CN117745741A - Medical image segmentation method integrating survey area and image area - Google Patents

Abstract

The invention provides a medical image segmentation method for fusing a measurement region and an image region, which is used for solving the difficult segmentation problems of weak boundary, low contrast and the like in medical image segmentation. The method comprises the following steps: selecting a mark point according to the medical image, and solving a threshold geodesic distance by using a generalized Eikonal equation; the geodesic distance and the deep learning are fused to construct a network optimization problem, and the segmentation results of the image domain and the region to be tested are respectively learned by utilizing a double-branch U-net network; and fusing the image domain and the region measurement result by using the conditional random field to obtain a final segmentation image. The marking point strategy based on the geodesic distance improves the marking strategy, saves the cost, and the network part can simultaneously extract medical structure information so as to obtain a better segmentation structure and better segment the weak boundary and the low-contrast image. The method is verified in a plurality of challenging medical image segmentation tasks, and experiments show that the method can well segment medical images.

Description

Medical image segmentation method integrating survey area and image area

Technical Field

The invention relates to the technical field of medical image segmentation, in particular to a medical image segmentation method integrating a measurement region and an image region.

Background

Medical image segmentation plays a vital role in medical image processing, and by segmenting organs or lesion areas from images, doctors can more accurately locate during diagnosis and treatment. The existing segmentation methods are mainly divided into two types: semantic segmentation and selective segmentation. Semantic segmentation aims at separating foreground objects from the background, whereas selective segmentation separates specific objects or regions of interest (ROIs) in the foreground from the image. Although selective segmentation has made significant progress over the past decades, medical images are often affected by factors such as noise, artifacts, low contrast, and differences between patients, making it challenging to achieve consistent and accurate segmentation with significant anatomical variations and complex pathological conditions.

Thus, selective segmentation of medical images is of major concern, aimed at achieving sufficiently accurate and robust results in clinical applications. In general, the selective segmentation utilizes labeling information of the user to guide the segmentation process, thereby speeding up the segmentation speed of the ROI and improving accuracy. Conventional selective segmentation methods typically compute shallow image features and utilize annotation information to minimize some energy functions. However, shallow features may not adequately capture contextual information of the image, particularly in the case of low contrast or images with weak boundaries. An effective approach is to combine some a priori annotation information with the active contour model to improve segmentation defects. However, to achieve accurate segmentation, these methods rely heavily on manual features and still require a significant amount of user interaction.

In recent years, deep learning methods have achieved breakthrough results in image segmentation due to their ability to automatically learn advanced semantic features. To further improve accuracy and robustness, some interactive segmentation methods based on deep learning have been proposed. However, it is difficult to extract complex textures using only simple click and box annotations. For this purpose, some students use geodesic distance as a priori information to provide context information for deep learning. But these geodesic distances perform poorly in the face of low contrast or weak boundary images. The ideal geodesic distance should be consistent with the segmentation target region. And meanwhile, the fusion of the geodesic distance and the deep learning is also a challenge.

The invention patent with application number 202310485694.1 discloses a weak supervision medical image segmentation method based on a depth generation model, which utilizes the generated weak supervision segmentation model to identify focus areas and normal areas by means of ideas of class activation images and generation models, and optimizes MSE loss through generated false images and real images; finally, the model generated lesion segmentation area is post-processed using a conditional random field (Dense CRF) to generate a final lesion segmentation. The invention improves the dependence of medical influence focus segmentation on pixel-level labels, can train in a network model by using the class labels of the images, and finally achieves the aim of focus segmentation; can help medical staff to realize rapid diagnosis, greatly saves the time of the medical staff, and thereby meets the requirement of quick patient seeing. However, the generated image is different from the actual image in the above-described invention, and the lesion area is easily erroneously recognized, thereby generating an inaccurate segmented structure.

Disclosure of Invention

Aiming at the technical problem that the existing medical image segmentation method is difficult to segment images with low contrast and weak boundaries, the invention provides a medical image segmentation method for fusing a measurement region and an image region, and the medical segmentation is carried out by fusing the measurement region and the image region.

In order to achieve the above purpose, the technical scheme of the invention is realized as follows: a medical image segmentation method integrating a measurement region and an image region comprises the following steps:

step one: selecting a mark point according to the medical image, and solving a threshold geodesic distance by using a generalized Eikonal equation;

step two: the geodesic distance and the deep learning are fused to construct a network optimization problem, and the segmentation results of the image domain and the region to be tested are respectively learned by utilizing a double-branch U-net network;

step three: and fusing the image domain and the region measurement result by using the conditional random field to obtain a final segmentation image.

Preferably, the geodesic distance is the minimum of the weight function integral of all paths between two points according to the Riemann metric, the geodesic distance between the two points being:

where P (x, y) represents the set of all segmented smooth paths connecting point x to point y, the geodetic curve γ (t) ∈p (x, y) satisfies γ (0) =x and γ (1) =y, γ' (t) is the derivative of geodetic curve γ (t), and H (γ (t)) represents the riman metric function related to geodetic curve γ (t);

in image segmentation, the Riemann metric is selected as an edge detection function related to the gradient norms of the input medical image I (x) such that the geodesic distance within the region of interest is small relative to the geodesic distance of neighboring pixels on the object boundary; given a set of starting pointsThe geodesic distance is:

wherein M represents a set of marker points,representing the mark point, x is other pixel points, < ->Representing the other pixel points x to the mark point +.>Is a geodesic distance.

Preferably, the geodesic distance map D (x) satisfies the generalized Eikonal equation:

wherein, ||·| denotes a norm, and the number is represented by a gradient operator, H (x) represents a riman metric function related to the pixel point x.

Preferably, generalized Eikonal equations are generalized, and the approximate constant region is punished by Euclidean distance, so that generalized Eikonal equations are obtained:

defining a diffusion function:

wherein epsilon and beta are respectively smaller and larger constants,is regional weight, T is threshold, sigma > 1 is control parameter, D _e (x) For the normalized Euclidean distance, S (-) represents the filter operator.

Preferably, the filtering operator S (·) selects gaussian filtering;

the promoted Eikonal equation utilizes a fast travelling algorithm to obtain a numerical solution, and the Skfmm library function is called in Python software to solve.

Preferably, for the diffusion function d (x), whenThe region is considered as a boundary, at which time the distance diffusion rate is determined by a larger constant β; when->The region is considered as a flat region and the region weight α (x) is used to distinguish between foreground and background: the Euclidean distance from the foreground pixel to the mark point is smaller so that alpha (x) is approximately equal to 0, and at the moment, the diffusion speed of the geodesic distance is determined by a constant epsilon, so that the geodesic distance is slowly increased or not increased in the target area; the Euclidean distance of the background pixel to the marker point is far enough that α (x) > 0, the geodesic distance increases rapidly in the background region.

Preferably, one of the two-branch U-net networks is used for learning regional information and the other is used for learning image domain information; the two U-net networks interact through the same loss function and update network parameters in the back propagation; each U-net network includes five convolutional layers as encoders and five deconvolution layers as decoders, replacing the batch normalization layer with an instance normalization layer, and reducing the number of network feature layers by a factor of four.

Preferably, the network optimization problem is:

wherein θ is a network parameter, θ ^* For the optimal parameters obtained after data set training, Z (x) is the labeled label image, D (x|I (x)) and D (x|Z (x)) respectively represent geodesic distances of the input medical image I (x) and the label image Z (x), and f _θ (I (x)) represents the segmentation result, g, obtained by training the image domain U-net network _θ (D (x|I (x))) represents a segmentation result obtained by U-net network training of the region to be measured;

the loss function of the U-net network training is

Where λ and ω are empirically selected regularized term parameters;

in the training process, normalizing and scaling the distance between an input image to be segmented and a threshold geodesic wire to be within the range of [0,1], and reversing the geodesic image during input; the U-net network was trained for 300 epochs using the Adam optimization algorithm.

Preferably, the method for fusing the image domain and the region measurement result by the conditional random field is as follows: a random variable ζ (x _i ) Wherein ζ (x) _i ) E {0,1} for i=1, 2, …, N is the number of pixels in the input medical image I (x); let X be the final segmentation result, then the random variable ζ (X) follows Gibbs distribution:

wherein P (x=ζ (X) |i (X)) is a conditional distribution function of the random variable ζ (X), and pi (I (X)) is a normalization factor; the energy function is:

preferably, the unitary potential function ψ of the conditional random field _u (ζ (x)) and a binary potential function ψ _p (ξ(x _i ),ξ(x _j ) Respectively is:

wherein,respectively obtaining segmentation results by using the trained U-net network, wherein tau is a control parameter;

conditional random fields are solved using pydensecrf library functions in Python software.

Compared with the prior art, the invention has the beneficial effects that:

1. according to the invention, the Eikonal equation is promoted, the threshold geodesic distance is provided, the Euclidean distance is used for punishing the approximate constant region, and the threshold geodesic distance is kept consistent in the ROI region according to the self-property of the image, and meanwhile, the foreground and the background can be well distinguished.

2. The invention proposes a new marking point strategy based on the threshold geodesic distance property, only one point needs to be marked inside the region of interest (ROI), which is determined by the consistency of the diffusion function in the same region, and additional points may need to be added when larger or more complex ROI regions are processed. The marking point strategy greatly simplifies the marking flow of the interactive method and saves the marking cost.

3. The invention utilizes the threshold geodesic distance and the image domain information to construct a parallel network architecture, converts geodesic distance and image input deep learning into a network optimization problem, obtains the segmentation results of the image domain and the geodesic domain, ensures that the results of the two domains are consistent by constructing a loss function, can fully capture the image characteristic information, and provides for obtaining accurate segmentation results.

4. The method utilizes the conditional random field to fuse the measured region and the image region results, and reconstructs a unitary potential function and a binary potential function; through the post-processing of the conditional random field, finer segmentation results can be obtained. The method can be applied to medical images of different modes, such as CT images and MR images, and satisfactory segmentation results can be obtained on the medical images of different modes by utilizing the fusion of region measurement information and image domain information.

The marking point strategy based on the geodesic distance improves the marking strategy, saves the cost, and can simultaneously extract medical structure information by the network part so as to obtain a better segmentation structure. The invention can better divide the weak boundary and the low contrast image.

Drawings

In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.

FIG. 1 is a flow chart of the present invention.

Fig. 2 is an overall frame diagram of the present invention.

FIG. 3 shows the threshold geodesic distances obtained by selecting different parameters according to the present invention.

Fig. 4 shows the segmentation results of the present invention and the prior art method applied to CT and MR images, respectively.

FIG. 5 shows the segmentation results of the present invention at different viewing angles, using only cross-sectional data for training, and using the training network to test the cross-section, sagittal plane and coronal plane, respectively.

Fig. 6 shows the segmentation result under different marking point strategies according to the present invention, wherein five marking strategies are respectively adopted: center point one mark point, center one point plus random one point, random one mark point, random two mark points and random three mark points.

Detailed Description

The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without any inventive effort, are intended to be within the scope of the invention.

As shown in fig. 1, a medical image segmentation method integrating a geodesic region and an image region provides a threshold geodesic distance, and the geodesic distance of a target region is kept consistent according to the nature of the image; the method Deep Threshold Geodesic Distance (DTGD) mainly utilizes the threshold geodesic distance and the image domain information to construct a parallel network architecture, and the segmentation results of the image domain and the geodesic region are respectively obtained; and finally, fusing the results of the image domain and the region to be measured by using a conditional random field to obtain a final segmentation image. The performance of the DTGD is widely verified in a plurality of challenging medical image segmentation tasks, and experiments show that the method can well solve the problems of low contrast, difficult segmentation of weak boundaries and the like of the medical image at present. The specific steps of the invention are as follows:

step one: and selecting a mark point according to the medical image, and solving a threshold geodesic distance by using a generalized Eikonal equation.

The geodesic distance is defined as: the minimum of the weight function integral of all paths between two points according to the Riemann metric. The local Riemann metric H (x) allows a global metric to be defined over geodetic space in order to find the geodetic curve γ (t).

The geodesic distance between two points is defined as:

where P (x, y) represents the set of all segmented smooth paths connecting point x to point y, the geodetic curve γ (t) ∈p (x, y) satisfies γ (0) =x and γ (1) =y, γ' (t) is the derivative of geodetic curve γ (t), H (γ (t)) represents the metric function related to geodetic curve γ (t), and can be designed according to specific problems.

In practice, the Riemann metric is chosen according to the particular problem. In the case of image segmentation, the Riemann metric is selected as an edge detection function related to the gradient norms of the input medical image I (x) such that the geodesic distance within the region of interest (ROI) is small relative to the geodesic distance of neighboring pixels on the object boundary. In general, it is not necessary to calculate the geodesic distance of any two points. For the image segmentation problem, given a group of mark points M in a target area to be segmented, the geodesic distance from the rest pixel points to the nearest mark point is calculated. Thus, a set of starting points is givenThe geodesic distance of (2) is defined as follows:

wherein M represents a set of marker points,representing the mark point, x is other pixel points, < ->Representing point x to mark point->Is a geodesic distance.

Whereas geodesic distance map D (x) satisfies the generalized ekonal equation:

wherein, for matrices A and B, the B norm is defined as Representing the gradient operator, H (x) represents the metric function associated with pixel x.

The invention provides a generalized Eikonal equation, which constructs a measurement function H (x) to punish an approximate constant region through Euclidean distance, and provides a threshold geodesic distance:

defining a diffusion function:

where ε, β are the smaller and larger constants, respectively, typically ε=10 ^-3 ，β＝10 ³ The diffusion speed of different areas is controlled,is a regionWeight, T is threshold, T.epsilon.0, 1]Setting according to a specific data set, wherein sigma > 1 is used as a control parameter D _e (x) Is the normalized euclidean distance. S (·) represents a filtering operator, and Gaussian filtering is selected in the invention. The promoted Eikonal equation can be used for solving a numerical solution by using a fast travelling algorithm, and the skfmm library function can be directly called in Python.

For the diffusion function d (x), whenThe region is considered to be a boundary where the distance diffusion rate is determined by a larger constant beta, i.e. it is desired that the geodesic distance undergoes a step change at the boundary. When->The region is considered to be a flat region and the region weight α (x) is used to distinguish between foreground and background. For the foreground pixels, the Euclidean distance to the mark point is small, so that alpha (x) is approximately equal to 0, and at the moment, the diffusion speed of the geodesic distance is mainly determined by a constant epsilon, and the geodesic distance is slowly increased or not increased in the target area. For background pixels, the Euclidean distance to the marker point is far, so that α (x) > 0, the geodesic distance will increase rapidly in the background area. Different parameters T and σ are chosen as shown in fig. 3, and the influence of the parameters on the geodesic distance is explored. As can be seen from fig. 3, when a suitable parameter is selected, the threshold geodesic distance can be well distinguished from the foreground while the ROI area is kept consistent by setting the segmented diffusion function d (x). The selection of the marker points requires only one point to be marked inside the region of interest (ROI), which is determined by the consistency of the diffusion function in the same region. Additional points may need to be added when processing larger or more complex ROI areas.

Step two: and (3) fusing geodesic distance and deep learning to construct a network optimization problem, and respectively learning the segmentation results of the image domain and the geodesic region by using a double-branch U-net network.

The present invention aims to combine geodesic distance with deep learning to better segment target boundaries. The geodesic distance measures the proximity of each pixel to the marker point under the Riemann metric. Meanwhile, the image itself contains structural information about the foreground and the background. The invention adopts the concept of a double-branch network, and utilizes two independent U-net networks, one is used for learning regional information and the other is used for learning image domain information. The two networks interact through the same loss function and update the network parameters as they back-propagate to ensure that the segmentation results for the two domains are as close as possible. Each independent branch includes approximately five convolutional layers as encoders and five deconvolution layers as decoders, replacing the batch normalization layer with an example normalization layer, and reducing the number of network feature layers by a factor of four to balance performance, memory consumption, and time cost. In addition, in order to perform feature extraction in the measurement region, inversion is performed in input and output of the measurement region, that is, input of the measurement region U-net is 1-D (x).

As shown in fig. 2, consider the following network optimization problem:

wherein θ is a network parameter, θ ^* Z (x) is a label image marked by a professional doctor for the optimal parameters obtained after the data set training. D (x|I (x)) and D (x|Z (x)) represent geodesic distances, f, of the input image I (x) and the label image Z (x), respectively _θ (I (x)) represents the segmentation result obtained by training with the image domain U-net, and g _θ (D (x|I (x))) represents the segmentation result obtained by the region measurement U-net training. And the segmentation results of the measured region and the image region are obtained simultaneously by solving the optimization problem.

Constructing a loss function

Where λ and ω are empirically selected regularized term parameters, λ=0.05, ω=0.05 is set in the present invention. The first two terms are fidelity terms, and measure the difference between the predicted result and the real result. The third item and the fourth item respectively describe sparsity of image domain and region measurement results. The last term is a cross term, minimizing the difference between the segmentation results in the image domain and the survey domain. The network is trained by the loss function, and the trained network is used for respectively obtaining the segmentation results of the image domain and the region to be tested during the test. In the training process, in order to facilitate network decoding, the input image to be segmented and the threshold geodesic distance are normalized and scaled to [0,1]]And inverts the geodetic image at the time of input. The network was trained for 300 epochs, and the weight decay was 10 using Adam optimization algorithm ^-4 。

Step three: and fusing the image domain and the region measurement result by using the conditional random field to obtain a final segmentation image.

And (3) carrying out post-processing by using a Conditional Random Field (CRF) to fuse the segmentation results of the image domain and the region to be measured to obtain a final segmentation result. A random variable ζ (x _i ) Wherein ζ (x) _i ) E {0,1} for i=1, 2, …, N, where N is the number of pixels in the input image I (x). Let X be the final segmentation result, then for the random variable ζ (X), it follows the Gibbs distribution:

where P (x=ζ (X) |i (X)) is a conditional distribution function of the random variable ζ (X), and pi (I (X)) is a normalization factor. Here the energy function is defined as:

wherein psi of conditional random field _u (ζ (x)) and ψ _p (ξ(x _i ),ξ(x _j ) A unitary potential function and a binary potential function, respectively, defined as:

wherein,and respectively obtaining segmentation results by using the trained U-net network, wherein tau is a control parameter. If the random variable ζ (x _i )≠ξ(x _j ) The oscillometric function mu (xi (x) _i ),ξ(x _j ) () =1, otherwise μ (ζ (x) _i ),ξ(x _j ) =0. Unitary potential function ψ _u (ζ (x)) combines the predicted result f of the U-net network in the image domain and the measurement domain _θ* (I (x)) and->It is intended to keep the prediction results in the two domains as consistent as possible. Binary potential function ψ _p (ξ(x _i ),ξ(x _j ) Forcing pixels with similar image gray values to be assigned the same label, i.e. gray value I (x _i )≈I(x _j ) Then xi (x) _i )＝ξ(x _j ). When assigned to different labels with pixels of similar gray values, the display function μ (ζ (x _i ),ξ(x _j ) A penalty is imposed. Under the action of potential function, binary segmentation result xi (x) is obtained. The conditional random field can be solved using pydensecrf library functions in Python.

The experimental platform of the invention is as follows: AMD Ryzen 7 5800H with Radeon Graphics 3.20GHz personal notebook. Both the numerical experiments and the network framework were performed under the PyTorch framework.

Specific experiment one:

the effects of the threshold geodesic distance provided by the invention under different parameters are compared, and the influence of the threshold T and the control parameter sigma on the threshold geodesic distance is discussed respectively. For this purpose, the control parameter σ is first fixed to 20, and the threshold T is set to 0, 0.01, 0.05, 0.1, 0.5. Then, the threshold T is fixed to 0.05, and the control parameter σ is set to 1,2, 10, 50, 100. Solving the generalized Eikonal equation can result in threshold geodesic distances under different parameters, as shown in FIG. 3. It can be observed that the threshold T mainly controls the extent of the flat area. As the threshold T increases, more pixels are considered to belong to a flat region, so that the region has the same diffusion rate. The control parameter σ mainly affects the area weight α (x) of the diffusion speed in the flat area. When the control parameter σ is smaller, the weighted region weight is also smaller, which is insufficient to penalize the background region away from the marker point. As the control parameter σ increases, the euclidean distance provides spatial information, resulting in a greater penalty to be imposed on the background area away from the marker point. At this time, the region weight α (x) of the target region tends to be 0, so that the distance between the target region pixel and the mark point is also close to 0. By selecting proper parameters, the foreground and the background can be better distinguished, and the geodetic information can be better extracted by helping the geodetic region U-net, so that a better geodetic region segmentation result is obtained. In the experiments of the present invention we selected t=0.05, σ=20. For other data sets, adjustments may be made according to the actual situation.

And a specific experiment II:

fig. 4 shows the visualization results of the present invention on a public dataset liver CT image and a left atrium MR image, respectively. This is compared with several selective segmentation methods, such as depth-limited cutting (DEXTR), minimal intervention segmentation framework based on deep learning (midepseg), efficient GCN-based interactive framework (igmediseg), and a U-Net network (SDU-Net) modified by combining compressed attention (SA) and Dense space pooling (Dense ASPP) modules. Several standard medical image datasets are used for comparison. It can be seen that SDU-Net has difficulty in locating boundary information accurately due to lack of a priori information. On the other hand, in the face of more complex shapes, the segmentation performance of the dexter is affected because it is challenging to precisely label the extreme points. Compared with the MIDeeppeg and the IGMedseg, the segmentation result of the invention is closer to the real segmentation result. The present invention can still achieve satisfactory segmentation results when facing weak boundary and low contrast images.

Furthermore, the invention is extended to multiple organs of the same structure, such as lung CT images. Since DEXTR and igmediseg can only segment a single object, the present invention uses a method of separately segmenting a single object and then adds the segmentation results to obtain an overall segmentation result. Notably, to verify the generalization ability of the present invention, three-dimensional data was sliced in different directions, distributed to obtain cross-sectional, sagittal and coronal slices. Only cross-sectional data is used during training. In the test, the performance of the invention between the transverse, sagittal and coronal planes was evaluated, respectively. Fig. 5 shows the visual segmentation results of lung sections from three different view planes. The segmentation results in the cross-sectional view are superior to the sagittal and coronal planes due to the use of cross-sectional data during the training phase. But lacking prior information from the marker points, SDU-Net shows a lower generalization ability, DEXTR shows poor segmentation performance on images with complex edges, midepseg and igmediseg show a degree of generalization ability on sagittal and coronal planes, but still not as good as the present invention. It is apparent that the present invention can more robustly segment lung slices, particularly for corner regions (see enlarged sagittal view) and complex structural regions (see enlarged coronal view).

And a specific experiment III:

in order to further verify the robustness of the threshold geodesic distance proposed by the present invention and evaluate the association between the number and location of marker points and segmentation accuracy, five different marker strategies were used: marking a single mark point at the center, marking a single point at the center and attaching an additional point for supplemental information, randomly marking a single point, randomly marking two points, and randomly marking three points. The threshold geodesic distances obtained under different strategies are used as the input of the invention, and corresponding segmentation results are obtained, as shown in fig. 6. It can be seen that the present invention achieves better segmentation results even when there is only one marker point. Further, it can be seen from a longitudinal comparison that the resulting geodesic distances under different strategies do not greatly affect the segmentation results, which is determined by the nature of the threshold geodesic distances having the same diffusion rate in the same region. Meanwhile, the method has excellent generalization performance. Even when the mark points are randomly selected, a better segmentation result can be obtained, which shows that the generalization performance of the method provided by the invention is better.

The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, alternatives, and improvements that fall within the spirit and scope of the invention.

Claims (10)

1. A medical image segmentation method integrating a measurement region and an image region is characterized by comprising the following steps:

step one: selecting a mark point according to the medical image, and solving a threshold geodesic distance by using a generalized Eikonal equation;

step two: the geodesic distance and the deep learning are fused to construct a network optimization problem, and the segmentation results of the image domain and the region to be tested are respectively learned by utilizing a double-branch U-net network;

step three: and fusing the image domain and the region measurement result by using the conditional random field to obtain a final segmentation image.

2. The medical image segmentation method for fusing a geodetic region and an image region according to claim 1, wherein the geodetic distance is a minimum value of a weight function integral of all paths between two points according to a Riemann metric, and the geodetic distance between the two points is:

where P (x, y) represents the set of all segmented smooth paths connecting point x to point y, the geodetic curve γ (t) ∈p (x, y) satisfies γ (0) =x and γ (1) =y, γ' (t) is the derivative of geodetic curve γ (t), and H (γ (t)) represents the riman metric function related to geodetic curve γ (t);

in image segmentation, the Riemann metric is selected as an edge detection function related to the gradient norms of the input medical image I (x) such that the geodesic distance within the region of interest is small relative to the geodesic distance of neighboring pixels on the object boundary; given a set of starting pointsThe geodesic distance is:

wherein M represents a set of marker points,representing the mark point, x is other pixel points, < ->Representing the other pixel points x to the mark point +.>Is a geodesic distance.

3. The medical image segmentation method for fusing geodesic and image domains according to claim 2, wherein the geodesic distance map D (x) satisfies the generalized Eikonal equation:

wherein, I.I the norms are represented by the numbers,representing the gradient operator, H (x) represents the Riemann metric function associated with pixel point x.

4. The medical image segmentation method for fusing a survey area and an image area according to claim 3, wherein generalized Eikonal equations are generalized, and the approximate constant area is punished by euclidean distance, so that generalized Eikonal equations are obtained:

defining a diffusion function:

wherein epsilon and beta are respectively smaller and larger constants,is regional weight, T is threshold, sigma > 1 is control parameter, D _e (x) For the normalized Euclidean distance, S (-) represents the filter operator.

5. The medical image segmentation method integrating a survey area and an image area according to claim 4, wherein the filtering operator S (·) selects gaussian filtering;

the promoted Eikonal equation utilizes a fast travelling algorithm to obtain a numerical solution, and the Skfmm library function is called in Python software to solve.

6. The method for medical image segmentation of fused regions and image regions according to claim 4, characterized in that for the diffusion function d (x), whenThe region is considered as a boundary, at which time the distance diffusion rate is determined by a larger constant β; when->The region is considered as a flat region and the region weight α (x) is used to distinguish between foreground and background: the Euclidean distance from the foreground pixel to the mark point is smaller so that alpha (x) is approximately equal to 0, and at the moment, the diffusion speed of the geodesic distance is determined by a constant epsilon, so that the geodesic distance is slowly increased or not increased in the target area; the Euclidean distance of the background pixel to the marker point is far enough that α (x) > 0, the geodesic distance increases rapidly in the background region.

7. The medical image segmentation method combining a geodetic region and an image domain according to any one of claims 1-6, wherein one of the two-branch U-net networks is used for learning geodetic region information and the other is used for learning image domain information; the two U-net networks interact through the same loss function and update network parameters in the back propagation; each U-net network includes five convolutional layers as encoders and five deconvolution layers as decoders, replacing the batch normalization layer with an instance normalization layer, and reducing the number of network feature layers by a factor of four.

8. The method for medical image segmentation fusing a survey area and an image area of claim 7, wherein the network optimization problem is:

wherein θ is a network parameter, θ ^* For the optimal parameters obtained after data set training, Z (x) is the labeled label image, D (x|I (x)) and D (x|Z (x)) respectively represent geodesic distances of the input medical image I (x) and the label image Z (x), and f _θ (I (x)) represents the segmentation result, g, obtained by training the image domain U-net network _θ (D (x|I (x))) represents a segmentation result obtained by U-net network training of the region to be measured;

the loss function of the U-net network training is

Where λ and ω are empirically selected regularized term parameters;

in the training process, normalizing and scaling the distance between an input image to be segmented and a threshold geodesic wire to be within the range of [0,1], and reversing the geodesic image during input; the U-net network was trained for 300 epochs using the Adam optimization algorithm.

9. The method for medical image segmentation for fusion of a geodetic region and an image region according to claim 8, wherein the method for fusion of image region and geodetic region results by a conditional random field is as follows: a random variable ζ (x _i ) Wherein ζ (x) _i ) E {0,1} for i=1, 2, …, N is the number of pixels in the input medical image I (x); let X be the final segmentation result, then the random variable ζ (X) follows Gibbs distribution:

wherein P (x=ζ (X) |i (X)) is a conditional distribution function of the random variable ζ (X), and pi (I (X)) is a normalization factor; the energy function is:

10. the method for medical image segmentation of fused geodetic and image domains according to claim 9, wherein the univariate potential function ψ of the conditional random field _u (ζ (x)) and a binary potential function ψ _p (ξ(x _i ),ξ(x _j ) Respectively is:

wherein,respectively obtaining segmentation results by using the trained U-net network, wherein tau is a control parameter;

conditional random fields are solved using pydensecrf library functions in Python software.