Involute surface image sub-pixel level rotation simulation method

Abstract

The present application relates to image simulation, data enhancement technical field, especially to a kind of involute surface image subpixel level rotation simulation method, comprising: S1, establish multidimensional conversion relationship, establish the mapping rule of image pixel and three-dimensional space point in world coordinate system;S2, determine the continuous space-time motion trajectory of surface point, and establish the dynamic corresponding relationship between the trajectory and image pixel;S3, solve the instantaneous surface point corresponding to target pixel in world coordinate system at t time and its involute angle;Original pixel and its original pixel value corresponding to the instantaneous surface point at initial time are deduced reversely;S4, original pixel value is corrected, and instantaneous gray value is obtained;S5, double integration operation is carried out on the motion trajectory corresponding to target pixel in space and time dimension;Synthesis has physical consistency motion blur image.The present application can efficiently generate dynamic blur image with space-time consistency and geometric reality.

Description

Technical Field

[0001] This invention relates to the fields of image simulation and data augmentation technology, and in particular to a subpixel-level rotation simulation method for involute surface images. Background Technology

[0002] In the field of industrial visual inspection and intelligent recognition, online condition monitoring of high-speed rotating equipment (such as mechanical components with involute tooth structures like gears and turbines) places extremely high demands on imaging quality. However, during actual acquisition, due to factors such as high-speed rotation of the target object, system vibration, and transient illumination changes, the acquired images generally exhibit complex motion blur. This type of blur not only severely degrades image edge details and texture features but also significantly reduces the robustness and accuracy of subsequent recognition, measurement, and defect detection algorithms.

[0003] Early image enhancement methods primarily relied on geometric transformations (such as affine and perspective transformations) and color space perturbations (such as brightness and contrast adjustments). While these methods could expand the training samples to some extent, their generation mechanisms lacked modeling of the real imaging physical processes, especially neglecting the spatiotemporal evolution characteristics of dynamic blur in industrial scenes. These methods typically assume that image degradation is static or quasi-static, failing to reflect the nonlinear and time-varying blurring effects caused by high-speed rotation. This results in a significant domain offset between the generated samples and real-world conditions, limiting their generalization ability.

[0004] In recent years, with the rapid development of generative artificial intelligence technologies (such as Generative Adversarial Networks (GANs) and Diffusion Models), researchers have been able to synthesize highly realistic image data, effectively alleviating the problem of scarce training samples. However, most existing generative models are based on static tooth surface images for enhancement or style transfer, and their training objectives focus on pixel-level fidelity or perceptual similarity, without deeply coupling the geometric constraints of the imaging system and the dynamic behavior of the target object. Therefore, it is difficult to accurately reproduce the complex motion blur patterns caused by high-speed rotation—especially for involute surfaces with nonlinear trajectories, whose blur morphology dynamically changes with rotation angle, angular velocity, and exposure time, exhibiting strong spatiotemporal nonuniformity and direction dependence.

[0005] Current mainstream motion blur modeling methods are mostly based on the assumptions of uniform linear motion and spatiotemporal invariance, suitable for translational blur scenes, but unable to effectively characterize the curvature changes and sub-pixel displacement accumulation effects of pixel trajectories under rotational motion. More importantly, the geometric properties of the involute surface (such as the base circle radius and aspect ratio) and the intrinsic and extrinsic parameters of the imaging system jointly determine the spatial distribution of the blur kernel, while existing methods neither establish this geometric-optical coupling relationship nor have a precise inverse mapping mechanism for sub-pixel motion trajectories. In addition, physical factors such as rotation center deviation, non-integer coordinate sampling during exposure integration, and the directional consistency of grayscale distribution within pixel grids further exacerbate the modeling difficulty.

[0006] Therefore, how to efficiently generate dynamic blurred images with spatiotemporal consistency and geometric realism, thereby significantly improving the generalization ability and detection accuracy of industrial vision recognition systems under high-speed rotating conditions, has become an urgent problem to be solved. Summary of the Invention

[0007] To address the aforementioned shortcomings of existing technologies, the present invention aims to provide a subpixel-level rotation simulation method for involute surface images, which can efficiently generate dynamic blurred images with spatiotemporal consistency and geometric realism, thereby significantly improving the generalization ability and detection accuracy of industrial vision recognition systems under high-speed rotation conditions.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0009] A subpixel-level rotation simulation method for involute surface images includes the following steps:

[0010] S1. Establishment of imaging system calibration and spatiotemporal mapping relationship:

[0011] Obtain the intrinsic and extrinsic parameter matrices of the imaging system. The intrinsic parameter matrix includes scaling factors and principal point coordinates, and the extrinsic parameter matrix includes rotation and translation matrices. Based on the intrinsic and extrinsic parameter matrices, establish a multidimensional transformation relationship between the image pixel coordinate system, the camera coordinate system, and the world coordinate system, and establish the mapping rules between image pixels and three-dimensional spatial points in the world coordinate system.

[0012] S2. Modeling of rotating surface motion based on the involute equation:

[0013] By introducing the involute parametric equation defined by the base circle radius and the development angle, a geometric model is performed on a target rotating object with an involute surface, and the three-dimensional spatial distribution of the surface points of the object is obtained.

[0014] By combining the set average rotation speed, a continuous evolution equation of the rotation angle of the surface point at any time during the exposure time is constructed, thereby determining the continuous spatiotemporal motion trajectory of the surface point during the rotation process, and establishing a dynamic correspondence between the trajectory and the image pixel.

[0015] S3. Sub-pixel-level reverse spatial positioning based on the sine theorem:

[0016] Construct a pixel grid for the motion-blurred image to be synthesized. For any target pixel in the pixel grid, use the mapping rule established in S1 and the dynamic correspondence established in S2 to inversely map the target pixel to the world coordinate system.

[0017] Considering the rotation center deviation, a geometric solution model is constructed using the sine theorem to solve for the instantaneous surface point and its involute angle in the world coordinate system corresponding to the target pixel at time t.

[0018] Based on the involute angle and mapping rule, the original pixel point and its original pixel value corresponding to the instantaneous surface point at the initial moment are derived in reverse.

[0019] S4. Adaptive grayscale correction based on depth orthogonal distance:

[0020] Construct a grayscale correction function and use it to correct the original pixel values ​​obtained in S3 to obtain the instantaneous grayscale value at time t.

[0021] S5, Spatiotemporal double integral imaging synthesis:

[0022] During the exposure time, the instantaneous grayscale values ​​at each moment after S4 correction are subjected to double integration operations in spatial and temporal dimensions on the motion trajectory corresponding to the target pixel.

[0023] In the double integral operation, the integral dimension is simplified based on the consistency characteristics of the gray-level distribution of pixels in a specific direction within the pixel grid, and the gray-level values ​​at non-integer coordinate positions are processed to synthesize a motion-blurred image with physical consistency.

[0024] Compared with the prior art, the present invention has the following advantages:

[0025] 1. A nonlinear motion blur model that strictly conforms to physical mechanisms was constructed. Unlike existing techniques that are mostly based on uniform linear motion or static image transformation, this method accurately describes the continuous spatiotemporal evolution trajectory of points on the surface of a rotating object within the exposure time by introducing involute parametric equations defined by the base circle radius and the unfolding angle. This method breaks through the simplistic assumption of "spatiotemporal invariance" in traditional models, and can realistically reproduce the complex blurred textures generated by nonlinear motion under high-speed rotation conditions, solving the problem of lack of physical consistency in existing generated samples.

[0026] 2. Subpixel-level spatial positioning accuracy and geometric fidelity are achieved. To address the minute displacements caused by high-speed rotation, this method utilizes the sine theorem to construct a geometric solution model. Considering the rotation center deviation, it achieves subpixel-level reverse positioning from image pixels to instantaneous surface points in the world coordinate system. Compared to traditional integer-pixel-level mapping methods, this technique effectively eliminates aliasing and geometric distortion caused by coordinate rounding, ensuring that the generated blurred image maintains strict geometric correspondence at the microscopic scale, significantly improving the precision of the simulated image.

[0027] 3. Adaptive grayscale correction is introduced to enhance the realism of dynamic lighting. Unlike conventional methods that directly sample original pixel values, this method constructs an adaptive grayscale correction function based on depth orthogonal distance. This mechanism dynamically adjusts the instantaneous grayscale value according to the depth changes and lighting angle changes of surface points during rotation, thereby simulating the brightness changes and shadow effects caused by object rotation in real industrial scenes. This results in generated images that not only contain motion blur but also possess realistic photometric consistency, further reducing the distribution difference between simulated data and real-world acquired data.

[0028] 4. High-fidelity motion-blurred images synthesized via spatiotemporal double integration. This method abandons simple frame stacking or linear convolution processing, and uses spatiotemporal double integration to synthesize instantaneous grayscale values ​​within the exposure time. By utilizing the consistent characteristics of grayscale distribution within the pixel grid for dimensionality simplification during the integration process, and accurately handling interpolation at non-integer coordinate positions, this method can generate motion-blurred images with continuous and smooth transition characteristics. This processing method is not only computationally efficient, but also perfectly reproduces the accumulation process of light energy by the camera sensor during exposure, ensuring the physical authenticity of the imaging results.

[0029] In summary, this method can efficiently generate dynamic blurred images with spatiotemporal consistency and geometric realism, thereby significantly improving the generalization ability and detection accuracy of industrial vision recognition systems under high-speed rotating conditions.

[0030] Preferably, in step S1, the intrinsic parameter matrix includes an X-axis scaling factor a, a Y-axis scaling factor b, and principal point coordinates (u0, v0); the extrinsic parameter matrix includes a rotation matrix R and a translation matrix T. r The rotation matrix R is composed of rotation angles α, β, and γ about each coordinate axis of the world coordinate system, and the translation matrix T... r The translation component t of the camera origin relative to the origin of the world coordinate system x t y t z constitute.

[0031] This setup improves the geometric accuracy and adaptability of multidimensional coordinate system transformations. Existing technologies often employ simplified camera models (such as assuming pixels are squares or ignoring principal point offset), which introduces systematic errors in precision industrial measurements. This scheme, by introducing independent X / Y axis scaling factors and precise principal point coordinates, can more accurately describe the non-uniform sampling characteristics and optical center offset that may exist in actual imaging sensors. Simultaneously, by explicitly decomposing extrinsic parameters into three-dimensional rotation angle and translation components, a more rigorous "pixel-camera-world" multidimensional transformation rule is established. This refined parameter definition eliminates geometric distortions caused by idealized assumptions, ensuring high fidelity in the mathematical solutions of subsequent sub-pixel-level reverse localization (S3) and motion trajectory calculation (S2), laying a precise geometric foundation for generating physically consistent simulation images.

[0032] Preferably, in step S2, the involute parametric equation is:

[0033] ;

[0034] Where r0 is the radius of the base circle. For the exhibition angle;

[0035] The equation for the continuous evolution of the rotation angle is:

[0036] ;

[0037] in, Let be the angle through which the surface point rotates in time t; Let be the initial angle of the surface point, and n be the average rotational speed over time t.

[0038] This setup enables accurate physical reproduction of nonlinear surface motion. Existing image enhancement techniques often rely on simple rigid body transformations or linear blur kernels, which struggle to simulate the realistic motion characteristics of complex surfaces such as gears. This solution introduces standard involute parametric equations, ensuring the accuracy of the simulated object's geometry from a mathematical perspective. Simultaneously, by combining continuous evolution equations, discrete rotational speed parameters are transformed into continuous angular displacement variables in the time domain. This dual modeling approach of "geometry + dynamics" accurately captures the nonlinear trajectory of surface points changing over time during high-speed rotation, overcoming the motion blur distortion problem caused by neglecting surface curvature changes in traditional methods. This results in simulation data that conforms to the true physical imaging mechanism in both microscopic texture and macroscopic morphology.

[0039] Preferably, in step S3, the construction of the geometric solution model using the sine theorem includes:

[0040] The target pixel is inversely mapped to the X coordinate system of the world coordinate system. w OYw The plane is used to obtain its surface reference point P at time zero. w0 ;

[0041] Through the surface reference point P w0 Establish an extended straight line l, the equation of which is y = kx + b, where k and b are determined by the surface reference point P. w0 The coordinates are determined;

[0042] The world coordinate system is equivalently rotated to time t, such that the involute surface profile at time t intersects the extended straight line l at the instantaneous surface point P. wt Wherein, the involute surface profile at time t is the involute trajectory after rotation based on the continuous evolution equation of the rotation angle;

[0043] The point formed by the center of rotation, the intercept of the extended line l, and the instantaneous surface point P. wt Within the triangle formed, the instantaneous surface point P is solved using the sine theorem. wt The coordinates in the equivalent rotated coordinate system are obtained, and the corresponding instantaneous involute angle θ is obtained. ’ wt .

[0044] This setup enables high-precision sub-pixel inverse positioning under complex nonlinear motion. Existing techniques often employ iterative approximation or linear interpolation to address the complex nonlinear correspondence between pixels and object surface points during rotational motion, resulting in high computational cost and limited accuracy. This solution innovatively utilizes "equivalent rotation of the coordinate system" to transform the dynamic problem into a static geometric intersection problem, and constructs an analytical solution model using the sine theorem. This method avoids tedious numerical iterations and can directly and quickly calculate the sub-pixel-level precise coordinates and involute angle of surface points at any time t. This not only significantly improves the computational efficiency of inverse mapping but also fundamentally eliminates positioning errors caused by approximation algorithms, ensuring the geometric consistency of texture sampling in simulated images under high-speed rotation conditions.

[0045] Preferably, in S3, the instantaneous involute angle θ is used as the basis for the transformation relationship between pixel coordinates and world coordinates. ’ wt Reverse derive the original pixel:

[0046] ;

[0047] ;

[0048] Where (u,v) are the original pixel coordinates to be obtained; r ij For each element of the rotation matrix R, i = 1, 2 represents a row, j = 1, 2, 3 represents a column; z w Let P be the instantaneous surface pointwt Z-axis coordinates in the world coordinate system For θ ’ wt The corresponding angle of display.

[0049] This setup ensures both texture sampling accuracy and geometric consistency in dynamic blur synthesis. Existing techniques often neglect the 3D curvature changes of object surfaces or the nonlinear distortion of camera imaging when processing motion blur, leading to texture stretching errors or geometric distortion in the generated blurred images. This solution constructs a rigorous closed-loop inverse mapping system by deeply fusing the camera imaging model with the involute geometric equation. It can backtrack to the corresponding position in the original sharp image at the sub-pixel level based on the precise spatial pose and depth changes of the object at any given time. This method effectively overcomes the errors introduced by the traditional planar projection assumption, ensuring that every grayscale value in the simulated image originates from the correct texture sampling of the real physical scene during high-speed rotation and nonlinear motion, greatly improving the geometric fidelity of the synthesized data.

[0050] Preferably, in step S4, the grayscale correction function H is:

[0051] H=(d0 / d t ) k ;

[0052] Where d0 is the initial orthogonal distance of the instantaneous surface point relative to the camera optical center at the initial moment, d t t represents the instantaneous orthogonal distance of a point on the surface at time t relative to the optical center of the camera, and k is the adaptive correction exponent.

[0053] This setup achieves realistic lighting compensation based on changes in physical depth. In rotational motion simulations, the distance between points on the object's surface and the camera dynamically changes due to the surface contour and rotational attitude, resulting in a gradual change in brightness that follows the inverse square law in actual imaging. Existing methods often ignore this effect or use fixed gain, causing the synthesized image to lack realistic lighting and shadow levels. This scheme addresses this by adjusting the instantaneous distance d... t Using the ratio of light intensity to the initial distance d0 as the core variable, supplemented by an adjustable exponent k, the physical law of light intensity changing with object distance can be accurately simulated. This allows the generated blurred image to not only contain motion trajectory information, but also simultaneously restore the natural light attenuation or enhancement effects caused by three-dimensional spatial displacement, significantly improving the visual realism and physical consistency of the simulated image.

[0054] Preferably, the initial orthogonal distance d0 and the instantaneous orthogonal distance d t Calculated in the following way:

[0055] The instantaneous surface point P wt instantaneous involute angle θ’ wt and corresponding display angles Substituting into the involute parametric equation, we obtain its world coordinates;

[0056] Then, using the coordinate system transformation relationship established in S1, the world coordinates are converted into coordinates in the camera coordinate system, and the depth component along the camera optical axis is extracted as the initial orthogonal distance d0 or the instantaneous orthogonal distance d. t .

[0057] This setup establishes a physically consistent foundation for dynamic object distance perception and illumination modeling. Existing motion blur simulations often assume objects are planar or ignore depth variations, resulting in images lacking realistic perspective scaling and illumination attenuation effects. This scheme, by strictly adhering to involute geometric constraints and the camera imaging model, mathematically guarantees that the object distance value at each sampling point originates from its true 3D spatial trajectory. This chain-like calculation method of "geometry → coordinates → depth" not only avoids errors caused by approximate estimation but also provides a high-precision, physically interpretable distance input for the subsequent grayscale correction function H. This allows the final synthesized blurred image to naturally present the gradations of brightness and depth of field effects caused by surface rotation, greatly enhancing the realism of the data and the effectiveness of algorithm training.

[0058] Preferably, the adaptive correction exponent k is determined by the following iterative optimization method:

[0059] Step A: Acquire a real dynamic blur image based on the actual imaging system as the reference image;

[0060] Step B: Set a set of candidate correction index k values;

[0061] Step C: Iterate through the candidate correction index k values, and for each k value, execute steps S3 to S5 in sequence to generate the corresponding synthetic motion blur image;

[0062] Step D: Calculate the point-by-point peak signal-to-noise ratio (P-PSNR) between each of the synthesized motion-blurred images and the reference image;

[0063] Step E: Select the candidate k value that maximizes the P-PSNR as the optimal solution for the adaptive correction exponent k.

[0064] This setup enables physically scene-adaptive calibration of the grayscale correction parameters, significantly improving the visual fidelity of simulated images. Traditional methods often rely on experience or fixed formulas to set the illumination attenuation coefficient, making it difficult to adapt to different materials, lighting environments, or camera response characteristics, resulting in distortion of brightness in the synthesized images. This solution introduces real images as supervisory signals and utilizes the fine-grained evaluation metric P-PSNR to perform a global search in the parameter space, ensuring that the selected k value can maximally reproduce the light and shadow variations in the real scene. This "simulation-experimental closed-loop optimization" mechanism makes the grayscale correction function H no longer a theoretical model, but an empirically verified physical mapping, thereby ensuring that the generated blurred image is highly consistent with the actual shooting results in terms of texture details and brightness distribution, greatly enhancing the reliability and practicality of the data.

[0065] Preferably, in step S5, the simplification of the integration dimension includes: based on the characteristic that points with the same Y coordinate value in the same pixel grid of the camera coordinate system and perpendicular to the motion trajectory direction have approximately the same gray value, in the double integration operation, the Y coordinate component is taken as the arithmetic mean of the Y coordinates of the starting point and the ending point of the motion trajectory.

[0066] An interpolation algorithm is used to process the grayscale values ​​at non-integer coordinate positions.

[0067] This setup significantly improves the computational efficiency of motion blur synthesis while maintaining visual fidelity. This solution cleverly utilizes the characteristic of "smooth and continuous grayscale within small regions" in imaging systems, transforming complex two-dimensional area integrals into efficient one-dimensional line integrals, and compensating for the accuracy loss caused by discretization through interpolation. This combination of "dimensionality reduction + interpolation" strategy greatly reduces redundant computation without sacrificing final image quality, enabling the system to achieve rapid rendering and mass production while maintaining high realism. It is particularly suitable for scenarios with stringent requirements for data throughput and timeliness, such as industrial vision algorithm training.

[0068] Preferably, the rotating object with an involute surface includes an involute spur gear, an involute helical gear, an involute spline shaft, an involute cam, or a rotating workpiece with an involute tooth profile.

[0069] This setup, through the refined definition of the target object, successfully focuses general motion fuzzy simulation technology on the most challenging and commercially valuable industrial sub-scenarios, achieving a key leap from "theoretically feasible" to "engineerably usable," and providing a solid data foundation and algorithmic support for building intelligent vision inspection systems for high-end equipment manufacturing. Attached Figure Description

[0070] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0071] Figure 1 This is a flowchart of the method;

[0072] Figure 2 This is a schematic diagram of the spatiotemporal dimensionality increase mapping of the image-camera-world coordinate system in Example 1;

[0073] Figure 3 A schematic diagram illustrating the grayscale correction in section one;

[0074] Figure 4 This is a two-dimensional planar schematic diagram of the gear in Embodiment 1;

[0075] Figure 5 The corresponding example diagram is shown in Example 1. Detailed Implementation

[0076] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0077] 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 only a part of the embodiments of the present invention, not all of them. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to represent selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0078] It should be noted that similar reference numerals and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the figures, or the orientation or positional relationship commonly used when the product is in use. They are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. Furthermore, the terms "first," "second," and "third," etc., are only used to distinguish descriptions and should not be construed as indicating or implying relative importance. In addition, the terms "horizontal," "vertical," etc., do not indicate that the component is required to be absolutely horizontal or suspended, but can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted. In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0079] Example 1

[0080] like Figure 1 As shown, this invention provides a subpixel-level rotation simulation method for involute surface images, comprising the following steps:

[0081] S1. Establishment of imaging system calibration and spatiotemporal mapping relationship, such as Figure 2 As shown:

[0082] Obtain the intrinsic and extrinsic parameter matrices of the imaging system. The intrinsic parameter matrix includes scaling factors and principal point coordinates, and the extrinsic parameter matrix includes rotation and translation matrices. Based on the intrinsic and extrinsic parameter matrices, establish a multidimensional transformation relationship between the image pixel coordinate system, the camera coordinate system, and the world coordinate system, and establish the mapping rules between image pixels and three-dimensional spatial points in the world coordinate system.

[0083] In specific implementation, the intrinsic parameter matrix includes the X-axis scaling factor a, the Y-axis scaling factor b, and the principal point coordinates (u0, v0); the extrinsic parameter matrix includes the rotation matrix R and the translation matrix T. rThe rotation matrix R is composed of rotation angles α, β, and γ about each coordinate axis of the world coordinate system, and the translation matrix T... r The translation component t of the camera origin relative to the origin of the world coordinate system x t y t z constitute.

[0084] Existing technologies often employ simplified camera models (such as assuming pixels are square or ignoring principal point offset), which introduces systematic errors in precision industrial measurements. This approach, by introducing independent X / Y axis scaling factors and precise principal point coordinates, more accurately describes the non-uniform sampling characteristics and optical center offset that may exist in actual imaging sensors. Simultaneously, by explicitly decomposing extrinsic parameters into three-dimensional rotation angle and translation components, a more rigorous "pixel-camera-world" multidimensional transformation rule is established. This refined parameter definition eliminates geometric distortions caused by idealized assumptions, ensuring high fidelity in the mathematical solutions of subsequent sub-pixel-level reverse localization (S3) and motion trajectory calculation (S2), laying a precise geometric foundation for generating physically consistent simulation images.

[0085] S2. Modeling of rotating surface motion based on the involute equation:

[0086] By introducing the involute parametric equation defined by the base circle radius and the development angle, a geometric model is performed on a target rotating object with an involute surface, resulting in the three-dimensional spatial distribution of points on the object's surface. The rotating object with an involute surface includes an involute spur gear, an involute helical gear, an involute spline shaft, an involute cam, or a rotating workpiece with an involute tooth profile.

[0087] By combining the set average rotation speed, a continuous evolution equation for the rotation angle of the surface point at any time during the exposure time is constructed, thereby determining the continuous spatiotemporal motion trajectory of the surface point during the rotation process, and establishing a dynamic correspondence between the trajectory and the image pixel.

[0088] In specific implementation, the involute parametric equation is as follows:

[0089] ;

[0090] in, The radius of the base circle, For the exhibition angle; , The pressure angle at surface point P;

[0091] The equation for the continuous evolution of the rotation angle is:

[0092] ;

[0093] in, Let be the angle through which the surface point rotates in time t; Let be the initial angle of the surface point, and n be the average rotational speed over time t.

[0094] Existing image enhancement techniques often rely on simple rigid body transformations or linear blur kernels, making it difficult to simulate the realistic motion characteristics of complex surfaces such as gears. This solution introduces standard involute parametric equations, ensuring the accuracy of the simulated object's geometry from a mathematical perspective. Simultaneously, by combining continuous evolution equations, discrete rotational speed parameters are transformed into continuous angular displacement variables in the time domain. This dual modeling approach of "geometry + dynamics" accurately captures the nonlinear trajectory of surface points changing over time during high-speed rotation, overcoming the motion blur distortion problem caused by neglecting surface curvature changes in traditional methods. This results in simulation data that conforms to the real physical imaging mechanism in both microscopic texture and macroscopic morphology.

[0095] S3. Sub-pixel-level reverse spatial positioning based on the sine theorem:

[0096] Construct a pixel grid for the motion-blurred image to be synthesized. For any target pixel in the pixel grid, use the mapping rule established in S1 and the dynamic correspondence established in S2 to inversely map the target pixel to the world coordinate system.

[0097] Considering the rotation center deviation, a geometric solution model is constructed using the sine theorem to solve for the instantaneous surface point and its involute angle in the world coordinate system corresponding to the target pixel at time t.

[0098] Based on the involute angle and mapping rule, the original pixel point and its original pixel value corresponding to the instantaneous surface point at the initial moment are derived in reverse.

[0099] In specific implementation, the construction of the geometric solution model using the sine theorem includes:

[0100] The target pixel is inversely mapped to the X coordinate system of the world coordinate system. w OY w The plane is used to obtain its surface reference point P at time zero. w0 ;

[0101] Through the surface reference point P w0 Establish an extended straight line l, the equation of which is y = kx + b, where k and b are determined by the surface reference point P. w0 The coordinates are determined;

[0102] The world coordinate system is equivalently rotated to time t, such that the involute surface profile at time t intersects the extended straight line l at the instantaneous surface point P. wtWherein, the involute surface profile at time t is the involute trajectory after rotation based on the continuous evolution equation of the rotation angle;

[0103] The point formed by the center of rotation, the intercept of the extended line l, and the instantaneous surface point P. wt Within the triangle formed, the instantaneous surface point P is solved using the sine theorem. wt The coordinates in the equivalent rotated coordinate system are obtained, and the corresponding instantaneous involute angle θ is obtained. ’ wt .

[0104] To address the complex nonlinear correspondence between pixels and points on an object's surface during rotational motion, existing techniques often employ iterative approximation or linear interpolation, resulting in high computational costs and limited accuracy. This innovative approach transforms the dynamic problem into a static geometric intersection problem using "equivalent coordinate system rotation," and constructs an analytical solution model based on the sine theorem. This method avoids tedious numerical iterations, enabling direct and rapid calculation of the sub-pixel-level precise coordinates and involute angle of surface points at any given time t. This not only significantly improves the computational efficiency of inverse mapping but also fundamentally eliminates positioning errors caused by approximation algorithms, ensuring the geometric consistency of texture sampling in simulated images under high-speed rotation conditions.

[0105] In practice, the following transformation relationship between pixel coordinates and world coordinates is used, based on the instantaneous involute angle θ. ’ wt Reverse derive the original pixel:

[0106] ;

[0107] ;

[0108] Where (u,v) are the original pixel coordinates to be obtained; r ij For each element of the rotation matrix R, i = 1, 2 represents a row, j = 1, 2, 3 represents a column; z w Let P be the instantaneous surface point wt Z-axis coordinates in the world coordinate system For θ ’ wt The corresponding angle of display.

[0109] Existing technologies for handling motion blur often ignore the three-dimensional curvature changes of object surfaces or the nonlinear distortion of camera imaging, leading to texture stretching errors or geometric distortion in the generated blurred images. This solution constructs a rigorous closed-loop inverse mapping system by deeply fusing the camera imaging model with the involute geometric equations. It can backtrack to the corresponding position in the original sharp image at the sub-pixel level based on the precise spatial pose and depth changes of the object at any given time. This method effectively overcomes the errors introduced by the traditional planar projection assumption, ensuring that every grayscale value in the simulated image originates from the correct texture sampling of the real physical scene during high-speed rotation and nonlinear motion, greatly improving the geometric fidelity of the synthesized data.

[0110] S4. Adaptive grayscale correction based on depth orthogonal distance:

[0111] Construct a grayscale correction function and use it to correct the original pixel values ​​obtained in S3 to obtain the instantaneous grayscale value at time t.

[0112] In specific implementation, the grayscale correction function H is:

[0113] H=(d0 / d t ) k ;

[0114] Where d0 is the initial orthogonal distance of the instantaneous surface point relative to the camera optical center at the initial moment, d t t represents the instantaneous orthogonal distance of a point on the surface at time t relative to the optical center of the camera, and k is the adaptive correction exponent.

[0115] A schematic diagram of grayscale correction is shown below. Figure 3 As shown.

[0116] In rotational motion simulations, the distance between points on an object's surface and the camera dynamically changes due to the surface profile and rotational attitude, resulting in a gradual change in brightness that follows the inverse square law in actual imaging. Existing methods often ignore this effect or use fixed gain, causing the synthesized image to lack realistic light and shadow levels. This scheme addresses this by dynamically adjusting the instantaneous distance d... t Using the ratio of light intensity to the initial distance d0 as the core variable, supplemented by an adjustable exponent k, the physical law of light intensity changing with object distance can be accurately simulated. This allows the generated blurred image to not only contain motion trajectory information, but also simultaneously restore the natural light attenuation or enhancement effects caused by three-dimensional spatial displacement, significantly improving the visual realism and physical consistency of the simulated image.

[0117] Wherein, the initial orthogonal distance d0 and the instantaneous orthogonal distance d t Calculated in the following way:

[0118] The instantaneous surface point P wtinstantaneous involute angle θ ’ wt and corresponding display angles Substituting into the involute parametric equation, we obtain its world coordinates;

[0119] Then, using the coordinate system transformation relationship established in S1, the world coordinates are converted into coordinates in the camera coordinate system, and the depth component along the camera optical axis is extracted as the initial orthogonal distance d0 or the instantaneous orthogonal distance d. t .

[0120] Existing motion blur simulations often assume objects are planar or ignore depth variations, resulting in images lacking realistic perspective scaling and illumination attenuation effects. This proposed solution, by strictly adhering to involute geometric constraints and the camera imaging model, mathematically guarantees that the object distance value at each sampling point originates from its true 3D spatial trajectory. This chain-like calculation method of "geometry → coordinates → depth" not only avoids errors caused by approximate estimations but also provides a high-precision, physically interpretable distance input for the subsequent grayscale correction function H. This allows the final synthesized blurred image to naturally present the gradations of brightness and depth of field effects caused by surface rotation, greatly enhancing the realism of the data and the effectiveness of algorithm training.

[0121] In specific implementation, the adaptive correction index k is determined through the following iterative optimization method:

[0122] Step A: Acquire a real dynamic blur image based on the actual imaging system as the reference image;

[0123] Step B: Set a set of candidate correction index k values;

[0124] Step C: Iterate through the candidate correction index k values, and for each k value, execute steps S3 to S5 in sequence to generate the corresponding synthetic motion blur image;

[0125] Step D: Calculate the point-by-point peak signal-to-noise ratio (P-PSNR) between each of the synthesized motion-blurred images and the reference image;

[0126] Step E: Select the candidate k value that maximizes the P-PSNR as the optimal solution for the adaptive correction exponent k.

[0127] Traditional methods often rely on experience or fixed formulas to set the illumination attenuation coefficient, making it difficult to adapt to different materials, lighting environments, or camera response characteristics, resulting in distortion of brightness and darkness in the synthesized image. This solution introduces real images as supervisory signals and utilizes P-PSNR, a fine-grained evaluation metric, to perform a global search in the parameter space, ensuring that the selected k value can maximally reproduce the light and shadow variations in the real scene. This "simulation-experimental closed-loop optimization" mechanism makes the grayscale correction function H no longer a theoretical model, but an empirically verified physical mapping, thus guaranteeing that the generated blurred image is highly consistent with the actual shooting results in terms of texture detail and brightness distribution, greatly enhancing the reliability and practicality of the data.

[0128] S5, Spatiotemporal double integral imaging synthesis:

[0129] During the exposure time, the instantaneous grayscale values ​​at each moment after S4 correction are subjected to double integration operations in spatial and temporal dimensions on the motion trajectory corresponding to the target pixel.

[0130] In the double integral operation, the integration dimension is simplified based on the consistent characteristics of the gray-level distribution of pixels in a specific direction within the pixel grid, and an interpolation algorithm is used to process the gray-level values ​​at non-integer coordinate positions to synthesize a motion-blurred image with physical consistency.

[0131] In specific implementation, the simplification of the integration dimension includes: based on the characteristic that points with the same Y coordinate value in the same pixel grid in the camera coordinate system and perpendicular to the motion trajectory direction have approximately the same gray value, in the double integration operation, the Y coordinate component is taken as the arithmetic mean of the Y coordinates of the starting point and the ending point of the motion trajectory.

[0132] In this way, this solution cleverly utilizes the characteristic of "smooth and continuous grayscale within small regions" in imaging systems to transform complex two-dimensional area integrals into efficient one-dimensional line integrals, and compensates for the accuracy loss caused by discretization through interpolation. This combination of "dimensionality reduction + interpolation" strategy significantly reduces redundant computation without sacrificing the final image quality, enabling the system to achieve rapid rendering and mass production while maintaining high realism. It is particularly suitable for scenarios with stringent requirements for data throughput and timeliness, such as industrial vision algorithm training.

[0133] To facilitate a better understanding of the principles of this method by those skilled in the art, the following detailed steps are provided.

[0134] Step 1: Based on the calibration parameters, calculate the XY axis scaling factors a=82584.1 and b=67765.3 from the pixel coordinates and the camera coordinate system. Based on the characteristics of the telecentric imaging system, the tilt factor s=0, and the principal point coordinates are set to the origin (u0=v0=0). Substitute into equation (1) to obtain the transformation equation of any point between the image-camera-world.

[0135] (1);

[0136] Step 2: Calculate the rotation and translation matrices R and T from the camera coordinate system to the world coordinate system. r As shown in equation (2), the rotation angles of the coordinate transformation are α=90°, β=0°, and γ=45-50°, and the relative coordinates of the origin are t. x =-18.13、t y =10、t z =138.

[0137] (2);

[0138] Step 3: Calculate the rotating surface point P at time t. t (x t ,y t According to formula (3), based on the angle θ between the point in the plane of rotation and the x-axis... t The radius of rotation r and the z-coordinate are the independent variables, f X f Y It is a parametric equation.

[0139] (3);

[0140] Step 4: Calculate P t The rotation angle within time t, according to formula (4), θ t P represents t The angle rotated within time t, where n is the average rotational speed (r / s) within time t, with positive values ​​for counterclockwise rotation.

[0141] (4);

[0142] Step 5: Introduce the involute equation into equation (5)-(6) to instantiate equation (3), α p φ is the pressure angle at point P, φ is the expansion angle at P, and r0 is the base circle radius.

[0143] (5);

[0144] (6);

[0145] Step 6: By combining formulas (1)-(6), a spatiotemporal dimensionality-upgrading mapping from a two-dimensional image to a three-dimensional surface is established.

[0146] Step 7: s0, s t Let P represent the transverse tangents on the gear surface at time 0 and time t, respectively. c (x c ,y c ,z c This is equivalent to simplifying to the camera coordinate system X. c OZ c P c (x c ,0), P w0 Given point P c Mapped to world coordinate system X at time 0 w OY w Let the involute surface point s0 correspond to the extended equation l: y = kx + b. Through X w OY w The relationship between the intercepts of the two coordinate axes on the plane is used to derive the equation shown in equation (7), where γ is a scalar with a rotational direction. Figure 4 In the case of a negative value, at time t, l and s t Intersect at P wt Rotate the world coordinate system to the X-axis. wt OY wt , forming △Z w BB t We then use the sine theorem to solve for the corresponding intercepts.

[0147] (7);

[0148] Step 8: At time t, l is in X wt OY wt The equation is shown in equation (8), and P is obtained by calculation through (5), (6), and (8). wt In X wt OY wt The included angle θ wt .

[0149] (8);

[0150] Step 9: Using equation (9), calculate the transformation between any point (θ,z) on the surface of the gear involute and the pixel point (u,v) at time t=0.

[0151] (9);

[0152] Step 10: Calculate θ from (8) ’ wtSubstituting the value into equation (9), we can obtain P. wt The coordinates P' of the camera coordinate system corresponding to the zero-time coordinates c (x' c Substituting ,0) into equation (10), we can obtain the required original pixel values, providing a reliable reverse positioning and value calculation method for subsequent motion blur modeling.

[0153] (10);

[0154] Step 11: Given a fixed optical hardware photosensitive configuration, the orthogonal distance information Z... c Coupled with the grayscale dynamic response, a depth-based correction function H(x,y,t) is constructed to effectively compensate for the real grayscale shift caused by the dynamic changes in reflected light during motion. As shown in equation (11), d0 and d t denoted by , where represents the distance at the corresponding moment, and k represents the adaptive correction exponent considering the influence of the system's optical arrangement and the micro-rotation angle of the surface point.

[0155] (11);

[0156] Step 12: In Figure 4 In the middle, d0 and d t Represents Z at the corresponding time. c Coordinate value, i.e., P wt’ P c’ With P wt P c The length of θ can be obtained by substituting the gear involute equation (5) into (1) to obtain the corresponding solution equation (12), where θ ’ wt It is P ’ wt The involute angle, φ ’ wt It is the corresponding expansion angle, which can be calculated using equation (9).

[0157] (12);

[0158] Step 13: Calculate the motion blur image of the rotating involute surface according to equation (13). The coordinates of a pixel region g in the camera coordinate system are (x... c (y), after exposure time T, it moves to (x) ceLet G be the grayscale function of the point (u,v,t), where V(u,v,t) represents the original grayscale value of the surface point corresponding to the image coordinates (u,v) at time t, and H(u,v,t) represents the change function of the original grayscale value of the surface point corresponding to the image coordinates (u,v) at time t. Theoretically, each surface point reflects light from the lens surface with a different intensity, corresponding to a grayscale value under grayscale imaging conditions. However, due to hardware imaging limitations, within any pixel grid of the camera coordinate system, all points with the same x or y value have identical pixel values. During rotation, we let the y variable in G take the value (y,v,t). e +y s The formula ) / 2 can compress the molecular part to a double integral, which simplifies the calculation while maintaining the granularity of the simulation.

[0159] (13).

[0160] Unlike existing techniques that are mostly based on uniform linear motion or static image transformation, this method introduces an involute parametric equation defined by the base circle radius and the unfolding angle to accurately describe the continuous spatiotemporal evolution trajectory of points on the surface of a rotating object within the exposure time. This method breaks through the simplistic assumption of "spatiotemporal invariance" in traditional models, and can realistically reproduce the complex blurred textures generated by nonlinear motion under high-speed rotation conditions, solving the problem of lack of physical consistency in existing generated samples. In addition, for the tiny displacements caused by high-speed rotation, this method uses the sine theorem to construct a geometric solution model, achieving sub-pixel-level reverse localization from image pixels to instantaneous surface points in the world coordinate system while considering the rotation center deviation. Compared with traditional integer pixel-level mapping methods, this technique effectively eliminates the aliasing effect and geometric distortion caused by coordinate rounding, ensuring that the generated blurred image still maintains a strict geometric correspondence at the microscale, significantly improving the precision of the simulated image.

[0161] Unlike conventional methods that directly sample raw pixel values, this method constructs an adaptive grayscale correction function based on depth orthogonal distance. This mechanism dynamically adjusts instantaneous grayscale values ​​according to the depth changes and illumination angle changes of surface points during rotation, thereby simulating the brightness changes and shadow effects caused by object rotation in real industrial scenes. This results in generated images that not only contain motion blur but also possess realistic photometric consistency, further reducing the distribution difference between simulated and real-world acquired data. Furthermore, this method abandons simple frame stacking or linear convolution processing, employing spatiotemporal double integration to synthesize instantaneous grayscale values ​​within the exposure time. By utilizing the consistency characteristics of grayscale distribution within pixel grids for dimensionality simplification during integration and accurately handling interpolation at non-integer coordinate positions, this method can generate motion-blurred images with continuous and smooth transition characteristics. This processing approach is not only computationally efficient but also perfectly reproduces the accumulation process of light energy by the camera sensor during exposure, ensuring the physical realism of the imaging results.

[0162] This method can efficiently generate dynamic blurred images with spatiotemporal consistency and geometric realism, thereby significantly improving the generalization ability and detection accuracy of industrial vision recognition systems under high-speed rotating conditions.

[0163] Example 2

[0164] To better illustrate the effectiveness of this method, the following experiment was conducted.

[0165] The dataset is derived from multiple batches of involute gear samples with known machining dimensions. Through partial shearing of the involute surface, an original dataset D of 5258 was formed. r This dataset contains an equal number of one-to-one paired blurred / sharp images (D). rb / D rs The blurred image size is 250×250 pixels, designed to simulate a realistic motion blur calculation scenario as closely as possible. A 50-pixel margin is left on each side of the clear image in the horizontal direction, resulting in a size of 350×250 pixels. Performance comparisons and validations of the experimental model are conducted within the 250×250 pixel range for image matching. To ensure data reliability, the blurred image is subjected to various speeds × exposure times × Z-axis measurements. c -X w Captured under the angled grouping.

[0166] To address the issue of grayscale fitting of surface points after minute rotations under specific environmental lighting configurations and surface features, a suitable adaptive correction exponent k value needs to be determined. First, static-dynamic image sampling is performed on the involute surface under the actual lighting conditions of the acquisition system. Then, by substituting the specific k value into the proposed method, a corresponding simulated motion-blurred image is generated based on the aforementioned static image. Based on the definition of k, only the grayscale value changes of the same surface point at the beginning and end of a minute rotation are considered, without considering factors such as the structural similarity of image quality indicators, thus introducing P-PSNR. The generated blurred image under specific k-value conditions is compared with the real motion-blurred image as an evaluation of the k-value's fit. Through grouping and statistical analysis of different k values, the k value with the highest fit is finally obtained.

[0167] Based on the above process, from D rs 10% of the images in each group are randomly sampled, and 5% of the pixel rows are drawn from them at equal intervals. Simulated pixel rows are generated using this method under different k values ​​(0.1 division value). In order to evaluate the point-by-point pixel unit similarity under the sampling conditions, P-PSNR is introduced, as shown in Equation (14).

[0168] (14);

[0169] Experimental results show that under small rotation conditions, grayscale shift no longer strictly follows the inverse square law of ideal static conditions, and is significantly affected by the actual illumination intensity arrangement and three-dimensional surface features of the system. Furthermore, introducing a grayscale correction mechanism can enhance the pixel-by-pixel simulation performance by up to 0.18 dB. Setting the k value of equation (14) to -14.4 yields a better overall correction effect, and batches of D... rs Equal number and approximating the real blurred image D rb Full-size blurred image dataset D gb .

[0170] The proposed method generates an equal-quantity blurred image. It is worth mentioning that, in actual calculation, the double integral of equation (2) is optimized by interpolation within the pixel unit, as shown in equation (15):

[0171] (15);

[0172] While significantly reducing computational load, the accuracy of generated images (less than 1 grayscale value) was maintained. Several blurring methods based on different principles were selected for comparative experiments, and the parameters of each method were adjusted for different groupings to match real-world physical scenes. Through multiple comparative experiments under different combinations of rotation speed and exposure time, the mean performance indicators for each method processing all combinations of image datasets are listed in Table 1. Corresponding examples are provided. Figure 5 As shown.

[0173] Table 1

[0174]

[0175] Clearly, Gaussian blur, mean blur, and rectangular motion blur cannot approximate the true 3D rotation pattern by adjusting the point spread function, resulting in significantly distorted images with low similarity. Theoretically, linear neighborhood mean blur and linear motion blur can approximate dynamic surface imaging features, but due to the fundamental limitation of integer kernel size, their granularity cannot match the continuity of sub-pixel-level motion trajectories, leading to differences from true rotational blur. Furthermore, none of the above methods possess nonlinear gain for pixel units, failing to simulate blur pattern changes caused by involute phase angle differences. In contrast, this method, by introducing continuous spatiotemporal upscaling mapping and an adaptive grayscale correction mechanism, effectively overcomes the accuracy loss caused by traditional convolution kernel discretization, exhibiting superior pixel-level similarity under various rotation speeds and exposure conditions.

[0176] In summary, our proposed method achieves the best results in FID, PSNR, and SSIM metrics, outperforming the suboptimal methods by 16.4%, 2.9%, and 1.2%, respectively. This validates the effectiveness and superiority of our method in generating realistic 3D rotated surface blurred images, significantly outperforming traditional methods based on blur kernel convolution. This simulation generation method not only reduces the dependence on dynamic image acquisition from actual equipment but also provides high-quality, scalable data support for model training in dynamic blurred scenarios. For any combination of speed-exposure products, our method is equivalent to traditional motion blur methods; for example, the blur simulation effect of a set of n*T images is the same as that of 10n*0.1T. Therefore, the feasibility and superiority of our verified method can be extended to a wider range of industrial applications, especially dynamic blurred environments caused by higher-speed rotation.

[0177] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit the technical solutions. Those skilled in the art should understand that any modifications or equivalent substitutions to the technical solutions of the present invention without departing from the spirit and scope of the present invention should be covered within the scope of the claims of the present invention.

Claims

1. A sub-pixel-level rotation simulation method for involute surface images, characterized in that, Includes the following steps: S1. Establishment of imaging system calibration and spatiotemporal mapping relationship: Obtain the intrinsic and extrinsic parameter matrices of the imaging system. The intrinsic parameter matrix includes scaling factors and principal point coordinates, and the extrinsic parameter matrix includes rotation and translation matrices. Based on the intrinsic and extrinsic parameter matrices, establish a multidimensional transformation relationship between the image pixel coordinate system, the camera coordinate system, and the world coordinate system, and establish the mapping rules between image pixels and three-dimensional spatial points in the world coordinate system. S2. Modeling of rotating surface motion based on the involute equation: By introducing the involute parametric equation defined by the base circle radius and the development angle, a geometric model is performed on a target rotating object with an involute surface, and the three-dimensional spatial distribution of the surface points of the object is obtained. By combining the set average rotation speed, a continuous evolution equation of the rotation angle of the surface point at any time during the exposure time is constructed, thereby determining the continuous spatiotemporal motion trajectory of the surface point during the rotation process, and establishing a dynamic correspondence between the trajectory and the image pixel. S3. Sub-pixel-level reverse spatial positioning based on the sine theorem: Construct a pixel grid for the motion-blurred image to be synthesized. For any target pixel in the pixel grid, use the mapping rule established in S1 and the dynamic correspondence established in S2 to inversely map the target pixel to the world coordinate system. Considering the rotation center deviation, a geometric solution model is constructed using the sine theorem to solve for the instantaneous surface point and its involute angle in the world coordinate system corresponding to the target pixel at time t. Based on the involute angle and mapping rule, the original pixel point and its original pixel value corresponding to the instantaneous surface point at the initial moment are derived in reverse. S4. Adaptive grayscale correction based on depth orthogonal distance: Construct a grayscale correction function and use it to correct the original pixel values ​​obtained in S3 to obtain the instantaneous grayscale value at time t. S5, Spatiotemporal double integral imaging synthesis: During the exposure time, the instantaneous grayscale values ​​at each moment after S4 correction are subjected to double integration operations in spatial and temporal dimensions on the motion trajectory corresponding to the target pixel. In the double integral operation, the integral dimension is simplified based on the consistency characteristics of the gray-level distribution of pixels in a specific direction within the pixel grid, and the gray-level values ​​at non-integer coordinate positions are processed to synthesize a motion-blurred image with physical consistency.

2. The sub-pixel level rotation simulation method for involute surface images as described in claim 1, characterized in that: In step S1, the intrinsic parameter matrix includes the X-axis scaling factor a, the Y-axis scaling factor b, and the principal point coordinates (u0, v0); the extrinsic parameter matrix includes the rotation matrix R and the translation matrix T. r The rotation matrix R is composed of rotation angles α, β, and γ about each coordinate axis of the world coordinate system, and the translation matrix T... r The translation component t of the camera origin relative to the origin of the world coordinate system x t y t z constitute.

3. The sub-pixel level rotation simulation method for involute surface images as described in claim 2, characterized in that: In step S2, the involute parametric equation is: ； Where r0 is the radius of the base circle. For the exhibition angle; The equation for the continuous evolution of the rotation angle is: ； in, Let be the angle through which the surface point rotates in time t; Let be the initial angle of the surface point, and n be the average rotational speed over time t.

4. The sub-pixel level rotation simulation method for involute surface images as described in claim 3, characterized in that: In step S3, the construction of the geometric solution model using the sine theorem includes: The target pixel is inversely mapped to the X coordinate system of the world coordinate system. w OY w The plane is used to obtain its surface reference point P at time zero. w0 ; Through the surface reference point P w0 Establish an extended straight line l, the equation of which is y = kx + b, where k and b are determined by the surface reference point P. w0 The coordinates are determined; The world coordinate system is equivalently rotated to time t, such that the involute surface profile at time t intersects the extended straight line l at the instantaneous surface point P. wt Wherein, the involute surface profile at time t is the involute trajectory after rotation based on the continuous evolution equation of the rotation angle; The point formed by the center of rotation, the intercept of the extended line l, and the instantaneous surface point P. wt Within the triangle formed, the instantaneous surface point P is solved using the sine theorem. wt The coordinates in the equivalent rotated coordinate system are obtained, and the corresponding instantaneous involute angle θ is obtained. ’ wt .

5. The sub-pixel level rotation simulation method for involute surface images as described in claim 4, characterized in that: In S3, the following transformation relationship between pixel coordinates and world coordinates is used, based on the instantaneous involute angle θ. ’ wt Reverse derive the original pixel: ； ； Where (u,v) are the original pixel coordinates to be obtained; r ij For each element of the rotation matrix R, i = 1, 2 represents a row, j = 1, 2, 3 represents a column; z w Let P be the instantaneous surface point wt Z-axis coordinates in the world coordinate system For θ ’ wt The corresponding angle of display.

6. The sub-pixel level rotation simulation method for involute surface images as described in claim 5, characterized in that: In step S4, the grayscale correction function H is: H=(d0 / d t ) k ; Where d0 is the initial orthogonal distance of the instantaneous surface point relative to the camera optical center at the initial moment, d t t represents the instantaneous orthogonal distance of a point on the surface at time t relative to the optical center of the camera, and k is the adaptive correction exponent.

7. The sub-pixel level rotation simulation method for involute surface images as described in claim 6, characterized in that: The initial orthogonal distance d0 and the instantaneous orthogonal distance d t Calculated in the following way: The instantaneous surface point P wt instantaneous involute angle θ ’ wt and corresponding display angles Substituting into the involute parametric equation, we obtain its world coordinates; Then, using the coordinate system transformation relationship established in S1, the world coordinates are converted into coordinates in the camera coordinate system, and the depth component along the camera optical axis is extracted as the initial orthogonal distance d0 or the instantaneous orthogonal distance d. t .

8. The sub-pixel level rotation simulation method for involute surface images as described in claim 6, characterized in that: The adaptive correction index k is determined by the following iterative optimization method: Step A: Acquire a real dynamic blur image based on the actual imaging system as the reference image; Step B: Set a set of candidate correction index k values; Step C: Iterate through the candidate correction index k values, and for each k value, execute steps S3 to S5 in sequence to generate the corresponding synthetic motion blur image; Step D: Calculate the point-by-point peak signal-to-noise ratio (P-PSNR) between each of the synthesized motion-blurred images and the reference image; Step E: Select the candidate k value that maximizes the P-PSNR as the optimal solution for the adaptive correction exponent k.

9. The sub-pixel level rotation simulation method for involute surface images as described in claim 1, characterized in that: In step S5, the simplification of the integration dimension includes: based on the characteristic that points with the same Y coordinate value in the same pixel grid in the camera coordinate system and perpendicular to the motion trajectory direction have approximately the same gray value, in the double integration operation, the Y coordinate component is taken as the arithmetic mean of the Y coordinates of the starting point and the ending point of the motion trajectory. An interpolation algorithm is used to process the grayscale values ​​at non-integer coordinate positions.

10. The sub-pixel level rotation simulation method for involute surface images as described in claim 1, characterized in that: The rotating object with an involute surface includes an involute spur gear, an involute helical gear, an involute spline shaft, an involute cam, or a rotating workpiece with an involute tooth profile.

Images