CN119169034A - Global image segmentation method based on global Gaussian distribution and statistical norm - Google Patents
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Abstract
The invention provides a global image segmentation method based on global Gaussian distribution and statistical norms, which relates to the technical field of image processing and application and comprises the steps of constructing an energy functional based on the global Gaussian distribution and the statistical norms; the method comprises the steps of obtaining pixel coordinates of an image to be segmented, inputting the pixel coordinates of the image to be segmented into the energy functional, carrying out iterative operation on the level set function in the energy functional until the difference between the energy functional value obtained by iterative calculation of the current round and the energy functional value obtained by iterative calculation of the previous round is smaller than a preset precision threshold value, ending iterative calculation, outputting a final level set function of the image to be segmented, updating the current level set function after each iterative calculation, and carrying out iterative update of the next round by utilizing the updated level set function if the condition of ending the iterative calculation is not reached. The scheme can improve the precision of image segmentation.
Description
Technical Field
The invention relates to the technical field of image processing and application, in particular to a global image segmentation method based on global Gaussian distribution and statistical norms.
Background
The image is one of carriers for transmitting information in daily life of people, the research of image technology is extended to various aspects, and the image is widely applied to the fields of target detection, medical image processing, industry, face recognition, intelligent transportation and the like. Image processing has become very important with the continuous progress of technology, and image segmentation is an important field in image processing. The image segmentation mainly divides an image into a plurality of non-overlapping areas, and segments a target area in the image, thereby providing basis for subsequent image analysis and image understanding. Therefore, how to obtain better image segmentation results and improve segmentation accuracy and efficiency have become one of the key problems of image segmentation.
The current common image segmentation mode is a segmentation mode based on a local level set, has a good effect on segmenting an image with uneven intensity, and can improve segmentation accuracy under the condition of uneven intensity by using local statistical characteristics. However, since this approach loses global features, it is highly sensitive to the initial position of the contour. Meanwhile, when the algorithm is processing high noise images, the existing scheme may also perform poorly because noise may cause local intensity variations, which may be erroneously captured by contours, resulting in erroneous segmentation. Therefore, the existing image segmentation scheme has poor accuracy in segmenting the image.
Disclosure of Invention
In view of the foregoing, it is necessary to propose a global image segmentation method based on global gaussian distribution and statistical norms to improve the accuracy of image segmentation.
In a first aspect, the present invention provides a global image segmentation method based on global gaussian distribution and statistical norms, including:
Constructing an energy functional based on global Gaussian distribution and a statistical norm, wherein the energy functional comprises a level set function for representing an image segmentation result;
acquiring pixel coordinates of an image to be segmented;
Inputting pixel coordinates of the image to be segmented into the energy functional, carrying out iterative operation on a level set function in the energy functional based on a gradient descent method until the difference between the energy functional value obtained by the iterative calculation of the current round and the energy functional value obtained by the iterative calculation of the previous round is smaller than a preset precision threshold, and ending the cyclic iterative calculation;
Outputting a final level set function of the image to be segmented;
And after each iterative calculation, if the condition of ending the cyclic iterative calculation is not met, updating the current level set function, and carrying out the iterative updating of the next round by utilizing the updated level set function.
Preferably, the construction of the energy functional based on the global Gaussian distribution and the statistical norm comprises the steps of starting from global information of an image, defining a global Gaussian distribution fitting energy for each pixel in the image to be segmented by taking a global mean value and a global variance as variables, and integrating the fitting energy of all pixel points to construct the energy functional.
Preferably, constructing the energy functional specifically includes:
the fitting energy is described statistically by global gaussian distributions of different mean and variance, respectively, and the following primary energy functional is constructed:
Wherein, Is a probability density function defined as the global region intensity of a gaussian distribution, i=1, 2, Ω 1 and Ω 2 are the inner and outer regions, respectively, of the image contour C to be segmented, the following energy functions can be obtained:
Wherein, The energy functional is characterized, phi is a level set function, x is the pixel coordinates in the image I (x) to be segmented, mu i (x) is the global mean,As a global variance of the values of the variables,For the degree of deviation of the gray value at x from the average intensity value μ i (x), λ (x) is a multiplier that adjusts the deviation from μ i (x), α 1 and α 2 are both fixed balance parameters, and H (Φ (x)) is a Heaviside function.
Preferably, the iterative operation is performed on the level set function in the energy functional based on the gradient descent method, including:
Step S31, configuring initial iteration parameters, wherein the iteration parameters comprise initial energy functional values;
Step S32, respectively calculating the current energy functional related mu i (x), Partial derivative of λ (x);
Step S33, making each calculated partial derivative be 0, and calculating mu i (x) by using pixel coordinates of the image to be segmented, A calculated value of λ (x);
step S34, calculating mu i (x), The calculated value of lambda (x) is brought into the current energy functional to obtain an energy functional value;
And step 35, judging whether the difference between the energy functional value obtained by current calculation and the energy functional value obtained by previous iterative calculation is smaller than a preset precision threshold, if so, ending iterative operation, otherwise, returning to step 32 for execution after updating the level set function in the current energy functional.
Preferably, in step S35, the updating the level set function in the current energy functional includes:
Calculating the partial derivative of the current energy functional with respect to a level set function;
And updating the level set function in the current energy functional by utilizing the partial derivative of the current energy functional with respect to the level set function, and taking a new energy functional formed after the level set function is updated as the energy functional of the next iterative operation.
Preferably, the updating the level set function in the current energy functional with respect to the partial derivative of the level set function by using the current energy functional includes:
updating the level set function using the following calculation formula:
Where Δt is the time step.
Preferably, after constructing the energy functional, further comprising:
correcting the constructed energy functional by using the following regularization term to ensure the smoothness of the level set function in the curve evolution process;
wherein p (phi (x)) is the regularization term, Gradient as a function of level set.
Preferably, the preset precision threshold is 10 -3.
In a second aspect, the present invention provides a computer readable storage medium having stored thereon a computer program which, when executed in a computer, causes the computer to perform the method according to any of the first aspects.
In a third aspect, the present invention provides a computing device comprising a memory having executable code stored therein and a processor, the processor implementing a method as in any of the first aspects when executing the executable code.
According to the technical scheme, when the global image is segmented based on the scheme, firstly, an energy functional is built based on global Gaussian distribution and statistical norms, then, pixel coordinates of the image to be segmented are acquired and then input into the energy functional, further, iterative operation is carried out on a level set function in the energy functional based on a gradient descent method until the difference value between the energy functional value obtained by current iterative calculation and the energy functional value obtained by the previous round is smaller than a preset precision threshold, and then, loop iterative calculation is ended, and a final level set function of the image to be segmented is output. Therefore, in order to solve the problem of high sensitivity to the initial position of the outline and noise caused by the lack of global features, the method constructs the energy functional based on the probability density function of the global area intensity of the Gaussian distribution with statistical rule characteristics from the global information of the image, not only can consider the features of each pixel point of the image to be segmented by taking the global mean value and the variance as variables, but also can measure the similarity among the pixels through the Gaussian distribution statistical characteristics, so that the boundary of the target area can be identified more accurately under the complex background. Therefore, the scheme can improve the precision of image segmentation.
Drawings
Fig. 1 is a flowchart of a global image segmentation method based on global gaussian distribution and statistical norms according to an embodiment of the present invention.
Fig. 2 shows image segmentation contrast results of different initial contours.
Fig. 3 shows image segmentation comparison results of different noise and different levels.
Fig. 4 shows the segmentation comparison result of the natural image.
Detailed Description
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
As shown in fig. 1, the present invention provides a global image segmentation method based on global gaussian distribution and statistical norms, which may include the following steps:
Step 101, constructing an energy functional based on global Gaussian distribution and statistical norms, wherein the energy functional comprises a level set function for representing an image segmentation result;
102, acquiring pixel coordinates of an image to be segmented;
Step 103, inputting pixel coordinates of an image to be segmented into an energy functional, carrying out iterative operation on a level set function in the energy functional based on a gradient descent method until the difference between the energy functional value obtained by iterative computation of the current round and the energy functional value obtained by iterative computation of the previous round is smaller than a preset precision threshold value, and ending the cyclic iterative computation, wherein after each iterative computation, if the condition of ending the cyclic iterative computation is not reached, updating the current level set function, and carrying out iterative update of the next round by utilizing the updated level set function;
and 104, outputting a final level set function of the image to be segmented.
In order to solve the problem that the initial position of the contour and noise are highly sensitive due to the lack of global features, the embodiment of the scheme starts from the global information of the image, constructs the energy functional based on the probability density function of the global area intensity of the Gaussian distribution with statistical rule characteristics, not only considers the feature of each pixel point of the image to be segmented by taking the global mean value and the variance as variables, but also can measure the similarity among pixels through the Gaussian distribution statistical characteristics, so that the boundary of the target area can be identified more accurately under the complex background. Therefore, the scheme can improve the precision of image segmentation.
For step 101, constructing an energy functional based on the global Gaussian distribution and the statistical norm, wherein the energy functional comprises a level set function for representing an image segmentation result;
In this embodiment, in order to solve the problem of high sensitivity to the initial position and noise of the contour caused by the lack of global features, consider that, starting from the global information of the image, for each pixel in the image to be segmented, a new global gaussian distribution fitting energy is defined by taking the global mean and variance as variables, and the fitting energy of all pixel points is integrated to form a data item of an energy function, namely an energy functional. Specifically, when constructing the energy functional, the fitting energy can be described by using global gaussian distribution of different mean and variance from the statistical perspective, and the following primary energy functional is constructed:
Wherein, p i,x(I(x),μi (x), Λ (x)) is a probability density function defined as the intensity of the global region of the gaussian distribution, where,Omega 1 and omega 2 are the inner and outer regions of the image contour C to be segmented, respectively, so that the following energy functions can be obtained:
Wherein, The energy functional is characterized, phi is a level set function, x is the pixel coordinates in the image I (x) to be segmented, mu i (x) is the global mean,As a global variance of the values of the variables,For the degree of deviation of the gray value at x from the average intensity value μ i (x), λ (x) is a multiplier that adjusts the deviation from μ i (x), α 1 and α 2 are both fixed balance parameters, and H (Φ (x)) is a Heaviside function.
For step 102, obtaining pixel coordinates of an image to be segmented;
In the step, firstly, an image to be segmented is obtained, then a pixel coordinate system of the image to be segmented is constructed, and further the pixel coordinate of the image to be segmented is obtained. For example, a two-dimensional coordinate system u-v in units of pixels is established with the upper left corner of the image to be segmented as the origin. The abscissa u and ordinate v of a pixel are the number of columns and rows, respectively, in the image array. The unit of the pixel coordinate system u-v is a pixel, which is a discrete image coordinate or pixel coordinate, with the origin in the upper left corner of the picture.
For step 103, inputting pixel coordinates of the image to be segmented into an energy functional, and carrying out iterative operation on a level set function in the energy functional based on a gradient descent method until the difference between the energy functional value obtained by the iterative computation of the current round and the energy functional value obtained by the iterative computation of the previous round is smaller than a preset precision threshold value, ending the cyclic iterative computation;
In the step, the energy functional value obtained after each iterative operation is compared with the energy functional value obtained by the previous iterative operation, and whether the difference value between the energy functional value and the energy functional value is smaller than a preset precision threshold value is judged. If so, the energy functional is not reduced continuously, namely the iterative operation reaches the precision requirement, the output level set function can meet the segmentation precision requirement, and if not, the iterative operation does not reach the precision requirement, the iterative operation is further continued. Specifically, step 103 may be implemented by performing an iterative operation on the level set function in the energy functional based on the gradient descent method as follows:
Step S31, configuring initial iteration parameters, wherein the iteration parameters comprise initial energy functional values;
Step S32, respectively calculating the current energy functional related mu i (x), Partial derivative of λ (x);
Step S33, making each calculated partial derivative be 0, and calculating mu i (x) by using pixel coordinates of the image to be segmented, A calculated value of λ (x);
step S34, calculating mu i (x), The calculated value of lambda (x) is brought into the current energy functional to obtain an energy functional value;
and step S35, judging whether the difference between the energy functional value obtained by current calculation and the energy functional value obtained by previous iterative calculation is smaller than a preset precision value, if so, ending iterative operation, otherwise, returning to step S32 for execution after updating the level set function in the current energy functional.
In this embodiment, during the iterative operation, each iteration parameter is initialized, for example, an initial energy functional value is given, and then the current energy functional is calculated with respect to μ i (x),Lambda (x) partial derivative. Specifically, the gradient descent flow is: where δ (φ (x)) is the derivative of H (φ (x)), i.e In the formula mu i (x),Λ (x) is unknown, so considering the partial derivative of the energy function and let the derivative equal to zero, it is possible to obtain:
Wherein:
Thus, the calculated mu i (x), And further judging the magnitude relation between the difference value between the current energy functional value and the energy functional value obtained in the previous round and the preset precision value. Of course, if the first iterative operation is performed, the energy functional value of the previous round is the set initial energy functional value. If the difference value of the energy functional values is smaller than a preset precision threshold value, for example, the difference value is smaller than 10 -3, the preset precision requirement is met, along with the progress of iterative operation, the energy functional does not evolve to the minimum, and at the moment, the level set function in the output energy functional is the final level set function of the image to be segmented, and the optimal segmentation curve of the image to be segmented is obtained. If the difference value of the energy functional values is larger than a preset precision threshold, namely the difference value is larger than 10 -3, the precision requirement is not met, and iterative operation is continued after the level set function is updated.
Further, in step S35, when updating the level set function in the current energy functional, the partial derivative of the current energy functional with respect to the level set is calculated, then the partial derivative of the current energy functional with respect to the level set function is utilized to update the level set function in the current energy functional, and the new energy functional formed after the level set function is updated is used as the energy functional of the next iteration operation. Specifically, when the level set function in the current energy functional is updated with respect to the partial derivative of the level set function, the level set function may be updated using the following calculation formula:
Where Δt is the time step.
In addition, in order to avoid the problem of reinitialization and ensure that the curve keeps the level set function smooth in the evolution process, the constructed energy functional can be modified by introducing regularization terms. The specific regularization term may be obtained as follows:
Where p (phi (x)) is a regularization term, Gradient as a function of level set.
And when the regularization term is used for correcting the energy functional, the following new energy functional can be obtained:
in practice, iterative operation can be performed by using the regularized and corrected energy functional, so that a more accurate image segmentation result is obtained.
The effects of the present solution are further described below with reference to specific application examples.
In order to verify the effectiveness of the scheme on natural images, 6 natural images are selected in BSDS data sets to be tested, and the segmentation performance of the scheme is measured according to the following 4 objective evaluation indexes, namely, a Jaccard index (JSC) rate, a Dice Similarity Coefficient (DSC) rate, a Recall rate (Recall) and a Precision rate (Precision). Specifically, each evaluation index is:
in the above four objective evaluation indexes, G s is a divided image, G GT is a GT image, |·|indicates the number of pixels in the region, TP indicates a true example, FP indicates a false positive example, and FN indicates a false negative example.
(1) Verifying the robustness of an initial contour
Experiments were performed by setting initial contours of different sizes and shapes, and the segmentation results are shown in fig. 2. As can be seen from fig. 2, in (a 0)-(a3), a green rectangle represents an initial contour and red represents a division result, in (b 0)-(b3), a green triangle represents an initial contour and red represents a division result, in (c 0)-(c3), a green circle represents an initial contour and red represents a division result, and in (d 0)-(d3), a green trapezoid represents an initial contour and red represents a division result. The whole segmentation result shows that whether the shape of the initial contour is rectangular, round, triangular or trapezoidal, or the initial contour comprises one target area, two target areas, three target areas and even no target area, the scheme can accurately segment the image.
(2) Robustness to noise
In order to verify the robustness of the scheme to noise, the method is verified from two aspects of subjective evaluation and objective evaluation.
1) Subjective evaluation
Setting the initial contour as a circle, selecting a real image, sequentially adding a mean value of 0, gaussian noise with variances of 0.015,0.02,0.025 and 0.03 and spiced salt noise with variances of 0.01,0.012,0.014 and 0.016 into the image, and dividing the image into a segmentation result shown in figure 3. Wherein, (a 0)-(a3) adds the segmentation result of different levels of gaussian noise to the image respectively, and (b 0)-(b3) adds the segmentation result of different levels of salt-and-pepper noise to the image respectively. The segmentation result of fig. 3 shows that the scheme can realize image segmentation of Gaussian noise with different levels and salt and pepper noise with different levels, and has good robustness to Gaussian noise and salt and pepper noise.
The segmentation results of the natural image as shown in fig. 4, (a 1)-(a6) are six different scene segmentation results without noise, and (b 1)-(b6) are six different scene segmentation results with different noise. As can be seen from fig. 4, the present solution can realize the segmentation of natural images under different scenes, and also can realize the segmentation of noise natural images under different scenes. Thereby verifying the feasibility and effectiveness of the scheme on natural image segmentation.
2) Objective evaluation
For better analysis of the experimental results, the above-described fig. 4 was objectively evaluated by four objective evaluation indexes, and the evaluation results are shown in table 1 below:
TABLE 1
Table 1 shows objective evaluation results of the present embodiment on natural image segmentation. The four objective indexes have the value ranges of [0,1], and the closer the objective evaluation value is to 1, the better the segmentation effect is, the closer to 0 is, and the worse the segmentation effect is. From table 1, it can be seen that, for the DSC evaluation index, the segmentation accuracy is in the range of 97.79% -99.48%, for the Precision index, the segmentation accuracy is in the range of 98.67% -99.99%, for the Recall evaluation index, the segmentation accuracy is in the range of 97.16% -99.36%, and for the JSC index, the segmentation accuracy is in the range of 95.68% -99.14%, so that the effectiveness of the scheme in segmenting images is further verified.
The present specification also provides a computer readable storage medium having stored thereon a computer program which, when executed in a computer, causes the computer to perform the method of any of the embodiments of the specification.
The present specification also provides a computing device comprising a memory having executable code stored therein and a processor which when executing the executable code implements the method of any of the embodiments of the specification.
The modules or units in the device of the embodiment of the invention can be combined, divided and deleted according to actual needs. The foregoing disclosure is illustrative of the preferred embodiments of the present invention, and is not to be construed as limiting the scope of the invention, as it is understood by those skilled in the art that all or part of the above-described embodiments may be practiced with equivalents thereof, which fall within the scope of the invention as defined by the appended claims.
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