An improved RPCA infrared small target detection method based on scale space theory

Abstract

The application discloses an infrared small target detection method. Due to a long imaging distance, a small target is small in size and low in contrast in an infrared image, so that the small target is easily disturbed by a background and noise in the infrared image, and a traditional target detection method has great limitations in infrared small target detection. Therefore, in the application, a Laplacian of Gaussian operator based on a scale space theory is used to process an original image to obtain a candidate target point. The image range to be decomposed is determined according to the candidate target point. The original image is decomposed through a low-rank sparse theory, and a real target is detected under the guidance of the candidate target point. On one hand, the introduction of the scale space theory improves the robustness of the algorithm and suppresses the influence of the background; on the other hand, the low-rank sparse theory converts the background and target separation problem in the traditional algorithm into a robust principal component analysis problem, and effectively improves the target detection success rate.

Description

TECHNICAL FIELD

[0001] The application relates to the fields of image processing, target detection and image segmentation, and particularly relates to an improved RPCA infrared small target detection method based on scale space theory. BACKGROUND

[0002] The scale space theory considers that a sequence of transformed images under different scale factors can be obtained by introducing a scale factor into an image, performing scale transformation on the image and continuously transforming the scale factor. An infrared small target appears as a spot on an image under the influence of a series of factors such as atmospheric conditions and lens imaging. The infrared small target can be described by a point spread function target model. According to the point spread function, the intensity value of the infrared small target approximately satisfies Gaussian distribution. Therefore, the responses of the infrared small target and the infrared background to the scale transformation are quite different in the sequence of transformed images. The response of the infrared small target is relatively sharp, and the response of the infrared background is relatively flat. The candidate target region can be determined according to the phenomenon.

[0003] The low-rank sparse theory considers that a matrix can be decomposed into a low-rank matrix and a sparse matrix, and the robust principal component analysis (RPCA) is a method for matrix decomposition. For an image matrix containing a target to be detected, the RPCA decomposes the image matrix into a target matrix (sparse part) and a background matrix (low-rank part), and detects the target by extracting effective information of the target matrix. However, the RPCA is sensitive to noise and background interference. Therefore, in a relatively complex scene, part of the background region may be misjudged as a target, causing false alarm. Therefore, the scale space theory can be introduced to determine the real target region in a relatively complex scene. SUMMARY

[0004] The application aims to provide an improved RPCA infrared small target detection method based on scale space theory, which can effectively suppress background interference and improve the target detection success rate in infrared small target detection.

[0005] The technical scheme adopted by the application is as follows: an improved RPCA infrared small target detection method based on scale space theory, which has the following steps:

[0006] Step (1), obtaining a single-frame infrared small target original image, referred to as an original image;

[0007] Step (2), performing LoG scale transformation on the original image to obtain a candidate target matrix;

[0008] Step (3), determining the range of the original image that needs to be decomposed by RPCA according to the coordinates of each point in the candidate target matrix;

[0009] Step (4), according to the range determined in step (3), the original image obtained in step (1) is subjected to RPCA decomposition, matrix filling and the like to obtain a target image matrix;

[0010] Step (5), the intersection of the candidate target matrix obtained in step (2) and the target image matrix obtained in step (4) is taken to obtain a significant target matrix;

[0011] Step (6), the global threshold of the significant target matrix is calculated, and the real target image matrix is obtained through image segmentation according to the threshold.

[0012] Further, in step (1), the image processed is an infrared image, and the target size is usually not greater than 5*5 pixels, and the image is referred to as an original image.

[0013] Further, in step (2), the original image is subjected to LoG scale space transformation, points similar to the transformation features of small targets are marked as candidate target points, a zero matrix with the same size as the original image is set, and the pixel point values in the matrix consistent with the coordinates of the candidate target points are set to 1 to obtain a candidate target matrix.

[0014] Further, in step (3), the range subjected to RPCA decomposition is divided according to the coordinate range of the pixel points of the candidate target matrix. In order to prevent the target from being located at the edge of the range and causing subsequent failure to be detected, the range is respectively expanded by 1 / 16 of the maximum value of the original image size in four directions.

[0015] Further, in step (4), the original image is cropped to obtain an image matrix according to the range determined in step (3), the image matrix is subjected to RPCA decomposition to obtain a background matrix and a target matrix, and the target matrix is filled to be consistent with the size of the original image to obtain a target image matrix.

[0016] Further, in step (5), the intersection of the candidate target matrix and the target image matrix is taken to obtain a significant target matrix.

[0017] Further, in step (6), the global threshold of the significant target matrix is used for image segmentation to obtain a real target image matrix.

[0018] Compared with the prior art, the present application has the following advantages:

[0019] (1) The scale space theory is introduced into the RPCA target detection algorithm, which can effectively improve the target detection rate and robustness of the method.

[0020] (2) The present application optimizes the selection logic of the candidate target region of the scale space theory, and improves the detection efficiency of the method.

[0021] (3) The application uses a candidate target region for RPCA, reduces the operation amount, and improves the detection speed of the method. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 A flowchart of the application;

[0023] Figure 2 Detection results of different algorithms;

[0024] Figure 3 SCRG values of the original image. DETAILED DESCRIPTION

[0025] The application will be further described below in combination with the drawings and specific embodiments.

[0026] As Figure 1 shown, the target detection method process is represented in the form of a flowchart.

[0027] The specific flow steps of the improved RPCA infrared small target detection method based on the scale space theory are as follows:

[0028] Step (1), obtaining a single-frame infrared small target original image, referred to as an original image;

[0029] Step (2), performing LoG scale transformation on the original image to obtain a candidate target matrix;

[0030]

[0031] wherein, σ represents a variable scale factor, and L(x, y, σ) represents the LoG operator of the pixel point (x, y) under the scale factor σ.

[0032]

[0033] wherein, I(x, y) represents the single-frame infrared small target original image obtained in step (1), represents a convolution operation, and S(x, y, σ) represents the response intensity of the pixel point (x, y) after convolution under the scale factor σ.

[0034] It can be known from the expression of LoG that when the operator is used to perform convolution on the image, a large response value will be generated for the high-frequency region of the image; and the response value is close to 0 for the low-frequency region of the image. According to the mathematical model of the infrared small target established by the point spread function, when the center of the LoG operator coincides with the center of the small target, a large response value will appear, and the diameter d of the small target is approximately equal to Therefore, S(x, y) has different response values under different scale factors σ. Selecting a point (x, y) under a scale factor σ, a 5x5x5 pixel cube space M(x, y, σ) is constructed:

[0035] M(x, y, σ) = {x, y, σ | x+2≥x≥x-2, y+2≥y≥y-2, σ+2≥σ≥σ-2}

[0036] For a cube space M(x n ,y n ,σ n ), if the response value S(x n ,y n ,σ n ) of the center point (x n ,y n ,σ n ) is the largest, the point (x n ,y n ,σ n ) is marked as the center point of a candidate target, and the size of the candidate target is Traverse the sequence, and mark all pixel points satisfying the above conditions as candidate target points. Set a full zero matrix with the same size as the original image, and place all candidate target points in the matrix according to the coordinate positions and assign a value of 1. The matrix is called a candidate target matrix, denoted as K.

[0037] Step (3), according to the coordinates of each point in the candidate target matrix, determine the range of the original image that needs to be decomposed by RPCA;

[0038]

[0039] wherein G(x, y) represents the range that needs to be decomposed by RPCA, x max represents the maximum value of the horizontal axis coordinates of all candidate target points, x min represents the minimum value of the horizontal axis coordinates of all candidate target points, y max represents the maximum value of the vertical axis coordinates of all candidate target points, y min represents the minimum value of the vertical axis coordinates of all candidate target points, size x represents the width of the original image, and size y represents the height of the original image. In order to prevent the target from being located at the edge of the range and causing failure to detect, the range is extended by 1 / 16 of the image size in four directions respectively.

[0040] Step (4), according to the range determined in step (3), the original image obtained in step (1) is decomposed by RPCA, matrix filling and other operations to obtain a target image matrix;

[0041] Applying the range G(x,y) obtained in step (3) to the original image, we crop the image matrix D to obtain the image matrix that needs to be decomposed using RPCA. According to the theory of Principal Component Analysis (PCA), the image matrix D with a determined range contains two main parts: the background and the target. It can be decomposed into a low-rank matrix B and a sparse matrix T:

[0042] D = B + T

[0043] Where B is the background matrix and T is the target matrix.

[0044] According to RPCA theory, the above equation can be transformed into a convex optimization problem:

[0045] min||B|| * +λ||T||1 st D=B+T

[0046] Among them ||·|| * Let ||·||1 represent the nuclear norm, ||·||1 represent the l1 norm, and λ (λ>0) is the regularization coefficient.

[0047] The convex optimization problem is solved using the Accelerated Proximal Gradient (APG) algorithm. The background matrix B and the objective matrix T are obtained.

[0048] In more complex scenarios, the target matrix T contains not only the real target but also background elements that are mistakenly identified as targets. Since the matrix size used for RPCA decomposition may differ from the original image size, a zero-matrix is ​​set, and the target matrix T is placed into the range G(x,y) corresponding to this zero-matrix. The resulting matrix is ​​denoted as the target image matrix N.

[0049] Step (5): Take the intersection of the candidate target matrix obtained in step (2) and the target image matrix obtained in step (4) to obtain the salient target matrix;

[0050] The intersection of the candidate target matrix K and the target image matrix N yields the salient target matrix I, where ⊙ represents the intersection operation:

[0051] I = K⊙N

[0052] Step (6): Calculate the global threshold of the salient target matrix, and perform image segmentation based on the threshold to obtain the real target image matrix.

[0053] The salient target matrix I may contain some noise that could cause false alarms. Therefore, it is necessary to calculate the global threshold for the non-zero elements in I.

[0054] thresh = mean(I) + k·std(I)

[0055] where thresh is the calculated global threshold, mean(·) represents the mean value of non-zero elements of the matrix, std(·) represents the standard deviation of non-zero elements of the matrix, and k is a weighting factor, which in this method k is in the range of k ∈ [1, 5]. The global threshold is applied to I to obtain the real target.

[0056] To prove the effectiveness and detection ability of the method, three infrared small target images in complex cloud background are selected for verification, and compared with other commonly used target detection methods. The other three comparison algorithms are: local contrast enhancement algorithm (LCM), Top-Hat filtering algorithm and RPCA algorithm. The detection comparison results are shown in Figure 2 . Among them, column (a) is the original image, column (b) is the LCM algorithm processing result, column (c) is the Top-Hat algorithm processing result, column (d) is the RPCA algorithm processing result, and column (e) is the processing result of the method.

[0057] In order to quantitatively compare the advantages and disadvantages of each algorithm, the signal-to-clutter ratio gain (SCRG) is introduced:

[0058]

[0059] where the signal-to-clutter ratio (SCR) is expressed as:

[0060]

[0061] where μ t is the mean value of the gray value of the target area, μ b is the mean value of the gray value of the background area, and σ b is the standard deviation of the gray value of the background area. SCRG represents the enhancement effect of the algorithm on the target, and the larger the SCRG value, the better the detection effect of the algorithm.

[0062] Figure 3 The SCRG value in Figure 2 shows the detection effect of each algorithm on Figure 2 . Combined with Figure 3 , it proves that the method has good detection ability for infrared small targets in complex background.

[0063] The above merely illustrates the specific embodiments of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can understand and conceive the transformation or replacement within the technical range disclosed by the present application, which should be covered in the inclusive scope of the present application. The contents not described in detail in the specification belong to the prior art known by the professional technicians.

Claims

1. An improved RPCA infrared small target detection method based on scale-space theory, characterized in that, The method comprises the following steps: Step (1): Obtain a single-frame original image of a small infrared target, which is called the original image; Step (2): Perform LoG scaling transformation on the original image to obtain the candidate target matrix; Step (3): Determine the range in the original image that needs to be decomposed by RPCA based on the coordinates of each point in the candidate target matrix; Step (4): For the original image obtained in step (1), perform RPCA decomposition and matrix filling operations according to the range determined in step (3) to obtain the target image matrix; Step (5): Take the intersection of the candidate target matrix obtained in step (2) and the target image matrix obtained in step (4) to obtain the salient target matrix; Step (6): Calculate the global threshold of the salient target matrix, and perform image segmentation based on the threshold to obtain the real target image matrix.

2. The improved RPCA infrared small target detection method based on scale space theory according to claim 1, characterized in that: In step (1), the image being processed is an infrared image with a target size no larger than 5×5 pixels. This image is called the original image.

3. The improved RPCA infrared small target detection method based on scale space theory according to claim 1, characterized in that: In step (2), the original image is transformed by LoG scale space, and points with similar transformation features to the small target are marked as candidate target points. A zero matrix with the same size as the original image is set, and the pixel values ​​in the matrix that are consistent with the coordinates of the candidate target points are set to 1 to obtain the candidate target matrix.

4. The improved RPCA infrared small target detection method based on scale space theory according to claim 1, characterized in that: In step (3), the range to be decomposed by RPCA is divided according to the coordinate range of the candidate target matrix pixels. In order to prevent the target from being located at the edge of the range and thus being unable to be detected, the range is expanded by 1 / 16 of the maximum value of the original image size in four directions.

5. The improved RPCA infrared small target detection method based on scale space theory according to claim 1, characterized in that: In step (4), the original image is cropped according to the range determined in step (3) to obtain an image matrix. The image matrix is ​​decomposed by RPCA to obtain a background matrix and a target matrix. The target matrix is ​​then filled to match the size of the original image to obtain the target image matrix.

6. The improved RPCA infrared small target detection method based on scale space theory according to claim 1, characterized in that: In step (5), the intersection of the candidate target matrix and the target image matrix is ​​taken to obtain the salient target matrix.

7. The improved RPCA infrared small target detection method based on scale space theory according to claim 1, characterized in that: In step (6), the global threshold of the salient target matrix is ​​used to perform image segmentation to obtain the real target image matrix.

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