CN111583286B - Abdomen MRI (magnetic resonance imaging) image contour extraction method based on Flow-XDoG operator - Google Patents
Abdomen MRI (magnetic resonance imaging) image contour extraction method based on Flow-XDoG operator Download PDFInfo
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Abstract
The invention discloses an abdomen MRI image contour extraction method based on a Flow-XDoG operator, which comprises the following steps: preprocessing an abdominal MRI image, reducing interference caused by noise and a deviation field, and enhancing and smoothing the image; extracting the edges of tissues or organs, respectively extracting the edges of the preprocessed MRI images by using two Flow-XDoG operators with different parameters, and obtaining a preliminary result through edge connection; removing error edge interference; and removing the false edge, thinning the edge and finishing the extraction of the abdominal MRI image contour. Compared with the classic edge extraction operator and the edge extraction method of non-photorealistic drawing, the abdomen MRI image contour extraction method based on the Flow-XDoG operator has the advantages that the extracted edge is clearer, more complete and more accurate, the network training is not depended on, the problem of the data volume of a training set does not need to be solved, and the abdomen MRI image contour extraction method based on the Flow-XDoG operator is very suitable for contour extraction of abdomen MRI images or other images with complex graphic mechanisms and texture structures.
Description
Technical Field
The invention relates to the field of medical image processing, in particular to an abdominal nuclear Magnetic Resonance (MRI) image contour extraction method Based on a Flow-Based Extended Difference-of-Gaussians (Flow-Based Extended Difference) operator.
Background
With the continuous emergence of medical Imaging equipment such as Computed Tomography (CT), magnetic Resonance Imaging (MRI), and Positron Emission Tomography (PET), the revolutionary development of modern computer science and technology has brought about a dramatic progress in medical image processing and analysis technology. Today, medical image processing and analysis techniques are widely used to assist physicians in performing accurate and clear clinical diagnosis. At present, the technology for analyzing and processing MRI images or CT images of brain, lung, blood vessels, bones and other parts is mature, but the research on abdominal MRI images is less, so the technology for processing and analyzing abdominal MRI images has very important practical significance.
Edge extraction is an important component of computer graphics processing techniques. The clear and complete contour is extracted, and the method can provide help for subsequent image processing analysis operations such as image segmentation and target recognition. The abdominal nuclear magnetic resonance image has the characteristic of complex graphic structure and texture structure, and the common edge extraction method cannot meet the requirement of practical application. The classical image edge extraction algorithm mainly utilizes detection operators such as a Sobel operator, a Laplace operator and a Canny operator to extract edge features. The detection operators have the advantages of small calculation amount, high calculation speed and strong real-time performance, but are sensitive to illumination and noise, and have poor detection effect on image edges under the conditions of poor illumination conditions and noise pollution. The contour extraction method based on the neural network and the deep learning is also a popular research direction in recent years, but because a large number of training samples are needed, and a large amount of manpower is needed for calibrating the medical images, how to solve the problem of the number of training sets becomes a big problem. Therefore, the method for extracting the edge without depending on the neural network and the deep learning and capable of extracting the complete and clear outline has very important significance.
In many practical applications, people pay attention to only a part of an image, and other details are ignored, such as in the fields of medicine, video communication, archaeology and the like. Non-photorealistic rendering (NPR) is an artistic approach to represent a scene by means of no pursuit of reality, which generally does not show the real and specific details of an object, but shows an image in a structured and simplified style focused by an observer, which is easier to show non-real details, emphasizes certain information capable of representing image features, and ignores secondary information. The edge extraction of the image is a process for extracting the outline and the shape of the image, and therefore can be regarded as extraction of the image skeleton or extraction of the image structural features. Therefore, non-photorealistic rendering (NPR) is of great significance for realizing contour extraction of images. Commonly used non-photorealistic rendering (NPR) methods include Flow-Based Difference of gaussian (FDoG) and Flow-Based Extended Difference of gaussian (Flow-XDoG). However, many false edges may occur in the extraction result of the NPR edge extraction method, so an improved contour extraction method based on a non-photorealistic rendering technology is urgently needed.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides an abdominal nuclear Magnetic Resonance (MRI) image contour extraction method Based on a Flow-Based Extended Difference-of-Gaussians (Flow-Based Extended Difference-of-Gaussians) operator.
The technical purpose of the invention is realized by the following technical scheme.
A Flow-XDoG operator-based abdominal MRI image contour extraction method comprises the following steps:
in the step 1, bilateral filtering is carried out on the image, so that the interference of noise and a deviation field to contour extraction is reduced; enhancing the texture details of the image by using fractional order differential filtering, and reserving a smooth area in the image;
in step 1, the fractional order differential template used by the fractional order differential filtering is a Tiansi operator.
in step 2, the Flow-XDoG operator is an anisotropic filter that extracts a set of smoothed and abstracted edge curves from an image; the edge extraction process for the preprocessed MRI image using the Flow-XDoG operator is as follows:
(1) Calculating the image gradient to obtain a gradient image;
(2) Constructing Edge Tangential Flow (ETF);
(3) Extracting a line profile using extended gaussian differential filtering (XDoG);
(4) Threshold segmentation;
(5) Filtering a connected domain threshold;
in step 2, the Flow-XDoG operators with different parameters have different edge extraction effects, in order to reduce adjustable parameters as much as possible, the Flow-XDoG operators with two different parameters rho are respectively used for carrying out edge extraction on the preprocessed MRI image, and an image A corresponding to a smaller rho value and an image B corresponding to a larger rho value are obtained; the parameter rho is used for controlling the number of lines extracted by an operator, and the larger the rho value is, the more lines are extracted;
in step 2, the edge connection refers to the case that each edge pixel (x) of the image A is connected i ,y i ) Edge points (x ') exist in the neighborhood of the corresponding position of image B' i ,y′ i ) Then locate in (x ') in figure A' i ,y′ i ) Is set as an edge point.
Step 3, removing error edge interference;
in step 3, by obtaining difference information between images and connected domain threshold filtering, erroneous edges due to noise and other interference factors and erroneous edges located inside organs are removed.
in step 4, the neighborhood Total variation can reflect the spectral variation degree in the neighborhood, the edge has a larger response value, and considering that each pixel has different contributions to the neighborhood Total variation, the Weighted neighborhood Total variation (WTV) is used for further filtering the false edge generated in the process of edge extraction, and the edge is preliminarily refined;
in step 4, the calculation formula of the weighted neighborhood total variation is as follows:
wherein (x, y) represents the coordinates of a pixel point in the image, (x) 0 ，y 0 ) Indicating the coordinates of a certain pixel in the image, D indicating the point (x) 0 ,y 0 ) Is given as a weighted neighborhood total variation value, Ω is expressed in (x) 0 ,y 0 ) A neighborhood space, central, h (x, y) denotes a gaussian function, v (x, y) denotes a gradient;
in step 4, the edge is further refined through a skeleton extraction algorithm to obtain a final edge refinement result.
Compared with the prior art, the method has the advantages that the influence of noise and image self-texture interference on the extraction result is reduced by utilizing bilateral filtering and fractional order differential filtering, the number of parameters to be adjusted is reduced by adopting two Flow-XDoG operators with given different parameters, the extracted error edge is removed through connected domain threshold analysis, image difference information and weighted total variation edge judgment, and the edge extraction quality is improved; compared with the classical edge extraction operator and the nonphotorealistic drawn edge extraction method, the Flow-XDoG operator-based abdomen MRI image contour extraction method has the advantages that the extracted edges are clearer, more complete and more accurate, the method does not depend on network training, and the problem of training set data volume does not need to be solved; the method is very suitable for contour extraction of abdominal MRI images or other images with complex graphical mechanisms and textures.
Description of the drawings:
FIG. 1 is a flow chart of the contour extraction of the present invention;
FIG. 2 is a schematic diagram of a four-direction Tiansi template decomposed according to coordinate axes;
FIG. 3 is a template of a sobel in eight orientations;
FIG. 4 is a graph showing the effect of pretreatment according to the present invention; fig. 4 (a) is an original image, fig. 4 (b) is a bilateral filtering effect diagram, and fig. 4 (c) is a fractional differential filtering effect diagram;
FIG. 5 is a graph illustrating the effect of connected domain threshold filtering according to the present invention; wherein, fig. 5 (a) is a Flow-XDoG operator extraction effect graph with ρ =0.99, fig. 5 (b) is a connected domain threshold value filtering effect graph with ρ =0.99, fig. 5 (c) is a Flow-XDoG operator extraction effect graph with ρ =1.0, and fig. 5 (d) is a connected domain threshold value filtering effect graph with ρ = 1.0;
FIG. 6 is a diagram illustrating the effect of edge connection according to the present invention;
FIG. 7 is a diagram illustrating the effect of the present invention after obtaining an image difference and removing false edge interference;
FIG. 8 is a Zhang-Suen refinement algorithm pseudo-code; wherein, fig. 8 (a) is a schematic diagram of 8 neighborhoods, and fig. 8 (b) is pseudo code of Zhang-Suen refinement algorithm;
FIG. 9 is a graph of edge refinement results of the present invention; wherein, fig. 9 (a) is a weighted total variation edge determination process, and fig. 9 (b) is a Zhang-Suen refinement algorithm effect diagram;
FIG. 10 is a comparison of different contour extraction methods; wherein, fig. 10 (a) is the Sobel operator edge extraction result, fig. 10 (b) is the fuzzy inference-based edge extraction result, fig. 10 (c) is the single Flow-XDoG operator edge extraction result, and fig. 10 (d) is the edge extraction result of the method of the present invention.
Detailed Description
The method of the present invention will be described in detail with reference to specific embodiments.
In consideration of the influence of Image noise and complex Image texture on contour extraction, bilateral filtering and fractional differential filtering are adopted to preprocess an abdominal nuclear Magnetic Resonance Image (MRI), two Flow-XDoG operators with different parameters are used to extract edge lines and perform edge connection on the Image, residual noise and error edges caused by Image texture are removed by obtaining difference information between the images and analyzing a connected domain, weighted Total Variation (WTV) and skeleton extraction are used to realize false edge removal and edge refinement, and finally the extraction of the abdominal nuclear Magnetic Resonance Image (MRI) contour is realized.
The data of the invention is derived from the public data set provided by the SPIE-AAPM-NCI PROSTATex competition, and the extraction flow chart is shown in figure 1.
The invention discloses an abdomen MRI image contour extraction method based on a Flow-XDoG operator, which comprises the following steps:
carrying out bilateral filtering on the image to reduce the interference of noise and a deviation field to contour extraction; using fractional order differential filtering to enhance the image texture details and keep smooth areas in the image, the specific process is as follows:
(1) The image is subjected to bilateral filtering, so that the interference of noise and a deviation field to contour extraction is reduced, and the calculation formula is as follows:
wherein (x) 0 ，y 0 ) Coordinates, f' (x), of a certain pixel point in the image 0 ,y 0 ) Is filtered at (x) 0 ,y 0 ) The pixel value of (f, x, y) is (x) before filtering 0 ,y 0 ) The pixel value, k and l, of a certain pixel point in the neighborhood are respectively expressed by (x) 0 ，y 0 ) The length and width of the central neighborhood window; w (x) 0 ,y 0 X, y) is the weight of a point (x, y) that depends on the spatial domain kernel d (x, y) 0 ,y 0 X, y) and a value range kernel r (x) 0 ,y 0 X, y), the calculation formula is as follows:
wherein σ d And σ r Filtering parameters for the spatial domain and the value domain, respectively.
(2) Because the abdominal MRI image has the characteristics of multiple organ tissues and complex image texture, the fractional differentiation is adopted to enhance the image texture details and keep a smooth region in the image. Decomposing an operator into four small templates of 3 × 3 along the coordinate axis direction by using the most widely applied fractional order differential template, namely the Tiansi operator, respectively performing enhancement processing on the pixel points to be processed by using each small template, and decomposing the operator into four templates such as the Tiansi operator along the coordinate axis directionAs shown in fig. 2. In FIG. 2, a 0 ＝1，a 1 ＝-v，
v is the fractional order of differentiation;
in the processing process, the pixel point (x, y) to be processed is a constant coefficient 2a 0 At the position, performing convolution operation on each pixel point in the image by using four 3 x 3 templates in the figure 2 respectively to obtain four convolution values M corresponding to the coordinate axis direction respectively 1 、M 2 、M 3 、M 4 (ii) a For a pixel point (x, y) to be processed in an image, the pixel value of the point is s, and s can be M 1 、M 2 、M 3 、M 4 To indicate that:
respectively carrying out edge extraction on the preprocessed MRI images by using two Flow-XDoG operators with different rho values to obtain an image A (smaller rho) with less edge information and an image B (larger rho) with more edge information, and then carrying out edge connection on the image A by taking the image B as a guide image, wherein the specific process is as follows:
(1) The Flow-XDoG operator is an anisotropic filter that extracts a set of smooth and abstract edge curves from an image; the edge extraction process for the preprocessed MRI image using the Flow-XDoG operator is as follows:
1) Calculating image gradient to obtain gradient image
And (3) respectively performing convolution calculation on the image by using the sobel operators in the eight directions, wherein the direction with the maximum gradient assignment is taken as the gradient of the current point, and the sobel operator templates in the eight directions are shown in FIG. 3.
2) Construction Edge tangential Flow (Edge indexed Flow, ETF)
For a given input image, defining the vector perpendicular to the image gradient as the edge tangent vector, denoted by t (x, y), which can be regarded as the local edge curve direction in a sense, the specific construction formula is as follows:
wherein omega μ Is used to denote by (x) 0 ,y 0 ) A centered, μ radius kernel, (x, y) is used to denote (x) 0 ,y 0 ) The pixels in the neighborhood, k, are used to represent the normalization factor, t n (. Cndot.) represents an iteratively determined local edge tangent vector of period 2 π, and specifies t 0 (. Is) an image gradient vector, phi (x) 0 ,y 0 X, y) denotes two t n Angle relation of (c) (. Alpha.), w s (x 0 ,y 0 X, y) is a spatial weighting function, w m (x 0 ,y 0 X, y) is a magnitude weighting function, w d (x 0 ,y 0 X, y) represents a direction weight function; their calculation formulas are shown in formulas (6) to (9):
w d (x 0 ,y 0 ,x,y)＝|t n-1 (x 0 ,y 0 )·t n-1 (x,y)| (9)；
wherein the content of the first and second substances,
represents a normalized gradient magnitude; to ensure smoothness of the edge, the number of iterations is set to 3.
3) Contour line extraction using extended Gaussian differential filtering (XDoG)
And (3) applying extended Gaussian difference filtering (XDoG) to the obtained edge tangential flow graph to extract a contour line, wherein the application formula is as follows:
wherein, G σ Representing a Gaussian function, x representing a pixel (x) 0 ,y 0 ) S represents an arc length parameter, T represents the size of the Gaussian function kernel, + -S represents the upper and lower integral limits of the arc length parameter S, I (l) x,s (t)) is represented by x,s A pixel value at (t); l x,s (t) represents a tangent line segment perpendicular to and intersecting a certain curve at an intersection point of (x) 0 ,y 0 )；D σ,k,ρ (t) represents extended Gaussian difference Filter (XDoG), and the calculation formula is shown in formula (11), σ m The size of S is determined:
wherein the content of the first and second substances,
and
representing a Gaussian operator, σ c And σ s Denotes the scale size of a Gaussian template, let σ denote s ＝1.6σ c ，σ c =1.0, for the following edge join, here two different values of ρ are taken, where ρ can control the number of lines extracted by the operator, the larger the value of ρ the more lines are extracted, where ρ is 1 ＝0.99、ρ 2 =1.0, each contour extraction is performed on an image, and the extraction result is thresholded by a threshold function of formula (12) to obtain a final contour extraction graph:
wherein, T ε (u) represents the output pixel value after thresholding, u represents the input pixel value to the thresholding function, ε represents the error coefficient,
representing a luminance parameter.
4) Threshold segmentation
Because the extracted line profile image is not a binary image and cannot be subjected to connected domain threshold filtering, an Otsu threshold method is applied to carry out binarization processing on the image; for a given image, T is recorded as a segmentation threshold value of the foreground and the background, and the proportion of the number of foreground points in the image is p 0 Average gray level of u 0 The background point number is p in the proportion of the image 1 Traversing T from the minimum gray value to the maximum gray value, and when the variance value delta is maximum by T, the T is the optimal threshold for segmentation, wherein the variance value delta is calculated according to the following formula:
δ＝p 0 ·p 1 ·(u 0 -u 1 ) 2 (13)。
5) Connected-domain threshold filtering
Due to the influence of residual noise and complex texture information, the extracted contour has many false interference edges, and a part of interference items can be removed by analyzing the connected domain and setting an area threshold, and an effect schematic diagram is shown in fig. 5.
(2) Edge connection, the specific process is as follows:
in FIG. 5 (b) and FIG. 5 (d), respectively, are ρ 1 ＝0.99、ρ 2 An outline extraction diagram when =1.0, in fig. 5 (b), there are fewer error edges but an edge missing phenomenon, and in fig. 5 (d), there are a large number of error edges but the details of the edges are rich, so that an edge connection scheme is applied to process fig. 5 (b), and the specific process is as follows: for each edge pixel (x) in FIG. 5 (b) i ,y i ) Finding whether there is an edge point (x ') in the neighborhood of the corresponding position of FIG. 5 (d)' i ,y′ i ) If any, the bit in FIG. 5 (b) is located at (x' i ,y′ i ) Until the complete image is traversed, the join effect is as shown in fig. 6.
Step 3, removing error edge interference:
as can be seen from the results shown in fig. 6, there are still false edges inside the organ, and to solve this problem, image subtraction is applied to obtain the difference image of fig. 6 and fig. 5 (b); the erroneous edges that need to be removed are then selected by connected component analysis and removed in fig. 6, resulting in the results shown in fig. 7.
And 4, removing the false edge, performing edge thinning, and finishing the extraction of the abdominal MRI image contour, wherein the specific process is as follows:
(1) Weighted neighborhood Total variation (WTV)
The neighborhood Total variation reflects the spectral change degree in the neighborhood, has a larger response value at the edge, considers that each pixel has different contributions to the neighborhood Total variation, uses Weighted neighborhood Total variation (WTV) to further filter out the false edge generated in the process of edge extraction, and preliminarily refines the edge, and the calculation formula is as follows:
wherein D represents a point (x) 0 ,y 0 ) The weighted neighborhood total variation value of (x) is expressed by Ω 0 ,y 0 ) A neighborhood space that is centered, h (x, y) represents a gaussian function, and ^ (x, y) represents a gradient; in the neighborhood, if the weighted total variation of the point is greater than the weighted total variation of more than half of the points in the neighborhood, the point can be reserved as an edge point, otherwise, the point is removed; because the relation between the current point and the window neighboring point and the relation between the windows are considered, the method not only can preliminarily refine the edges, but also can better filter the false edges caused by noise and tiny ground feature details.
(2) Image skeleton extraction
It is actually the central pixel contour of the object on the image, and the main idea is to extract the central pixel contour from the imageContinuously corroding and thinning the target by using the characteristic of a 3-by-3 pixel window taking the pixel to be detected as the center from the periphery of the target to the center of the target until the target is corroded to be incapable of corroding any more (the width of a single-layer pixel), thereby obtaining the edge of the width of the single-layer pixel; here, zhang-Suen refinement algorithm (pseudo code is shown in FIG. 8) is applied to achieve edge refinement, where A (P) 1 ) Is from P 9 Go back to P 1 From 0 to 1, B (P) 1 ) Is P 1 The number of non-zero neighborhood pixels.
As can be seen from fig. 4, the bilateral filtering can not only smooth the image noise but also retain the edge information, and the fractional differential filtering can further smooth the texture structure inside the organ or tissue, thereby reducing the influence on the extraction result.
As can be seen from FIG. 5, as ρ increases, the extracted edge information is richer and the number of false edges is larger, and connected domain threshold filtering is introduced to remove part of false edges and reduce the number of false edges in the image.
As shown in fig. 6, the method using neighborhood search can connect the fracture edges in fig. 5 (b), but adds many error edges, which indicates that the Flow-XDoG operator using only two parameters cannot meet the requirement of practical application, and further processing is required on the extraction result.
As can be seen from fig. 7, the edge extraction result after the post-processing is introduced is clearer and more complete, and the number of false edges is less, which illustrates the necessity of the method of the present invention, but the edge is too coarse and has too large difference with the actual edge, so that the edge discrimination and edge refinement steps of the weighted total variation are introduced, and as can be seen from fig. 9 (b), the edge of the refined result is clearer and more complete, and the number of false edges is less.
As can be seen from fig. 10, the edge of the image contour extracted by the Flow-XDoG operator-based abdominal MRI image contour extraction method is clearer and more complete, and has less interference, and especially when the edge in an area where gradient change is not significant is extracted, the effect is better than that of other prior art. Therefore, the method provided by the invention is suitable for extracting the outline of the abdominal Magnetic Resonance Image (MRI).
Compared with the classical edge extraction operator and the nonphotorealistic drawing edge extraction method, the Flow-XDoG operator-based abdomen MRI image contour extraction method has the advantages that the extracted edges are clearer, more complete and more accurate, the method does not depend on network training, the problem of training set data volume does not need to be solved, and the method is very suitable for contour extraction of abdomen MRI images or other images with complex graphic mechanisms and texture structures.
Although the methods and techniques of the present invention have been described in terms of preferred embodiments, it will be apparent to those of ordinary skill in the art that variations and/or rearrangements of the methods and techniques described herein may be made without departing from the spirit and scope of the invention. It is expressly intended that all such similar substitutes and modifications apparent to those skilled in the art are deemed to be within the spirit, scope and content of the invention.
Claims (8)
1. A Flow-XDoG operator-based abdominal MRI image contour extraction method is characterized by comprising the following steps:
step 1, abdominal MRI image preprocessing: reducing the interference caused by noise and deviation fields, and enhancing and smoothing the image;
step 2, extracting the edges of the tissues or organs: respectively carrying out edge extraction on the preprocessed MRI image by using two Flow-XDoG operators with different parameters, and obtaining a preliminary result through edge connection;
respectively using Flow-XDoG operators with two different parameters rho to carry out edge extraction on the preprocessed MRI image to obtain an image A corresponding to a smaller rho value and an image B corresponding to a larger rho value; the parameter rho is used for controlling the number of lines extracted by an operator, and the larger the rho value is, the more lines are extracted;
the edge connection refers to the case that each edge pixel (x) of the image A is connected i ,y i ) Edge points (x ') exist in the neighborhood of the corresponding position of image B' i ,y′ i ) Then it is located at (x 'in graph A' i ,y′ i ) Setting the point of (a) as an edge point;
step 3, removing error edge interference;
and 4, removing the false edge, and performing edge thinning to finish the extraction of the abdominal MRI image contour.
2. The abdomen MRI image contour extraction method based on the Flow-XDoG operator according to the claim 1, characterized in that, in the step 1, the image is filtered bilaterally, and the interference of noise and deviation field to the contour extraction is reduced; and (3) enhancing the texture details of the image and reserving a smooth area in the image by using fractional order differential filtering.
3. The abdomen MRI image contour extraction method based on the Flow-XDoG operator according to claim 2, wherein in step 1, the fractional differential template used by the fractional differential filtering is Tiansi operator.
4. The abdomen MRI image contour extraction method based on the Flow-XDoG operator according to claim 1, wherein in the step 2, the edge extraction process of the preprocessed MRI image by using the Flow-XDoG operator is as follows:
(1) Calculating the image gradient to obtain a gradient image;
(2) Constructing Edge Tangential Flow (ETF);
(3) Extracting a line profile by using extended Gaussian difference filtering (XDoG);
(4) Threshold segmentation;
(5) And filtering a connected component threshold.
5. The abdomen MRI image contour extraction method based on the Flow-XDoG operator according to claim 1, characterized in that, in step 3, by obtaining the difference information between the images and the connected domain threshold filtering, the false edges generated due to noise and other interference factors and the false edges located inside the organ are removed.
6. The abdomen MRI image contour extraction method based on the Flow-XDoG operator according to claim 1, characterized in that in step 4, the weighted neighborhood total variation is used to filter out the false edges generated in the edge extraction process, and the edges are preliminarily refined.
7. The abdomen MRI image contour extraction method based on the Flow-XDoG operator according to claim 6, wherein in the step 4, the calculation formula of the weighted neighborhood total variation is as follows:
wherein (x, y) represents the coordinates of a pixel point in the image, (x) 0 ,y 0 ) Indicating the coordinates of a certain pixel in the image, D indicating the point (x) 0 ,y 0 ) Is given as a weighted neighborhood total variation value, Ω is expressed in (x) 0 ,y 0 ) A neighborhood space of the center, h (x, y) represents a Gaussian function,
representing a gradient.
8. The abdomen MRI image contour extraction method based on the Flow-XDoG operator according to claim 6, wherein in step 4, the edge is further refined by a skeleton extraction algorithm to obtain a final edge refinement result.
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