Image edge detection method based on adaptive extended state observer

Abstract

The present invention discloses an image edge detection method based on an adaptive extended state observer, which uses ESO as an image noise filtering operator (filter) and a differential operator (differentiator) at the same time, and has higher detection accuracy and better anti-noise ability. The optimized pole configuration method is used to select the gain coefficient of ESO, which is more conducive to ensuring numerical stability and is more suitable for filtering out noise in the image and improving the image edge detection ability. An adaptive learning mechanism is introduced to adjust the ESO bandwidth according to the gradient size, and the position of the noise point is determined according to the noise estimation value, so that good edge detection can be achieved under different noise intensity conditions. In view of the problem that the shape of the image edge may be irregular, edge detection is performed from multiple directions to obtain multi-directional edge information; in view of the phase lag problem caused by unidirectional differentiation, a two-way differential averaging method is used to offset the influence of the phase lag, thereby improving the detection accuracy.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and in particular to an image edge detection method based on an adaptive dilated state observer. Background Technology

[0002] In practical image processing problems, image edges, as fundamental features, contain important image information and have wide applications in image segmentation and object recognition. Typical edge detection methods are based on the first or second derivative of the image to detect edge points, primarily using differential edge detection operators such as Robert, Sobel, Prewitt, Canny, Log, and Laplacian. While these edge detection algorithms are relatively mature, their performance on noisy images is still not ideal, exhibiting poor noise resistance and a tendency to misidentify high-frequency noise points as edges. To remove noise, most edge detection algorithms perform image smoothing preprocessing, but image smoothing can easily lead to the loss of edge information. Furthermore, edge detection based on numerical differentiation suffers from phase lag, resulting in low accuracy. Therefore, performing edge detection directly on noisy images is of great significance in the field of image processing. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings and disadvantages of the prior art and provide an image edge detection method based on an adaptive extended state observer (ESO). This method integrates noise filtering and differentiation, and introduces the concept of an extended state observer (ESO) to extract noisy image edges. This method can automatically adjust the filtering bandwidth parameter according to the noise level, effectively solving the problem that the edge detection effect of traditional edge detection methods is sensitive to noise, and achieving accurate detection of image edges and effective suppression of noise.

[0004] To achieve the above objectives, the technical solution provided by this invention is: an image edge detection method based on an adaptive dilated state observer, comprising the following steps:

[0005] The gradient of the image to be edge detected is calculated using the first-order differential signal obtained by ESO, and the bandwidth of ESO is changed according to the gradient. The bandwidth of ESO is also adjusted by the real-time value of the image gray-level change rate estimated by third-order ESO.

[0006] The noise intensity of the image is estimated by using the second-order differential signal obtained from ESO, and the location of extreme noise points is determined.

[0007] The above-mentioned ESO is used to calculate the differential of image pixels from multiple directions to reduce the influence of the initial direction on the edge position. The gradient of the image is obtained by multi-directional synthesis in both positive and negative directions, and the image is filtered according to the position of noise points.

[0008] The non-maximum suppression method is used to accurately locate edge points, and the double thresholding method is used to determine the connection of the edges, thus obtaining the final edge image.

[0009] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0010] 1. This invention innovatively uses ESO as both an image noise filtering operator (filter) and a differential operator (differentiator) to achieve noise-resistant edge detection, which has higher detection accuracy and better noise resistance than existing edge detection methods.

[0011] 2. An optimized pole placement method is used to select the gain coefficient of ESO. Compared with the traditional bandwidth method, it is more conducive to ensuring numerical stability and is more suitable for filtering noise in the image and improving the image edge detection capability.

[0012] 3. An adaptive learning mechanism is introduced to adjust the bandwidth of ESO according to the gradient magnitude and determine the location of noise points according to the noise estimate, so as to achieve good edge detection performance under different noise intensity conditions.

[0013] 4. To address the issue of potentially irregular image edge shapes, edge detection is performed from multiple directions to obtain multi-directional edge information. To address the phase lag problem caused by unidirectional differentiation, a bidirectional (forward and reverse) differentiation averaging method is used to offset the effect of phase lag, thereby improving detection accuracy. Attached Figure Description

[0014] Figure 1 This is a flowchart of the method of the present invention.

[0015] Figure 2 This is a sample image of the original image with noise.

[0016] Figure 3a This is the gradient image in the horizontal (0°) direction.

[0017] Figure 3b This is a gradient image at a 45° angle.

[0018] Figure 3c This is the gradient image in the vertical (90°) direction.

[0019] Figure 3d This is a gradient image in the 135° direction.

[0020] Figure 4 An image synthesized from gradient images in four directions.

[0021] Figure 5 The flowchart shows the algorithm for nonmaximum suppression and double thresholding.

[0022] Figure 6 This is the edge image after nonmaximum suppression and double thresholding. Detailed Implementation

[0023] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0024] like Figure 1 As shown, this embodiment discloses an image edge detection method based on an adaptive extended state observer. First, Step 001 is run, inputting the image to be edge detected, for example... Figure 2 The original image shown is contaminated with noise. To verify the denoising performance of the algorithm, Gaussian noise with a variance of 0.5% and salt-and-pepper noise with a density of 0.5% are added to the original grayscale image. In Step 002, gradient detection is performed on the original image, using bidirectional adaptive ESO gradient detection from four directions, resulting in the following... Figures 3a-3d Four gradient images from different orientations are used to synthesize the gradient magnitude and direction of the image pixels, as shown below. Figure 4 The image shown is followed by Steps 003 and 004, and then... Figure 5 The algorithm flow, sequentially... Figure 4 The image is subjected to non-maximum suppression and double threshold segmentation edge connection to obtain, as shown below. Figure 6 The final edge image is shown, and the edge image is output through Step005.

[0025] In the image processing of Step002, extraction is performed from four directions. Figure 2 The first-order differential signal is obtained by bidirectional averaging, where the first-order differential signal is extracted using a third-order ESO. The discrete form of the third-order ESO is as follows:

[0026] (1);

[0027] Nonlinear function , The definition is as follows:

[0028] (2);

[0029] (3);

[0030] In the formula, and These are the current pixel and the next pixel, respectively. This is the integration step size; The input signal is the gray value of a pixel in a certain direction in the image; This is the grayscale output for the pixel at the current moment. For the grayscale tracking output of the next pixel, The output is the first-order derivative of the gray level of the pixel at the current moment. The first-order derivative of the pixel's grayscale value is output at the next time step. The output is the second-order derivative of the grayscale value of the pixel at the current moment. The second-order derivative of the pixel's grayscale value is output at the next time step. The input control quantity serves as a differentiator for image processing. , To control the gain, because The value is 0, so this control gain does not need to be considered in subsequent calculations; It is the tracking error of ESO, that is, the difference between the gray value estimated by ESO and the actual gray value of the image; nonlinear function , To quickly control the optimal synthesis function, , , It is the gain coefficient of ESO; , A parameter representing the change in the error exponent; The size of the linear variation region representing the observation error, with a value range of [value missing]. ;

[0031] , , The value of plays a crucial role in the observation capability and disturbance estimation capability of ESO. This invention employs an optimized pole placement method to select the gain coefficient of ESO. , and This reduces high-frequency noise interference in images and improves edge detection accuracy. The characteristic polynomial of the observation error matrix of a third-order ESO is... , represented as:

[0032] (4);

[0033] In the formula, For the Laplace operator, the optimized extreme point is obtained experimentally. , , That is:

[0034] (5);

[0035] From formulas (4) and (5), the gain coefficient of ESO can be obtained as follows:

[0036] (6);

[0037] In the formula, The bandwidth of the ESO determines its tracking speed and noise immunity. Figure 2 The parameters of ESO are taken as the integration step size. =0.02, bandwidth =40, then the gain coefficient of ESO =104, =2000, =6400; Nonlinear function , In =0.9, =0.45, =0.1.

[0038] Given that the ESO has already observed the current image pixel position once, the first-order differential signal is used. To adjust bandwidth The size of the ESO is adjusted to achieve adaptive adjustment, which is very effective for filtering Gaussian noise.

[0039] (7);

[0040] In the formula, This represents the upper limit of ESO bandwidth. This represents the lower limit of ESO bandwidth. This represents the maximum value of the image grayscale change rate. These parameters are determined offline to represent the minimum rate of change of image grayscale. It is the real-time value of the image grayscale change rate estimated by ESO.

[0041] First, select a sufficiently large initial bandwidth offline. When applying ESO for edge detection, if the image edges are clear and noise points are mostly filtered out, then both noise filtering and differentiation are good. It can be determined as And it is acceptable =0.707 The corresponding edge for , Desirable 10% of =0.1 If the initial bandwidth If image edge sharpness cannot be guaranteed, the bandwidth can be increased in increments of 20% until the image edges are sharp; if the initial bandwidth... While ensuring clear image edges, if there are many noise points, the noise level can be reduced by 15% until the image edges are clear. After finalizing the ESO parameters, perform edge detection on the resulting image. Figure 2 Initial bandwidth =40, at the edge value =600.

[0042] At the same time, using the second-order differential signal To determine the location of extreme noise points, a pixel is identified as a noise point if it meets the conditions shown in the following formula. This method is particularly effective for salt-and-pepper noise.

[0043] (8);

[0044] In the formula, As a dimensional scaling factor, the second-order differential signal Equivalent to and The total change with the same dimensions These parameters were determined offline to determine the noise threshold; It is the real-time value of the rate of change of the image grayscale change rate estimated by ESO.

[0045] Dimensional scaling factor It can be any non-zero positive number, usually taken as... To achieve dimensional transformation of second-order differential signals; threshold You can take it first. The value is increased by 50% at a time until the noise point is accurately located and subsequent filtering can effectively remove the noise. For Figure 2 scaling factor =0.5, threshold =2500.

[0046] The above ESO method is used to extract the first-order differential signal of the original image from four directions. The origin of the image coordinate system is located at the upper left corner of the image, and the horizontal direction is... The axis (0°) is to the right, and the perpendicular direction is... The axis (90°) is downwards, with the positive direction being downwards. Assume... Represents image pixels grayscale value, point Indicates the tracking start point; therefore, the initial conditions for ESO are: the input signal... , To track the starting point The grayscale value, the signal tracking output The first-order differential output of the signal The second-order differential output of the signal .

[0047] For each pixel in the image First, perform a forward traversal from four directions: horizontal (0°), 45°, vertical (90°), and 135°, and then apply ESO to obtain the first-order differential signal. , , and .

[0048] Traverse from left to right in the horizontal (0°) direction, and take... Given the grayscale value in the horizontal direction, we get:

[0049] (9);

[0050] In the formula, This outputs the grayscale value of the pixel at the current moment during horizontal traversal. The grayscale tracking output of the next pixel in the horizontal traversal; This is the first-order derivative of the grayscale value of the pixel at the current moment during horizontal traversal. The first-order derivative of the grayscale of the pixel at the next time step during the horizontal traversal is output. This is the second-order derivative of the grayscale value of the pixel at the current moment during horizontal traversal. The second-order derivative of the grayscale value of the pixel at the next time step of the horizontal traversal is output. This is the input signal at the current moment, i.e., the grayscale value of the current pixel. This serves as the input for the signal at the next moment, i.e., the grayscale value of the next pixel. This represents the grayscale value of the pixel whose horizontal coordinate has shifted one grid to the right. For pixels during horizontal traversal The gradient;

[0051] Traverse from the top right corner to the bottom left corner in a 45° direction, and take... Given the grayscale value at a 45° angle, we get:

[0052] (10);

[0053] In the formula, This outputs the grayscale value of the pixel at the current moment during a 45° traversal. The grayscale tracking output of the next pixel in the 45° traversal direction; This is the first-order derivative output of the grayscale value of the pixel at the current moment during a 45° traversal. The first-order derivative of the grayscale value of the pixel at the next time step after traversing the 45° direction is output. This is the second-order derivative output of the grayscale value of the pixel at the current moment during a 45° traversal. The second-order derivative of the grayscale value of the pixel at the next time step after traversing in the 45° direction is output. This is the input signal at the current moment, i.e., the grayscale value of the current pixel. This serves as the input for the signal at the next moment, i.e., the grayscale value of the next pixel. This represents the grayscale value of a pixel whose horizontal coordinate is shifted one unit to the left and whose vertical coordinate is shifted one unit down. Pixels when traversing in a 45° direction The gradient;

[0054] Traverse vertically (90º) from top to bottom, and take... Given the grayscale value in the vertical direction, we get:

[0055] (11);

[0056] In the formula, This is the grayscale tracking output of the pixel at the current moment during vertical traversal. This is the grayscale tracking output of the next pixel in the vertical traversal. This is the first-order derivative of the grayscale value of the pixel at the current moment during vertical traversal. The first-order derivative of the grayscale value of the pixel at the next time step during vertical traversal is output. This is the second-order derivative of the grayscale value of the pixel at the current moment during vertical traversal. The second-order derivative of the grayscale value of the pixel at the next time step in the vertical traversal is output. This is the input signal at the current moment, i.e., the grayscale value of the current pixel. This serves as the input for the signal at the next moment, i.e., the grayscale value of the next pixel. This represents the grayscale value of the pixel whose vertical coordinate has shifted down one grid. For vertical traversal of pixels The gradient;

[0057] Traverse from the top left corner to the bottom right corner in a 135° direction, and take... Given the grayscale value at 135°, we get:

[0058] (12);

[0059] In the formula, This is the grayscale tracking output of the pixel at the current moment during a 135° traversal. The grayscale tracking output of the next pixel in the 135° traversal direction; This is the first-order derivative output of the grayscale value of the pixel at the current moment during a 135° traversal. The first-order derivative of the grayscale value of the pixel at the next time step after traversing the 135° direction is output. This is the second-order derivative output of the grayscale value of the pixel at the current moment during a 135° traversal. The second-order derivative of the grayscale value of the pixel at the next time step after traversing the 135° direction; This is the input signal at the current moment, i.e., the grayscale value of the current pixel. This serves as the input for the signal at the next moment, i.e., the grayscale value of the next pixel. This represents the grayscale value of a pixel whose horizontal coordinate is shifted one unit to the right and whose vertical coordinate is shifted one unit down. Pixels when traversing in a 135° direction The gradient;

[0060] Then, by performing a reverse traversal from each of the four directions, the first-order differential signal can be obtained. , , and ;

[0061] Traverse from right to left in the horizontal (0°) direction, and take... The horizontally reversed grayscale value is obtained as follows:

[0062] (13);

[0063] In the formula, This is the grayscale tracking output of the current pixel during horizontal reverse traversal. This is the grayscale tracking output of the next pixel in the horizontal reverse traversal. This is the first-order derivative of the grayscale value of the pixel at the current time step during the horizontal reverse traversal. The first-order derivative of the grayscale value of the pixel at the next time step of the horizontal reverse traversal is output. This is the second-order derivative of the grayscale value of the pixel at the current time step during the horizontal reverse traversal. The second-order derivative of the grayscale of the pixel at the next time step after the horizontal reverse traversal; This is the input signal at the current moment, i.e., the grayscale value of the current pixel. This serves as the input for the signal at the next moment, i.e., the grayscale value of the next pixel. This represents the grayscale value of the pixel whose horizontal coordinate has shifted one grid to the left. For pixels during horizontal reverse traversal The gradient;

[0064] Traverse from the bottom left to the top right in a 45° direction, and take... The grayscale value after a 45° inversion is obtained as follows:

[0065] (14);

[0066] In the formula, This is the grayscale tracking output of the current pixel during a 45° reverse traversal. The grayscale tracking output of the next pixel in the 45° reverse traversal; This is the first-order derivative output of the grayscale value of the pixel at the current time point after a 45° reverse traversal. The first-order derivative output of the grayscale of the pixel at the next time step after a 45° reverse traversal; This is the second-order derivative output of the grayscale value of the pixel at the current moment after a 45° reverse traversal. The second-order derivative output of the grayscale of the pixel at the next time step after a 45° reverse traversal; This is the input signal at the current moment, i.e., the grayscale value of the current pixel. This serves as the input for the signal at the next moment, i.e., the grayscale value of the next pixel. This represents the grayscale value of a pixel whose horizontal coordinate is shifted one unit to the right and whose vertical coordinate is shifted one unit upward. Pixels during 45° reverse traversal The gradient;

[0067] Traverse vertically (90º) from bottom to top, and take... For the vertically reversed grayscale values, we get:

[0068] (15);

[0069] In the formula, This is the grayscale tracking output of the current pixel during vertical reverse traversal. This is the grayscale tracking output of the next pixel in the vertical reverse traversal. This is the first-order derivative of the grayscale value of the pixel at the current moment during the vertical reverse traversal. The first-order derivative of the grayscale value of the pixel at the next time step of the vertical reverse traversal is output. This is the second-order derivative output of the grayscale value of the pixel at the current moment during the vertical reverse traversal. The second-order derivative of the grayscale of the pixel at the next time step after the vertical reverse traversal; This is the input signal at the current moment, i.e., the grayscale value of the current pixel. This serves as the input for the signal at the next moment, i.e., the grayscale value of the next pixel. The grayscale value of the pixel whose vertical coordinate has shifted upwards by one grid. For vertical reverse traversal of pixels The gradient;

[0070] Traverse from the bottom right corner to the top left corner in a 135° direction, and take... The grayscale value after a 135° inversion is obtained as follows:

[0071] (16);

[0072] In the formula, This is the grayscale tracking output of the pixel at the current moment during a 135° reverse traversal. The grayscale tracking output of the next pixel in the 135° reverse traversal; This is the first-order differential output of the grayscale value of the pixel at the current moment after a 135° reverse traversal. The first-order derivative output of the grayscale of the pixel at the next time step after a 135° reverse traversal; This is the second-order derivative output of the grayscale value of the pixel at the current moment after a 135° reverse traversal. The second-order derivative output of the grayscale of the pixel at the next time step after a 135° reverse traversal; This is the input signal at the current moment, i.e., the grayscale value of the current pixel. This serves as the input for the signal at the next moment, i.e., the grayscale value of the next pixel. This represents the grayscale value of a pixel whose horizontal coordinate is shifted one unit to the left and whose vertical coordinate is shifted one unit upward. For pixels during 135° reverse traversal The gradient.

[0073] The differential signals obtained from the forward and reverse traversals are averaged to eliminate errors caused by phase lag, resulting in the average gradients in four directions. , , and The gradient image corresponding to each direction is as follows: Figures 3a-3b As shown.

[0074] (17);

[0075] (18);

[0076] (19);

[0077] (20);

[0078] The gradient magnitude is usually calculated using the formula (21), but the calculation of the square and square root is computationally expensive. Therefore, this invention calculates the gradient magnitude of the entire image by taking the absolute values ​​of the gradient components in the four directions and summing them, as shown in formula (22). The gradient magnitude image synthesized from the four directions is as follows: Figure 4 As shown.

[0079] (twenty one);

[0080] (twenty two);

[0081] In the formula, Represents image pixels The gradient value, the gradient direction at 0° horizontally and 90° vertically is obtained by the following formula, and its phase... Represented as:

[0082] (twenty three);

[0083] The gradient directions at 45° and 135° are obtained by the following formula, and their phases are... Represented as:

[0084] (twenty four);

[0085] Based on the previously determined locations of extreme noise points, these noise points are filtered on the gradient magnitude image.

[0086] (25);

[0087] In the formula, the set This indicates that the filter window size is 3×3. , All are sets Any one of the values ​​in the table represents the grayscale value of the noise point. It is the gray value of the 8-neighborhood of the noise point. To take the median, This represents the grayscale value of the noise point after filtering.

[0088] In the image processing of Step 003, non-maximum suppression is used to accurately locate edge feature points. According to... Figure 5 In the non-maximum suppression method, Step 501 inputs the gradient magnitude image; then, in Step 502, the gradient normal vector is calculated from four directions. When gradient changes indicate an edge, due to the wide change area, the gradient normal vector needs to be calculated in four directions: horizontal, vertical, 45°, and 135°. Next, in Step 503, it is determined whether there is a local maximum in the normal direction. If so, it proceeds to Step 504 to retain the current pixel; otherwise, it proceeds to Step 505 to suppress the grayscale value of the current pixel to 0. Then, in Step 506, the entire image is traversed, retaining only pixels with local maxima in the edge directions, and the non-maximum suppressed image is output. Through multi-directional non-maximum suppression, the blurring effect caused by edge detection is eliminated, making the edges of the target image clearer and more detailed.

[0089] In the image processing of Step 004, a double thresholding method is used to determine the edge connections. After non-maximum suppression, although the edge information of the target image is significantly improved, discontinuities may occur at the edges due to some interference factors when extracting the edge lines. To make the edge information of the image clearer and ensure edge coherence, according to... Figure 5 The double-threshold edge determination algorithm uses two thresholds on the image after non-maximum suppression. and The image is thresholded and segmented, and edge connections are performed. In Step 507, the image pixels are determined. gradient magnitude Is it greater than the high threshold? If yes, proceed to Step 510; this point must be an edge point and will be retained. If not, proceed to Step 508, where the gradient magnitude will be determined. Whether it falls between two thresholds, i.e. If so, proceed to Step 509 to perform connectivity analysis on the 8-neighborhood of the pixel to find the point. If there are any pixels in the 8-neighborhood that exceed a high threshold, proceed to Step 510. If the current pixel is an edge pixel, it is used to connect strong edge points. Otherwise, proceed to Step 511. If the current pixel is not an edge point, it is treated as an isolated noise point and discarded. In Step 508, if the gradient magnitude... Less than the low threshold If the current pixel is not an edge point, proceed to Step 511. Since it is not an edge point, suppress its grayscale value to 0. Finally, in Step 512, set the grayscale value of edge points to 255 and the grayscale value of non-edge points to 0, forming the edge contour and obtaining a binarized edge image as the final edge image. Figure 4 Apply high threshold =70, low threshold Double thresholding and edge concatenation with a threshold of 30 result in the following edge image: Figure 6 As shown. Comparison Figure 2 and Figure 6 It can be seen that, Figure 6 It extracted very well Figure 2 The edges of the image are filtered out, which removes a lot of noise while preserving the texture information and local features of the image.

[0090] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be considered as equivalent replacement methods and are included in the scope of protection of the present invention.

Claims

1. An image edge detection method based on an adaptive extended state observer, characterized in that: The following steps are involved: The gradient of the image to be detected is calculated by the first-order differential signal obtained by ESO, and the bandwidth of ESO is changed according to the gradient. The bandwidth of ESO is adjusted by the real-time value of the image grayscale change rate estimated by the third-order ESO. The second-order differential signal obtained by ESO is used to estimate the noise intensity of the image and determine the location of the extreme noise point; The above ESO is applied to calculate the differential of image pixels from multiple directions to reduce the influence of the initial direction on the edge position. The gradient of the image is obtained through forward and reverse multi-directional synthesis, and the image is filtered according to the position of the noise point. The non-maximum suppression method is used to accurately locate edge points, and the double threshold method is used to determine the edge connection line to obtain the final edge image; The first-order differential signal of the image to be detected is extracted from the horizontal, 45°, vertical and 135° directions in both directions, and the first-order differential signal of the two directions is averaged. The first-order differential signal is extracted by the third-order ESO. The discrete form of the third-order ESO is: （1）； The nonlinear function , The definition is as follows: （2）； （3）； In the formula, and are the current pixel and the next pixel respectively. is the integration step length; is the input of the signal, that is, the gray value of the pixel in a certain direction in the image; is the grayscale tracking output of the pixel at the current moment, is the grayscale tracking output of the pixel at the next moment, is the first-order differential output of the grayscale of the pixel at the current moment, is the first-order differential output of the grayscale of the pixel at the next moment, is the second-order differential output of the grayscale of the pixel at the current moment, It is the second-order differential output of the grayscale of the pixel at the next moment; is the input control quantity, which is used as the differentiator for image processing , is the control gain, due to If it is 0, the control gain does not need to be considered in subsequent calculations; is the tracking error of ESO, that is, the difference between the gray value estimated by ESO and the gray value of the actual image; Nonlinear functions , To quickly control the optimal comprehensive function, , , is the gain coefficient of ESO; , Parameter representing the exponential change of the error; Represents the size of the linear change area of ​​the observation error, and its value range is ; , , The value of plays a key role in the observation capability and disturbance estimation capability of ESO. The optimal pole configuration method is used to select the gain coefficient of ESO. , and , reduce the interference of high-frequency noise in the image and improve the accuracy of image edge detection; the characteristic polynomial of the observation error matrix of the third-order ESO , expressed as: （4）； In the formula, is the Laplace transform operator, and the optimized poles obtained through experiments are , , , that is: （5）； From formula (4) and formula (5), the gain coefficient of ESO is: （6）； In the formula, It is the bandwidth of the ESO that determines the tracking speed and noise immunity of the ESO.

2. The image edge detection method based on adaptive extended state observer according to claim 1, characterized in that: When ESO has made one observation of the current image pixel position, the first-order differential signal is used To adjust the bandwidth of ESO The size of can realize the adaptive adjustment of ESO, as shown in the following formula (7): （7）； In the formula, is the upper limit of ESO bandwidth, is the lower limit of ESO bandwidth, is the maximum value of the image grayscale change rate, is the minimum value of the grayscale change rate of the image, the first-order differential signal It is the real-time value of the image grayscale change rate estimated by ESO.

3. The image edge detection method based on adaptive extended state observer according to claim 2 is characterized in that: parameter , , and Through offline determination, first select an initial bandwidth offline , apply ESO for edge detection. If the image edge is clear and the noise points are filtered out, then Can be determined as , and can take =0.707 , the corresponding edge for , Can take 10% of =0.1 ; If the initial bandwidth If the image edge cannot be guaranteed to be clear, the bandwidth can be increased by 20% until the image edge is clear. Although the image edge is clear, there are many noise points, which can be reduced by 15% until the image edge is clear.

4. The image edge detection method based on adaptive extended state observer according to claim 3 is characterized in that: If the current pixel satisfies the condition shown in the following formula (8), it is an extreme noise point; （8）； In the formula, is the dimensionless proportional factor, and the second-order differential signal Equivalent to The total change of the same dimension, To determine the noise threshold, the second-order differential signal is the real-time value of the rate of change of the image grayscale change rate estimated by ESO, Contains noise intensity information.

5. The image edge detection method based on adaptive extended state observer according to claim 4 is characterized in that: The dimension scale factor Can be any non-zero positive number, take , realize the dimensional conversion of the second-order differential signal; threshold Can take first The value of is increased by 50% until the noise point is accurately located and the subsequent filtering can effectively filter out the noise point.

6. The image edge detection method based on adaptive extended state observer according to claim 5, characterized in that: ESO is used to extract the first-order differential signal of the image to be edge detected from four directions. The origin of the image coordinate system is located in the upper left corner of the image, and the horizontal direction is The axis is 0°, the right is the positive direction, and the vertical direction is The axis is 90°, with downward being the positive direction; assuming Represents image pixels Gray value, point represents the tracking starting point, then the initial condition of ESO is: the input signal , Starting point for tracking Gray value, signal tracking output , the first-order differential output of the signal , the second-order differential output of the signal ; For each pixel in the image First, perform forward traversal from the horizontal direction (0°, 45°, vertical direction (90°, and 135°) respectively, and apply ESO to obtain the first-order differential signal , , and ; Traverse from left to right in the horizontal direction, that is, in the 0° direction, and take is the gray value in the horizontal direction, we get: （9）； In the formula, is the grayscale tracking output of the current pixel point traversed horizontally, It is the grayscale tracking output of the pixel point at the next moment of horizontal traversal; is the first-order differential output of the grayscale of the pixel at the current moment traversed horizontally, It is the first-order differential output of the grayscale of the pixel point at the next moment of horizontal traversal; is the second-order differential output of the grayscale of the pixel at the current moment traversed horizontally, It is the second-order differential output of the grayscale of the pixel point at the next moment of horizontal traversal; is the input of the signal at the current moment, that is, the grayscale value of the current pixel; is the input of the signal at the next moment, that is, the grayscale value of the next pixel; The gray value of the pixel whose horizontal coordinate moves one grid to the right; Pixel points when traversing horizontally The gradient of Traverse from the upper right corner to the lower left corner in the 45° direction and take is the gray value in the 45° direction, we get: （10）； In the formula, It is the grayscale tracking output of the pixel at the current moment traversed in the 45° direction. It is the grayscale tracking output of the pixel point at the next moment of traversal in the 45° direction; It is the first-order differential output of the grayscale of the pixel at the current moment traversed in the 45° direction. It is the first-order differential output of the grayscale of the pixel point at the next moment of traversal in the 45° direction; It is the second-order differential output of the grayscale of the pixel at the current moment traversed in the 45° direction. It is the second-order differential output of the grayscale of the pixel point at the next moment of traversal in the 45° direction; is the input of the signal at the current moment, that is, the grayscale value of the current pixel; is the input of the signal at the next moment, that is, the grayscale value of the next pixel; The gray value of the pixel whose horizontal coordinate moves one grid to the left and whose vertical coordinate moves one grid downward; Pixel points when traversing in the 45° direction The gradient of Traverse vertically from top to bottom at 90°. is the gray value in the vertical direction, we get: （11）； In the formula, is the grayscale tracking output of the current pixel point traversed in the vertical direction, It is the grayscale tracking output of the pixel point at the next moment of vertical traversal; is the first-order differential output of the grayscale of the pixel at the current moment traversed in the vertical direction, It is the first-order differential output of the grayscale of the pixel point at the next moment of vertical traversal; is the second-order differential output of the grayscale of the pixel at the current moment traversed in the vertical direction, It is the second-order differential output of the grayscale of the pixel point at the next moment of vertical traversal; is the input of the signal at the current moment, that is, the grayscale value of the current pixel; is the input of the signal at the next moment, that is, the grayscale value of the next pixel; The gray value of the pixel point whose vertical coordinate moves down one grid; Pixel points when traversing vertically The gradient of Traverse from the upper left corner to the lower right corner in the 135° direction and take is the gray value in the 135° direction, we get: （12）； In the formula, It is the grayscale tracking output of the pixel at the current moment of traversal in the 135° direction. It is the grayscale tracking output of the pixel point at the next moment of traversal in the 135° direction; It is the first-order differential output of the grayscale of the pixel at the current moment traversed in the 135° direction. It is the first-order differential output of the grayscale of the pixel point at the next moment of traversal in the 135° direction; It is the second-order differential output of the grayscale of the pixel at the current moment traversed in the 135° direction. It is the second-order differential output of the grayscale of the pixel point at the next moment of traversal in the 135° direction; is the input of the signal at the current moment, that is, the grayscale value of the current pixel; is the input of the signal at the next moment, that is, the grayscale value of the next pixel; The grayscale value of the pixel whose horizontal coordinate moves one grid to the right and whose vertical coordinate moves one grid downward; Pixel points when traversing in the 135° direction The gradient of Then traverse backward from four directions to obtain the first-order differential signal , , and ; Traverse from right to left in the horizontal direction, that is, in the 0° direction, and take is the horizontally reversed grayscale value, we get: （13）； In the formula, is the grayscale tracking output of the current pixel point in the horizontal reverse traversal, It is the grayscale tracking output of the pixel point at the next moment of horizontal reverse traversal; is the first-order differential output of the grayscale of the pixel at the current moment of horizontal reverse traversal, It is the first-order differential output of the grayscale of the pixel point at the next moment of horizontal reverse traversal; is the second-order differential output of the grayscale of the pixel at the current moment of horizontal reverse traversal, It is the second-order differential output of the grayscale of the pixel point at the next moment of horizontal reverse traversal; is the input of the signal at the current moment, that is, the grayscale value of the current pixel; is the input of the signal at the next moment, that is, the grayscale value of the next pixel; The gray value of the pixel whose horizontal coordinate moves one grid to the left; Pixel point when traversing horizontally in reverse The gradient of Traverse from the lower left corner to the upper right corner in the 45° direction and take is the gray value of the 45° reverse direction, we get: （14）； In the formula, It is the grayscale tracking output of the pixel at the current moment of the 45° reverse traversal. It is the grayscale tracking output of the pixel point at the next moment of 45° reverse traversal; It is the first-order differential output of the grayscale of the pixel at the current moment of the 45° reverse traversal. It is the first-order differential output of the grayscale of the pixel point at the next moment of 45° reverse traversal; It is the second-order differential output of the grayscale of the pixel at the current moment of the 45° reverse traversal. It is the second-order differential output of the grayscale of the pixel point at the next moment of 45° reverse traversal; is the input of the signal at the current moment, that is, the grayscale value of the current pixel; is the input of the signal at the next moment, that is, the grayscale value of the next pixel; The gray value of the pixel whose horizontal coordinate moves one grid to the right and whose vertical coordinate moves one grid upward; Pixel point when traversing in the reverse direction at 45° The gradient of Traverse vertically, i.e., 90°, from bottom to top. is the vertically reversed grayscale value, we get: （15）； In the formula, is the grayscale tracking output of the current pixel point in the vertical reverse traversal, It is the grayscale tracking output of the pixel point at the next moment of vertical reverse traversal; is the first-order differential output of the grayscale of the pixel at the current moment of vertical reverse traversal, It is the first-order differential output of the grayscale of the pixel point at the next moment of vertical reverse traversal; is the second-order differential output of the grayscale of the pixel at the current moment of vertical reverse traversal, It is the second-order differential output of the grayscale of the pixel point at the next moment of vertical reverse traversal; is the input of the signal at the current moment, that is, the grayscale value of the current pixel; is the input of the signal at the next moment, that is, the grayscale value of the next pixel; The gray value of the pixel point that moves one grid upward on the vertical coordinate; Pixel point when traversing vertically in reverse direction The gradient of Traverse from the lower right corner to the upper left corner in the 135° direction and take is the gray value of the 135° reverse direction, we get: （16）； In the formula, It is the grayscale tracking output of the pixel at the current moment of the 135° reverse traversal. It is the grayscale tracking output of the pixel point at the next moment of the 135° reverse traversal; is the first-order differential output of the grayscale of the pixel at the current moment of the 135° reverse traversal, It is the first-order differential output of the grayscale of the pixel point at the next moment of the 135° reverse traversal; It is the second-order differential output of the grayscale of the pixel at the current moment of the 135° reverse traversal. It is the second-order differential output of the grayscale of the pixel point at the next moment of the 135° reverse traversal; is the input of the signal at the current moment, that is, the grayscale value of the current pixel; is the input of the signal at the next moment, that is, the grayscale value of the next pixel; The grayscale value of the pixel whose horizontal coordinate moves one grid to the left and whose vertical coordinate moves one grid upward; Pixel point when traversing in reverse direction at 135° The gradient of The differential signals obtained by the forward and reverse traversals are averaged to eliminate the error caused by the phase lag and obtain the average gradient in the four directions. , , and , as shown below: （17）； （18）； （19）； （20）； The absolute values ​​of the gradient components in the four directions are taken and summed to obtain the gradient amplitude of the entire image, and the gradient amplitude image is obtained. As shown in formula (21), the gradient amplitude synthesized in the four directions is As shown below: （21）； The gradient directions of horizontal 0° and vertical 90° are obtained by the following formula, and their phase It is expressed as: （22）； The gradient directions of 45° and 135° are obtained by the following formula, and their phases are It is expressed as: （23）； According to the previously determined extreme noise point positions, these noise points are filtered on the gradient magnitude image, as shown in the following formula: （24）； In the formula, the set Indicates that the filter window size is 3×3, , All are collections Any value in is the gray value of the noise point. is the gray value of the 8-neighborhood point of the noise point, To take the median value, is the gray value of the noise point after filtering.

7. The image edge detection method based on adaptive extended state observer according to claim 6, characterized in that: The non-maximum suppression method is used to accurately locate edge points, as follows: For the gradient amplitude image, the gradient normal vector is calculated from four directions. When the gradient changes to show an edge, due to the wide change area, the gradient normal vector needs to be calculated in the horizontal, 45°, vertical and 135° directions. In the normal direction, it is determined whether it is a local maximum. If so, the current pixel point is retained, otherwise the grayscale value of the current pixel point is suppressed to 0; then the entire image is traversed, only the pixels with the local maximum value in the edge direction are retained, and a non-maximum suppressed image is output; finally, through multi-directional non-maximum suppression, the blurring effect caused by edge detection is eliminated, making the edge of the target image clearer and more detailed.

8. The image edge detection method based on adaptive extended state observer according to claim 7, characterized in that: The double threshold method is used to determine the edge connection line, as follows: After non-maximum suppression, although the edge information of the target image is significantly improved, the edge may be discontinuous due to some interference factors when extracting the edge line. In order to make the edge information of the image clearer and ensure the continuity of the edge, two thresholds are used for the image after non-maximum suppression. , Perform threshold segmentation and edge connection; first, determine the image pixel points The gradient magnitude Is it greater than the high threshold? If yes, then the point must be an edge point and is retained. If not, the gradient amplitude is determined. Is it between two thresholds? , Between If so, then the 8-neighborhood of the pixel is subjected to connectivity analysis to find the pixel Are there any pixels in the 8 neighboring pixels greater than the high threshold? If there is a pixel point, the current pixel point is an edge pixel point, which is used to connect strong edge points. Otherwise, the current pixel point is not an edge point and is regarded as an isolated noise point to be removed. If the gradient amplitude Less than low threshold , then the current pixel is definitely not an edge point, and its grayscale value is suppressed to 0; finally, the grayscale value of the edge point is set to 255, and the grayscale value of the non-edge point is set to 0 to form an edge contour, and a binary edge image is obtained as the final edge image.

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