CN108416792B - Medical computed tomography image segmentation method based on active contour model - Google Patents
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Abstract
The invention discloses a medical computed tomography image segmentation method based on an active contour model, and belongs to the field of medical image processing. Firstly, a GAC model and an SBGFRLS model are combined by using a weight function, so that the possibility of zero-level set inspection of the multi-layer contour of the medical image is improved; secondly, in order to further simplify the level set algorithm in the model, a Gaussian filtering technology is introduced, and the convergence rate of the segmentation model is improved; and finally, the Hausdorff distance is introduced to measure the distance between the targets, so that the problem of poor segmentation effect of the traditional model on the convex region in the medical image is solved, the capture capability of the multi-target object edge in the medical computed tomography image is improved, and the segmentation precision is high.
Description
Technical Field
The invention relates to the field of image processing, in particular to a medical computed tomography image segmentation method based on an active contour model, which has high convergence rate and high robustness to initial contour curve positions and noise.
Background
Image segmentation is one of the most basic and important problems in the field of image processing. Although many researchers have proposed various image segmentation methods such as a morphological watershed-based segmentation method, a grayscale threshold-based segmentation method, an edge detection-based segmentation method, a partial differential equation-based segmentation method, and the like, an image segmentation method suitable for all applications has not appeared at present.
With the continuous innovation and development of medical imaging equipment and examination technology, digital imaging enables computer-aided detection and computer-aided diagnosis, and imaging examination is increasingly applied to clinical disease diagnosis, and especially shows more and more important roles in tumor 'precise medical treatment' planning. In order to accurately judge the disease condition of a patient, a doctor needs to effectively segment a lesion site included in a medical image. Medical image segmentation is the basis for extracting a mutation region, measuring a specific tissue and realizing reconstruction of three dimensions, is an important step for distinguishing and sketching a focus region, is also the basis and the key of accurate medical treatment, and the quality of segmentation directly influences whether a clinician diagnoses the state of an illness of a patient. However, according to the introduction of the imaging department doctor, on one hand, due to the influence of many factors such as the physiology of the patient, the body position movement, the acquisition system and the like, the quality of the acquired medical image is sometimes low; on the other hand, due to the different tissues to be segmented and the different imaging mechanisms, the segmentation methods are often inconsistent. Therefore, when the clinical treatment is carried out, the doctor still needs to segment the focus and the peripheral tissues of the patient through manual operation, which wastes time and labor and affects the diagnosis efficiency of the clinician. Moreover, although Computed Tomography (CT) images have high resolution and are relatively accurate in locating lesion regions, doctors have certain difficulty in determining tumor positions and boundaries when there is no significant difference in the density between tissues with tumor infiltration and normal tissues. As such, there is an urgent need for a practical segmentation method for specific medical images.
Jehan-Besson et al propose a medical image segmentation method based on an extreme learning machine, which reduces segmentation time, but has low precision. The royal yog et al propose a multi-threshold medical image segmentation algorithm based on one-dimensional Otsu, and though the segmentation precision is improved to a certain extent, the segmentation effect on the deep convex region is poor. In view of the characteristics of uneven gray distribution, fuzzy edge, high noise intensity and the like of medical images, variation models have shown greater and greater application potential in recent years. The variation model is a model driven by 'internal force' constraint and 'external force', and has a good segmentation effect on medical images. The Mumford and J.Shah firstly propose a Mumford-Shah variation model, and firstly expand a partial differential model based on image recovery to the image segmentation field. Chan et al simplify the Mumford-Shah model and then propose a CV model, which has the advantages that the segmentation result is independent of the initial contour position, the boundary of the image can be accurately extracted, and the robustness to noise is high. However, since the level set function is introduced, the computation amount of the CV model is high, the level set function needs to be reinitialized, and the gradient descent is easy to fall into a local minimum value. In addition, since the CV model is based on global gray scale fitting, it is not suitable for medical image segmentation with uneven gray scale distribution. For this reason, Li et al propose a RSF (regional Scalable fixing) model containing a regional Scalable energy term, which is capable of segmenting images with non-uniform gray levels, but is sensitive to the initial position of the active contour and noise. Zhang et al further introduces global information of the CV model into a gac (geodesic Active content) model, proposes a Level Set segmentation model sbgfrls (selected and filtered regulated Level Set gaussian) model based on a region, considers region information and edge information of an image, reduces sensitivity of the model to an initial contour position, but cannot effectively segment heterogeneous images with uneven gray levels, such as medical images.
Disclosure of Invention
The invention aims to solve the technical problems in the prior art and provides a medical computed tomography image segmentation method based on an active contour model, which has high convergence rate and high robustness on the initial contour curve position and noise.
The technical solution of the invention is as follows: a medical computed tomography image segmentation method based on an active contour model is characterized by comprising the following steps:
step 1, establishing a moving contour segmentation model of the medical computed tomography image, wherein the definition of a level set evolution equation is given by a formula (1):
the above-mentionedRepresenting the sign pressure function for controlling the direction of evolution of the curve,representing the image in coordinatesThe value of the pixel of (a) is,the function of the level set is represented,the gradient operator is represented by a gradient operator,representing information about an initial input imageThe weight function of (a) is determined,indicating an expectation of 0 and a standard deviation ofThe gaussian kernel function of (a) is,the divergence operator is represented by a vector of vectors,represents the normalized Hausdorff distance,andare all scale factors, wherein the weight functionIs given by equation (2):
the above-mentionedIndicating an expectation of 0 and a standard deviation ofA gaussian kernel function of ""represents a convolution operation, and the definition of the normalized Hausdorff distance is given by equation (3):
the above-mentionedRepresenting the Hausdorff distance between the gray information in the inner and outer local regions of the active contour curve, the definition of which is given by equation (4):
the above-mentionedA set of pixels representing an inner region of the active contour curve,set of pixels, coordinates, representing the outer region of the active contour curveThe pixel value of (b) is given by equation (6) -equation (7):
the above-mentionedRepresents the Heaviside function, the definition of which is given by equation (8):
step 2, inputting the medical computed tomography image to be segmentedSetting a relevant Gaussian kernel function and calculating a weight function by using the formula (2);
Step 3, ifIf the image is a CT image or an MRI image, the step 3.1 is carried out; if it isTurning to step 3.2 for the PET image;
the above-mentionedAndthe average pixel values representing the inner and outer regions of the active contour, respectively, are defined by equations (10) and (11), respectively:
turning to the step 4;
the above-mentionedA gray threshold value representing a judgment tumor region, whose definition is given by equation (13):
the above-mentionedThe derivative function, representing the Weibull probability distribution function, is defined by equation (14):
the above-mentionedIs a shape parameter of the probability distribution function,scale parameters of the probability distribution function;
Step 5, calculating the normalized Hausdorff distance calculation of the pixel values of the inner and outer regions of the active contour by using a formula (3);
Step 7, checking whether the evolution curve is stably converged, if so, stopping iteration, and ending the algorithm; otherwise, go to step 3.
Compared with the prior art, the invention has the following advantages: firstly, the convergence rate of the segmentation is improved by utilizing the normalized Hausdorff distance; secondly, the introduction of Gaussian filtering simplifies the evolution process of the level set; thirdly, the capability of detecting the multilayer outline of the object by adopting the weight function is improved, and the capturing capability of the deep convex region and the multi-target object edge in the computed tomography image is also improved.
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FIG. 1 is a graph comparing the CT or MRI image segmentation results with other methods according to the present invention.
FIG. 2 is a graph comparing the segmentation results of PET images according to the embodiment of the present invention and other methods.
Detailed Description
The invention relates to a medical computed tomography image segmentation method based on an active contour model, which is carried out according to the following steps:
step 1, establishing a moving contour segmentation model of the medical computed tomography image, wherein the definition of a level set evolution equation is given by a formula (1):
the above-mentionedRepresenting the sign pressure function for controlling the direction of evolution of the curve,representing the image in coordinatesThe value of the pixel of (a) is,the function of the level set is represented,the gradient operator is represented by a gradient operator,representing information about an initial input imageThe weight function of (a) is determined,indicating an expectation of 0 and a standard deviation ofThe gaussian kernel function of (a) is,the divergence operator is represented by a vector of vectors,represents the normalized Hausdorff distance,andare all scale factors, wherein the weight functionIs given by equation (2):
the above-mentionedIndicating an expectation of 0 and a standard deviation ofA gaussian kernel function of ""represents a convolution operation, and the definition of the normalized Hausdorff distance is given by equation (3):
the above-mentionedRepresenting the Hausdorff distance between the gray information in the inner and outer local regions of the active contour curve, the definition of which is given by equation (4):
the above-mentionedA set of pixels representing an inner region of the active contour curve,set of pixels, coordinates, representing the outer region of the active contour curveThe pixel value of (b) is given by equation (6) -equation (7):
the above-mentionedRepresents the Heaviside function, the definition of which is given by equation (8):
step 2, inputting the medical computed tomography image to be segmentedSetting the associated Gaussian kernel functionAnd calculating a weight function using the formula (2);
Step 3, ifIf the image is a CT image or an MRI image, the step 3.1 is carried out; if it isTurning to step 3.2 for the PET image;
the above-mentionedAndthe average pixel values representing the inner and outer regions of the active contour, respectively, are defined by equations (10) and (11), respectively:
turning to the step 4;
the above-mentionedA gray threshold value representing a judgment tumor region, whose definition is given by equation (13):
the above-mentionedThe derivative function, representing the Weibull probability distribution function, is defined by equation (14):
the above-mentionedIs a shape parameter of the probability distribution function,scale parameters of the probability distribution function;
Step 5, calculating the normalized Hausdorff distance calculation of the pixel values of the inner and outer regions of the active contour by using a formula (3);
Step 7, checking whether the evolution curve is stably converged, if so, stopping iteration, and ending the algorithm; otherwise, go to step 3.
The embodiment of the invention and other methods compare the segmentation results of CT or MRI images as shown in figure 1: from left to right are (a) original images; (b) the embodiment of the invention divides the result; (c) a segmentation result based on an extreme learning machine proposed by Jehan-Besson; (c) the one-dimensional Otsu-based multi-threshold segmentation result proposed by Queen yog.
The embodiment of the invention and other methods compare the segmentation results of the PET image as shown in FIG. 2: from left to right are (a) original images; (b) the embodiment of the invention divides the result; (c) a segmentation result based on an extreme learning machine proposed by Jehan-Besson; (c) the one-dimensional Otsu-based multi-threshold segmentation result proposed by Queen yog.
The iteration number and time ratio required for segmenting 3 CT or MRI images (figure 1) by the embodiment of the invention and other methods are shown in table 1.
The error rate ratio of 3 CT or MRI images (FIG. 1) segmented by the embodiment of the invention and other methods is shown in Table 2.
The number of iterations and time ratio required to segment 3 PET images (fig. 2) for embodiments of the present invention and other methods are shown in table 3.
The error rate ratio of 3 PET images (FIG. 2) segmented by the embodiment of the present invention and other methods is shown in Table 4.
TABLE 1 iteration count vs. time (units: seconds) for the 3 images of FIG. 1
TABLE 2 segmentation error Rate comparison of the 3 images of FIG. 1
TABLE 3 iteration count vs. time (units: seconds) for the 3 images of FIG. 2
TABLE 4 segmentation error Rate comparison of the 3 images of FIG. 2
The comparison result shows that: the invention can more accurately segment the heterogeneous medical computed tomography image with low contrast and uneven gray scale in a short time.
Claims (1)
1. A medical computed tomography image segmentation method based on an active contour model is characterized by comprising the following steps:
step 1, establishing a moving contour segmentation model of a medical computed tomography image, wherein the definition of a level set evolution equation is given by a formula (1):
spf (-) denotes a symbolic pressure function for controlling the direction of curve evolution, i (x) denotes the pixel value of the image at coordinate x, phi denotes a level set function,representing the gradient operator, v (u)0(x) Is shown with respect to the initial input image u0(x) Weight function of δσ(. represents desirably 0,Gaussian kernel function with standard deviation σ, div denotes the divergence operator, DHExpressing the normalized Hausdorff distance, α and μ are both scale factors, where the definition of the weight function v is given by equation (2):
the G isσRepresenting a gaussian kernel with a desired 0 and standard deviation σ, "# represents a convolution operation, and the definition of the normalized Hausdorff distance is given by equation (3):
d isHRepresenting the Hausdorff distance between the gray information in the inner and outer local regions of the active contour curve, the definition of which is given by equation (4):
dH=max(d(Ω1,Ω2),d(Ω2,Ω1)) (4)
the d represents the distance of two discrete point sets a and B, the definition of which is given by equation (5):
the omega1Set of pixels, Ω, representing the inner region of the active contour curve2A set of pixels representing the area outside the active contour curve, the pixel value at coordinate x being given by equation (6) -equation (7):
said Hε(φ) represents the Heaviside function, the definition of which is given by equation (8):
step 2, inputting a medical computed tomography image u to be segmented0(x) Setting a relevant Gaussian kernel function, and calculating a weight function v by using a formula (2);
step 3. if u0(x) If the image is a CT image or an MRI image, the step 3.1 is carried out; if u0(x) Turning to step 3.2 for the PET image;
step 3.1 calculates the value of the spf (-) function using equation (9):
c is mentioned1And c2The average pixel values representing the inner and outer regions of the active contour, respectively, are defined by equations (10) and (11), respectively:
turning to the step 4;
step 3.2 calculates the value of the spf (-) function using equation (12):
the th represents a threshold value of the gray scale for judging the tumor region, and the definition is given by equation (13):
the f' (a) represents the derivative function of the Weibull probability distribution function, the definition of which is given by equation (14):
k is a shape parameter of the probability distribution function, and lambda is a scale parameter of the probability distribution function;
step 4, initializing a level set function phi (x, t) to be 0, and making alpha to be-0.1 and mu to be 0.1;
step 5, calculating the normalized Hausdorff distance calculation of the pixel values of the inner and outer regions of the active contour by using a formula (3);
step 6, updating the level set function phi (x, t) by using a finite difference method and a formula (1);
step 7, checking whether the evolution curve is stably converged, if so, stopping iteration, and ending the algorithm; otherwise, go to step 3.
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