Underwater Distorted Image Restoration Method for Cracks Detection of Bridge Piers by Underwater Robots

Abstract

The present invention discloses an underwater distorted image restoration method for detecting pier cracks by an underwater robot, including: observing the water conditions around the pier in real time and establishing a fluid stress model and its coordinate system accordingly; calculating the specific acting force range of the turbulent flow around the pier; calculating the offset displacement of the pixel points of the target image according to the specific acting force range of the turbulent flow around the pier; establishing a coordinate set of the original pixel points in the characteristic distortion points according to the obtained pixel point offset displacement; compensating the adjacent points around the original pixel points in the coordinate set by using an optical flow method based on polynomial expansion; repeating the steps until N pixel points and their adjacent point sets are obtained, and expanding the point set to obtain the restored image. The whole process of the present invention corrects the root cause of image distortion, which is the distortion of pixel points, rather than estimating the underwater space distortion situation, is more suitable for the image restoration of the deep water area of the pier, and is not affected by the interference of vortex turbulence, whether shallow or deep, on the quality of the final restored image.

Description

Technical Field

[0001] The present invention belongs to the field of underwater robot image processing, relates to underwater distorted image restoration technology, and specifically relates to an underwater distorted image restoration method applied to underwater robot pier crack detection. Background Art

[0002] In recent years, fully autonomous underwater robots have been widely used in the field of state observation and crack repair of the underwater part of piers because they can replace divers to work in dangerous environments with fast-flowing water for a long time. In this process, accurate underwater video images are an important basis for judging the state of piers and formulating repair plans. However, when the water flows at high speed past a fixed pier, regular vortices are formed on both sides of the pier. These vortices interfere with the density distribution of the water body, easily causing deformation and distortion of the underwater images collected by the underwater robot, thus affecting the formulation of the plan. Therefore, designing a technology that can eliminate periodic image distortion and distortion caused by vortices is of great help for the full-automatic observation and repair of piers.

[0003] For the technology of restoring distorted images of underwater robots, there are currently mainly methods such as constructing a water surface wave equation, compressive sensing, and lucky block fusion. The method of constructing a water surface wave equation and estimating the underwater space distortion accordingly to remove the image distortion caused by turbulence is only applicable to shallow waters and cannot be migrated to the deep water area of the pier. The compressive sensing method is highly sensitive to the initial value. Due to the interference of vortex turbulence, the choice of the initial value is easily affected by the shallow and deep water areas. Therefore, this method does not have stable accuracy for image processing when the underwater robot is operating on the pier. The lucky block fusion selects some parts of the distorted image blocks with higher quality in the video sequence for splicing to obtain the final complete image. Similarly, it is also affected by the shallow and deep of vortex turbulence, which affects the final splicing quality. Summary of the Invention

[0004] Object of the Invention: In order to overcome the deficiencies in the prior art, the present invention provides an underwater distorted image restoration method applied to underwater robot pier crack detection.

[0005] Technical Solution: To achieve the above object, the present invention provides an underwater distorted image restoration method applied to underwater robot pier crack detection, including the following steps:

[0006] S1: Real-time observe the water conditions around the pier through an underwater robot and establish a fluid stress model and its coordinate system accordingly;

[0007] S2: Based on the fluid stress model, calculate the specific acting force range of the turbulent flow around the pier;

[0008] S3: According to the specific acting force range of the turbulent flow around the pier, calculate the offset displacement of the target image pixel points;

[0009] S4: establishing a coordinate set of the original pixel points in the feature distortion point according to the obtained pixel point offset displacement;

[0010] S5: using an optical flow method based on polynomial expansion to compensate for the surrounding adjacent points of the original pixel in the coordinate set of step S4;

[0011] S6: Repeat steps S4 to S5 until N pixel points and their adjacent point sets are obtained, and expand the point set to obtain a restored image.

[0012] Furthermore, the specific forces of turbulence around the bridge pier in step S2 include the left wing vortex force in a top-down perspective, the right wing vortex force in a top-down perspective, and the bottom vortex force in a side perspective.

[0013] Furthermore, the calculation method of the left wing vortex force range in the top view is:

[0014] F is the stress of the bridge pier caused by turbulence impact, O is the stress center point of the bridge pier affected by a section of turbulence impact, F L is the initial stress decomposed from F around point O toward the left wing, F L 'For F L The maximum stress diffused around the left wing of the pier; the x-axis is the two opposite tangents passing through point O, the y-axis is perpendicular to the x-axis, and α is the angle between F and the x-axis;

[0015] Take the length ds L is the microelement of the left wing arch section in the coordinate system xOy; due to the viscous drag of the medium around the turbulent flow and the attenuation caused by the arc shape of the bridge pier, in order to obtain the initial decomposed stress F L , define a curvature rapid descent formula:

[0016]

[0017] Among them, F x is the x-direction component of F, F y is the y-direction component of F, ε refers to the viscosity coefficient of the medium surrounding the turbulence, and ds L / dr represents the micro-radian of the left wing arch segment; then F L The size is:

[0018]

[0019] When F L Diffusion to F L ', F's x L The axial force decays to 0, that is:

[0020]

[0021] Then F LThe size of ' is:

[0022]

[0023] In order to obtain F L The diffusion range of the L , using △F L Indicates F L The diffusion range, △F L The vector representation of is the size of the diffusion range, and the vector relationship is:

[0024]

[0025] Obtain That is, △F L Size, that is, F L The diffusion range of

[0026]

[0027] Where L is F L and △F L Angle.

[0028] Furthermore, the calculation method of the right wing vortex force range under the top view is:

[0029] F R is the initial stress decomposed from F around point O toward the left wing, F R 'For F R The maximum stress spreading around the right wing of the pier; take the length ds R is the infinitesimal element of the right wing arch section in the coordinate system xOy; by the curvature rapid drop formula, we can get:

[0030]

[0031] Among them, ds R / dr represents the micro-radian of the right wing arch segment; then F R The size is:

[0032]

[0033] When F R Diffusion to F R ', F's x R The axial force decays to 0, that is:

[0034]

[0035] Then F R The size of ' is:

[0036]

[0037] To obtain the diffusion range of F R the size of, introduce △F R , and use △F R to represent the diffusion range of F R . For the vector representation of △F R , then is the size of the diffusion range, and from the vector relationship, we get:

[0038]

[0039] Obtain That is, the size of △F R , which is the size of the diffusion range of F R :

[0040]

[0041] where R is the angle between F R and △F R .

[0042] Furthermore, the calculation method of the bottom vortex acting force range under the side view angle is as follows:

[0043] The z-axis is along the vertical upward direction of the pier, the y-axis is along the outward direction of the force application point O of the pier, and β is the angle between F and the z-axis; F H is the initial anti-seismic force after the turbulent flow F impacts the pier, and F H ' is the maximum stress of F H diffusing along the vertical direction of the pier to the bottom;

[0044] Take a longitudinal section of the pier with a height of h; due to the viscous drag of the medium around the turbulent flow and the longitudinal attenuation with height after the anti-seismic action of the pier with a certain stiffness, in order to obtain the initial anti-seismic force F H , define a speed reduction formula for anti-seismic attenuation:

[0045]

[0046] where 1 / εσ is the attenuation coefficient, ε refers to the viscosity coefficient of the medium around the turbulent flow, and σ refers to the stiffness of the pier; F z is the z-direction component force of F, then the size of F H is:

[0047]

[0048] When F H diffuses to F H ', the z-axis direction component force of F decays to 0, that is:

[0049]

[0050] Then F H ’s magnitude is:

[0051]

[0052] To obtain the diffusion range magnitude of F H , introduce △F H , and use △F H to represent the diffusion range of F H . For the vector representation of △F H , then is the magnitude of the diffusion range, and from the vector relationship, we get:

[0053]

[0054] Obtain That is, the magnitude of △F H , which is the diffusion range magnitude of F H :

[0055]

[0056] where H is the angle between F H and △F H .

[0057] Furthermore, the calculation method of the pixel point offset displacement in step S3 is specifically:

[0058] According to the stress model, the maximum action range △F L , △F R , △F H of the vortex diffusion formed after the turbulent flow impacts the bridge pier is obtained, and there is the vortex diffusion speed caused by each component force; it can be deduced from Newton's second law that the diffusion speed is:

[0059]

[0060] Then the magnitudes of the diffusion speeds in each direction are:

[0061]

[0062] where C is the integration constant; from the relationship between velocity and displacement, the magnitudes of the offset displacements S of the pixel points in each direction under the diffusion action are:

[0063]

[0064] Furthermore, step S4 is specifically:

[0065] The video frame sequence is drawn by the trajectories of a number of image pixels; the point trajectories are generated based on N feature distortion points captured by the camera in a certain frame:

[0066]

[0067] Among them, the coordinates (P xit , P yit ) represent the i-th pixel point among the N distortion points captured in a certain frame;

[0068] The displacement set of the i-th original pixel point obtained from step S3 is given as:

[0069]

[0070] Among them, S xit = S L - S R represents the horizontal point trajectory displacement of the original pixel point. When S L < S R that is, S xit < 0, the original pixel point is mainly affected by the right-wing vortex in the horizontal direction and is displaced to P xit on the right side of the pier; when S L > S R that is, S xit > 0, the original pixel point is mainly affected by the left-wing vortex in the horizontal direction and is displaced to P xit on the left side of the pier; S yit = S H represents the vertical point trajectory displacement of the original pixel point, that is, the original pixel point is displaced to P yit by the bottom vortex in the vertical direction to the pier foundation;

[0071] Thus, the coordinate set of the i-th original pixel point among the N distortion points captured in a certain frame is derived as:

[0072]

[0073] Further, the specific step S5 is as follows:

[0074] 1) Select a pixel point in the video sequence of a certain frame expressed as a second-order polynomial:

[0075]

[0076] 2) Assume that the distance between the selected point and the adjacent point gives the polynomial expansion of the unknown adjacent point:

[0077]

[0078] Among them, d is the assumed distance between the two points, are unknown adjacent points; A in formulas (29) and (30) 1 , A 2 , B 1 , B 2 are polynomial coefficients;

[0079] 3) Making the polynomial coefficients equal gives:

[0080] A 1 = A 2

[0081] B 1 = B 2 + A 1 d (31)

[0082] 4) Solving for the adjacent distance d gives:

[0083] d = A 1 -1 (B 1 - B 2 ) (32)

[0084] 5) The coordinate set of the adjacent points is represented as:

[0085]

[0086] Furthermore, the restored image in step S6 is represented as:

[0087]

[0088] Advantageous effects: Compared with the prior art, the present invention has the following advantages:

[0089] 1. By establishing a model based on real-time water conditions without relying on initial value sampling, the accuracy of the final image restoration result is improved.

[0090] 2. The whole process corrects the root cause of image distortion, which is the distortion of pixel points, rather than estimating the underwater space distortion. It is more suitable for image restoration in the deep water area of bridge piers and is not affected by vortex turbulence, ensuring the quality of the restored image. The quality of the image restoration is well guaranteed. Brief Description of the Drawings

[0091] Figure 1 is a schematic diagram of a fluid stress model and its coordinate system;

[0092] Figure 2 is a schematic diagram of a target distorted image;

[0093] Figure 3 is a comparison diagram of restored images. DETAILED DESCRIPTION

[0094] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0095] like Figure 1 As shown, the present invention provides an underwater distorted image restoration method for underwater robot pier crack detection, comprising the following steps:

[0096] S1: Use underwater robots to observe the water conditions around the bridge piers in real time and establish a fluid stress model and its coordinate system based on the water conditions;

[0097] When a bridge pier is impacted by a turbulent flow, it can be simplified into a stream of water spreading around the bridge pier to the two wings and the bottom with the impact point as the center, thus forming a vortex with a certain pattern. When the camera takes an image of the underwater part of the bridge pier, the strong vortex will cause the deformation and distortion of the target image, which will seriously affect the judgment of the state of the bridge pier. In order to eliminate the image distortion of the underwater part of the bridge pier, the present invention establishes the following Figure 1 The fluid stress model and its coordinate system are shown.

[0098] S2: Based on the fluid stress model, the specific force range of turbulent flow around the bridge pier is calculated;

[0099] The specific forces of turbulence around the bridge pier include the left wing vortex force from a top-down perspective, the right wing vortex force from a top-down perspective, and the bottom vortex force from a side perspective.

[0100] Reference Figure 1 , the calculation method of the left wing vortex force range from the top view is:

[0101] F is the stress of the bridge pier caused by turbulence impact, O is the stress center point of the bridge pier affected by a section of turbulence impact, F L is the initial stress decomposed from F around point O toward the left wing, F L 'For F L The maximum stress diffused around the left wing of the pier; the x-axis is the two opposite tangents passing through point O, the y-axis is perpendicular to the x-axis, and α is the angle between F and the x-axis;

[0102] Take the length ds L is the microelement of the left wing arch section in the coordinate system xOy; due to the viscous drag of the medium around the turbulent flow and the attenuation caused by the arc shape of the bridge pier, in order to obtain the initial decomposed stress F L , define a curvature rapid descent formula:

[0103]

[0104] Among them, F x is the x-direction component of F, F y is the y-direction component of F, ε refers to the viscosity coefficient of the medium around the turbulence (ε here has a real physical meaning, which can be measured in advance. Further measurement steps can be to collect water samples, let the measured liquid pass through the capillary at a certain flow rate with a metering pump, and then use a differential pressure gauge to measure the pressure difference at both ends of the capillary, which can represent the viscosity coefficient of the medium around the turbulence), ds L / dr represents the micro-radian of the left wing arch segment; then F L The size is:

[0105]

[0106] When F L Diffusion to F L ', F's x L The axial force decays to 0, that is:

[0107]

[0108] Then F L The size of ' is:

[0109]

[0110] Using △F L Indicates F L The diffusion range, △F L The vector representation of is the size of the diffusion range, and the vector relationship is:

[0111]

[0112] Obtain That is, △F L Size, that is, F L The diffusion range of

[0113]

[0114] Where L is F L and △F L Angle.

[0115] Reference Figure 1 , the calculation method of the right wing vortex force range from the top view is:

[0116] F R is the initial stress decomposed from F around point O toward the left wing, F R 'For F R The maximum stress spreading around the right wing of the pier; take the length dsR is the micro-element of the right-wing arch segment of the coordinate system x-O-y; similarly obtained from the curvature rapid decline formula:

[0117]

[0118] where, ds R / dr represents the radian of the micro-element of the right-wing arch segment; then the magnitude of F R is:

[0119]

[0120] When F R diffuses to F R ’, the x R -axis component force of F decays to 0, that is:

[0121]

[0122] Then the magnitude of F R ’ is:

[0123]

[0124] Use △F R to represent the diffusion range of F R , is the vector representation of △F R , then is the magnitude of the diffusion range, and from the vector relationship:

[0125]

[0126] Obtain That is, the magnitude of △F R , which is the magnitude of the diffusion range of F R :

[0127]

[0128] where, R is the angle between F R and △F R .

[0129] Referring to Figure 1 , the calculation method of the bottom vortex acting force range under the side view angle is:

[0130] The z-axis is along the vertical upward direction of the pier, the y-axis is along the outward direction of the force application point O of the pier, and β is the angle between F and the z-axis; F H is the initial anti-seismic force after the turbulent flow F impacts the pier, and F H ’ is the maximum stress when F H diffuses along the vertical direction of the pier to the bottom;

[0131] Take the longitudinal section of the pier with height h; due to the viscous drag of the medium around the turbulence and the longitudinal attenuation with height after the pier with a certain stiffness undergoes anti-seismic vibration, in order to obtain the initial anti-seismic force F H , define a speed reduction formula for anti-seismic attenuation:

[0132]

[0133] Among them, 1 / εσ is the attenuation coefficient, specifically caused by two parts of attenuation factors. ε refers to the viscosity coefficient of the medium around the turbulence (such as the curvature speed reduction formula before), and σ refers to the stiffness of the pier (which can be directly measured by an instrument according to the pier material), which is the main reason for the anti-seismic vibration in the longitudinal direction of the turbulence section. F z is the z-direction component force of F, then the magnitude of F H is:

[0134]

[0135] When F H diffuses to F H ’, the z-axis direction component force of F attenuates to 0, that is:

[0136]

[0137] Then the magnitude of F H ’ is:

[0138]

[0139] Use △F H to represent the diffusion range of F H , is the vector representation of △F H , then is the magnitude of the diffusion range. From the vector relationship, we get:

[0140]

[0141] Obtain That is, the magnitude of △F H , which is the magnitude of the diffusion range of F H :

[0142]

[0143] Among them, H is the included angle between F H and △F H .

[0144] S3: Calculate the offset displacement of the target image pixel points according to the specific acting force range of the turbulence around the pier;

[0145] According to the stress model, the maximum acting range △F of the eddy diffusion formed by the turbulence after impacting the pier is obtainedL , △F R , △F H , referring to Figure 1 , there is a vortex diffusion speed caused by each component force; the diffusion speed can be derived from Newton's second law as :

[0146]

[0147] Then the diffusion speed in each direction is:

[0148]

[0149] where C is the integration constant; from the relationship between velocity and displacement, the magnitude of the offset displacement S of each pixel point under the diffusion effect is:

[0150]

[0151] S4: According to the obtained offset displacement of the pixel points, establish the coordinate set of the original pixel points in the characteristic distortion points (i.e., the points captured by the camera);

[0152] The video frame sequence is drawn by the trajectories of a number of image pixel points; generate a point trajectory according to the N characteristic distortion points captured by the camera in a certain frame:

[0153]

[0154] where the coordinate (P xit , P yit ) represents the i-th pixel point among the N distorted points captured in a certain frame;

[0155] The displacement set of the i-th original pixel point obtained from step S3 is given as:

[0156]

[0157] where S xit = S L - S R represents the horizontal point trajectory displacement of the original pixel point. When S L < S R i.e., S xit < 0, the original pixel point is mainly affected by the right-wing vortex in the horizontal direction and is displaced to the right side of the pier to P xit ; when S L > S R i.e., S xit > 0, the original pixel point is mainly affected by the left-wing vortex in the horizontal direction and is displaced to the left side of the pier to P xit ; S yit = S HRepresents the displacement of the point trajectory in the vertical direction of the original pixel point, that is, the original pixel point is displaced to P in the vertical direction by the bottom vortex towards the pier foundation yit ;

[0158] From this, the coordinate set of the i-th original pixel point among the N distorted points captured in a certain frame is deduced as:

[0159]

[0160] S5: Since the camera only obtains a limited number of N feature distorted points, the original pixel points obtained in step S4 are also limited. The adjacent points around the original pixel points in the coordinate set obtained in step S4 are compensated by using the optical flow method based on polynomial expansion, specifically

[0161] 1) Select a pixel point in a video sequence of a certain frame Expressed as a second-order polynomial:

[0162]

[0163] 2) Assume the distance between the selected point and the adjacent point and give the polynomial expansion of the unknown adjacent point:

[0164]

[0165] Among them, d is the assumed distance between the two points, is the unknown adjacent point; A in formulas (29) and (30) 1 , A 2 , B 1 , B 2 are polynomial coefficients;

[0166] 3) Let the polynomial coefficients be equal to obtain:

[0167] A 1 = A 2

[0168] B 1 = B 2 + A 1 d (31)

[0169] 4) Solve for the adjacent distance d as:

[0170] d = A 1 -1 (B 1 - B 2 ) (32)

[0171] 5) The coordinate set of the adjacent point is expressed as:

[0172]

[0173] S6: Repeat steps S4 - S5 until N pixel points and their adjacent point sets are obtained, and expand the point set to obtain the restored image. The restored image is represented as:

[0174]

[0175] To verify the effectiveness and effect of the method of the present invention, in this embodiment, the method of the present invention is compared with existing image restoration methods by examples as follows:

[0176] In the experiment of this embodiment, a PVC pipe is used to simulate a bridge pier, and a target image with the mark of "three English words arranged in three lines and aligned left and right" is drawn on it. Then it is vertically placed in the experimental pool to simulate the actual work of detecting bridge pier cracks. By rotating the paddle at the bottom of the experimental pool to simulate the turbulent environment in the deep water area of the bridge pier, the target image is distorted, specifically as Figure 2 shown. Subsequently, the distorted image obtained by taking a forward photo with a camera is restored using the method of the present invention and three existing image restoration methods: constructing a water surface wave equation, compressive sensing, and lucky block fusion, specifically as Figure 3 shown. Figure 3 (a), (b), (c), and (d) in respectively represent the restored images of the method of constructing a water surface wave equation, the compressive sensing method, the lucky block fusion method, and the method of the present invention.

[0177] To objectively compare and evaluate the restoration method of the present invention and existing image restoration methods, structural similarity (SSIM) and image entropy are introduced as relevant evaluation indicators, as shown in Table 1.

[0178] Table 1 Evaluation indicators SSIM and image entropy

[0179]

[0180] Comparison Figure 2 and Figure 3 , the restored images of each method have been improved in clarity and recognition. Comparing the evaluation indicators in Table 1, the SSIM of the restoration method provided by the present invention is improved compared with existing image restoration methods, and the image entropy is reduced compared with existing image restoration methods. And the image quality is positively correlated with SSIM and negatively correlated with image entropy, indicating that the method of this patent has a certain improvement in the restoration effect compared with existing image restoration methods. Therefore, the underwater image distortion restoration method of the present invention is more suitable for the work of underwater robot detecting bridge pier cracks.

Claims

1. An underwater distorted image restoration method for underwater robot bridge pier crack detection, characterized in that: The steps include: S1: Use underwater robots to observe the water conditions around the bridge piers in real time and establish a fluid stress model and its coordinate system based on the water conditions; S2: Based on the fluid stress model, the specific force range of turbulent flow around the bridge pier is calculated; S3: Calculate the offset displacement of the pixel point of the target image according to the specific force range of the turbulent flow around the bridge pier; S4: establishing a coordinate set of the original pixel points in the feature distortion point according to the obtained pixel point offset displacement; S5: using an optical flow method based on polynomial expansion to compensate for the surrounding adjacent points of the original pixel in the coordinate set of step S4; S6: repeat steps S4 to S5 until N pixel points and their adjacent point sets are obtained, and expand the point sets to obtain the restored image; The specific forces of turbulence around the bridge pier in step S2 include the left wing vortex force in a top-down perspective, the right wing vortex force in a top-down perspective, and the bottom vortex force in a side perspective; The calculation method of the left wing vortex force range under the top view is: F is the stress of the bridge pier caused by turbulence impact, O is the stress center point of the bridge pier affected by a section of turbulence impact, F L is the initial stress decomposed from F around point O toward the left wing, F L 'For F L The maximum stress diffused around the left wing of the pier; the x-axis is the two opposite tangents passing through point O, the y-axis is perpendicular to the x-axis, and α is the angle between F and the x-axis; Take the length ds L is the microelement of the left wing arch section in the coordinate system xOy; due to the viscous drag of the medium around the turbulent flow and the attenuation caused by the arc shape of the bridge pier, in order to obtain the initial decomposed stress F L , define a curvature rapid descent formula: Among them, F x is the x-direction component of F, F y is the y-direction component of F, ε refers to the viscosity coefficient of the medium surrounding the turbulence, and ds L / dr represents the micro-radian of the left wing arch segment; then F L The size is: When F L Diffusion to F L ', F's x L The axial force decays to 0, that is: Then F L The size of ' is: In order to obtain F L The diffusion range of the L , using △F L Indicates F L The diffusion range, △F L The vector representation of is the size of the diffusion range, and the vector relationship is: Obtain That is, △F L Size, that is, F L The diffusion range of Where L is F L and △F L The angle of The calculation method of the right wing vortex force range under the top view is: F R is the initial stress decomposed from F around point O toward the left wing, F R 'For F R The maximum stress spreading around the right wing of the pier; take the length ds R is the infinitesimal element of the right wing arch section in the coordinate system xOy; by the curvature rapid drop formula, we can get: Among them, ds R / dr represents the micro-radian of the right wing arch segment; then F R The size is: When F R Diffusion to F R ', F's x R The axial force decays to 0, that is: Then F R The size of ' is: In order to obtain F R The diffusion range of the R , using △F R Indicates F R The diffusion range, △F R The vector representation of is the size of the diffusion range, and the vector relationship is: Obtain That is, △F R Size, that is, F R The diffusion range of Where R is F R and △F R The angle of The calculation method of the bottom vortex force range under the side view is: The z-axis is in the upward direction along the plumb bob of the bridge pier, and the y-axis is in the outward direction along the force point O of the bridge pier. β is the angle between F and the z-axis; F H is the initial force of the turbulent flow F after it impacts the bridge pier, F H 'For F H The maximum stress spreading along the plumb bob of the pier to the bottom; Take the longitudinal section of the bridge pier with a height of h; due to the viscous drag of the medium around the turbulent flow and the longitudinal attenuation of the bridge pier with a certain stiffness after the shock, in order to obtain the initial shock force F H , define a rapid descent formula for anti-shock attenuation: Among them, 1 / εσ is the attenuation coefficient, ε refers to the viscosity coefficient of the medium surrounding the turbulence, and σ refers to the stiffness of the bridge pier; F z is the z-direction component of F, then F H The size is: When F H Diffusion to F H ', the z-axis component of F decays to 0, that is: Then F H The size of ' is: In order to obtain F H The diffusion range of the H , using △F H Indicates F H The diffusion range, △F H The vector representation of is the size of the diffusion range, and the vector relationship is: Obtain That is, △F H Size, that is, F H The diffusion range of Where H is F H and △F H The angle of The calculation method of the target image pixel offset displacement in step S3 is specifically as follows: According to the stress model, the maximum range of eddy diffusion formed by turbulence after impacting the bridge pier is obtained. L , △F R , △F H , there is the vortex diffusion speed caused by each component force; the diffusion speed can be derived from Newton's second law for: The diffusion speed in all directions The size is: Among them, C is the integral constant; from the relationship between velocity and displacement, the magnitude of the offset displacement S of the pixel point in each direction due to diffusion is: The step S4 is specifically as follows: The video frame sequence is drawn from the trajectories of several image pixel points; the point trajectory is generated according to the N characteristic distortion points captured by the camera in a certain frame: Among them, the coordinate (P xit ,P yit ) represents capturing the i-th pixel point among N distorted points in a certain frame; The displacement set of the i-th original pixel point obtained in step S3 is given as: Among them, S xit =S L -S R Represents the horizontal point trajectory displacement of the original pixel point. When S L <S R That is S xit When <0, the original pixel point is mainly affected by the right wing vortex in the horizontal direction and moves to the right side of the bridge pier to P xit ; When S L >S R That is S xit When >0, the original pixel point is mainly affected by the left wing vortex in the horizontal direction and moves to the left side of the pier to P xit ; S yit =S H represents the point trajectory displacement in the vertical direction of the original pixel point, that is, the original pixel point is vertically displaced to the pier foundation by the bottom vortex to P yit ; It is deduced that the coordinate set of the i-th original pixel point among the N distorted points captured in a certain frame is:

2. The underwater distorted image restoration method for underwater robot pier crack detection according to claim 1 is characterized in that: The step S5 is specifically as follows: 1) Select a pixel in a certain frame of the video sequence Expressed as a second-order polynomial: 2) Assume that the distance between the selected point and the adjacent point gives the polynomial expansion of the unknown adjacent points: Where d is the distance between the two assumed points. are unknown adjacent points; in formulas (29) and (30), A1, A2, B1, B2 are polynomial coefficients; 3) Let the polynomial coefficients be equal to obtain: A1=A2 B1=B2+A1d (31) 4) Solve the adjacent distance d to be: <h2 style=";text-align:left;direction:ltr">d=A1<h2 style=";text-align:left;direction:ltr"> -1 <h2 style=";text-align:left;direction:ltr"> (B1-B2) (32) 5) Adjacent points The coordinate set of is expressed as:

3. The underwater distorted image restoration method for underwater robot pier crack detection according to claim 2 is characterized in that: The restored image in step S6 is represented as:

Images