Fourier-Mellin transform image geometric matching method and system for pole-logarithm domain decoupling

Abstract

The invention provides a Fourier-Mellin transform image geometric matching method and system for pole-logarithm domain decoupling, and the method comprises the steps: estimating a rotation angle through Fourier-Mellin transform, rotating a to-be-matched image of a current frame relative to a template image of a previous frame, and obtaining an axially aligned image search region; converting the template image and the to-be-matched image from a Cartesian coordinate system to a logarithmic polar coordinate system to obtain an image search area corresponding to the logarithmic polar coordinate system; sequentially segmenting the to-be-matched image and the image search area corresponding to the template image along the theta-axis direction according to a set proportion; splicing the horizontally related image area and the vertically related image area into two twin image search areas; calculating a cross power spectrum through phase correlation to obtain scale factors in horizontal and vertical directions; and aligning the images to be matched according to the scale factors in the two directions. The method provided by the invention has equal-proportion scale estimation and rotation estimation capability, scale self-adaption, and robustness to out-of-plane overturning and rotation of a target object.

Description

Technical Field

[0001] The present invention relates to the technical field of image registration, and in particular to a Fourier-Mellin transform image geometric matching method and system based on extremum domain decoupling. Background Art

[0002] The Fourier-Mellin transform image registration method is an image pair matching algorithm based on the Fourier shift theory strategy and phase correlation method. It can be used to solve image detection and image registration problems. Compared with traditional methods such as SI FT and SURF, it can effectively achieve accurate geometric matching when there is a large angle rotation between matching images and consume less time. The traditional Fourier-Mellin transform and improved image matching method have a default premise, that is, the template and the two images to be registered can only have the same aspect ratio, such as a large round coin and a round coin, a large square block and a small square block, and the scale and rotation estimation are proportional. Therefore, this method is only applicable to similarity transformations with two degrees of freedom. However, when the target is rotated out of plane, the aspect ratio will inevitably change, and the scale changes in the width and length directions are not consistent. This makes the single scale factor estimated by the traditional Fourier-Mellin transform unable to represent the scale changes in both the width and height directions.

[0003] At present, there are extensions and application solutions based on Fourier-Mellin transform, such as patent number CN202010794306.4, named "An extended Fourier-Mellin positioning algorithm for multi-depth scenes", which uses interval sampling to obtain scale vectors and combines Fourier-Mellin transform to realize the positioning and navigation of multi-depth scene robots, so as to solve the problem that the original Fourier-Mellin algorithm can only be applied to planar scenes and the scenes need to be parallel to the camera imaging plane. However, it relies on multiple matching and has high time complexity. Another example is patent number CN201910345255.4, named "A cargo positioning method based on Fourier-Mellin transform", which is based on the traditional Fourier-Mellin transform image registration, and calculates the position relationship between the cargo and the picking mechanism to achieve high-precision positioning of various shelves and cargo. However, when the target is flipped out of the plane in the camera, this method cannot obtain accurate positioning.

[0004] Therefore, for fast image geometry matching in high-dynamic and large-angle scenes, traditional image matching methods and various matching methods based on Fourier-Mellin transform cannot take into account matching accuracy, computational efficiency and adaptability to size changes. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a Fourier-Mellin transform image geometric matching method and system with decoupling in the extreme logarithmic domain, aiming to solve the problems that traditional matching methods such as SI FT cannot accurately geometrically match large-angle rotations, and that the size estimation of the Fourier-Mellin transform matching method cannot adapt to changes in image aspect ratio without increasing the computational complexity.

[0006] The technical solution adopted by the present invention is as follows:

[0007] The present invention provides a Fourier-Mellin transform image geometric matching method with extremal domain decoupling, comprising the following steps:

[0008] Estimating the rotation angle using Fourier-Mellin transform Rotate the image to be matched in the current frame i relative to the template image in the previous frame i-1 Get the axis-aligned image search region p i ;

[0009] The template image and the image to be matched are transformed from the Cartesian coordinate system to the logarithmic polar coordinate system to obtain the image search area p i Corresponds to the image search area in log-polar coordinates

[0010]

[0011] in, and are the image search areas corresponding to the i-1th frame and the i-th frame respectively; ρ represents the polar axis along the Cartesian coordinate x, θ represents the angle between the pixel and ρ, and θ0 represents and An increment in the θ direction, logs represents and An increment in the ρ-axis direction;

[0012] According to the different phases of the image area, the image search area p i Divide into five parts along the θ axis according to the set ratio Image area Only related to the scale change in the horizontal direction, the image area and Only relevant to scale changes in the vertical direction;

[0013] will be searched with the image region Do image search region matching on template image Divide into five parts in sequence along the axis θ according to the set ratio Image area Only related to the scale change in the horizontal direction, the image area and Only relevant to scale changes in the vertical direction;

[0014] Sequential splicing The image area related to the scale change in the horizontal direction is obtained to obtain a new image search area

[0015] Sequential splicing The image area related to the scale change in the vertical direction is obtained to obtain a new image search area

[0016] Sequential splicing The image area related to the scale change in the horizontal direction is obtained to obtain a new image search area

[0017] Sequential splicing The image area related to the scale change in the vertical direction is obtained to obtain a new image search area

[0018] Registration and Get the horizontal scale factor s h , registration and Get the vertical scale factor s v ;

[0019] Using the scale factor s in two directions h 、s v The image to be matched is affine transformed to align the image scales and obtain the final matching result.

[0020] The setting ratio is 1:2:2:2:1.

[0021] The registration and Get the horizontal scale factor s h , registration and Get the vertical scale factor s v ,include:

[0022] Calculate the cross power spectrum of the search area of ​​the two images to be registered in the frequency domain:

[0023]

[0024] In the formula, represents the cross power spectrum in the Fourier domain, ω h,v ,ξ h,vThey represent the horizontal and vertical coordinates after frequency shift in the Fourier domain, respectively. The subscripts h and v represent the horizontal and vertical directions, respectively. Represents the region after reorganization or express The discrete Fourier transform form of ; express The complex conjugate of express The discrete Fourier transform form of Represents the region after reorganization or

[0025] Calculate the Dirac function:

[0026]

[0027] Among them, δ(x dfm ,y dfm ) represents the horizontal and vertical coordinates x in the spatial domain dfm ,y dfm The Dirac function value of represents inverse Fourier transform;

[0028] Find the Dirac function δ(x dfm ,y dfm ), take the peak value coordinates to get the displacement <x dfm ,y dfm >, according to the displacement <x dfm ,y dfm > Calculate the rotation angle θ and the scale factor s.

[0029] The rotation angle θ and the scale factor s are calculated as follows:

[0030]

[0031] Where s is the scale factor in the horizontal direction h Or the vertical scale factor s v ; L is the length of the θ axis, κ represents the limiting factor; is the maximum value of the response, represents the undecoupled cross power spectrum, <x dfm ,y dfm > represents the undecoupled displacement.

[0032] The angle θ between the pixel and the polar axis ρ along the Cartesian coordinate x is calculated by the following formula:

[0033]

[0034] Where y is the Cartesian ordinate and (x0, y0) represents the axis point.

[0035] The present invention also provides a Fourier-Mellin transform image geometric matching system with extremal domain decoupling, comprising:

[0036] Matching image rotation alignment module, which estimates the rotation angle using Fourier-Mellin transform Rotate the image to be matched in the current frame i relative to the template image in the previous frame i-1 Get the axis-aligned image search region p i ;

[0037] The image logarithmic polar coordinate transformation module transforms the template image and the image to be matched from the Cartesian coordinate system to the logarithmic polar coordinate system to obtain the image search area p i Corresponds to the image search area in log-polar coordinates

[0038]

[0039] in, and are the image search areas corresponding to the i-1th frame and the i-th frame respectively; ρ represents the polar axis along the Cartesian coordinate x, θ represents the angle between the pixel and ρ, and θ0 represents and An increment in the θ direction, logs represents and An increment in the ρ-axis direction;

[0040] The region segmentation module in the logarithmic polar coordinate system divides the image search area into Divide into five parts along the θ axis according to the set ratio Image area Only related to the scale change in the horizontal direction, the image area and Only relevant to scale changes in the vertical direction;

[0041] will be searched with the image region Do image search region matching on template image Divide into five parts in sequence along the axis θ according to the set ratio Image area Only related to the scale change in the horizontal direction, the image area and Only relevant to scale changes in the vertical direction;

[0042] Image block screening and splicing module, which is used to:

[0043] Sequential splicing The image area related to the scale change in the horizontal direction is obtained to obtain a new image search area

[0044] Sequential splicing The image area related to the scale change in the vertical direction is obtained to obtain a new image search area

[0045] Sequential splicing The image area related to the scale change in the horizontal direction is obtained to obtain a new image search area

[0046] Sequential splicing The image area related to the scale change in the vertical direction is obtained to obtain a new image search area

[0047] Phase correlation calculation dual scale factor module, which is registered by and Get the horizontal scale factor s h , registration and Get the vertical scale factor s v ;

[0048] Matching image scale alignment module, which uses s h 、s v The image to be matched is affine transformed to align the image scales and obtain the final matching result.

[0049] The setting ratio is 1:2:2:2:1.

[0050] The registration and Get the horizontal scale factor s h , registration and Get the vertical scale factor s v ,include:

[0051] Calculate the cross power spectrum of the search area of ​​the two images to be registered in the frequency domain:

[0052]

[0053] In the formula, represents the cross power spectrum in the Fourier domain, ω h,v ,ξ h,vThey represent the horizontal and vertical coordinates after frequency shift in the Fourier domain, respectively. The subscripts h and v represent the horizontal and vertical directions, respectively. Represents the region after reorganization or express The discrete Fourier transform form of ; express The complex conjugate of express The discrete Fourier transform form of Represents the region after reorganization or

[0054] Calculate the Dirac function:

[0055]

[0056] Among them, δ(x dfm ,y dfm ) represents the horizontal and vertical coordinates x in the spatial domain dfm ,y dfm The Dirac function value of represents inverse Fourier transform;

[0057] Find the Dirac function δ(x dfm ,y dfm ), take the peak value coordinates to get the displacement <x dfm ,y dfm >, according to the displacement <x dfm ,y dfm > Calculate the rotation angle θ and the scale factor s.

[0058] The rotation angle θ and the scale factor s are calculated as follows:

[0059]

[0060] Where s is the scale factor in the horizontal direction h Or the vertical scale factor s v ; L is the length of the θ axis, κ represents the limiting factor; is the maximum value of the response, represents the undecoupled cross power spectrum, <x dfm ,y dfm > represents the undecoupled displacement.

[0061] The angle θ between the pixel and the polar axis ρ along the Cartesian coordinate x is calculated by the following formula:

[0062]

[0063] Where y is the Cartesian ordinate and (x0, y0) represents the axis point.

[0064] The beneficial effects of the present invention are as follows:

[0065] The present invention expands the degree of freedom of the traditional Fourier-Mellin transform, making it adaptive to changes in scale aspect ratio, and does not significantly increase the computational complexity, solving the problem that traditional matching methods such as SIFT cannot accurately geometrically match large-angle rotations, and the size estimation of the Fourier-Mellin transform matching method cannot adapt to changes in image aspect ratio. The present invention obtains the Fourier-Mellin transform method of scale transformation independence through image decoupling, and has similarity transformation (equal-proportional scale estimation and rotation estimation) capabilities and scale adaptation, which can be used for scale-rotation adaptive visual recognition and positioning, and is robust to out-of-plane flipping and rotation of the target object.

[0066] The decoupled Fourier-Mellin transform proposed in the present invention utilizes log-polar domain conversion and Fourier shift objectives, combines the Fourier-Mellin transform matching method with the independence of image scale changes in log-polar coordinates, solves the scale factors in two directions respectively, and expands the equal-width-height ratio scale estimation to the more general arbitrary-width-height ratio scale estimation, realizes three-degree-of-freedom rotation and scale estimation, and greatly improves the accuracy and efficiency of image geometric matching.

[0067] Other features and advantages of the present invention will be set forth in the following description or may be learned by practicing the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 Schematic diagram of the process of the embodiment of the present invention.

[0069] Figure 2 The schematic diagram is a principle diagram of a method according to an embodiment of the present invention using a standard diagram as an example.

[0070] Figure 3 Schematic diagram of the principle of independence of scale changes in a logarithmic polar coordinate system of the method of an embodiment of the present invention.

[0071] Figure 4 The figure is a schematic diagram of the result obtained during the processing of a specific image to be matched by the method of an embodiment of the present invention. DETAILED DESCRIPTION

[0072] The specific implementation of the present invention is described below with reference to the accompanying drawings.

[0073] Example 1

[0074] See also Figure 1 , a Fourier-Mellin transform image geometric matching method with pole-logarithmic domain decoupling in this embodiment comprises the following steps:

[0075] S1. Estimating the rotation angle using Fourier-Mellin transform Rotate the image to be matched in the current frame i relative to the template image in the previous frame i-1 Get the axis-aligned image search region p i .

[0076] Among them, the image search area p i It is an area on the image to be matched that is larger than the minimum rectangular box that contains the target to be tracked.

[0077] S2. According to the properties of logarithmic polar coordinate mapping, the template image and the image to be matched are transformed from the Cartesian coordinate system to the logarithmic polar coordinate system to obtain the image search area p i Corresponds to the image search area in log-polar coordinates

[0078]

[0079] Among them, the logarithmic polar coordinate transformation has scale change and rotation invariance. In the above formula, and are the image search areas corresponding to the i-1th frame and the i-th frame respectively; ρ represents the polar axis along the Cartesian coordinate x, θ represents the angle between the pixel and ρ, and θ0 represents and An increment in the θ direction, logs represents and An increment in the ρ-axis direction;

[0080] Wherein, the angle θ between the pixel and the polar axis ρ along the Cartesian coordinate x is calculated by the following formula:

[0081]

[0082] Where y is the Cartesian ordinate and (x0, y0) represents the axis point.

[0083] S3, based on the independence of scale changes in logarithmic polar coordinates, according to the different phases of the image area, the image search area Divide into five parts along the θ axis according to the set ratio Image area Only related to the scale change in the horizontal direction, the image area and Only relevant to scale changes in the vertical direction;

[0084] will be searched with the image region Do image search region matching on template image Divide into five parts in sequence along the axis θ according to the set ratio Image area Only related to the scale change in the horizontal direction, the image area and Only relevant for scale changes in the vertical direction.

[0085] Among them, the setting ratio is 1:2:2:2:1.

[0086] S4. After dividing the area, sequential splicing The image area related to the scale change in the horizontal direction is obtained to obtain a new image search area

[0087] Sequential splicing The image area related to the scale change in the vertical direction is obtained to obtain a new image search area

[0088] Sequential splicing The image area related to the scale change in the horizontal direction is obtained to obtain a new image search area

[0089] Sequential splicing The image area related to the scale change in the vertical direction is obtained to obtain a new image search area

[0090] S5. Registration and Get the horizontal scale factor s h , registration and Get the vertical scale factor s v . Specifically include:

[0091] Calculate the cross power spectrum of the search area of ​​the two images to be registered in the frequency domain:

[0092]

[0093] In the formula, To express the cross power spectrum in the Fourier domain by utilizing the time-shift characteristic of the Fourier transform, ω h,v ,ξ h,v They represent the horizontal and vertical coordinates after frequency shift in the Fourier domain, respectively. The subscripts h and v represent the horizontal and vertical directions, respectively. Represents the region after reorganization or express The discrete Fourier transform form of ; express The complex conjugate of express The discrete Fourier transform form of Represents the region after reorganization or

[0094] Calculate the Dirac function:

[0095]

[0096] Among them, δ(x dfm ,y dfm ) represents the Dirac function value of the horizontal and vertical coordinates xdfm, ydfm in the spatial domain, represents inverse Fourier transform;

[0097] Find the Dirac function δ(x dfm ,y dfm ), take the peak value coordinates to get the displacement <x dfm ,y dfm >, according to the displacement <x dfm ,y dfm >, calculate the rotation angle θ and the scale factor s according to the following formula:

[0098]

[0099] Where s is the scale factor in the horizontal direction h Or the vertical scale factor s v ; L is the length of the θ axis, κ represents a limiting factor used to control the strength of the decoupling effect; is the maximum value of the response, represents the undecoupled cross power spectrum, <x dfm ,y dfm > represents the undecoupled displacement.

[0100] S6. Using the scale factor s in two directions h 、s v The image to be matched is affine transformed to align the image scales and obtain the final matching result.

[0101] See also Figure 2 , which uses a standard graphic example to explain the method conception of the present embodiment for graphic transformation, namely, the operation mode of scale and rotation estimation based on the decoupled Fourier-Mellin transform. Figure 2 middle That is, and and That is, and and As can be seen from the figure, different image regions represent different colors. Only related to the scale change in the horizontal direction, the image area and Only related to the scale change in the vertical direction; similarly, the image area and Only related to the scale change in the horizontal direction, the image area and It is only related to the scale change in the vertical direction. Therefore, according to the different phases of the image area, the two twin pixel areas are decoupled in the logarithmic polar coordinate system, and the two areas contain scale information in different directions. The decoupled images are combined and spliced ​​according to the scale information contained to obtain two new pixel areas, and the phase is correlated with the template to obtain the final scale factor.

[0102] Figure 3 Schematic diagram of the independence of scale changes in logarithmic polar coordinates in this embodiment. Figure 3 As shown in the figure, the sample image (a) is regarded as the template image, and the other three sample images (b), (c), and (d) are the enlarged images of the template. The first row and the first column are the logarithmic polar coordinate transformations of the four sample images. In order to highlight the area of ​​redundant pixels, the pixel values ​​of the template (a′) are added to the pixel values ​​of the enlarged images (a′), (b′), and (c′) to obtain the new image shown in the second row. It can be clearly seen that the scale in the horizontal direction is expanded, which is shown as two continuous areas of the same color in the figure; the scale in the vertical direction is expanded, which is shown as three continuous areas of the same color in the figure.

[0103] Figure 4 This is a specific example diagram of decoupled Fourier-Mellin transform for scale estimation in this embodiment. In order to highlight the scale change, Figure 4Two frames of images with significant changes in aspect ratio are selected. The two input images in the first column are obtained from the same target by UAV from different angles, so the scale and aspect ratio (aspect ratio) of the target in these two frames are inconsistent. It can be seen that the template and the image to be matched are transformed into log polar coordinates. According to the change of the target from the first column to the second column, the effect of log polar coordinate transformation on the image pixels can be clearly seen, that is, in the Cartesian coordinate system, the pixel values ​​in the same direction from the center of the target to the periphery are mapped to the same phase (θ axis) in the log polar coordinate system. Then, the horizontal and vertical directions of the image search area of ​​the target are segmented and reorganized to obtain the twin image search area, and the twin image search area is represented as two inverted triangle areas in the Cartesian coordinate system. Through decoupling and phase correlation operations in log polar coordinates, two different phase correlation responses in the fourth column can be obtained. In the horizontal direction, the phase correlation response of the twin image search area obtains a scale factor of 1.3611; similarly, a scale factor of 1.0539 is obtained in the vertical direction, which is basically consistent with the intuitive scale of the target in the two input images. However, when the traditional Fourier-Mellin transform is used, the scale factor calculated by phase correlation is 1.0653. A single scale factor cannot represent two directions, so it cannot adapt to the aspect ratio change. Although phase correlation processing is used twice to solve the aspect ratio adaptability problem, only half of the image search area is input each time, so the running time does not increase directly. Compared with other scale estimation methods, this embodiment is more effective and robust for out-of-plane rotation.

[0104] Example 2

[0105] This embodiment provides a Fourier-Mellin transform image geometric matching system with pole-logarithm domain decoupling corresponding to the method of Embodiment 1, and the system includes:

[0106] Matching image rotation alignment module, which estimates the rotation angle using Fourier-Mellin transform Rotate the image to be matched in the current frame i relative to the template image in the previous frame i-1 Get the axis-aligned image search region p i ;

[0107] The image logarithmic polar coordinate transformation module transforms the template image and the image to be matched from the Cartesian coordinate system to the logarithmic polar coordinate system to obtain the image search area p i Corresponds to the image search area in log-polar coordinates

[0108]

[0109] in, and are the image search areas corresponding to the i-1th frame and the i-th frame respectively; ρ represents the polar axis along the Cartesian coordinate x, θ represents the angle between the pixel and ρ, and θ0 represents and An increment in the θ direction, logs represents and An increment in the ρ-axis direction;

[0110] The region segmentation module in the logarithmic polar coordinate system divides the image search area into Divide into five parts along the θ axis according to the set ratio Image area Only related to the scale change in the horizontal direction, the image area and Only relevant to scale changes in the vertical direction;

[0111] will be searched with the image region Do image search region matching on template image Divide into five parts in sequence along the axis θ according to the set ratio Image area and Only related to the scale change in the horizontal direction, the image area and Only relevant to scale changes in the vertical direction;

[0112] Image block screening and splicing module, which is used to:

[0113] Sequential splicing The image area related to the scale change in the horizontal direction is obtained to obtain a new image search area

[0114] Sequential splicing The image area related to the scale change in the vertical direction is obtained to obtain a new image search area

[0115] Sequential splicing The image area related to the scale change in the horizontal direction is obtained to obtain a new image search area

[0116] Sequential splicing The image area related to the scale change in the vertical direction is obtained to obtain a new image search area

[0117] Phase correlation calculation dual scale factor module, which is through registration and Get the horizontal scale factor sh , registration and Get the vertical scale factor s v ;

[0118] Matching image scale alignment module, which uses s h 、s v The image to be matched is affine transformed to align the image scales and obtain the final matching result.

[0119] In summary, the present invention takes into account the difficulty of decomposing the scale change of the target in the Cartesian coordinate system and the independence of the scale changes in the horizontal and vertical directions in the logarithmic polar coordinates. The Fourier-Mellin transform matching method is combined with the independence of the scale change of the image in the logarithmic polar coordinates, and the scale factors in the two directions are solved respectively. The equal width and height ratio scale estimation is extended to the more general arbitrary width and height ratio scale estimation, and three-degree-of-freedom rotation and scale estimation are realized, which greatly improves the accuracy and efficiency of image geometric matching.

[0120] Those skilled in the art can understand that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention is described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions recorded in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A Fourier-Mellin transform image geometric matching method with decoupling in the extreme logarithmic domain, characterized in that: The following steps are involved: Estimating the rotation angle using Fourier-Mellin transform Rotate the image to be matched in the current frame i relative to the template image in the previous frame i-1 Get the axis-aligned image search region p i ; The template image and the image to be matched are transformed from the Cartesian coordinate system to the logarithmic polar coordinate system to obtain the image search area p i Corresponds to the image search area in log-polar coordinates in, and are the image search areas corresponding to the i-1th frame and the i-th frame respectively; ρ represents the polar axis along the Cartesian coordinate x, θ represents the angle between the pixel and ρ, and θ0 represents and An increment in the θ direction, logs represents and An increment in the ρ-axis direction; According to the different phases of the image area, the image search area Divide into five parts along the θ axis according to the set ratio Image area Only related to the scale change in the horizontal direction, the image area and Only relevant to scale changes in the vertical direction; will be searched with the image region Do image search region matching on template image Divide into five parts in sequence along the axis θ according to the set ratio Image area and Only related to the scale change in the horizontal direction, the image area and Only relevant to scale changes in the vertical direction; Sequential splicing The image area related to the scale change in the horizontal direction is obtained to obtain a new image search area Sequential splicing The image area related to the scale change in the vertical direction is obtained to obtain a new image search area Sequential splicing The image area related to the scale change in the horizontal direction is obtained to obtain a new image search area Sequential splicing The image area related to the scale change in the vertical direction is obtained to obtain a new image search area Registration and Get the horizontal scale factor s h , registration and Get the vertical scale factor s v ; Using the scale factor s in two directions h 、s v The image to be matched is affine transformed to align the image scales and obtain the final matching result.

2. The method according to claim 1, characterized in that The setting ratio is 1:2:2:2:

1.

3. The method according to claim 1, characterized in that The registration and Get the horizontal scale factor s h , registration and Get the vertical scale factor s v ,include: Calculate the cross power spectrum of the search area of ​​the two images to be registered in the frequency domain: In the formula, represents the cross power spectrum in the Fourier domain, ω h,v ,ξ h,v They represent the horizontal and vertical coordinates after frequency shift in the Fourier domain, respectively. The subscripts h and v represent the horizontal and vertical directions, respectively. Represents the region after reorganization or express The discrete Fourier transform form of ; express The complex conjugate of express The discrete Fourier transform form of Represents the region after reorganization or Calculate the Dirac function: Among them, δ(x dfm ,y dfm ) represents the horizontal and vertical coordinates x in the spatial domain dfm ,y dfm The Dirac function value of represents inverse Fourier transform; Find the Dirac function δ(x dfm ,y dfm) The peak value of the peak value is obtained by taking the coordinates of the peak value. <x dfm ,y dfm >, according to the displacement <x dfm ,y dfm > Calculate the rotation angle θ and the scale factor s.

4. The method according to claim 3, characterized in that The rotation angle θ and the scale factor s are calculated as follows: Where s is the scale factor in the horizontal direction h Or the vertical scale factor s v ; L is the length of the θ axis, κ represents the limiting factor; is the maximum value of the response, represents the undecoupled cross power spectrum, <x dfm ,y dfm > represents the undecoupled displacement.

5. The method according to claim 1, characterized in that The angle θ between the pixel and the polar axis ρ along the Cartesian coordinate x is calculated by the following formula: Where y is the Cartesian ordinate and (x0, y0) represents the axis point.

6. A Fourier-Mellin transform image geometric matching system with decoupling in the extreme logarithmic domain, characterized in that: include: Matching image rotation alignment module, which estimates the rotation angle using Fourier-Mellin transform Rotate the image to be matched in the current frame i relative to the template image in the previous frame i-1 Get the axis-aligned image search region p i ; The image logarithmic polar coordinate transformation module transforms the template image and the image to be matched from the Cartesian coordinate system to the logarithmic polar coordinate system to obtain the image search area p i Corresponds to the image search area in log-polar coordinates in, and are the image search areas corresponding to the i-1th frame and the i-th frame respectively; ρ represents the polar axis along the Cartesian coordinate x, θ represents the angle between the pixel and ρ, and θ0 represents and An increment in the θ direction, logs represents and An increment in the ρ-axis direction; The region segmentation module in the logarithmic polar coordinate system divides the image search area into Divide into five parts along the θ axis according to the set ratio Image area Only related to the scale change in the horizontal direction, the image area and Only relevant to scale changes in the vertical direction; will be searched with the image region Do image search region matching on template image Divide into five parts in sequence along the axis θ according to the set ratio Image area and Only related to the scale change in the horizontal direction, the image area and Only relevant to scale changes in the vertical direction; Image block screening and splicing module, which is used to: Sequential splicing The image area related to the scale change in the horizontal direction is obtained to obtain a new image search area Sequential splicing The image area related to the scale change in the vertical direction is obtained to obtain a new image search area Sequential splicing The image area related to the scale change in the horizontal direction is obtained to obtain a new image search area Sequential splicing The image area related to the scale change in the vertical direction is obtained to obtain a new image search area Phase correlation calculation dual scale factor module, which is registered by and Get the horizontal scale factor s h , registration and Get the vertical scale factor s v ; Matching image scale alignment module, which uses s h 、s v The image to be matched is affine transformed to align the image scales and obtain the final matching result.

7. The system according to claim 6, characterized in that The setting ratio is 1:2:2:2:

1.

8. The system according to claim 6, characterized in that The registration and Get the horizontal scale factor s h , registration and Get the vertical scale factor s v ,include: Calculate the cross power spectrum of the search area of ​​the two images to be registered in the frequency domain: In the formula, represents the cross power spectrum in the Fourier domain, ω h,v ,ξ h,v They represent the horizontal and vertical coordinates after frequency shift in the Fourier domain, respectively. The subscripts h and v represent the horizontal and vertical directions, respectively. Represents the region after reorganization or express The discrete Fourier transform form of ; express The complex conjugate of express The discrete Fourier transform form of Represents the region after reorganization or Calculate the Dirac function: Among them, δ(x dfm ,y dfm ) represents the horizontal and vertical coordinates x in the spatial domain dfm ,y dfm The Dirac function value of represents inverse Fourier transform; Find the Dirac function δ(x dfm ,y dfm ), take the peak value coordinates to get the displacement <x dfm ,y dfm >, according to the displacement <x dfm ,y dfm > Calculate the rotation angle θ and the scale factor s.

9. The system according to claim 8, characterized in that The rotation angle θ and the scale factor s are calculated as follows: Where s is the scale factor in the horizontal direction h Or the vertical scale factor s v ; L is the length of the θ axis, κ represents the limiting factor; is the maximum value of the response, represents the undecoupled cross power spectrum, <x dfm ,y dfm > represents the undecoupled displacement.

10. The system according to claim 6, characterized in that The angle θ between the pixel and the polar axis ρ along the Cartesian coordinate x is calculated by the following formula: Where y is the Cartesian ordinate and (x0, y0) represents the axis point.

Images