A Super-Resolution Reconstruction Method for Infrared Images Based on Thermal Imager Blur Kernel Calibration

Abstract

This invention provides a method for super-resolution reconstruction of infrared images based on thermal imager fuzzy kernel calibration, comprising the following steps: constructing a multi-aperture calibration target image acquisition system; acquiring a set of target images using an infrared thermal imager to be calibrated; detecting the position of each circle center in each target image, determining the thermal imager's attitude, and generating a corresponding high-resolution target image; simultaneously inputting the actual target image and the generated high-resolution target image into a fuzzy kernel solving network to obtain the fuzzy kernel calibration result for the corresponding region; dividing the low-resolution image to be reconstructed into multiple image blocks, simultaneously inputting the image blocks and the fuzzy kernel of the corresponding region into a non-blind super-resolution reconstruction network to obtain reconstructed image blocks; and merging the reconstructed image blocks to obtain the final super-resolution reconstructed image. This invention provides a method for super-resolution reconstruction of infrared images based on thermal imager fuzzy kernel calibration, which can accurately calibrate the spatially non-uniform fuzzy kernel caused by the optical system, thereby improving the super-resolution reconstruction effect of infrared images.

Description

Technical Field

[0001] This invention belongs to the field of infrared image processing technology, specifically relating to an infrared image super-resolution reconstruction method based on thermal imager fuzzy kernel calibration. Background Technology

[0002] Infrared imaging offers advantages such as near-all-day and near-all-weather operation, leading to its increasingly widespread applications in security, industry, and remote sensing. However, the complex manufacturing process of infrared detectors and the difficulty in preparing large-size, highly uniform infrared crystal materials result in low yields and high costs for large-area, high-resolution focal plane array devices. Furthermore, the longer wavelength of infrared light and the larger diffraction spot limit the improvement of infrared sensor resolution. Therefore, infrared image super-resolution reconstruction methods have significant application value.

[0003] Currently, numerous infrared image super-resolution reconstruction methods exist. While these methods have achieved satisfactory results on simulated images, they are prone to artifacts or excessive blurring when tested on real-world images. This is primarily because they assume a globally invariant blur kernel, estimating only one kernel for the entire image. However, real-world infrared optical systems, due to aberrations and thermal defocusing, are not strictly linear spatially motion-invariant systems. Therefore, these methods still struggle to achieve ideal results for real-world scene images. Research on spatially non-uniform blur kernels largely focuses on motion blur caused by camera shake or object movement, paying less attention to blurring caused by the optical system itself. Some deep learning-based methods directly estimate spatially non-uniform blur kernels from low-resolution images, but because blur kernel estimation is an ill-posed problem, it is difficult to achieve ideal results, particularly for weakly textured areas and single-edge regions. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes an infrared image super-resolution reconstruction method based on thermal imager fuzzy kernel calibration. This method can accurately estimate the fuzzy kernel at each spatial location of the thermal imager, thereby improving the super-resolution reconstruction effect. Furthermore, for any infrared imaging device, using the technology of this invention, only a set of multi-hole target images covering all regions of the image needs to be acquired to achieve spatially non-uniform fuzzy kernel calibration, resulting in a small workload and ease of implementation.

[0005] The technical solution adopted by the present invention to achieve the above objectives is as follows:

[0006] A method for super-resolution reconstruction of infrared images based on thermal imager fuzzy kernel calibration includes the following steps:

[0007] 1) Acquire a set of target images, detect the position of each circle center in each target image, determine the thermal imager attitude, and generate the corresponding high-resolution target image;

[0008] 2) Input the acquired original target image and the corresponding generated high-resolution target image into the fuzzy kernel solving network simultaneously to obtain the fuzzy kernel calibration results for the corresponding region;

[0009] 3) Divide the low-resolution image to be reconstructed into multiple image blocks, and simultaneously input the image blocks and the blur kernels of the corresponding regions into the non-blind super-resolution reconstruction network to obtain the reconstructed image blocks;

[0010] 4) Merge the reconstructed image blocks to obtain the final super-resolution reconstructed image.

[0011] Step 1) includes the following steps:

[0012] 1.1) Establish the image coordinate system and the target coordinate system respectively, and use the OpenCV circle center detection algorithm to calculate the center p1 to p2 of each circle in the image. n The pixel coordinates (u1, v1) ~ (u n v n );

[0013] 1.2) Based on the physical dimensions of the target, obtain the corresponding center p. 1 1~p ′ n The physical coordinates (x1, y1) ~ (x n ,y n );

[0014] 1.3) Calculate the homography matrix H between pixel coordinates and physical coordinates.

[0015]

[0016] 1.4) Traverse the pixel coordinates (u) in the high-resolution image to be determined. HR ,v HR ), calculate its corresponding pixel coordinates (u) in the low-resolution image. LR ,v LR ), and calculate (u) based on the homography matrix H. LR ,v LR The corresponding physical coordinates (x, y)

[0017]

[0018]

[0019] Where s is the super-resolution magnification;

[0020] 1.5) Determine the distance from the physical coordinates (x, y) of each pixel to the center p of each circle. ′ 1~p ′ nIf the distances of the coordinates are all greater than the radius of the circle, then the corresponding pixel is assigned the average gray value of the background outside the circle; otherwise, the corresponding pixel is assigned the average gray value of the area inside the circle, thus obtaining a high-resolution target image.

[0021] Step 1) further includes the following steps:

[0022] 1.6) The obtained high-resolution image is divided into multiple regions to solve for the blur kernel of each region, specifically:

[0023] Choose the center of any circle that is not on the boundary as the center. Select the four circles that are adjacent to it and whose center is the shortest distance from the center. Use 1.5 times the distance between any two adjacent centers of these four circles as the side length to cut out a square region. Each region contains five complete circles.

[0024] Step 2) includes the following steps:

[0025] 2.1) Simulation to generate training data for the fuzzy kernel solver network:

[0026] 2.2) Using the training data, train the fuzzy kernel solver network:

[0027] The fuzzy kernel k of the network output is obtained by solving the fuzzy kernel problem. i With the fuzzy kernel k generated by simulation gt The L1 loss between the two is used as the loss function for supervised training;

[0028] 2.3) Input the actual target image and the generated high-resolution target image into the trained fuzzy kernel solving network at the same time, perform network inference, and obtain the fuzzy kernel solving results for the corresponding region.

[0029] Step 2.1) includes the following steps:

[0030] 2.1.1) Randomly generate the attitude angle and focal length of the virtual thermal imager, and calculate the homography matrix H. t

[0031] H t =K v R rot R el R az

[0032] Among them, R az R el and R rot These are the rotation matrices corresponding to the heading, pitch, and roll attitude angles of the virtual thermal imager, respectively, K. v This is the intrinsic parameter matrix of the virtual camera;

[0033]

[0034] Among them, f x f y The focal ratio, W, is obtained by adding a random error of 10% to the focal ratio of the thermal imager under test. t ×H t The resolution of the generated image;

[0035] 2.1.2) Using the homography matrix H t Generate simulated high-resolution images;

[0036] 2.1.3) Randomly generate anisotropic Gaussian blur kernel k gt (i,j)

[0037]

[0038] Where N is the normalization parameter, C is the spatial coordinate, and Σ is the covariance matrix.

[0039]

[0040] Where θ is the rotation angle, and λ1 and λ2 are both eigenvalues;

[0041] 2.1.4) The generated blur kernel is used to blur and downsample the simulated high-resolution image, and Gaussian random noise is added to obtain a low-resolution image, which is used as training data.

[0042] The fuzzy kernel solving network consists of a shallow feature extraction module, a deep feature extraction module, and a fuzzy kernel reconstruction module connected in sequence, wherein:

[0043] The shallow feature extraction module extracts low-resolution image features and high-resolution image features respectively, and obtains shallow features by dimensional concatenation;

[0044] The deep feature extraction module sequentially passes the shallow features through the residual module, downsampling module, and upsampling module to obtain the extracted deep features;

[0045] The fuzzy kernel reconstruction module sequentially passes deep features through a first convolutional layer, a global average pooling layer, a second convolutional layer, and a soft threshold activation layer to obtain a reconstructed fuzzy kernel.

[0046] Step 3) includes the following steps:

[0047] 3.1) Divide the low-resolution image to be reconstructed into multiple image blocks using overlapping image blocks;

[0048] 3.2) Input the image patch and the corresponding fuzzy kernel of the image patch calculated by the fuzzy kernel solution network into the trained non-blind super-resolution reconstruction network to obtain the reconstructed image patch.

[0049] Step 4) includes the following steps:

[0050] 4.1) Remove the boundaries of each reconstructed image patch;

[0051] 4.2) Calculate the Euclidean distance from the pixels in the overlapping region to the center of the image block;

[0052] 4.3) Perform weighted average fusion based on Euclidean distance.

[0053] An infrared image super-resolution reconstruction system based on thermal imager fuzzy kernel calibration includes:

[0054] The high-resolution target image generation module is used to acquire a set of target images, detect the position of each circle center in each target image, determine the thermal imager attitude, and generate the corresponding high-resolution target image.

[0055] The fuzzy kernel calibration module is used to simultaneously input the acquired original target image and the corresponding generated high-resolution target image into the fuzzy kernel solving network to obtain the fuzzy kernel calibration result of the corresponding region;

[0056] The image reconstruction module is used to divide the low-resolution image to be reconstructed into multiple image blocks, and simultaneously input the image blocks and the blur kernels of the corresponding regions into the non-blind super-resolution reconstruction network to obtain the reconstructed image blocks.

[0057] The image stitching module is used to merge reconstructed image blocks to obtain the final super-resolution reconstructed image.

[0058] The present invention has the following beneficial effects and advantages:

[0059] The infrared image super-resolution reconstruction method based on thermal imager blur kernel calibration can calibrate the spatial non-uniform blur caused by the optical system. The super-resolution reconstruction method using the calibrated blur kernel and image block can significantly improve the super-resolution reconstruction effect. Attached Figure Description

[0060] Figure 1 This is a schematic diagram of the multi-hole calibration target pattern in an embodiment of the present invention;

[0061] Figure 2 This is a schematic diagram of a target image actually captured by a thermal imager in an embodiment of the present invention;

[0062] Figure 3 This is a schematic diagram of the image coordinate system and physical coordinate system constructed by solving the thermal imager attitude in an embodiment of the present invention;

[0063] Figure 4 This is a schematic diagram of high / low resolution target image pairs captured in an embodiment of the present invention;

[0064] Figure 5This is a diagram of the fuzzy kernel solving network structure in an embodiment of the present invention;

[0065] Figure 6 This is a schematic diagram of the blur kernel calibration result of a thermal imager in an embodiment of the present invention;

[0066] Figure 7 This is a block diagram illustrating the principle of super-resolution reconstruction in an embodiment of the present invention;

[0067] Figure 8 This is a comparison chart of the reconstruction results of this method with two other methods in this embodiment of the invention;

[0068] Figure 9 This is a flowchart of the present invention. Detailed Implementation

[0069] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0070] This invention provides a method for super-resolution reconstruction of infrared images based on thermal imager fuzzy kernel calibration, such as... Figure 9 As shown, it includes the following steps:

[0071] Step S1: Set up a target image acquisition system and use the thermal imager to be calibrated to acquire a set of images of a multi-hole calibration target.

[0072] Specifically, such as Figure 1 As shown, the calibration target pattern in this embodiment consists of 13 regularly arranged circular holes. Its main advantages are that it contains gradient information in all directions, which can be used for anisotropic blur kernel estimation; the center coordinates can be accurately extracted through the center detection algorithm, thereby determining the camera pose without the need for auxiliary features such as corner points; and based on the determined camera pose, an ideal high-resolution image can be quickly generated.

[0073] Specifically, the target image acquisition system in this embodiment consists of a blackbody, a multi-aperture calibration target, a collimator, a rotating platform, a thermal imager to be calibrated, and a computer. The infrared thermal imager is fixed to a two-axis rotating platform, with its optical axis aligned with the collimator. Figure 2 The image shown is a target image actually captured by the thermal imager in this embodiment.

[0074] Furthermore, since the target image cannot cover the entire field of view, the rotating platform is used to drive the thermal imager to perform horizontal and vertical scanning movements to acquire a set of target images, thereby achieving full coverage of the field of view.

[0075] Step S2: For each target image, detect the position of each circle center in the image, determine the thermal imager attitude, and generate the corresponding high-resolution target image;

[0076] Specifically, high-resolution target generation includes the following steps:

[0077] S201: As Figure 3 As shown, this embodiment establishes an image coordinate system and a target coordinate system, which is beneficial for the OpenCV circle center detection algorithm to calculate the circle centers p1 to p2 in the image. 13 The pixel coordinates (u1, v1) ~ (u 13 ,v 13 );

[0078] S202: Based on the physical dimensions of the target, obtain the corresponding center p. ′ 1~p ′ 13 The physical coordinates (x1, y1) ~ (x 13 ,y 13 ).

[0079] S203: Calculate the transformation matrix H between image coordinates and physical coordinates using the following formula.

[0080]

[0081] S204: Traverse the pixel coordinates (u) in the high-resolution image to be determined HR ,v HR ), calculate its pixel coordinates (u) in the low-resolution image. LR ,v LR )

[0082]

[0083] Calculate (u) based on the homography matrix H. LR ,v LR The corresponding physical coordinates (x, y)

[0084]

[0085] S205: Determine the distance from the physical coordinates (x, y) to each circle center p. ′ 1~p ′ 13 If the distances of the coordinates are all greater than the radius of the circle, then the corresponding pixel is assigned the average gray value of the background outside the circle; otherwise, the corresponding pixel is assigned the average gray value of the area inside the circle, thus obtaining a high-resolution target image.

[0086] Furthermore, with centers p4, p5, p9, and p respectively... 10 Centered on the image, and with a side length 1.5 times the distance between p4 and p5, a square image region is extracted. Each region essentially contains 5 complete circles, resulting in the following: Figure 4 The image pair shown is used to solve for the blur kernel in this region.

[0087] Step S3: Simultaneously input the acquired target image and the generated high-resolution target image into the fuzzy kernel solving network to obtain the fuzzy kernel calibration result of the target region;

[0088] Specifically, such as Figure 5 The diagram shows the network structure for solving the fuzzy kernel in this embodiment. The fuzzy kernel estimation network consists of a shallow feature extraction module, a deep feature extraction module, and a fuzzy kernel reconstruction module. The shallow feature extraction module extracts low-resolution and high-resolution image features and obtains a shallow feature representation through dimensional concatenation. The deep feature extraction module adopts a UNet structure, consisting of a residual module, a downsampling module, and an upsampling module, to extract deep features. The fuzzy kernel reconstruction module consists of a first convolutional layer, a global average pooling layer, a second convolutional layer, and a soft-thresholding (softmax) activation layer, reconstructing the fuzzy kernel using the deep features.

[0089] Furthermore, the fuzzy kernel solution network training process shown includes the following steps:

[0090] S301: Simulate and generate training data for the fuzzy kernel solver network.

[0091] Specifically, the attitude angle and focal length of the virtual thermal imager are randomly generated, and the homography matrix is ​​calculated according to the formula.

[0092] H t =K v R rot R el R az

[0093] Where R az R el and R rot These are the rotation matrices corresponding to the heading, pitch, and roll attitude angles of the virtual thermal imager, respectively. The heading and pitch angles are uniformly distributed within (-10°, 10°), and the roll angle is uniformly distributed within (-5°, 5°); K v Intrinsic parameter matrix of virtual camera

[0094]

[0095] Where f x f y The focal ratio, W, is obtained by adding a random error of 10% to the focal ratio of the thermal imager under test. t ×H t The resolution of the generated image.

[0096] Furthermore, using the homography matrix H t Following steps S204 to S205, a simulated high-resolution image is generated;

[0097] Furthermore, anisotropic Gaussian blur kernels are randomly generated.

[0098]

[0099] Where N is the normalization parameter, C is the spatial coordinates, i,j∈[-r,r], the size of the fuzzy kernel is (2r+1)×(2r+1), and Σ is the covariance matrix.

[0100]

[0101] Where θ is the rotation angle, and λ1 and λ2 are both eigenvalues.

[0102] Furthermore, the generated blur kernel is used to blur and downsample the high-resolution image, and Gaussian random noise is added to obtain a low-resolution image.

[0103] S302: Use simulation-generated data to train fuzzy kernel solution network parameters.

[0104] Specifically, the fuzzy kernel j output by the network i With the fuzzy kernel k generated by simulation gt The L1 loss between the two is used as the loss function for supervised training.

[0105] S303: Input the actual target image output in step 2 and the generated high-resolution target image into the fuzzy kernel solving network simultaneously, perform network inference, and obtain the fuzzy kernel solving results for the corresponding region.

[0106] like Figure 6 The image shown is a blur kernel for a thermal imager calibrated in this embodiment.

[0107] like Figure 7 The diagram shown illustrates the principle block diagram of image super-resolution reconstruction provided in this embodiment. Specifically, it includes two steps, s4 and s5.

[0108] Step S4: Divide the low-resolution image to be reconstructed into n image blocks, and simultaneously input the image blocks and the corresponding blur kernels into the non-blind super-resolution reconstruction network to obtain the reconstructed image blocks.

[0109] Specifically, step S4 includes the following steps:

[0110] S401: Divide the low-resolution image to be reconstructed into n image blocks using overlapping image blocks. Each image block is 128×128 in size, with 40 columns overlapping between adjacent left and right image blocks and 40 rows overlapping between adjacent top and bottom image blocks.

[0111] S402: Input the image patch and its corresponding blur kernel simultaneously into the trained UsrNet super-resolution reconstruction network to obtain the reconstructed image patch. UsrNet can also be replaced with other non-blind super-resolution reconstruction networks.

[0112] Step S5: Merge the n reconstructed image blocks to obtain the final super-resolution reconstructed image.

[0113] Specifically, step S5 includes the following steps:

[0114] S501: For each reconstructed 128×128 image block, remove the boundaries and retain the center 120×120 pixels;

[0115] S502: Calculate the Euclidean distance from the pixels in the overlapping region to the center of the image block;

[0116] S503: Weighted average fusion based on Euclidean distance.

[0117] like Figure 8 The image shows a comparison of the super-resolution reconstruction results of the method in this embodiment with two other methods. (a) represents the Bicubic method, (b) the MANet+RRDB-SFT method, and (c) the method provided by this invention. The method of this invention achieves higher edge sharpness and clearer weak textures in the reconstructed image, resulting in better performance.

Claims

1. A method for super-resolution reconstruction of infrared images based on thermal imager fuzzy kernel calibration, comprising the following steps: 1) Acquire a set of target images, detect the position of each circle center in each target image, determine the thermal imager attitude, and generate the corresponding high-resolution target image; 2) Input the acquired original target image and the corresponding generated high-resolution target image into the fuzzy kernel solving network simultaneously to obtain the fuzzy kernel calibration results for the corresponding region; 3) Divide the low-resolution image to be reconstructed into multiple image blocks, and simultaneously input the image blocks and the blur kernels of the corresponding regions into the non-blind super-resolution reconstruction network to obtain the reconstructed image blocks; 4) Merge the reconstructed image patches to obtain the final super-resolution reconstructed image; Step 2) includes the following steps: 2.1) Simulate and generate training data for the fuzzy kernel solver network; 2.2) Using the training data, train the fuzzy kernel solver network: Solving the fuzzy kernel of the network output using fuzzy kernels With the fuzzy kernel generated by simulation Between The loss is used as a loss function for supervised training; 2.3) Input the actual target image and the generated high-resolution target image into the trained fuzzy kernel solving network at the same time, perform network inference, and obtain the fuzzy kernel solving results for the corresponding region; Step 2.1) includes the following steps: 2.1.1) Randomly generate the attitude angle and focal length of the virtual thermal imager, and calculate the homography matrix. : ； in, , and These are the rotation matrices corresponding to the heading, pitch, and roll attitude angles of the virtual thermal imager, respectively. This is the intrinsic parameter matrix of the virtual camera; ； in, , The focal ratio is obtained by adding a 10% random error to the focal ratio of the thermal imager being tested. The resolution of the generated image; 2.1.2) Using the homography matrix Generate simulated high-resolution images; 2.1.3) Randomly generate anisotropic Gaussian blur kernels : ； in, N For normalization parameters, C For spatial coordinates, Σ Here is the covariance matrix: ； in, For rotation angle, and All are eigenvalues; 2.1.4) The generated blur kernel is used to blur and downsample the simulated high-resolution image, and Gaussian random noise is added to obtain a low-resolution image, which is used as training data.

2. The infrared image super-resolution reconstruction method based on thermal imager fuzzy kernel calibration according to claim 1, characterized in that, Step 1) includes the following steps: 1.1) Establish the image coordinate system and the target coordinate system respectively, and use the OpenCV circle center detection algorithm to calculate the center of each circle in the image. ~ pixel coordinates ~ ; 1.2) Based on the physical dimensions of the target, obtain the corresponding center point. ~ physical coordinates ~ ; 1.3) Calculate the homography matrix between pixel coordinates and physical coordinates. H： ； 1.4) Traverse the pixel coordinates in the high-resolution image to be determined. Calculate its corresponding pixel coordinates in the low-resolution image. And according to the homography matrix H calculate Corresponding physical coordinates : ； ； in, Super-resolution magnification; 1.5) Determine the physical coordinates of each pixel. To each center ~ If the distances of the coordinates are all greater than the radius of the circle, then the corresponding pixel is assigned the average gray value of the background outside the circle; otherwise, the corresponding pixel is assigned the average gray value of the area inside the circle, thus obtaining a high-resolution target image.

3. The infrared image super-resolution reconstruction method based on thermal imager fuzzy kernel calibration according to claim 2, characterized in that, Step 1) further includes the following steps: 1.6) The obtained high-resolution image is divided into multiple regions to solve for the blur kernel of each region, specifically: Choose the center of any circle that is not on the boundary as the center. Select the four circles that are adjacent to it and whose center is the shortest distance from the center. Use 1.5 times the distance between any two adjacent centers of these four circles as the side length to cut out a square region. Each region contains five complete circles.

4. The infrared image super-resolution reconstruction method based on thermal imager fuzzy kernel calibration according to claim 1, characterized in that, The fuzzy kernel solving network consists of a shallow feature extraction module, a deep feature extraction module, and a fuzzy kernel reconstruction module connected in sequence, wherein: The shallow feature extraction module extracts low-resolution image features and high-resolution image features respectively, and obtains shallow features by dimensional concatenation; The deep feature extraction module sequentially passes the shallow features through the residual module, downsampling module, and upsampling module to obtain the extracted deep features; The fuzzy kernel reconstruction module sequentially passes deep features through a first convolutional layer, a global average pooling layer, a second convolutional layer, and a soft threshold activation layer to obtain a reconstructed fuzzy kernel.

5. The infrared image super-resolution reconstruction method based on thermal imager fuzzy kernel calibration according to claim 1, characterized in that, Step 3) includes the following steps: 3.1) Divide the low-resolution image to be reconstructed into multiple image blocks using overlapping image blocks; 3.2) Input the image patch and the corresponding fuzzy kernel of the image patch calculated by the fuzzy kernel solution network into the trained non-blind super-resolution reconstruction network to obtain the reconstructed image patch.

6. The infrared image super-resolution reconstruction method based on thermal imager fuzzy kernel calibration according to claim 1, characterized in that, Step 4) includes the following steps: 4.1) Remove the boundaries of each reconstructed image patch; 4.2) Calculate the Euclidean distance from the pixels in the overlapping region to the center of the image block; 4.3) Perform weighted average fusion based on Euclidean distance.

7. An infrared image super-resolution reconstruction system based on thermal imager fuzzy kernel calibration, comprising: The high-resolution target image generation module is used to acquire a set of target images, detect the position of each circle center in each target image, determine the thermal imager attitude, and generate the corresponding high-resolution target image. The fuzzy kernel calibration module is used to simultaneously input the acquired original target image and the corresponding generated high-resolution target image into the fuzzy kernel solving network to obtain the fuzzy kernel calibration result of the corresponding region; The image reconstruction module is used to divide the low-resolution image to be reconstructed into multiple image blocks, and simultaneously input the image blocks and the blur kernels of the corresponding regions into the non-blind super-resolution reconstruction network to obtain the reconstructed image blocks. The image stitching module is used to merge reconstructed image blocks to obtain the final super-resolution reconstructed image; The fuzzy kernel calibration module performs the following steps: 2.1) Simulate and generate training data for the fuzzy kernel solver network; 2.2) Using the training data, train the fuzzy kernel solver network: Solving the fuzzy kernel of the network output using fuzzy kernels With the fuzzy kernel generated by simulation Between The loss is used as a loss function for supervised training; 2.3) Input the actual target image and the generated high-resolution target image into the trained fuzzy kernel solving network at the same time, perform network inference, and obtain the fuzzy kernel solving results for the corresponding region; Step 2.1) Includes the following steps: 2.1.1) Randomly generate the attitude angle and focal length of the virtual thermal imager, and calculate the homography matrix. : ； in, , and These are the rotation matrices corresponding to the heading, pitch, and roll attitude angles of the virtual thermal imager, respectively. This is the intrinsic parameter matrix of the virtual camera; ； in, , The focal ratio is obtained by adding a 10% random error to the focal ratio of the thermal imager being tested. The resolution of the generated image; 2.1.2) Using the homography matrix Generate simulated high-resolution images; 2.1.3) Randomly generate anisotropic Gaussian blur kernels : ； in, N For normalization parameters, C For spatial coordinates, Σ Here is the covariance matrix: ； in, For rotation angle, and All are eigenvalues; 2.1.4) The generated blur kernel is used to blur and downsample the simulated high-resolution image, and Gaussian random noise is added to obtain a low-resolution image, which is used as training data.

Images