A Method and System for Underwater Calibration of Composite Polarization States Based on an Equifocal Refraction Model

Abstract

This disclosure relates to a method and system for underwater calibration of composite polarization states based on an equal focal length refraction model. The method includes: approximating the incident angle of light under small-angle conditions by simultaneously applying geometrical optics imaging equations and Snell's law of refraction, obtaining the transformation relationship between the coordinates of the underwater imaging point and the coordinates of the theoretical imaging point in air, and establishing an equal focal length refraction mathematical model for the underwater camera and projector; designing a composite polarization state encoded sinusoidal projection calibration pattern based on this model; utilizing the polarized light projection characteristics, encoding the horizontally polarized light of the green channel of the calibration pattern into horizontal cosine fringes, and the vertically polarized light of the blue channel into vertical sine fringes; superimposing the cosine and sine fringes to generate two sets of orthogonal polarization state fringe patterns, and performing phase calculation and reprojection error optimization based on the equal focal length refraction mathematical model to achieve parameter calibration. This method can significantly improve the calibration accuracy and efficiency of underwater visual measurements.

Description

Technical Field

[0001] This disclosure relates to the field of computer vision, and in particular to a method and system for underwater calibration of composite polarization states based on an equal focal length refraction model. Background Technology

[0002] High-precision underwater 3D topography measurement is of irreplaceable value in key fields such as marine resource exploration, underwater engineering construction, archaeological excavation, and biological research. Optical 3D measurement technology, with its advantages of non-contact operation, high precision, and high resolution, is highly mature in air. However, when applied to underwater environments, the difference in refractive index between water and air causes unpredictable deflection of the path due to Insnell's law, leading to optical path distortion, imaging position shift, and drift of equivalent system parameters, rendering traditional air-based calibration models completely ineffective. Furthermore, multiple scattering caused by suspended particles in water significantly reduces fringe contrast, blurs image details, and introduces phase errors, severely degrading the signal-to-noise ratio and reconstruction accuracy. Existing methods for addressing refraction problems mainly include: direct underwater calibration, refraction compensation models, "virtual pinhole camera" models, and iterative optimization methods based on ray tracing. These methods are limited by the difficulty in balancing model complexity and accuracy, high sensitivity to window parameters (thickness, refractive index, pose), and a general lack of effective suppression mechanisms for scattering noise, resulting in significant noise interference in the extraction of calibration feature points.

[0003] Against this backdrop, the "equal focal length refraction model" provides a practical path for solving refraction problems. Research has found that when the camera's optical axis is strictly perpendicular to the planar window, underwater imaging can be equivalent to a "virtual camera" located on the air side, with its effective focal length matching the original air focal length and the principal point remaining essentially unchanged. However, its practical application is limited by installation errors due to non-strictly perpendicular optical axes, window non-idealities (such as uneven thickness and surface roughness), and interference from scattering noise on calibration feature extraction. To overcome the scattering noise bottleneck, polarization technology is introduced into the fringe projection system. However, the lack of a unified mathematical model that deeply couples the equal focal length refraction model with composite polarization coding makes it difficult to guide system optimization; the lack of a polarization encoding / decoding system architecture specifically designed for underwater fringe projection makes it impossible to maximize scattering suppression and feature enhancement effects; and the absence of an efficient and robust underwater calibration process based on polarization-enhanced images makes it impossible to systematically solve the problem of accurate calibration of internal / external parameters and interface parameters.

[0004] Therefore, developing a composite polarization state-coded fringe projection underwater calibration method and system based on an equal focal length refraction model, deeply integrating a simplified geometric optics model with polarization physics information processing, is an inevitable direction to overcome the dual constraints of refraction and scattering and achieve high-precision, high-efficiency, and high-robustness underwater three-dimensional measurement. Summary of the Invention

[0005] To address the issues of missing point cloud information in the 3D topography of underwater stripe patterns due to phase unfolding calculation errors, non-sinusoidal distribution errors, and phase saturation errors caused by HDR object surfaces, this disclosure proposes a composite polarization state underwater calibration method based on an equal focal length refraction model to solve these problems.

[0006] According to one aspect of this disclosure, an underwater calibration method for composite polarization states based on an equal focal length refraction model is provided, comprising:

[0007] S10. By combining the geometric optical imaging equations and Snell's law of refraction, the incident angle of light is approximated under small angle conditions to obtain the transformation relationship between the underwater imaging point coordinates and the theoretical imaging point coordinates in the air. Based on the transformation relationship, an equal focal length refraction mathematical model for the underwater camera and projector is established.

[0008] S20. Based on the aforementioned equal focal length refraction mathematical model, design a composite polarization state encoded sinusoidal projection calibration pattern;

[0009] S30. Utilizing the characteristics of polarized light projection, the horizontally polarized light of the green channel of the composite polarization state encoded sinusoidal projection calibration pattern is encoded into a cosine fringe in the horizontal direction, and the vertically polarized light of the blue channel of the composite polarization state encoded sinusoidal projection calibration pattern is encoded into a sinusoidal fringe in the vertical direction.

[0010] S40. The cosine stripes in the horizontal direction and the sine stripes in the vertical direction are superimposed to generate two sets of orthogonal polarization stripe patterns.

[0011] S50. Based on the aforementioned equal focal length refraction mathematical model, phase calculation and reprojection error optimization are performed on the two sets of orthogonal polarization fringe patterns to achieve parameter calibration.

[0012] Preferably, by combining the geometrical optical imaging equations and Snell's law of refraction, an approximation is made for the incident angle of light under small angle conditions, which is expressed as:

[0013] ,

[0014] In the formula, The coordinates of the underwater imaging point, It represents the distance from the interface between the media and the outer focal point of the lens. Expressed as focal length, In the representation space X Axis coordinates In spatial coordinates Z Axis coordinates and These represent the refractive indices of water and air, respectively. and These are the angles between the imaging ray and the normals of the water and air interfaces, respectively.

[0015] Preferably, the conversion relationship between the underwater imaging point coordinates and the theoretical imaging point coordinates in air is as follows:

[0016] ,

[0017] In the formula, The coordinates of the underwater imaging point, These are the coordinates of the theoretical imaging point in the air.

[0018] Preferably, the horizontally polarized light of the green channel of the composite polarization state encoded sinusoidal projection calibration pattern is encoded into a cosine fringe in the horizontal direction, represented as:

[0019] ,

[0020] ,

[0021] ,

[0022] In the formula, The x-axis coordinate of the projector coordinate system For a period of time, It is a green light source. Let be the total green light intensity of a certain row of pixels. This represents the intensity distribution of the horizontal polarization state of the pixels in this row.

[0023] Preferably, the vertically polarized light of the blue channel of the composite polarization state encoded sinusoidal projection calibration pattern is encoded into sinusoidal fringes in the vertical direction, as follows:

[0024] ,

[0025] ,

[0026] ,

[0027] In the formula, The x-axis coordinate of the projector coordinate system For a period of time, It is a blue light source. Let be the total blue light intensity of a certain row of pixels. This represents the intensity distribution of the vertical polarization state of the pixels in this row.

[0028] Preferably, the cosine fringes in the horizontal direction and the sine fringes in the vertical direction are superimposed to generate two sets of orthogonal polarization fringe patterns, represented as follows:

[0029] ,

[0030] In the formula, The coordinates of the pixels. The image shows the cosine fringe pattern in the horizontal direction recorded by a polarizing camera when the front polarizer is set to 0°. The vertical sinusoidal fringe pattern recorded by the polarizing camera when the front polarizer is set to 90°.

[0031] Preferably, phase calculation and reprojection error optimization are performed on the two sets of orthogonal polarization fringe patterns to achieve parameter calibration, including:

[0032] The wrapping phase is extracted from two sets of orthogonal polarization fringe patterns using the phase-shifting method, and the two sets of wrapping phases are decoded using complementary Gray codes to obtain the absolute phase distribution.

[0033] The three-dimensional coordinates of the feature points on the calibration plate are calculated based on the two sets of orthogonal polarization stripe patterns.

[0034] Based on the transformation relationship between underwater imaging point coordinates and theoretical imaging point coordinates in air, a reprojection error function is constructed and the camera's intrinsic and extrinsic parameters are optimized until the error converges.

[0035] According to one aspect of this disclosure, a composite polarization state underwater calibration system based on an equal focal length refraction model is provided, comprising:

[0036] The equal focal length refraction mathematical model construction module, by combining the geometric optical imaging equations and Snell's law of refraction, approximates the incident angle of light under small angle conditions, and obtains the transformation relationship between the coordinates of the underwater imaging point and the coordinates of the theoretical imaging point in the air. Based on the transformation relationship, the equal focal length refraction mathematical model of the underwater camera and projector is established.

[0037] The composite polarization state encoded sinusoidal projection calibration pattern design module designs a composite polarization state encoded sinusoidal projection calibration pattern based on the aforementioned equal focal length refraction mathematical model.

[0038] The polarization light encoding module utilizes the polarization light projection characteristics to encode the horizontally polarized light of the green channel of the composite polarization state encoded sinusoidal projection calibration pattern into a cosine fringe in the horizontal direction, and to encode the vertically polarized light of the blue channel of the composite polarization state encoded sinusoidal projection calibration pattern into a sinusoidal fringe in the vertical direction.

[0039] The orthogonal polarization stripe pattern generation module superimposes the cosine stripes in the horizontal direction and the sine stripes in the vertical direction to generate two sets of orthogonal polarization stripe patterns.

[0040] The parameter calibration module, based on the equal focal length refraction mathematical model, performs phase calculation and reprojection error optimization on the two sets of orthogonal polarization fringe patterns to achieve parameter calibration.

[0041] According to one aspect of this disclosure, an electronic device is provided, comprising: a processor; a memory for storing processor-executable instructions; wherein the processor is configured to: execute the above-described underwater calibration method for composite polarization states based on an equal focal length refraction model.

[0042] According to one aspect of this disclosure, a computer-readable storage medium is provided that stores computer program instructions thereon, which, when executed by a processor, implement the above-described underwater calibration method for composite polarization states based on an equal focal length refraction model.

[0043] Compared to the prior art, the beneficial effects of this disclosure are as follows:

[0044] 1) This disclosure uses an equal focal length refraction model to linearly magnify the underwater image into an air image in order to complete the calibration of system parameters and effectively solve the problem of the influence of light refraction on the underwater imaging quality.

[0045] 2) This disclosure can obtain a set of phase-shifted fringe patterns with mutually perpendicular polarization states by calculating the composite polarization state projection fringe pattern captured by the camera, thereby reducing the number of projection fringe patterns required.

[0046] 3) This disclosure can significantly improve the accuracy of underwater calibration and has better equipment parameter calibration performance compared with the traditional gray stripe method.

[0047] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure.

[0048] Other features and aspects of this disclosure will become clear from the following detailed description of exemplary embodiments with reference to the accompanying drawings. Attached Figure Description

[0049] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the specification, serve to illustrate the technical solutions of this disclosure.

[0050] Figure 1 A flowchart of an underwater calibration method for composite polarization states based on an equal focal length refraction model is shown.

[0051] Figure 2 The flowchart for generating composite polarization state encoded fringes is shown;

[0052] Figure 3 This diagram illustrates the propagation of light in underwater camera imaging.

[0053] Figure 4 A stereoscopic view of the equivalent imaging plane of the underwater camera is displayed.

[0054] Figure 5This shows a schematic diagram of the composite polarization state encoded sinusoidal projection calibration pattern design;

[0055] Figure 6 A schematic diagram of the underwater calibration plate's pose is shown;

[0056] Figure 7 A schematic diagram of the orientation of the calibration plate in the air is shown;

[0057] Figure 8 A schematic diagram showing the positional relationship between the calibration plate, camera, and projector in the air is displayed.

[0058] Figure 9 A schematic diagram showing the positional relationship between the underwater calibration plate and the camera and projector is displayed.

[0059] Figure 10 This diagram illustrates the distribution of camera feature point reprojection errors.

[0060] Figure 11 This diagram illustrates the reprojection error distribution of feature points on the projector.

[0061] Figure 12 The diagram shows a structural block diagram of an underwater calibration system for composite polarization states based on an equal focal length refraction model, according to an embodiment of this disclosure. Detailed Implementation

[0062] Various exemplary embodiments, features, and aspects of this disclosure will now be described in detail with reference to the accompanying drawings. The same reference numerals in the drawings denote elements that have the same or similar functions. Although various aspects of the embodiments are shown in the drawings, they are not necessarily drawn to scale unless specifically indicated otherwise.

[0063] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments.

[0064] In this document, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Furthermore, the term "at least one" in this document means any combination of at least two of any one or more elements. For example, including at least one of A, B, and C can mean including any one or more elements selected from the set consisting of A, B, and C.

[0065] Furthermore, to better illustrate this disclosure, numerous specific details are set forth in the following detailed description. Those skilled in the art will understand that this disclosure can be practiced without certain specific details. In some instances, methods, means, components, and circuits well known to those skilled in the art have not been described in detail in order to highlight the main points of this disclosure.

[0066] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0067] Example 1

[0068] Based on the above ideas, this invention proposes an underwater calibration method for composite polarization states based on an equal focal length refraction model. Figure 1 A flowchart of an underwater calibration method for composite polarization states based on an equal focal length refraction model is shown. The method includes:

[0069] S10. By combining the geometric optical imaging equations and Snell's law of refraction, the incident angle of light is approximated under small angle conditions to obtain the transformation relationship between the underwater imaging point coordinates and the theoretical imaging point coordinates in the air. Based on the transformation relationship, an equal focal length refraction mathematical model for the underwater camera and projector is established.

[0070] S20. Based on the aforementioned equal focal length refraction mathematical model, design a composite polarization state encoded sinusoidal projection calibration pattern;

[0071] S30. Utilizing the characteristics of polarized light projection, the horizontally polarized light of the green channel of the composite polarization state encoded sinusoidal projection calibration pattern is encoded into a cosine fringe in the horizontal direction, and the vertically polarized light of the blue channel of the composite polarization state encoded sinusoidal projection calibration pattern is encoded into a sinusoidal fringe in the vertical direction.

[0072] S40. The cosine stripes in the horizontal direction and the sine stripes in the vertical direction are superimposed to generate two sets of orthogonal polarization stripe patterns.

[0073] S50. Based on the aforementioned equal focal length refraction mathematical model, phase calculation and reprojection error optimization are performed on the two sets of orthogonal polarization fringe patterns to achieve parameter calibration.

[0074] This disclosure provides an underwater calibration method for composite polarization states based on an equal focal length refraction model. It deeply integrates a simplified geometric optics model with polarization physics information processing, representing a necessary direction for overcoming the dual constraints of refraction and scattering to achieve high-precision, high-efficiency, and highly robust underwater three-dimensional measurement. This requires not only innovative polarization encoding / decoding architectures at the optical system design level, but also collaborative efforts in model construction (unified refraction-polarization model), information processing (multi-modal data fusion), and algorithm development (noise-resistant calibration process). Specifically, it includes the following steps:

[0075] S10. By combining the geometric optical imaging equations and Snell's law of refraction, the incident angle of light is approximated under small angle conditions to obtain the transformation relationship between the underwater imaging point coordinates and the theoretical imaging point coordinates in the air. Based on the transformation relationship, an equal focal length refraction mathematical model for the underwater camera and projector is established.

[0076] In this embodiment, an underwater measurement calibration system was constructed. The system mainly includes: a 3LCD-based projector (EPSON CB-FH52, 1920×1080 pixel), a polarized monochrome CMOS camera (FLIR BFS-U3-51S5P-C, 2448×2048 pixel), a precision-machined black-and-white dot calibration plate, and a customized transparent water tank. The calibration plate employs an 11×9 black-and-white circular array design with optimized contrast, containing five large white dots (5mm in diameter) for marking the calibration plate's direction during calibration, and smaller white dots (2.5mm in diameter). The center-to-center distance between each dot is 10mm. The experimental water tank is constructed from 60cm×30cm×30cm, 5mm thick PMMA (polymethyl methacrylate) acrylic glass.

[0077] Figure 2 The overall process from projecting composite polarization state-coded fringes to capturing an image with a polarization camera is shown. Among them, This represents four sinusoidal grayscale fringes with different phase shifts, vertical and horizontal. This represents four different phase-shifted horizontal polarization state encoded fringes. This represents four different phase-shifted vertical polarization state encoded fringes. This represents four different phase-shifted composite polarization state encoded fringes. These include sinusoidal fringes emitted by the projector in the vertical direction (green channel, encoded as 0° horizontal polarization) and in the horizontal direction (blue channel, encoded as 90° vertical polarization). The light in the green channel is modulated into a horizontal polarization state (0°), and the light in the blue channel is modulated into a vertical polarization state (90°). The final projected composite polarization state encoded fringes simultaneously contain two orthogonal polarization information.

[0078] Furthermore, by establishing a mathematical model of refraction at the same focal length for the underwater camera and projector, and by simultaneously applying the geometrical optical imaging equations and Snell's law of refraction, the following quantitative relationship can be established:

[0079] ,

[0080] In the formula, The coordinates of the underwater imaging point, It represents the distance from the interface between the media and the outer focal point of the lens. Expressed as focal length, In the representation space X Axis coordinates In spatial coordinates Z Axis coordinates and These represent the refractive indices of water and air, respectively. and These are the angles between the imaging ray and the normals of the water and air interfaces, respectively.

[0081] As can be seen from the above formula derivation, the relationship between the object and the imaging position during underwater imaging can no longer be directly applied using the optical imaging principles based on air media:

[0082] ,

[0083] A schematic diagram of light propagation in underwater camera imaging, as shown below. Figure 3 As shown. CCD represents the camera. Represents an underwater point. Indicates the imaging point, It represents the distance from the interface between the media and the outer focal point of the lens. Represented as the optical center, Expressed as focal length, and These represent the refractive indices of water and air, respectively. and The angle between the imaging ray and the normal to the water-air interface is shown in the diagram. The light path is as follows: Light emitted from an underwater object is refracted (bent) as it passes through the water and the camera's protective window before finally entering the camera to form an image. Because water has a higher refractive index than air, underwater images appear "magnified," with an actual focal length longer than in air (approximately 1.33 times). When the object is far from the camera, underwater imaging can be approximated as a simple magnification of air imaging, facilitating calibration calculations. The equivalent imaging plane of an underwater camera is shown in the diagram below. Figure 4 As shown, this visually demonstrates that underwater camera imaging can be equivalent to "shooting with a longer focal length in air." It's clear that the same object appears larger and closer underwater than in air. This is because underwater images cannot provide object distance. The three-dimensional spatial information, relying solely on the camera's intrinsic parameters, is the imaging point in the water medium. Theoretical imaging point in air It is difficult to establish a deterministic mapping relationship between them. Due to the limitations of two-dimensional projection, it is impossible to deduce the corresponding air medium imaging results from a single underwater image. When the incident angle... and When the incident angle is small, the sine and tangent of the angle can be approximated by the incident angle, and the above equation is equivalent to:

[0084] ,

[0085] By simplification and solution, we can obtain:

[0086] ,

[0087] The difference between underwater and air images can be seen by comparison.

[0088] ,

[0089] Furthermore, it can be concluded that the point P Distance from camera and At that time, it can be deduced that:

[0090] ,

[0091] The conversion relationship between the coordinates of underwater imaging points and the coordinates of theoretical imaging points in air is summarized as follows:

[0092] ,

[0093] In the formula, The coordinates of the underwater imaging point, These are the coordinates of the theoretical imaging point in the air.

[0094] As shown in the above equation, the imaging results in an underwater environment can be simplified to a linear magnification process of imaging in air. The magnification is determined by the ratio of the refractive indices of water and air. Decide.

[0095] S20. Based on the aforementioned equal focal length refraction mathematical model, design a composite polarization state encoded sinusoidal projection calibration pattern.

[0096] In this embodiment, a schematic diagram of the composite polarization state encoded sinusoidal projection calibration pattern design is shown below. Figure 5As shown in the figure, this pattern utilizes the polarization characteristics of a 3LCD projector, encoding the green channel as sinusoidal fringes in the horizontal direction (0° polarization state) and the blue channel as sinusoidal fringes in the vertical direction (90° polarization state). The two orthogonal polarization states of fringes are superimposed to form a composite coded pattern. The sinusoidal fringes presented in the figure exhibit periodic brightness variations, with a 90° phase difference between the horizontal and vertical fringes, distinguished by green and blue, corresponding to different polarization directions. This innovative design allows for the simultaneous acquisition of two orthogonal polarization information in a single projection, significantly improving the calibration efficiency and accuracy of underwater 3D measurement systems compared to traditional grayscale fringe methods that require multiple projections.

[0097] Regarding the stripe coding strategy, the mathematical characterization of the composite polarization state coded stripe system can be expressed as follows: assuming the green light source emitted by the projector is... Blue light source is The intensity function of its composite polarization state encoded sinusoidal fringes is periodic. T change.

[0098] S30. Utilizing the characteristics of polarized light projection, the horizontally polarized light of the green channel of the composite polarization state encoded sinusoidal projection calibration pattern is encoded into a cosine fringe in the horizontal direction, and the vertically polarized light of the blue channel of the composite polarization state encoded sinusoidal projection calibration pattern is encoded into a sinusoidal fringe in the vertical direction.

[0099] In this embodiment, when the horizontal axis coordinate of the projector coordinate system is used... When the independent variable is 'cosine', the horizontally polarized light of the green channel of the composite polarization state encoded sinusoidal projection calibration pattern is encoded into a cosine fringe in the horizontal direction, represented as:

[0100] ,

[0101] ,

[0102] ,

[0103] In the formula, The x-axis coordinate of the projector coordinate system For a period of time, It is a green light source. Let be the total green light intensity of a certain row of pixels. This represents the intensity distribution of the horizontal polarization state of the pixels in this row.

[0104] Encoding the vertically polarized light of the blue channel of the composite polarization-state encoded sinusoidal projection calibration pattern into sinusoidal fringes in the vertical direction is represented as:

[0105] ,

[0106] ,

[0107] ,

[0108] In the formula, The x-axis coordinate of the projector coordinate system For a period of time, It is a blue light source. Let be the total blue light intensity of a certain row of pixels. This represents the intensity distribution of the vertical polarization state of the pixels in this row.

[0109] S40. The cosine stripes in the horizontal direction and the sine stripes in the vertical direction are superimposed to generate two sets of orthogonal polarization stripe patterns.

[0110] In this embodiment, the composite polarization state encoded phase-shifting fringes have one and only two linear polarization states, and are formed by the superposition of two sets of mutually perpendicular polarization state fringes. The two sets of fringes have different polarization states. and By calculating two Stokes parameters of the stripe pattern captured by a polarizing camera. and This allows us to obtain a set of horizontal (0° polarization state) polarization sinusoidal structured light fringe patterns and another set of vertical (90° polarization state) polarization sinusoidal structured light fringe patterns.

[0111] By superimposing the cosine fringes in the horizontal direction and the sine fringes in the vertical direction, two sets of orthogonal polarization fringe patterns are generated, represented as follows:

[0112] ,

[0113] In the formula, The coordinates of the pixels. The image shows the cosine fringe pattern in the horizontal direction recorded by a polarizing camera when the front polarizer is set to 0°. The vertical sinusoidal fringe pattern recorded by the polarizing camera when the front polarizer is set to 90°.

[0114] Polarizing cameras can simultaneously record polarization patterns at 0° and 90° after a single exposure, thus allowing for the acquisition of one image in a single exposure. And a This means that after calculation, a sinusoidal calibration pattern of one vertical stripe (0° polarization state) and one horizontal stripe (90° polarization state) can be obtained simultaneously after one exposure for the calibration of underwater cameras and projectors.

[0115] S50. Based on the aforementioned equal focal length refraction mathematical model, phase calculation and reprojection error optimization are performed on the two sets of orthogonal polarization fringe patterns to achieve parameter calibration.

[0116] In this embodiment, the corresponding wrapping phase is obtained by phase shifting, and finally the absolute phase is obtained by decoding using complementary Gray code.

[0117] Phase calculation and reprojection error optimization are performed on two sets of orthogonal polarization fringe patterns to achieve parameter calibration. This includes: extracting the enclosed phase from the two sets of orthogonal polarization fringe patterns using the phase-shifting method; decoding the two sets of enclosed phases using complementary Gray codes to obtain the absolute phase distribution; calculating the three-dimensional coordinates of the feature points of the calibration plate based on the two sets of orthogonal polarization fringe patterns; and constructing a reprojection error function and optimizing the camera's intrinsic and extrinsic parameters based on the conversion relationship between the underwater imaging point coordinates and the theoretical imaging point coordinates in the air, until the error converges.

[0118] To evaluate the performance of the composite polarization state-coded fringe calibration for the equal focal length refraction model, a polarization camera and projector were calibrated using a calibration board in both air and water environments. During the calibration process, the positions of the polarization camera and projector remained fixed, while the calibration board underwent multiple movements and attitude changes. Figure 6 (a) and Figure 7 (a) shows partial images of the calibration board at different locations in 12 groups, taken by a polarization camera in both air and water environments. This embodiment displays the first image from each group. Notably, in some underwater images of the calibration board, obvious bright spots appear at the top and right side of the pattern, which is due to light reflected from the water tank.

[0119] Figure 6 (b) and Figure 7 The calibration plate center detection effect shown by the polarization imaging system in (b) indicates that the device achieves complete feature point recognition in different media environments.

[0120] Figure 8 and Figure 9 The spatial pose relationships of the camera-projector system in air and water environments are respectively represented, where, Figure 8 The numbers 1-12 represent the positional relationship between the 12 calibration plates captured by the polarization camera in the air and the camera and projector. Figure 8 (a) in the image shows a visualization of extrinsic parameters centered on the camera. Figure 8 (b) in the figure represents the visualization of extrinsic parameters centered on the projector; Figure 9 (a) in the image shows a visualization of extrinsic parameters centered on the camera. Figure 9 The numbers 1-12 represent the positional relationship between the 12 calibration plates, the camera, and the projector as captured by the polarization camera in the water. Figure 9 (b) shows the visualization of extrinsic parameters centered on the projector. Table 1 compares the calibration parameters of the polarization imaging system in a dual-medium environment of air and water.

[0121] Table 1 Comparison of calibration parameters in air and underwater

[0122]

[0123] Based on the comparison of calibration parameters in Table 1, the changing trends of focal length values ​​in underwater and air environments conform to the derivation results of the equal focal length refraction mathematical model. The experimentally measured underwater focal length value is approximately 1.33 times the air focal length value, a ratio that perfectly matches the refractive index of water (approximately 1.33).

[0124] To verify the accuracy of the calibration method, the parameters of the underwater camera and projector system were calibrated using the traditional gray-white stripe pattern and the composite polarization state coding method, respectively. Figure 10 In the image, 1-12 represents the reprojection error distribution of camera feature points on 12 calibration boards captured by a polarization camera in air. Figure 10 (a) and Figure 10 (b) in the figure shows the reprojection error distribution of the camera center coordinates calibrated by the method of this embodiment and by the conventional gray-white stripe calibration, respectively. Figure 11 In the image, 1-12 represents the reprojection error distribution of camera feature points on 12 calibration plates captured by a polarization camera in water. Figure 11 (a) and Figure 11 Figure (b) shows the reprojection error distribution of the projector's center coordinates. For... Figure 10 and Figure 11 The experimental figures presented are analyzed from two dimensions: spatial distribution characteristics and error concentration. Experimental data show that, compared with the diffuse reprojection error distribution of the traditional gray-white stripe method, the method proposed in this embodiment exhibits better spatial consistency and a more concentrated reprojection error distribution.

[0125] This disclosure proposes an underwater calibration method for composite polarization states based on an equifocal refraction model. A projector calibration system is constructed based on an "inverse camera" model. Combining the polarized light projection characteristics of a 3LCD projector, an innovative sinusoidal fringe calibration pattern containing composite polarization state encoding is designed. This is achieved by encoding horizontally polarized light in the green channel of the projector onto vertical sinusoidal fringes, and vertically polarized light in the blue channel onto horizontal sinusoidal fringes. By calculating the composite polarization state projected fringe pattern captured by the camera, a set of phase-shifted fringe patterns with mutually perpendicular polarization states can be obtained. This method replaces the gray-white fringe pattern in the traditional camera-projector inverse calibration method, reducing the number of projected fringe patterns. Simultaneously, an underwater equifocal refraction model is introduced to complete the calibration of system parameters. Compared to traditional methods, this significantly improves the calibration accuracy and measurement efficiency of the underwater visual measurement system.

[0126] Example 2

[0127] As another aspect of the embodiments of this disclosure, a composite polarization state underwater calibration system 100 based on an equal focal length refraction model is also provided, such as... Figure 12 As shown, it includes:

[0128] The equal focal length refraction mathematical model construction module 1, by combining the geometric optical imaging equations and Snell's law of refraction, approximates the incident angle of light under small angle conditions, and obtains the transformation relationship between the coordinates of the underwater imaging point and the coordinates of the theoretical imaging point in the air. Based on the transformation relationship, the equal focal length refraction mathematical model of the underwater camera and projector is established.

[0129] The composite polarization state encoded sinusoidal projection calibration pattern design module 2 designs a composite polarization state encoded sinusoidal projection calibration pattern based on the equal focal length refraction mathematical model.

[0130] The polarization light encoding module 3 utilizes the polarization light projection characteristics to encode the horizontally polarized light of the green channel of the composite polarization state encoded sinusoidal projection calibration pattern into a cosine fringe in the horizontal direction, and to encode the vertically polarized light of the blue channel of the composite polarization state encoded sinusoidal projection calibration pattern into a sinusoidal fringe in the vertical direction.

[0131] The orthogonal polarization stripe pattern generation module 4 superimposes the cosine stripes in the horizontal direction and the sine stripes in the vertical direction to generate two sets of orthogonal polarization stripe patterns.

[0132] The parameter calibration module 5, based on the equal focal length refraction mathematical model, performs phase calculation and reprojection error optimization on the two sets of orthogonal polarization fringe patterns to achieve parameter calibration.

[0133] Without causing contradictions, the above-described modules in the system of the present disclosure embodiments can implement any of the above-described methods.

[0134] Based on the description of the above embodiments, it can be seen that the embodiments of this disclosure can achieve the following technical effects:

[0135] 1) This disclosure uses an equal focal length refraction model to linearly magnify the underwater image into an air image in order to complete the calibration of system parameters and effectively solve the problem of the influence of light refraction on the underwater imaging quality.

[0136] 2) This disclosure can obtain a set of phase-shifted fringe patterns with mutually perpendicular polarization states by calculating the composite polarization state projection fringe pattern captured by the camera, thereby reducing the number of projection fringe patterns required.

[0137] 3) This disclosure can significantly improve the accuracy of underwater calibration and has better equipment parameter calibration performance compared with the traditional gray stripe method.

[0138] This disclosure also proposes an electronic device, including: a processor; and a memory for storing processor-executable instructions; wherein the processor is configured for the aforementioned underwater calibration method for composite polarization states based on an equal focal length refraction model. The electronic device can be provided as a terminal, a server, or other type of device.

[0139] This disclosure also proposes a computer-readable storage medium storing computer program instructions, which, when executed by a processor, implement the aforementioned underwater calibration method for composite polarization states based on an equal focal length refraction model. The computer-readable storage medium can be a non-volatile computer-readable storage medium.

[0140] Those skilled in the art will understand that, in the above-described method and system for underwater calibration of composite polarization states based on the equifocal refraction model in specific embodiments, the order in which each step is written does not imply a strict execution order and does not constitute any limitation on the implementation process. The specific execution order of each step should be determined by its function and possible internal logic.

[0141] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction containing one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0142] The various embodiments of this disclosure have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or technical improvements to the technology in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A method for underwater calibration of composite polarization states based on an equal focal length refraction model, characterized in that, Includes the following steps: S10. By combining the geometric optical imaging equations and Snell's law of refraction, the incident angle of light is approximated under small angle conditions to obtain the transformation relationship between the underwater imaging point coordinates and the theoretical imaging point coordinates in the air. Based on the transformation relationship, an equal focal length refraction mathematical model for the underwater camera and projector is established. Combining the geometrical optics imaging equations with Snell's law of refraction, we can approximate the incident angle of light at small angles as follows: ， In the formula, The coordinates of the underwater imaging point, It represents the distance from the interface between the media and the outer focal point of the lens. Expressed as focal length, In the representation space X Axis coordinates In spatial coordinates Z Axis coordinates and These represent the refractive indices of water and air, respectively. and These are the angles between the imaging ray and the normals of the water and air interfaces, respectively. S20. Based on the aforementioned equal focal length refraction mathematical model, design a composite polarization state encoded sinusoidal projection calibration pattern; S30. Utilizing the characteristics of polarized light projection, the horizontally polarized light of the green channel of the composite polarization state encoded sinusoidal projection calibration pattern is encoded into a cosine fringe in the horizontal direction, and the vertically polarized light of the blue channel of the composite polarization state encoded sinusoidal projection calibration pattern is encoded into a sinusoidal fringe in the vertical direction. S40. The cosine stripes in the horizontal direction and the sine stripes in the vertical direction are superimposed to generate two sets of orthogonal polarization stripe patterns. S50. Based on the aforementioned equal focal length refraction mathematical model, phase calculation and reprojection error optimization are performed on the two sets of orthogonal polarization fringe patterns to achieve parameter calibration.

2. The method according to claim 1, characterized in that, The conversion relationship between the coordinates of the underwater imaging point and the coordinates of the theoretical imaging point in air is as follows: ， In the formula, The coordinates of the underwater imaging point, These are the coordinates of the theoretical imaging point in the air.

3. The method according to claim 1, characterized in that, Encoding the horizontally polarized light of the green channel of the composite polarization state encoded sinusoidal projection calibration pattern into cosine fringes in the horizontal direction is represented as: ， ， ， In the formula, The x-axis coordinate of the projector coordinate system For a period of time, It is a green light source. Let be the total green light intensity of a certain row of pixels. This represents the intensity distribution of the horizontal polarization state of the pixels in this row.

4. The method according to claim 1, characterized in that, The vertically polarized light of the blue channel of the composite polarization-state encoded sinusoidal projection calibration pattern is encoded into sinusoidal fringes in the vertical direction, as follows: ， ， ， In the formula, The x-axis coordinate of the projector coordinate system For a period of time, It is a blue light source. Let be the total blue light intensity of a certain row of pixels. This represents the intensity distribution of the vertical polarization state of the pixels in this row.

5. The method according to claim 1, characterized in that, By superimposing the cosine fringes in the horizontal direction and the sine fringes in the vertical direction, two sets of orthogonal polarization fringe patterns are generated, represented as follows: ， In the formula, The coordinates of the pixels. The image shows the cosine fringe pattern in the horizontal direction recorded by a polarizing camera when the front polarizer is set to 0°. The vertical sinusoidal fringe pattern recorded by the polarizing camera when the front polarizer is set to 90°.

6. The method according to claim 1, characterized in that, Phase calculation and reprojection error optimization are performed on two sets of orthogonal polarization fringe patterns to achieve parameter calibration, including: The wrapping phase is extracted from two sets of orthogonal polarization fringe patterns using the phase-shifting method, and the two sets of wrapping phases are decoded using complementary Gray codes to obtain the absolute phase distribution. The three-dimensional coordinates of the feature points on the calibration plate are calculated based on the two sets of orthogonal polarization stripe patterns. Based on the transformation relationship between underwater imaging point coordinates and theoretical imaging point coordinates in air, a reprojection error function is constructed and the camera's intrinsic and extrinsic parameters are optimized until the error converges.

7. An underwater calibration system for composite polarization states based on an equal focal length refraction model, characterized in that, include: The equal focal length refraction mathematical model construction module, by combining the geometric optical imaging equations and Snell's law of refraction, approximates the incident angle of light under small angle conditions, and obtains the transformation relationship between the coordinates of the underwater imaging point and the coordinates of the theoretical imaging point in the air. Based on the transformation relationship, the equal focal length refraction mathematical model of the underwater camera and projector is established. Combining the geometrical optics imaging equations with Snell's law of refraction, we can approximate the incident angle of light at small angles as follows: ， In the formula, The coordinates of the underwater imaging point, It represents the distance from the interface between the media and the outer focal point of the lens. Expressed as focal length, In the representation space X Axis coordinates In spatial coordinates Z Axis coordinates and These represent the refractive indices of water and air, respectively. and These are the angles between the imaging ray and the normals of the water and air interfaces, respectively. The composite polarization state encoded sinusoidal projection calibration pattern design module designs a composite polarization state encoded sinusoidal projection calibration pattern based on the aforementioned equal focal length refraction mathematical model. The polarization light encoding module utilizes the polarization light projection characteristics to encode the horizontally polarized light of the green channel of the composite polarization state encoded sinusoidal projection calibration pattern into a cosine fringe in the horizontal direction, and to encode the vertically polarized light of the blue channel of the composite polarization state encoded sinusoidal projection calibration pattern into a sinusoidal fringe in the vertical direction. The orthogonal polarization stripe pattern generation module superimposes the cosine stripes in the horizontal direction and the sine stripes in the vertical direction to generate two sets of orthogonal polarization stripe patterns. The parameter calibration module, based on the equal focal length refraction mathematical model, performs phase calculation and reprojection error optimization on the two sets of orthogonal polarization fringe patterns to achieve parameter calibration.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the underwater calibration method for composite polarization states based on the equal focal length refraction model as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the underwater calibration method for composite polarization states based on the equal focal length refraction model as described in any one of claims 1 to 6.

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