Underwater distorted image restoration method applied to underwater robot pier crack detection

Abstract

The invention discloses an underwater distorted image restoration method applied to underwater robot bridge pier crack detection. The method comprises the following steps: observing the water condition around a bridge pier in real time and establishing a fluid stress model and a coordinate system thereof according to the water condition; calculating to obtain a specific acting force range of turbulent flow around the pier; according to the specific acting force range of turbulent flow around the pier, calculating to obtain the offset displacement of the pixel point of the target image; establishing a coordinate set of original pixel points in the feature distortion points according to the obtained pixel point offset displacement; compensating adjacent points around an original pixel point in the coordinate set by adopting an optical flow method based on polynomial expansion; and repeating the steps until N pixel points and an adjacent point set thereof are obtained, and expanding the point set to obtain a restored image. According to the method, correction is carried out by taking the root cause of image distortion as the distortion of the pixel points instead of estimating the distortion condition of the underwater space in the whole process, so that the method is more suitable for image restoration of the pier deepwater area, and the quality of the final restored image is not influenced by shallow depth interference of vortex turbulence.

Description

Technical Field

[0001] The 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 bridge pier crack detection. Background Art

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

[0003] At present, the main technologies for restoring distorted images of underwater robots include constructing water surface wave equations, compressed sensing, lucky block fusion, etc. The method of constructing water surface wave equations and estimating the distortion of underwater space based on them to remove image distortion caused by turbulence is only applicable to shallow waters and cannot be migrated to the deep water area of ​​bridge piers. The compressed sensing method is highly sensitive to the initial value. Since the interference of vortex turbulence has a great influence on the selection of initial values, this method does not have stable accuracy for the image processing of underwater robots when performing bridge pier operations. Lucky fast fusion selects some high-quality distorted image blocks in the video sequence to splice to obtain the final complete image. Similarly, the interference of vortex turbulence affects the final splicing quality. Summary of the invention

[0004] Purpose of the invention: In order to overcome the deficiencies in the prior art, a method for restoring underwater distorted images for use in underwater robot pier crack detection is provided.

[0005] Technical solution: To achieve the above-mentioned purpose, the present invention provides an underwater distorted image restoration method for underwater robot pier crack detection, comprising the following steps:

[0006] 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;

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

[0008] 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;

[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 arch segment 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-curvature of the 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 L The 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 arch segment in the coordinate system xOy; by the curvature rapid drop formula, we can get:

[0030]

[0031] Among them, ds R / dR represents the arc of the 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] 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:

[0038]

[0039] Obtain That is, △F R Size, that is, F R The diffusion range of

[0040]

[0041] Where R is F R and △F R Angle.

[0042] Furthermore, the calculation method of the bottom vortex force range under the side viewing angle is:

[0043] 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;

[0044] 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:

[0045]

[0046] 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:

[0047]

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

[0049]

[0050] Then F H The size of ' is:

[0051]

[0052] 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:

[0053]

[0054] Obtain That is, △F H Size, that is, F H The diffusion range of

[0055]

[0056] Where H is F H and △F H Angle.

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

[0058] 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:

[0059]

[0060] The diffusion speed in all directions The size is:

[0061]

[0062] 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:

[0063]

[0064] Furthermore, the step S4 is specifically as follows:

[0065] 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:

[0066]

[0067] Among them, the coordinate (P xit ,P yit ) represents capturing the i-th pixel point among N distorted points in a certain frame;

[0068] The displacement set of the i-th original pixel point obtained in 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 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 ;

[0071] 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:

[0072]

[0073] Furthermore, the step S5 is specifically as follows:

[0074] 1) Select a pixel in a certain frame of the video sequence 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 points:

[0077]

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

[0079] 3) Let the polynomial coefficients be equal to obtain:

[0080]

[0081] 4) Solve the adjacent distance d to be:

[0082]

[0083] 5) Adjacent points The coordinate set of is expressed as:

[0084]

[0085] Furthermore, the restored image in step S6 is represented as:

[0086]

[0087] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0088] 1. The model established through real-time water conditions does not rely on the sampling of initial values, thereby improving the accuracy of the final image restoration result.

[0089] 2. The whole process takes the distortion of pixels as the fundamental cause of image distortion as the object for correction, rather than estimating the distortion of underwater space. This method is more suitable for image restoration in deep water areas of bridge piers, and is not affected by the shallowness or depth of vortex turbulence, so the quality of the final restored image is well guaranteed. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 is a schematic diagram of the fluid stress model and its coordinate system;

[0091] Figure 2 Schematic diagram of the target distorted image;

[0092] Figure 3 Comparison chart of restored images. DETAILED DESCRIPTION

[0093] 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.

[0094] 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:

[0095] 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;

[0096] 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.

[0097] S2: Based on the fluid stress model, the specific force range of turbulent flow around the bridge pier is calculated;

[0098] 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.

[0099] Reference Figure 1 , the calculation method of the left wing vortex force range from the top view is:

[0100] 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;

[0101] Take the length ds L is the microelement of the arch segment 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:

[0102]

[0103] Among them, F x is the x-direction component of F, F yis 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-curvature of the arch segment; then F L The size is:

[0104]

[0105] When F L Diffusion to F L ', F's x L The axial force decays to 0, that is:

[0106]

[0107] Then F L The size of ' is:

[0108]

[0109] 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:

[0110]

[0111] Obtain That is, △F L Size, that is, F L The diffusion range of

[0112]

[0113] Where L is F L and △F L Angle.

[0114] Reference Figure 1 , the calculation method of the right wing vortex force range from the top view is:

[0115] 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 arch segment in the coordinate system xOy; by the curvature rapid drop formula, we can get:

[0116]

[0117] Among them, ds R / dR represents the arc of the arch segment; then F R The size is:

[0118]

[0119] When F R Diffusion to F R ', F's x R The axial force decays to 0, that is:

[0120]

[0121] Then F R The size of ' is:

[0122]

[0123] Use △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:

[0124]

[0125] Obtain That is, △F R Size, that is, F R The diffusion range of

[0126]

[0127] Where R is F R and △F R Angle.

[0128] Reference Figure 1 , the calculation method of the bottom vortex force range under the side view is:

[0129] 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;

[0130] 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 FH , define a rapid descent formula for anti-shock attenuation:

[0131]

[0132] Among them, 1 / εσ is the attenuation coefficient. Specifically, there are two attenuation factors. ε refers to the viscosity coefficient of the medium around the turbulence (such as the curvature drop formula above), and σ refers to the stiffness of the pier (which can be directly measured by the instrument according to the pier material), which is the main reason for the turbulent longitudinal section rebound. z is the z-direction component of F, then F H The size is:

[0133]

[0134] When F H Diffusion to F H ', the z-axis component of F decays to 0, that is:

[0135]

[0136] Then F H The size of ' is:

[0137]

[0138] Use △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:

[0139]

[0140] Obtain That is, △F H Size, that is, F H The diffusion range of

[0141]

[0142] Where H is F H and △F H Angle.

[0143] 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;

[0144] 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 , refer to Figure 1, there is the vortex diffusion speed caused by each component force; the diffusion speed can be derived from Newton's second law for:

[0145]

[0146] The diffusion speed in all directions The size is:

[0147]

[0148]

[0149] 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:

[0150]

[0151] S4: establishing a coordinate set of the original pixel point in the feature distortion point (i.e., the point captured by the camera) according to the obtained pixel point offset displacement;

[0152] 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:

[0153]

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

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

[0156]

[0157] 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 Hrepresents 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 ;

[0158] 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:

[0159]

[0160] S5: Since the camera only obtains a limited number of N characteristic distortion points, the original pixel points obtained in step S4 are also limited. The optical flow method based on polynomial expansion is used to compensate the surrounding adjacent points of the original pixel points in the coordinate set of step S4. Specifically,

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

[0162]

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

[0164]

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

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

[0167]

[0168] 4) Solve the adjacent distance d to be:

[0169] d=A 1 -1 (B 1 -B 2 ) (32)

[0170] 5) Adjacent points The coordinate set of is expressed as:

[0171]

[0172] S6: Repeat steps S4 to S5 until N pixel points and their adjacent point sets are obtained, and the point sets are expanded to obtain the restored image. The restored image is expressed as:

[0173]

[0174] In order to verify the effectiveness and effect of the method of the present invention, the method of the present invention is compared with the existing image restoration method in this embodiment, as follows:

[0175] In the experiment of this embodiment, a PVC tube is used to simulate a bridge pier, and a target image of "three English words in three lines aligned left and right" is drawn on it as a mark, and then it is placed vertically in an experimental pool to simulate the actual work of detecting cracks in bridge piers. The target image is distorted by rotating the paddle at the bottom of the experimental pool to simulate the turbulent environment in the deep water of the bridge pier. Figure 2 Then, the distorted image obtained by forward shooting with the camera is restored by using the method of the present invention and three existing image restoration methods, namely, constructing a water surface wave equation, compressed sensing, and lucky block fusion. Figure 3 shown. Figure 3 (a), (b), (c), and (d) represent the restored images of the water surface wave equation construction method, the compressed sensing method, the lucky block fusion method, and the method of the present invention, respectively.

[0176] In order to objectively compare and evaluate the restoration method of the present invention with the existing image restoration method, structural similarity (SSIM) and image entropy are introduced as relevant evaluation indicators, as shown in Table 1.

[0177] Table 1 Evaluation index SSIM and image entropy

[0178]

[0179] contrast 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 the existing image restoration method, and the image entropy is reduced compared with the existing image restoration method. The image quality is positively correlated with SSIM and negatively correlated with image entropy, indicating that the restoration effect of the patented method is improved compared with the existing image restoration method. Therefore, the underwater image distortion image restoration method of the present invention is more suitable for underwater robots to detect 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 set to obtain a restored image.

2. The underwater distorted image restoration method for underwater robot pier crack detection according to claim 1 is characterized in that: 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.

3. The underwater distorted image restoration method for underwater robot pier crack detection according to claim 2 is characterized in that: 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 arch segment 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-curvature of the 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 Angle.

4. The underwater distorted image restoration method for underwater robot pier crack detection according to claim 2 is characterized in that: 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 arch segment in the coordinate system xOy; by the curvature rapid drop formula, we can get: Among them, ds R / dR represents the arc of the 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 Angle.

5. The underwater distorted image restoration method for underwater robot pier crack detection according to claim 2 is characterized in that: 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 Angle.

6. The underwater distorted image restoration method for underwater robot pier crack detection according to claim 2 is characterized in that: The calculation method of the 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:

7. The underwater distorted image restoration method for underwater robot pier crack detection according to claim 6 is characterized in that: 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 >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:

8. The underwater distorted image restoration method for underwater robot pier crack detection according to claim 7 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: 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:

9. The underwater distorted image restoration method for underwater robot pier crack detection according to claim 8, characterized in that: The restored image in step S6 is represented as:

Images