Dark and weak point target image registration method based on RPSF

Abstract

According to the dark and weak point target image registration method based on the RPSF provided by the invention, the RPSF is adopted to convert and characterize a dark and weak non-feature point target in a spatial domain, affine transformation derivation and calculation are performed on the RPSF function, a rotation parameter and a translation parameter of the point target in the spatial domain are acquired, and parameter estimation of affine transformation is realized. Through integral operation of Radon transform, enhancement and anti-interference detection of a target signal under a low signal-to-noise ratio are realized. Algorithm simulation and parameter estimation are carried out on tiny translation and rotation transformation through different Radon transformation step lengths, and it is verified that the error of the method meets the sub-pixel level. Through a registration test of a space debris image collected by a ground-based telescope, the engineering application capability and robustness of the method under the condition of a low signal-to-noise ratio are verified.

Description

Technical Field

[0001] This invention belongs to the field of image processing technology, specifically to an image registration method for dim target images where translation or rotation of the image causes affine transformations (rotations and translations) in successive frames. By using Radon Point Spread Function (RPSF) modeling and parameter estimation, this method significantly improves the registration accuracy and detection reliability of dim target images. The method is applicable to detection of space targets, infrared targets, and radar electromagnetic targets. Background Art

[0002] In radar, infrared, and optical imaging, there is often a need to detect and identify point targets. Examples include radar and infrared detection of high-altitude aircraft, and reflection and scattering imaging of radiation sources in microwave focal plane imaging. These point targets have characteristics such as weak intensity and shapelessness. Due to the mobility of targets, consecutive frames of images during the imaging detection process often undergo affine transformations such as translation and rotation, resulting in mismatches between consecutive frames. Traditional image registration methods (such as SIFT and phase correlation methods based on feature point matching) rely on salient features of the target or background. However, in dark and weak point target scenarios, feature information is weak or even missing, leading to the following problems: 1. Low registration accuracy: Traditional methods have difficulty distinguishing between noise and real targets, and the affine transformation parameter estimation error is large; 2. High false alarm rate: Due to noise interference, mismatches often occur on a large scale in background images; 3. Sub-pixel registration is difficult: Existing technologies mostly remain at whole-pixel registration, which cannot meet the needs of high-resolution imaging.

[0003] Patent CN115564946A proposes an image rotation detection method based on geometric feature matching. This method selects fixed and moving points in the image, combines camera calibration principles to calculate world coordinates, and determines the parallelism of lines between the previous and next frames to detect the rotation angle and direction. While this method can effectively identify image rotation, it does not fully consider the compound impact of translation on image offset. Furthermore, in low-light or feature-sparse scenes such as point targets, the reliance on visual features is insufficiently stable, which can easily lead to misjudgments. Another patent, CN117808839A, employs an inertial sensor (IMU) and visual fusion strategy. The IMU calculates rotation and translation parameters, combines depth information to generate grid offset values, and uses bilinear interpolation to achieve pixel-level alignment. This method has advantages in low-light environments, but it relies too much on sensor accuracy and does not fully integrate the image's own characteristics for dynamic optimization. Therefore, there is an urgent need for a high-precision registration method that addresses the dim and shapeless characteristics of point targets. Summary of the Invention

[0004] This paper proposes a method for dim point target image registration based on the Radon point spread function (RPSF). This method uses the Radon point spread function to model the rotation and translation parameters of point targets, and combines multi-reference point phase analysis and parameter estimation to achieve sub-pixel registration. The specific technical solutions of this invention are as follows:

[0005] A dark point target image registration method based on RPSF includes the following steps:

[0006] S1: RPSF definition and affine transformation modeling;

[0007] The system function of Radon transform is defined as Radon Point Spread Function (RPSF), and the formula is as follows:

[0008] P(θ) [x,y] =x*cosθ+y*sinθ (1)

[0009] Where [x,y] is the pixel coordinate in the image domain, θ is the rotation angle in the Radon domain, and P(θ) [x,y] Indicates the amplitude of the corresponding sine function. For the Radon transform of a point target, P(θ) can be determined by taking the coordinate values ​​corresponding to the maximum values ​​of each column in the Radon domain.

[0010] Therefore, the translation, rotation, and scaling transformations of the Radon transform are derived under the representation of the RPSF as shown in (2), (3), and (4). Combining them with (1), we can solve the translation parameter [l,ψ], the rotation parameter β, and the scaling parameter A.

[0011] ρ(θ) Trans[(x,y)] =x*cosθ+y*sinθ+l*cos(θ-ψ) (2)

[0012] ρ(θ) Rotate[(x,y)] =x*cos(θ+β)+y*sin(θ+β) (3)

[0013] ρ(θ) Scale[(x,y)] =A*x*cosθ+A*y*sinθ (4)

[0014] For applications such as target detection, there are usually translation and rotation transformations between consecutive frame images. Therefore, the RSPF expression for affine transformation under translation and rotation can be derived as follows:

[0015] ρ(θ) R&T[(x,y)] =ρ(θ+β) T[(x,y)] =x*cos(θ+β)+y*sin(θ+β)+l*cos(θ+β-ψ) (5)

[0016] Define τ=θ+β, then the above equation can be further written as follows:

[0017] ρ(τ) T[(x,y)] =x*cos(τ)+y*sin(τ)+l*cos(τ-ψ) (6)

[0018] According to (1), a pixel point (x0, y0) of the original image can be expressed by RPSF as:

[0019]

[0020] In the formula Then formula (7) can be further expressed as:

[0021]

[0022] S2: rotation parameter estimation;

[0023] The affine transformation consisting of translation and rotation can be solved by combining (7) and (8). Without loss of generality, the RPSF of the point target before and after the affine transformation is defined as According to (7) and (8), we can infer that:

[0024]

[0025] in, are the translation distances between the two frames in the x and y directions, and β0 is the rotation angle. The purpose of image registration between consecutive frames is to obtain and β0. Define the coordinates of the same target point in two consecutive frames as (x1, y1) and (x2, y2), respectively. For the RPSF before the affine transformation of the two, let θ = 0 and θ = π / 2, respectively, and we can get:

[0026]

[0027] For the RPSF of the two reference points after affine transformation, let θ = 0, we can get:

[0028]

[0029] Subtracting (15) from (16) yields:

[0030]

[0031] Combining equations (11)-(14) with equation (17), we can obtain:

[0032]

[0033] To simplify formula (46), define

[0034] ξ=arctan(b / a), the above formula can be expressed as:

[0035]

[0036] By solving this equation, the expression of β can be obtained from (20):

[0037]

[0038] Where a and b can be obtained by equations (11)-(14). Here we can find the estimated value of the rotation angle β.

[0039] S3: translation parameter estimation;

[0040] When the rotation angle β0 is a known variable, it can be substituted into RPSF as

[0041] ρ1(θ+β0)=L1*cos(θ+β0-α1) (21)

[0042] The result of an affine transformation involving both rotation and translation operations can be written as:

[0043]

[0044] By combining the above two equations, we can get

[0045]

[0046] Let θ = 0 and θ = π / 2 respectively, then equation (23) can be written as:

[0047]

[0048] Combining the above two equations, we can get:

[0049]

[0050] ψ can be calculated using formula (27), where all input variables can be directly obtained through (24) and formula (25).

[0051]

[0052] l is the only parameter that needs to be solved. Combining formula (24) and formula (25), we can get:

[0053]

[0054] The same operation can be performed on the reference point (x2, y2) to obtain a second estimate of ψ and l. By averaging these two results to reduce the error, we can obtain the fixed ψ0, l0. Finally, the estimated translation component in Cartesian coordinates can be solved by the following equation.

[0055] (x0,y0)=(l0*cosψ0,l0*sinψ0) (29)

[0056] S4: Image registration and verification;

[0057] Based on S1-S3, we obtain estimates of the rotation parameter β and translation parameter (x0, y0) for each consecutive frame. By performing an affine transformation on the previous frame, with a rotation angle of β and a translation vector of (x0, y0), we can register it with the next frame. After registration, we evaluate the registration by calculating the root mean square error between the two frames.

[0058] The beneficial effects of the present invention are:

[0059] 1. The method of the present invention expands the dark point target in the image domain into a sine curve in the Radon domain through the RPSF characterization method, which increases the target features and information entropy, and provides accuracy and robustness for target detection.

[0060] 2. The algorithm of the present invention utilizes the integral characteristics of Radon transform in the case of low signal-to-noise ratio to reduce the interference of random noise, improve signal resolution and effectively suppress pseudo-peaks, and can perform affine transformation parameter estimation at the sub-pixel level. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. By referring to the drawings, the features and advantages of the present invention will be more clearly understood. The drawings are schematic and should not be understood as limiting the present invention in any way. Those skilled in the art can derive other drawings based on these drawings without inventive effort. Among them:

[0062] Figure 1 Schematic diagram of the correlation between the point target coordinates and the amplitude and phase of the Radon point spread function of the present invention;

[0063] Figure 2 is a translation vector parameter estimation error diagram of Example 1 of the present invention;

[0064] Figure 3 is a rotation vector parameter estimation error diagram when the step size is 1° in Example 1 of the present invention;

[0065] Figure 4 is a rotation vector parameter estimation error diagram when the step size is 0.1° in Example 1 of the present invention;

[0066] Figure 5 1 is a graph of rotation vector parameter estimation errors at different distances according to Example 1 of the present invention;

[0067] Figure 6 This is a schematic diagram of space debris image registration according to embodiment 2 of the present invention; DETAILED DESCRIPTION

[0068] The accompanying drawings are for illustrative purposes only and are not to be construed as limiting this patent;

[0069] In order to better illustrate this example, some parts in the drawings may be omitted, enlarged or reduced, and do not represent the actual product size;

[0070] It is understandable to those skilled in the art that some well-known structures and descriptions thereof may be omitted in the drawings.

[0071] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present invention and the features therein can be combined with each other without conflict.

[0072] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0073] In order to facilitate understanding of the above technical solutions of the present invention, the above technical solutions of the present invention are described in detail below through specific embodiments.

[0074] Example 1

[0075] This example experimentally tests simulated images with different translation and rotation vectors to verify the effectiveness and error tolerance of the method. In the simulations, the point target image data used was a grayscale image of type uint8. The point targets were simulated by setting the corresponding pixel value to 255. The image size was 4096 x 4096.

[0076] S1: Testing the error of the proposed translation transform parameter estimation method. Using the proposed method, the translation transform estimation results were verified. A translation vector (x, y) was applied to a simulated image, where the x and y ranges were [-1.6, 1.6] pixels. The step size on both the x and y axes was set to 0.1 pixels, while the Radon transform step size was configured to 1°. Figure 2The results show that the error in the estimation of the translation transformation parameters is of the order of 10 -15 , which can basically be ignored. The simulation test verifies the effectiveness and accuracy of the method proposed in this paper.

[0077] S2: Test the error of the rotation transformation parameter estimation method of the present invention. Perform Radon transformation and rotation monitoring with a step size of 1° in the rotation range of 0-180° to verify the effectiveness of the proposed method. The error results are as follows Figure 3 As shown in Figure 2, the average error is 0.26°, and the rotation error remains in the range of [0, 0.5°] and does not increase with the increase of the rotation angle. For comparison, we also performed a Radon transform with a step size of 0.1° and obtained Figure 4 The error results are shown. The average error is 0.06° when the step size is 0.1°. It can be seen that as the Radon transform step size decreases, the estimated rotation angle becomes more accurate.

[0078] S3: Test the rotation vector parameter estimation error under different distances of the present invention. When the rotation angle is fixed at 1 degree, the distance between the selected reference point and the rotation center is used as a variable, and the reference point is selected for rotation parameter estimation test. The results are as follows Figure 5 As shown in the figure, the horizontal axis represents the distance from the reference point to the rotation center, and the vertical axis represents the estimated error. It can be seen that the farther the reference point is from the rotation center, the smaller the error. For a Radon transform with a step size of 1°, the reference point should be at least 200 pixels away from the rotation center to minimize the impact of the error introduced by the reference point.

[0079] Example 2

[0080] In order to verify the effectiveness of the RPSF-based point target image registration method, we used real space debris images for experimental testing. The test dataset is from the space debris images captured by the National Astronomical Observatory of China, containing 52 images with a size of 4096x 4096 and a translation vector of (-49, 55) pixels. The detection results are as follows: Figure 6 As shown in Figure 3, the translation vector estimation error does not exceed 0.5 pixels on average.

[0081] The present invention proposes a dark point target image registration method based on RPSF, which uses RPSF to transform and characterize dark, featureless point targets in the spatial domain, derives and calculates the affine transformation of the RPSF function, obtains the rotation parameters and translation parameters of the point target in the spatial domain, and realizes the parameter estimation of the affine transformation. Through the integral operation of the Radon transform, the enhancement and anti-interference detection of the target signal under low signal-to-noise ratio are realized. The algorithm simulation and parameter estimation of small translation and rotation transformations are carried out with different Radon transform step sizes, which verifies that the error of the present method meets the sub-pixel level. The space debris image registration test collected by ground-based telescopes verifies the engineering application capability and robustness of the present method under low signal-to-noise ratio conditions. In summary, the method of the present invention has a guiding role and practicality for point target detection in engineering practice, and can be used for the registration of radar electromagnetic point target images, infrared point target images, and space debris point target images.

[0082] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A dark point target image registration method based on Radon point spread function (RPSF), characterized in that: The following steps are involved: S1: RPSF modeling and affine transformation derivation: Establish the mapping relationship between the spatial coordinates of the point target and the sine curve in the Radon domain; derive the mathematical representation of RPSF under translation and rotation transformation; S2: Rotation parameter estimation: Construct the rotation angle solution equation based on the RPSF difference between the two reference points; S3: Translation parameter estimation: use the rotation angle to calculate the translation amount and direction angle; S4: Image Registration and Verification: Apply rotation and translation parameters to perform affine transformation and calculate the registration error.

2. The method according to claim 1, characterized in that In step S1: the RPSF mapping relationship satisfies P(θ) [x,y] =x*cosθ+y*sinθ, where [x,y] is the pixel coordinate in the image domain, θ is the rotation angle in the Radon domain, P(θ) [x,y] Represents the amplitude of the corresponding sine function. The RPSF after translation and rotation transformation satisfies: ρ(θ) R&T[(x,y)] =x*cos(θ+β)+y*sin(θ+β)+l*cos(θ+β-ψ), where l is the translation amount, β is the rotation angle, and ψ is the translation direction angle.

3. The method according to claim 1 or 2, characterized in that The step S2 comprises: a) Select two reference points (x1, y1) and (x2, y2); b) Calculate the RPSF value at θ = 0 and θ = π / 2; c) Through the formula Solve for the rotation angle β, where a and b are determined by the difference in the reference point RPSF.

4. The method according to claim 3, characterized in that The step S3 comprises: a) Substitute the rotation angle β into the reference point RPSF equation; b) Through the formula Solve for the translation direction angle ψ; c) Through the formula Calculate the translation l.

5. The method according to claim 1, wherein In step S4, the registration error is calculated only for the overlapping area of ​​the images before and after the affine transformation; the newly added pixel area does not participate in the error evaluation.

6. The method according to claim 3, wherein: The distance between the reference point and the image center is greater than a preset threshold, and the preset threshold is set according to the Radon transform accuracy requirement.

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