold than the global threshold due to the uneven illumination of the image.

The specific steps of the Otsu calculation threshold are as follows:

(1) Set the _gray value of the image as G={0, 1, .

(2) Use P _i to represent the probability of the occurrence of a pixel whose gray value is i in the image, then we have

之间的所有像素点组成，C₁由图像中灰度值在

之间所有的像素点组成；(3) Select a threshold t, and divide the pixels in the image into two categories C ₀ and C ₁ , C ₀ is determined by the gray value in the image

All pixels in between, C ₁ consists of the gray value in the image at

All the pixels in between are composed;

P₁＝1-P₀；(4) Calculate the probabilities P ₀ and P ₁ of the two types of pixel point sets appearing:

P ₁ =1-P ₀ ;

(5) Calculate the average gray value μ ₀ and μ ₁ of the two types of pixels and the average gray value μ of the entire image:

(6) Calculate the between-class variance of C ₀ and C ₁ :

σ ² =P ₀ (μ-μ ₀ ) ² +P ₁ (μ-μ ₁ ) ² =P ₀ P ₁ (μ ₀ -μ ₁ ) ² (26)

(7) Traverse the gray value of the image, set each gray value as a threshold, and then calculate the inter-class variance, so that the threshold with the maximum inter-class variance is the optimal threshold.

In the third step, each threshold is used to threshold the respective regions to obtain a binary image. The left image in Figure 3 is the output image using global Otsu thresholding, and the right image is using local Otsu thresholding. It can be seen that due to the uneven illumination of the image, the shadow area is also misjudged as the foreground area by using the global Otsu thresholding, while the local Otsu thresholding is used. Otsu thresholding works well.

The thresholding process is specifically as follows

Thresholding is actually an extreme but very useful grayscale transformation. It compares the gray value of each pixel in the image with a preset value, that is, a threshold, and transforms the pixel of the point into one of two possible output gray levels according to the comparison result, usually Shown in black and white. Therefore, the image after thresholding is actually a binary image. You can set the original image to be f(x, y) and the thresholded image to be g(x, y), then

The fourth step is to use the edge detection operator to perform edge detection on the binary image to obtain an edge image. As shown in Figure 4, there are three problems with the edge detected by the Sobel operator directly: (1) isolated edge points; (2) pseudo-edges; (3) discontinuous edge points. However, although the edges detected directly by the Canny operator have good continuity, there are too many false edges. As shown in Figure 5, using the global Otsu thresholding method to detect edges, misjudging the image target directly leads to errors in the later edge detection effect. As shown in Figure 6, the edge detection result using local Otsu thresholding greatly improves the shortcomings of Sobel operator and Canny operator, and can extract edge lines more accurately, with good edge continuity and strong anti-noise performance. .

The edge detection operators are specifically Sobel operators and Canny operators.

Specifically, the Sobel operator is

The Sobel operator is a 3×3 template, which is an odd-sized template, so the pixel to be processed can be placed in the center of the template to calculate its gradient value. The Sobel operator strengthens the weights of the pixels in the four areas of the center pixel, and weights the gray values of the upper, lower, left and right areas of the pixel to be processed to reach the extreme value at the edge, highlighting the edge information of the image to detect the edge, Its expression is:

in

G _x =[f(x+1,y-1)+2f(x+1,y)+f(x+1,y+1)]-[f(x-1,y-1)+2f( x-1,y)+f(x-1,y+1)] (29)

G _y =[f(x-1,y+1)+2f(x,y+1)+f(x+1,y+1)]-[f(x-1,y-1)+2f( x,y-1)+f(x+1,y-1)] (30)

The two templates are:

The above two templates represent the horizontal and vertical gradients of the image, respectively.

The Sobel operator strengthens the center pixel point. Therefore, if an image with uniform noise is processed, false edges are prone to appear with the Sobel operator. However, if the noise of the image is distributed near the edge, the Sobel operator will perform well for detection.

Specifically, the Canny operator is mainly divided into the following four steps:

(1) First, use the first derivative of the two-dimensional Gaussian function to smooth the image. Let the two-dimensional Gaussian function be:

where σ is the variance parameter of the Gaussian function. Like the previous application of the LOG operator in edge detection, the size of the variance parameter also directly affects the smoothness of the image, so it is also necessary to appropriately select the variance parameter according to the actual situation.

(2) Then, calculate the gradient size and gradient direction of all pixels in the image. Let the first-order directional derivative of the Gaussian function in a certain direction:

为梯度矢量。Among them, n is the direction vector;

is the gradient vector.

的基础上，图像的边缘强度可以用平滑后的图像在待测像素点梯度的幅值来表示：The Canny operator is built in two dimensions

On the basis of , the edge strength of the image can be represented by the magnitude of the gradient of the smoothed image at the pixel to be measured:

The direction of the edge is expressed as:

(3) Apply "non-maximum suppression" to the magnitude of the gradient. Since the global gradient in the image cannot determine the edge, it is necessary to traverse the entire image. If the gray value of a pixel is not the largest compared with the gray values of the two pixels before and after its gradient direction, then set the pixel value to It is 0, that is, the local maxima points in the image gradient are retained, and other non-local maxima are set to zero to obtain refined edges. The gradient direction of the pixel should be quantified according to 8-connectivity, as shown in the figure below, if the gradient direction of the central pixel points to the direction of the C area, then the adjacent pixels that need to be compared when performing local non-maximum suppression are Two pixels on the top left and bottom right.

(4) "Hysteresis thresholding" of gradients and edge connections. The so-called "hysteresis thresholding" is to take two thresholds for the gradient, one strong threshold Th ₁ and one weak threshold Th ₂ , and the two thresholds satisfy Th ₁ =0.4·Th ₂ . Any pixel with a gradient magnitude smaller than the weak threshold is definitely not considered an edge point. Since the weak threshold is low, more edge information can be retained; all pixels with a gradient magnitude greater than the strong threshold are determined. considered as an edge point. At this time, because the value of the strong threshold is high, although most of the noise is removed, some edge information is also lost, so that the image with missing edge points cannot form a complete outline. At this time, the pixels whose gradient amplitude is between the two can be judged as edge points by examining their 8-connectivity with other edge points. If the gradient magnitude of a pixel point is greater than the weak threshold and less than the strong threshold, and there is a connected relationship with another edge point, the pixel can be regarded as an edge point; but a pixel that is not connected to any edge point cannot be identified as for pixel points. This makes it possible to connect missing edge points to form contours.

Using the edge detected by the Canny operator can reduce the edge interruption phenomenon in template detection, which is conducive to obtaining more complete edges, high positioning accuracy, and large signal-to-noise ratio. Some weak edges in the image background can also be detected. .

In summary, the algorithm proposed in the present invention improves the quality of edge detection, can effectively filter out noise, retain key edges, and obtain a single-pixel closed edge line with good continuity for subsequent feature extraction, target recognition, etc. provides a good foundation.

Finally, it should be pointed out that the above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: it is still possible to modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements to some of the technical features; and these Modifications or substitutions do not make the essence of the corresponding technical solutions depart from the spirit and scope of the technical solutions of the embodiments of the present invention. Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that Various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principle and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims (7)

1. The edge detection method based on local Otsu thresholding is characterized by comprising the following steps of:

s1, inputting an image, equally dividing the input image into four regions according to the area size;

s2, calculating the threshold value of each block of area by adopting an Otsu (maximum inter-class variance) algorithm to obtain four threshold values;

s3, performing thresholding processing on the respective region by using each threshold value to obtain a binary image;

and S4, finally, carrying out edge detection on the binary image by using an edge detection operator to obtain an edge image.

2. The edge detection method based on local Otsu thresholding as claimed in claim 1, wherein the step of Otsu algorithm in S2 is:

(1) let the gray scale value of the image be G ═ 0, 1, …, 255}, and use f as the number of all pixels with gray scale value i _i Representing, total pixel points are represented by N, then

(2) With P _i The probability of the pixel point with the gray value i in the image is represented, so that

(3) Selecting a threshold value t, and dividing pixel points in the image into two types C ₀ And C ₁ ，C ₀ From grey values in the image

All pixel points in between, C ₁ From grey values in the image

All the pixel points are formed;

(4) calculating the probability P of the occurrence of two types of pixel point sets ₀ And P ₁ ：

P ₁ ＝1-P ₀ ；

(5) Calculating the average gray value mu of two types of pixel points ₀ 、μ ₁ And average gray value μ of the entire image:

(6) calculating C ₀ And C ₁ Inter-class variance of (c):

σ ² ＝P ₀ (μ-μ ₀ ) ² +P ₁ (μ-μ ₁ ) ² ＝P ₀ P ₁ (μ ₀ -μ ₁ ) ² (4)；

(7) traversing the gray values of the image, setting each gray value as a threshold, and then solving the inter-class variance, so that the threshold with the maximum inter-class variance is the optimal threshold.

3. The edge detection method based on local Otsu thresholding as claimed in claim 1, wherein the thresholding process in S3 is specifically:

assuming that the original image is f (x, y) and the thresholded image is g (x, y), the method will be described

4. The edge detection method based on local Otsu thresholding as claimed in claim 1, characterized in that the edge detection operators in S4 are specifically Sobel operators and Canny operators.

5. The edge detection method based on local Otsu thresholding as claimed in claim 4, wherein the Sobel operator is:

the Sobel operator strengthens the weight of the pixels in the four fields of the central pixel, weights the gray values of the upper field, the lower field, the left field and the right field of the pixel to be processed, reaches an extreme value at the edge, and highlights the edge information of the image so as to detect the edge.

6. The edge detection method based on local Otsu thresholding as claimed in claim 4, characterized in that said Canny operator is specifically divided into the following 4 steps:

(1) firstly, smoothing an image by using a first derivative of a two-dimensional Gaussian function, wherein the two-dimensional Gaussian function is set as:

where σ is the variance parameter of the Gaussian function.

(2) Then, calculating the gradient size and the gradient direction of all pixel points in the image, and setting a first-order directional derivative of the Gaussian function in a certain direction:

wherein n is a direction vector;

is a gradient vector;

canny operator is built in two dimensions

On the basis, the edge strength of the image can be represented by the amplitude of the gradient of the smoothed image at the pixel point to be detected:

the direction of the edge is expressed as:

(3) for the amplitude of the gradient, if the gray value of a certain pixel is not the maximum compared with the gray values of two pixels in front and at the back in the gradient direction, setting the pixel value as 0, reserving a local maximum value point in the image gradient, and setting other non-local maximum values as zero to obtain a refined edge, wherein the gradient direction of the pixel point is quantized according to 8-connectivity, and if the gradient direction of a central pixel points to the direction of the C area, adjacent pixels needing to be compared during local non-maximum value suppression are two pixel points at the upper left and the lower right;

(4) double threshold for gradient, one strong threshold Th ₁ A weak threshold Th ₂ And two thresholds satisfy Th ₁ ＝0.4·Th ₂ 。

7. The edge detection method based on local Otsu thresholding as claimed in claim 1, wherein in S1, the input image is any one of a grayscale image or a color image.

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