Interactive image segmentation method based on multi-scale geodesic

Abstract

The present invention discloses an interactive image segmentation method based on multi-scale geodesics, comprising the following steps: step S100: inputting a grayscale image I: Ω→R, wherein Ω is the image domain of the grayscale image I and R is a real number space; adding noise to the grayscale image I to obtain a noisy grayscale image I0; step S200: performing pyramid decomposition on the noisy grayscale image I0 using a contourlet transform; step S300: performing threshold processing on the contourlet coefficients to reconstruct a denoised image I n (n≥2, n∈Z); Step S400: Calculate the denoised image I n The segmentation results of geodesics at different scales are shown in Figure 2. The multi-scale strategy and contourlet threshold are used in the minimum path model to reduce the influence of noise on image segmentation; and the computational complexity of the minimum path model is reduced by finding geodesics from coarse to fine.

Description

Technical Field

[0001] The present invention relates to the field of computer vision technology, and in particular to an interactive image segmentation method based on multi-scale geodesics. Background Art

[0002] The geodesic active contour model proposed by Caselles et al. originally realized curve evolution through the level set formula, but this method easily causes the curve to fall into a local minimum, resulting in unsatisfactory segmentation effect; to solve this problem, Cohen and Kimmel et al. introduced the minimum path model to find the global minimum of the energy functional of the geodesic active contour model, but the minimum path model does not work well for noisy images; similarly, the geodesic active contour model also does not work well for noisy images; for this reason, someone proposed a method of applying multi-scale to the geodesic active contour model, and experimental results show that this method works very well for noisy images.

[0003] In the existing technology, image segmentation using the minimum path model is performed at the same scale, which is not ideal for segmenting noisy images, resulting in inaccurate image segmentation or failure to fully reflect the pixel distribution of the image. At the same time, the acquisition of geodesics in the general minimum path model still has the problem of high computational complexity. People need an interactive image segmentation method based on multi-scale geodesics to solve these problems. Summary of the Invention

[0004] The object of the present invention is to provide an interactive image segmentation method based on multi-scale geodesics to solve the problems raised in the above background technology.

[0005] In order to solve the above technical problems, the present invention provides the following technical solution: an interactive image segmentation method based on multi-scale geodesics, comprising the following steps:

[0006] Step S100: Input a grayscale image I: Ω→R, where Ω is the image domain of the grayscale image I and R is the real number space; add noise to the grayscale image I to obtain a noisy grayscale image I0;

[0007] Step S200: performing pyramid decomposition on the noisy grayscale image I0 using Contourlet transform;

[0008] Step S300: Thresholding the contourlet coefficients to reconstruct a denoised image I with a scale of n n (n≥2, n∈Z);

[0009] Step S400: Calculate the denoised image I n Geodesics at different scales is the segmentation result of the target object.

[0010] Furthermore, the process of adding noise to the grayscale image I in step S100 is: adding Gaussian noise with a value of 0 and a standard deviation of σ to obtain a noisy grayscale image I0=I+σN, where N is a random number matrix of standard normal distribution and its dimension is the same as that of the grayscale image I.

[0011] Furthermore, the process of obtaining contourlet coefficients by decomposing the noisy grayscale image I0 in step S200 includes:

[0012] Step S201: Contourlet transform is a two-dimensional multi-scale directional filter bank composed of a Laplacian pyramid and a directional filter bank; assuming that the scale n is four consecutive values ​​j, j+1, j+2, and j+3, the noisy grayscale image I0 is subjected to pyramid decomposition to obtain contourlet coefficients at scales j, j+1, j+2, and j+3, where j≥2; the contourlet coefficients are divided into approximation coefficients and detail coefficients;

[0013] Step S202: Use the Laplacian pyramid and directional filter to perform Laplacian pyramid decomposition on the grayscale image I0, and output the approximate coefficient a with scale n being j+2 j+2 and detail coefficient b of scale n j+3 j+2 ;

[0014] Step S203: Use the Laplace pyramid to approximate the coefficient a j+2 Further decomposed into the approximate coefficient a with scale n=j+1 j+1 and detail coefficient b of scale n j+2 j+1 ;

[0015] Step S204: Use the Laplace pyramid to approximate the coefficient a j+1 Further decomposed into the approximate coefficient a of scale n j j and detail coefficient b of scale nj+1 j ;

[0016] Step S205: Use l j+2 The level directional filter bank will reduce the detail coefficient b j+2 Decompose into Directional coefficient where l j+2 is the decomposition level of the directional filter bank;

[0017] Step S206: Use l j+1 The level directional filter bank will reduce the detail coefficient b j+1 Decompose into Directional coefficient where lj+1 is the decomposition level of the directional filter bank;

[0018] Step S207: Use l j The level directional filter bank will reduce the detail coefficient b j Decompose into Directional coefficient where l j is the decomposition level of the directional filter bank.

[0019] Furthermore, the process of step S400 includes:

[0020] Step S401: Denoised image I n The geodesic obtained at scale n is denoted as Assume that the scale n is four consecutive values ​​j, j+1, j+2, j+3, where j≥2; in addition, when j=2, the resolution of the denoised image I2 is set to 64×64;

[0021] Step S402: When the scale n is j, find the denoised image I n The segmentation result of the target object on the geodesic

[0022] Step S403: When the scale n is j+1 or j+2 or j+3, calculate the denoised image I n The segmentation result of the target object on the geodesic The geodesic Is to calculate the geodesic Initialization.

[0023] Furthermore, the process of step S402 includes:

[0024] Step S402.1: Input a graffiti ξ as a foreground seed within the target object outline in the noisy grayscale image I0;

[0025] Step S402.2: Use a linear downsampling operator to downsample the graffiti ξ on the noisy grayscale image I0 to the denoised image I n On the denoised image I n Graffiti on the n ;

[0026] Step S402.3: Set graffiti n By pixel Composition, of which T n For graffiti n The total number of pixels; let the denoised image I n The image domain Ω n The boundary points are According to the formula:

[0027]

[0028] in, For graffiti n All pixels on With the denoised image I n The image domain Ω n All boundary points The geodesic distance between

[0029] for point with dot The geodesic between Lip([0,1],Ω n ) is the set of Lipschitz continuous curves; It is a geodesic The first derivative with respect to parameter u; yes The Euclidean norm of ;

[0030] is a scalar-valued potential energy function, α is a constant, is the gradient operator, (x, y) is the denoised image I n The image domain Ω n Any point in

[0031] Calculate the geodesic distance

[0032] Step S402.4: Find the two points that minimize the geodesic distance d. with dot According to the formula:

[0033]

[0034] Among them, the symbol argmin represents the Lip([0,1],Ω n ) that minimizes the value of the energy functional within the brackets {}∈ n ∈Lip([0,1],Ω n ).

[0035] Find the denoised image I n Cut ∈ n ;

[0036] Step S402.5: Find the cut ∈ n With the denoised image I n The intersection point of the target object contour on the n ;

[0037] Step S402.6: According to the formula:

[0038]

[0039] Combined with the back propagation algorithm to find the geodesic Among them, the set Θ n Specifically expressed as β is a constant, (x, y) is the image I n The image domain Ω n Any point in

[0040] Step S402.7: Calculate geodesic The computational complexity of .

[0041] Furthermore, the process of step S403 includes:

[0042] Step S403.1: Use the linear upsampling operator to upsample the geodesic at scale n-1. Upsample to scale n, and record the geodesic upsampled to scale n as

[0043] Step S403.2: According to the formula:

[0044]

[0045] in, For geodesics Euclidean distance graph, Ω n is the denoised image I n Image domain;

[0046] Geodesic Tubular structure neighborhood According to the formula:

[0047]

[0048] Among them, d is a constant that changes with the change of the image;

[0049] Step S403.3: Set graffiti n By pixel Composition, of which T n For graffiti n The total number of pixels; let the denoised image I n The image domain Ω n The boundary points are According to the formula:

[0050]

[0051] in, For graffiti n All pixels on With the denoised image I n The image domain Ω n All boundary points The geodesic distance between

[0052] for point with dot The geodesic between Lip([0,1],Ω n ) is the set of Lipschitz continuous curves;

[0053] P is the scalar-valued potential energy function, α is a constant, (x, y) is the image domain Ω n Any point in

[0054] Calculate the geodesic distance

[0055] Step S403.4: Find the two points that minimize the geodesic distance d. According to the formula:

[0056]

[0057] Among them, the symbol argmin represents the Lip([0,1],Ω n ) that minimizes the value of the energy functional within the brackets {}∈ n ∈Lip([0,1],Ω n );Find the denoised image I n Cut ∈ n ;

[0058] Step S403.5: Find the cut ∈ n With the denoised image I n The intersection point of the target object contour on the n ;

[0059] Step S403.6: According to the formula:

[0060]

[0061] Combined with the back propagation algorithm to find the geodesic Among them, the set Θ n Specifically expressed as β is a constant, (x, y) is the denoised image In The image domain Ω n Any point in

[0062] Step S403.7: Calculate geodesic The computational complexity of .

[0063] Compared with the existing technology, the beneficial effects achieved by the present invention are as follows: first, the present invention applies the multi-scale and multi-resolution method strategy to the minimum path model, calculates the geodesic at four scales, and adds the contour wave threshold in the calculation process, which can reduce the influence of noise on image segmentation and make up for the shortcoming of the original minimum path model in extracting noisy images; second, except for the geodesic with scale n=j, the minimum path model can be used to extract the image with the best performance. In image I n Except for the one calculated on the entire image domain, the remaining scales n are geodesics on j+1 or j+2 or j+3 Both are on the geodesic Tubular structure field The calculation is performed within, so that the geodesic calculation complexity of this model can be achieved much less than the geodesic calculation complexity of the original minimum path model. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0065] Figure 1 This is a method flow chart of the interactive image segmentation method based on multi-scale geodesics of the present invention. DETAILED DESCRIPTION

[0066] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0067] See also Figure 1 The present invention provides a technical solution: an interactive image segmentation method based on multi-scale geodesics, comprising the following steps:

[0068] Step S100: Input a grayscale image I: Ω→R, where Ω is the image domain of the grayscale image I and R is the real number space; add noise to the grayscale image I to obtain a noisy grayscale image I0;

[0069] Among them, the process of adding noise to the grayscale image I in step S100 is: adding Gaussian noise with a value of 0 and a standard deviation of σ to obtain a noisy grayscale image I0=I+σN, where N is a random number matrix of standard normal distribution and its dimension is the same as that of the grayscale image I.

[0070] Step S200: performing pyramid decomposition on the noisy grayscale image I0 using Contourlet transform;

[0071] The process of obtaining contourlet coefficients by decomposing the noisy grayscale image I0 in step S200 includes:

[0072] Step S201: Contourlet transform is a two-dimensional multi-scale directional filter bank composed of a Laplacian pyramid and a directional filter bank; assuming that the scale n is four consecutive values ​​j, j+1, j+2, and j+3, the noisy grayscale image I0 is subjected to pyramid decomposition to obtain contourlet coefficients at scales j, j+1, j+2, and j+3, where j≥2; the contourlet coefficients are divided into approximation coefficients and detail coefficients;

[0073] Step S202: Use the Laplacian pyramid and directional filter to perform Laplacian pyramid decomposition on the grayscale image I0, and output the approximate coefficient a with scale n being j+2 j+2 and detail coefficient b of scale n j+3 j+2 ;

[0074] Step S203: Use the Laplace pyramid to approximate the coefficient a j+2 Further decomposed into the approximate coefficient a with scale n=j+1 j+1 and detail coefficient b of scale n j+2 j+1 ;

[0075] Step S204: Use the Laplace pyramid to approximate the coefficient a j+1 Further decomposed into the approximate coefficient a of scale n j j and detail coefficient b of scale nj+1 j ;

[0076] Step S205: Use l j+2 The level directional filter bank will reduce the detail coefficient b j+2 Decompose into Directional coefficient where l j+2 is the decomposition level of the directional filter bank;

[0077] Step S206: Use l j+1 The level directional filter bank will reduce the detail coefficient b j+1 Decompose into Directional coefficient where l j+1 is the decomposition level of the directional filter bank;

[0078] Step S207: Use l j The level directional filter bank will reduce the detail coefficient b j Decompose into Directional coefficient where l j is the decomposition level of the directional filter bank.

[0079] Step S300: Perform threshold processing on the contourlet coefficients and reconstruct the denoised image I with a scale of n. n (n≥2, n∈Z);

[0080] Step S400: Calculate the denoised image I n Geodesics at different scales is the segmentation result of the target object.

[0081] The process of step S400 includes:

[0082] Step S401: Denoised image I n The geodesic obtained at scale n is denoted as Assume that the scale n is four consecutive values ​​j, j+1, j+2, j+3, where j≥2; in addition, when j=2, the resolution of the denoised image I2 is set to 64×64;

[0083] Step S402: When the scale n is j, find the denoised image I n The segmentation result of the target object on the geodesic

[0084] Step S403: When the scale n is j+1 or j+2 or j+3, calculate the denoised image I n The segmentation result of the target object on the geodesic The geodesic Is to calculate the geodesic Initialization.

[0085] The process of step S402 includes:

[0086] Step S402.1: Input a graffiti ξ as a foreground seed within the target object outline in the noisy grayscale image I0;

[0087] Step S402.2: Use a linear downsampling operator to downsample the graffiti ξ on the noisy grayscale image I0 to the denoised image I n On the denoised image I n Graffiti on then ;

[0088] Step S402.3: Set graffiti n By pixel Composition, of which T n For graffiti n The total number of pixels; let the denoised image I n The image domain Ω n The boundary points are According to the formula:

[0089]

[0090] in, For graffiti n All pixels on With the denoised image I n The image domain Ω n All boundary points The geodesic distance between

[0091] for point with dot The geodesic between Lip([0,1],Ω n ) is the set of Lipschitz continuous curves; It is a geodesic The first derivative with respect to parameter u; yes The Euclidean norm of ;

[0092] is a scalar-valued potential energy function, α is a constant, is the gradient operator, (x, y) is the denoised image I n The image domain Ω n Any point in

[0093] Calculate the geodesic distance

[0094] Step S402.4: Find the two points that minimize the geodesic distance d. with dot According to the formula:

[0095]

[0096] Among them, the symbol argmin represents the Lip([0,1],Ω n ) that minimizes the value of the energy functional within the brackets {}∈ n ∈Lip([0,1],Ωn ).

[0097] Find the denoised image I n Cut ∈ n ;

[0098] Step S402.5: Find the cut ∈ n With the denoised image I n The intersection point of the target object contour on the n ;

[0099] Step S402.6: According to the formula:

[0100]

[0101] Combined with the back propagation algorithm to find the geodesic Among them, the set Θ n Specifically expressed as β is a constant, (x, y) is the image domain Ω of image In n Any point in

[0102] Step S402.7: Calculate geodesic The computational complexity of .

[0103] The process of step S403 includes:

[0104] Step S403.1: Use the linear upsampling operator to upsample the geodesic at scale n-1. Upsample to scale n, and record the geodesic upsampled to scale n as

[0105] Step S403.2: According to the formula:

[0106]

[0107] in, For geodesics Euclidean distance graph, Ω n is the denoised image I n Image domain;

[0108] Geodesic Tubular structure neighborhood According to the formula:

[0109]

[0110] Among them, d is a constant that changes with the change of the image;

[0111] Step S403.3: Set graffitin By pixel Composition, of which T n For graffiti n The total number of pixels; let the denoised image I n The image domain Ω n The boundary points are According to the formula:

[0112]

[0113] in, For graffiti n All pixels on With the denoised image I n The image domain Ω n All boundary points The geodesic distance between

[0114] for point with dot The geodesic between Lip([0,1],Ω n ) is the set of Lipschitz continuous curves;

[0115] P is the scalar-valued potential energy function, α is a constant, (x, y) is the image domain Ω n Any point in

[0116] Calculate the geodesic distance

[0117] Step S403.4: Find the two points that minimize the geodesic distance d. According to the formula:

[0118]

[0119] Among them, the symbol argmin represents the Lip([0,1],Ω n ) that minimizes the value of the energy functional within the brackets {}∈ n ∈Lip([0,1],Ω n );Find the denoised image I n Cut ∈ n ;

[0120] Step S403.5: Find the cut ∈ n With the denoised image I n The intersection point of the target object contour on the n ;

[0121] Step S403.6: According to the formula:

[0122]

[0123] Combined with the back propagation algorithm to find the geodesic Among them, the set Θ n Specifically expressed as β is a constant, (x, y) is the denoised image I n The image domain Ω n Any point in

[0124] Step S403.7: Calculate geodesic The computational complexity of .

[0125] Input gray image I with a resolution of 512×512; add Gaussian noise with a value of 0 and a standard deviation of 0.15 to the gray image I to obtain a noisy grayscale image I0=I+0.15N; set the scale n∈(2,3,4,5);

[0126] The noisy grayscale image I0 is decomposed into a first-level Laplacian pyramid using the Laplacian pyramid of the "9-7" wavelet and the directional filter of the "pkva" wavelet, and the output is the approximate coefficient a4(x, y) on the scale n=4 and the detail coefficient b4(x, y) on the scale n=5; the Laplacian pyramid is used to further decompose a4(x, y) into the approximate coefficient a3(x, y) on the scale n=3 and the detail coefficient b3(x, y) on the scale n=4; the Laplacian pyramid is used to further decompose the approximate coefficient a3(x, y) into the approximate coefficient a2(x, y) on the scale n=2 and the detail coefficient b2(x, y) on the scale n=3; the l4-level directional filter group is used to decompose the detail coefficient b4(x, y) into Directional coefficient The detail coefficients b3(x, y) are decomposed into Directional coefficient The detail coefficients b2(x, y) are decomposed into Directional coefficient Perform threshold processing on the obtained contour wave and reconstruct the contour wave coefficient after threshold processing to obtain the denoised image I n ;

[0127] Input a graffiti ξ as the foreground seed within the boundary of the noisy grayscale image I0, and use a downsampling operator to downsample the graffiti ξ to the denoised image I2 of scale n = 2. The resolution of the denoised image I2 is 64×64. The graffiti on the denoised image I2 is denoted as ξ2. The graffiti ξ2 is represented by the pixel points s=1,2,...,64,the boundary points of the image domain Ω2 of the noisy image I2 are recorded as t=1,2,...,252;According to the formula Calculate all pixels on graffiti ξ2 All boundary points of the image domain with the denoised image I2 The geodesic distance between Take α=5 and find the two points that minimize the geodesic distance d.

[0128] By formula Get the cut ∈2 of the denoised image I2; find the intersection point p2 of the cut ∈2 and the target object contour on the denoised image I2;

[0129] By formula Find the geodesic in Take β = -5; the set Θ2 is specifically expressed as

[0130] N1=64×64=4096, and we get the geodesic The computational complexity is O(4096log(4096)).

[0131] Use a linear upsampling operator to upsample the geodesic at scale n = 2 Upsample to the denoised image I3 with scale n=3, and record the geodesic upsampled to scale n=3 as The resolution of the denoised image I3 is 128×128, according to the formula Find the geodesic Euclidean distance graph of By the formula Find the geodesic The tubular structure neighborhood;

[0132] The graffiti on the denoised image I3 is denoted as ξ3; the graffiti ξ3 is composed of pixel points s=1,2,...,128,the boundary points of the image domain Ω3 of the noisy image I3 are recorded as t=1,2,...,508;According to the formula Calculate all pixels on graffiti ξ3 All boundary points of the denoised image I3 image domain The geodesic distance between Take α=5 and find the two points that minimize the geodesic distance d.

[0133] By formula Get the cut ∈3 of the denoised image I3; find the intersection point p3 of the cut ∈3 and the target object contour on the denoised image I3;

[0134] By formula Find the geodesic in Take β = -5; the set Θ3 is specifically expressed as

[0135] After one experiment, the tubular structure neighborhood was obtained The number of pixels is 1985, so the geodesic The computational complexity is 0(1985log(1985)).

[0136] Use the linear upsampling operator to upsample the geodesic at scale n=3 Upsample to the denoised image I4 with scale n = 4, and record the geodesic upsampled to scale n = 4 as The resolution of the denoised image I4 is 256×256, according to the formula Find the geodesic Euclidean distance graph of By the formula Find the geodesic The tubular structure neighborhood;

[0137] The graffiti on the denoised image I4 is denoted as ξ4; the graffiti ξ4 is composed of pixel points s=1,2,...,256,the boundary points of the image domain Ω4 of the noisy image I4 are recorded as According to the formula Calculate all pixels on graffiti ξ4 All boundary points of the image domain with the denoised image I4 The geodesic distance between Take α=5 and find the two points that minimize the geodesic distance d.

[0138] By formula Get the cut ∈4 of the denoised image I4; find the intersection point p4 of the cut ∈4 and the target object contour on the denoised image I4;

[0139] By formula Find the geodesic in Take β = -5; the set Θ4 is specifically expressed as

[0140] After one experiment, the tubular structure neighborhood was obtained The number of pixels is 3045, so the geodesic The computational complexity is 0(3045log(3045)).

[0141] Use the linear upsampling operator to upsample the geodesic at scale n = 4 Upsample to the denoised image I5 with scale n=5, and record the geodesic upsampled to scale n=5 as The resolution of the denoised image I5 is 512×512, according to the formula Find the geodesic Euclidean distance graph of By the formula Find the geodesic The tubular structure neighborhood;

[0142] The graffiti on the denoised image I5 is denoted as ξ5; the graffiti ξ5 is composed of pixel points s=1,2,...,512,the boundary points of the image domain Ω5 of the noisy image I5 are recorded as According to the formula Calculate all pixels on graffiti ξ5 All boundary points of the image domain with the denoised image I5 The geodesic distance between Take α=5 and find the two points that minimize the geodesic distance d.

[0143] By formula Get the cut ∈5 of the denoised image I5; find the intersection point p5 of the cut ∈5 and the target object contour on the denoised image I5;

[0144] By formula Find the geodesic in Take β = -5; the set Θ5 is specifically expressed as

[0145] After one experiment, the tubular structure neighborhood was obtained The number of pixels is 6118, so the geodesic The computational complexity is 0(6118log(6118)).

[0146] Geodesic is the final segmentation result, so the geodesic calculation complexity of the scaled geodesic model is O(1985log(1985))+O(3045log(3045))+O(6118log(6118))+O(4096log(4096)).

[0147] The working principle of the present invention is as follows: the interactive image segmentation method based on multi-scale geodesics applies the multi-scale strategy to the minimum path model, and reduces the influence of noise on image segmentation through contourlet threshold processing, thereby achieving effective segmentation of noisy images and reducing the computational complexity of geodesics.

[0148] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus.

[0149] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art will be able to modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. An interactive image segmentation method based on multi-scale geodesics, characterized in that: The following steps are involved: Step S100: Input a grayscale image I:Ω→R, where Ω is the image domain of the grayscale image I and R is the real number space; add noise to the grayscale image I to obtain a noisy grayscale image I0; Step S200: performing pyramid decomposition on the noisy grayscale image I0 using Contourlet transform; Step S300: Thresholding the contourlet coefficients to reconstruct a denoised image I with a scale of n n ,n≥2,n∈Z; Step S400: Calculate the denoised image I n Geodesics at different scales is the segmentation result of the target object; The process of step S400 includes: Step S401: Denoised image I n The geodesic obtained at scale n is denoted as Assume that the scale n is four consecutive values ​​j, j+1, j+2, j+3, where j≥2, j∈Z; In addition, when j=2, the resolution of the denoised image I2 is set to 64×64; Step S402: When the scale n is j, find the denoised image I in the entire image domain n The segmentation result of the target object on the geodesic Step S403: When the scale n is j+1 or j+2 or j+3, on the geodesic Find the denoised image I in the tubular structure area n The segmentation result of the target object on the geodesic The geodesic Is to calculate the geodesic Initialization, geodesic To transform the geodesic on scale n-1 Upsampled to scale n.

2. The interactive image segmentation method based on multi-scale geodesics according to claim 1, characterized in that: The process of adding noise to the grayscale image I in step S100 is: adding Gaussian noise with a mean of 0 and a standard deviation of σ to obtain a noisy grayscale image I0=I+σN, where N is a random number matrix of standard normal distribution and its dimension is the same as that of the grayscale image I.

3. The interactive image segmentation method based on multi-scale geodesics according to claim 1, characterized in that: The process of obtaining contourlet coefficients by decomposing the noisy grayscale image I0 in step S200 includes: Step S201: Contourlet transform is a two-dimensional multi-scale directional filter bank composed of a Laplacian pyramid and a directional filter bank. Assume that the scale n is four consecutive values, namely j, j+1, j+2, and j+3. Contourlet coefficients at scales j, j+1, j+2, and j+3 are obtained by performing pyramid decomposition on the noisy grayscale image I0, where j≥2 and j∈Z. Contourlet coefficients are divided into approximation coefficients and detail coefficients. Step S202: Use the Laplacian pyramid and directional filter to perform Laplacian pyramid decomposition on the grayscale image I0, and output the approximate coefficient a with scale n being j+2 j+2 and detail coefficient b of scale n j+3 j+2 ; Step S203: Use the Laplace pyramid to approximate the coefficient a j+2 Further decomposed into the approximate coefficient a with scale n=j+1 j+1 and detail coefficient b of scale n j+2 j+1 ; Step S204: Use the Laplace pyramid to approximate the coefficient a j+1 Further decomposed into the approximate coefficient a of scale n j j and detail coefficient b of scale nj+1 j ; Step S205: Use The level directional filter bank will reduce the detail coefficient b j+2 Decompose into Directional coefficient in is the decomposition level of the directional filter bank; Step S206: Use The level directional filter bank will reduce the detail coefficient b j+1 Decompose into Directional coefficient in is the decomposition level of the directional filter bank; Step S207: Use The level directional filter bank will reduce the detail coefficient b j Decompose into Directional coefficient in is the decomposition level of the directional filter bank.

4. The interactive image segmentation method based on multi-scale geodesics according to claim 3, characterized in that: The process of step S402 includes: Step S402.1: Input a graffiti ξ as a foreground seed within the target object outline in the noisy grayscale image I0; Step S402.2: Use a linear downsampling operator to downsample the graffiti ξ on the noisy grayscale image I0 to the denoised image I n On the denoised image I n Graffiti on the n ; Step S402.3: Set graffiti n By pixel Composition, of which T n For graffiti n The total number of pixels; let the denoised image I n The image domain Ω n The boundary points are According to the formula: Calculate the geodesic distance in, For graffiti n All pixels on With the denoised image I n The image domain Ω n All boundary points The geodesic distance between for point with dot The geodesic between Lip([0,1],Ω n ) is the set of Lipschitz continuous curves; It is a geodesic The first derivative with respect to parameter u; yes The Euclidean norm of ; is a scalar-valued potential energy function, α is a constant, is the gradient operator, (x, y) is the denoised image I n The image domain Ω n Any point in Step S402.4: Find the two points that minimize the geodesic distance d. with dot According to the formula: Find the denoised image I n Cut ∈ n ; Among them, the symbol argmin represents the Lip([0,1],Ω n ) that minimizes the value of the energy functional within the brackets {}∈ n ∈Lip([0,1],Ω n ); Step S402.5: Find the cut ∈ n With the denoised image I n The intersection point of the target object contour on n ; Step S402.6: According to the formula: Combined with the back propagation algorithm to find the geodesic Among them, the set Θ n Specifically expressed as β is a constant, (x,y) is the image I n The image domain Ω n Any point in Step S402.7: Calculate geodesic The computational complexity of .

5. The interactive image segmentation method based on multi-scale geodesics according to claim 4, characterized in that: The process of step S403 includes: Step S403.1: Use the linear upsampling operator to upsample the geodesic at scale n-1. Upsample to scale n, and record the geodesic upsampled to scale n as Step S403.2: According to the formula: Get geodesic Euclidean distance graph of Among them, Ω n is the denoised image I n Image domain; According to the formula: Get geodesic Tubular structure neighborhood Among them, d is a constant that changes with the change of the image; Step S403.3: Set graffiti n By pixel Composition, of which T n For graffiti n The total number of pixels; let the denoised image I n The image domain Ω n The boundary points are According to the formula: Calculate the geodesic distance in, For graffiti n All pixels on With the denoised image I n The image domain Ω n All boundary points The geodesic distance between for point with dot The geodesic between Lip([0,1],Ω n ) is the set of Lipschitz continuous curves; P is the scalar-valued potential energy function, α is a constant, (x,y) is the image domain Ω n Any point in Step S403.4: Find the two points that minimize the geodesic distance d. According to the formula: Find the denoised image I n Cut ∈ n ; Among them, the symbol argmin means to find Lip([0,1],Ω n ) that minimizes the value of the energy functional within the brackets {}∈ n ∈Lip([0,1],Ω n ); Step S403.5: Find the cut ∈ n With the denoised image I n The intersection point of the target object contour on n ; Step S403.6: According to the formula: Combined with the back propagation algorithm to find the geodesic Among them, the set Θ n Specifically expressed as β is a constant, (x,y) is the denoised image I n The image domain Ω n Any point in Step S403.7: Calculate geodesic The computational complexity of .

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