CN116883672B - Image segmentation method based on clustering division differential evolution algorithm and OTSU algorithm - Google Patents
Image segmentation method based on clustering division differential evolution algorithm and OTSU algorithm Download PDFInfo
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Abstract
The invention belongs to the technical field of image processing, and particularly discloses an image segmentation method based on a clustering division differential evolution algorithm and an OTSU algorithm. Comprising the following steps: initializing a population, calculating individual fitness values and dividing the individual fitness values into 3 sub-populations; different mutation strategies are adopted in different iteration stages of the population, and the population evolution is adapted; adaptively updating control parameters F and CR values in a population, and generating offspring individuals through cross operation of the population; and finally, selecting operation to screen the individual with the optimal fitness value. And carrying out threshold segmentation on the gray level image to obtain an optimal fitness value, if the iteration number of the current population reaches the maximum iteration number or reaches the optimal fitness value, terminating the algorithm and outputting a final result, otherwise, continuing to carry out differential evolution operation. The invention not only can balance the global searching capability and convergence speed of the algorithm, but also can improve the image segmentation precision, has better application value, and can be widely applied to medical image processing and canopy image processing.
Description
Technical Field
The invention belongs to the technical field of image processing, and particularly relates to an image segmentation method based on a clustering division differential evolution algorithm and an OTSU algorithm.
Background
The image segmentation is a process of dividing an image into a plurality of parts and extracting the interested parts, and can provide basis for computer vision and subsequent image processing. For image segmentation, the most common image segmentation methods are a threshold segmentation method, an edge detection image segmentation method and a maximum entropy method, wherein the threshold segmentation method is the most extensive image segmentation method because of being simple, efficient and good in robustness. However, with the increase of the threshold number, the conventional threshold image segmentation method has the defects of high time complexity and reduced image segmentation quality. In the prior art, image segmentation is regarded as an optimization problem, and a differential evolution algorithm (Differential Evolution Algorithm, abbreviated as DE) is applied to image segmentation, and the accuracy of image segmentation can be improved by combining an OTSU (maximum inter-class variance method) segmentation algorithm, but local optimization and premature convergence are easy to fall into. Therefore, the method has important significance for solving the problems existing in the combination of the differential evolution algorithm and the OTSU algorithm.
Disclosure of Invention
Aiming at the problems, the invention provides an image segmentation method based on a clustering division differential evolution algorithm and an OTSU algorithm. The method adopts K-Means clustering to divide population, double mutation strategy and dynamic self-adaptive adjustment of control parameters F and CR values, which not only can greatly balance global searching capability and local searching capability of the algorithm, but also can improve image segmentation precision, and well solves the problems of easy optimum sinking and premature convergence existing in the prior art when two algorithms are combined.
In order to achieve the technical effects, the invention is mainly realized by the following technical scheme:
an image segmentation method based on a clustering division differential evolution algorithm and an OTSU algorithm comprises the following steps:
step 1: preprocessing an image to obtain a gray image;
step 2: initializing a population, and calculating the fitness value of individual vectors in the population according to an OTSU algorithm;
step 3: dividing the population cluster into a plurality of sub-populations by using a K-Means algorithm based on the fitness value of individual vectors in the population;
step 4: iteratively updating the population, and performing double mutation operation on the population, wherein the method specifically comprises the following steps: in the initial stage of algorithm evolution, the fitness value of individual vectors in a population is generally lower than the optimal fitness value, at the moment, a mutation strategy 1 is adopted, and a plurality of individual vectors which are different from each other are randomly selected from the divided population to be used as base vectors of the mutation strategy. Along with the continuous increase of the iteration times, the fitness value of individual vectors in the population is continuously increased. When the fitness value of the individual vector reaches the maximum, a mutation strategy 2 is adopted, and the optimal individual vector is selected from the global as the base vector of the mutation strategy;
step 5: and iteratively updating the population, and performing cross operation on the population, wherein in the initial stage of a differential evolution algorithm in the cross operation, the CR value of a cross factor is smaller, so that the population diversity is increased, and the global searching capability of the population is ensured. Along with the continuous increase of the iteration times of the population, the fitness value of individual vectors in the population is continuously increased, the optimal solution in the population is gradually concentrated in a certain local area, the CR value is gradually increased at the moment, and the larger CR value is beneficial to the population to inherit excellent individual vectors;
step 6: and iteratively updating the population, and carrying out selection operation on the population. Comparing the fitness value of the current offspring individual vector with the fitness value of the parent individual vector, and selecting the fitness value to be large into the next generation population; after the selection operation is finished, finishing one differential evolution operation;
step 7: judging whether the current iteration number reaches the maximum iteration number or the optimal fitness value, if so, entering a step 8, otherwise, adaptively updating control parameters F and CR, and performing mutation, crossover and selection operations of the population again to select the current optimal individual vector;
step 8: inversely mapping the optimal individual vectors into the population, and determining an optimal image segmentation threshold value by calculating the fitness value of the individual vectors in the population after a differential evolution algorithm;
step 9: and outputting the segmented image according to the optimal image segmentation threshold.
In an exemplary embodiment, in step 2, the specific steps of initializing the population are: NP individual vectors are randomly generated in D-dimensional space:wherein each individual vector consists of D variables, -/->Represents +.>Individual vector,/->、/>Respectively represent the first->Upper and lower bounds of the g generation of the individual,/->Representing a number randomly generated between (0, 1) subject to a uniform distribution.
In an exemplary embodiment, in step 3, the population clusters are divided into 3 sub-populations, specifically the steps are:
(1) Firstly, randomly selecting 3 initialization cluster centers according to individual vector fitness values;
(2) Calculating the distance between each individual vector and the selected 3 initialization cluster centers, dividing the individual vectors into the data class closest to the cluster centers, and forming 3 data sets after all the individual vectors are divided;
(3) Then, calculating the average value of the data objects of each data set again, and taking the average value as a new clustering center;
(4) Finally, calculating the distance from each individual vector to the new 3 initialization cluster centers, and re-dividing;
(5) After each partition, the initial cluster center needs to be recalculated, and the process is repeated until all individual vectors cannot be updated to other data sets.
In an exemplary embodiment, in step 4, the double mutation operation is specifically:
，
wherein,representing the target variant vector, ">、/>And +.>Respectively represent three randomly selected from 3 cluster populationsIndividual vectors, r 1 、r 2 And r 3 Is three mutually unequal random integers, < ->Is a global optimum individual vector of the vector,indicate->The individual vector, F, is a variation factor, representing the adaptive control variation rate adjustment parameter.
Through the advantage analysis of the mutation strategies and the combination of the population characteristics of differential evolution, the double mutation strategies are designed to respectively act on different stages of the population, and the two mutation strategies complement and cooperate with each other to greatly balance the diversity and convergence of the population. 3 individual vectors are randomly selected in the variation strategy 1, and the strategy is used in the initial stage of searching of the differential evolution algorithm, so that the global searching capability of the algorithm is enhanced, the population diversity is ensured, and the local convergence is avoided; the basis vectors in variation strategy 2 areThe global optimal individual vector is used for guiding searching, and the convergence is accelerated at the later stage of the population iteration along with the increase of the population iteration times, so that the local searching capability of the population is improved.
In an exemplary embodiment, in step 5, the target vector and the individual vector generated by the mutation are subjected to a mutation operation to perform binomial cross to generate a final experimental vector, and the adaptive cross factor CR is used to adjust the cross probability.
In an exemplary embodiment, step 7, adaptively updating the control parameter F is achieved by:
，
where gen is the algebra of the current population and generations is the total number of iterations. F (F) max Represents the maximum value of the mutation factor,F min representing the minimum value of the mutant factor. Above-mentionedExhibits a decreasing trend in dynamic changes of (c).
Further, set F max =0.8，F min =0.2。
According to the evolutionary characteristics of the differential evolutionary population, the difference of individual vectors in the population is larger at the initial stage of the algorithm, so as to ensure the diversity of the population and ensure the global searching capability of the population, and the value of the variation factor F is larger at the moment. Along with the increase of the iteration times, the fitness value of individual vectors in the population is gradually increased, the optimal solution of the algorithm is gradually concentrated in a local area, the convergence is accelerated at the moment, the local searching capability of the algorithm is improved, and therefore the value of F is gradually reduced along with the iteration times.
In an exemplary embodiment, step 7, the adaptive updating of the control parameter CR is achieved by:
，
where gen represents the algebra of the current population and generations represents the total number of iterations; CR (computed radiography) min Representing the minimum value of the crossover factor,refers to random numbers in the (0, 1) range. Above->The variation of (c) exhibits a monotonically increasing trend.
Further, CR is set min =0.2。
In the initial stage of the differential evolution algorithm, the CR value of the cross factor is smaller, which is favorable for increasing the diversity of the population and ensuring the global searching capability of the population. Along with the continuous increase of the iteration times of the population, the fitness value of individual vectors in the population is continuously increased, the optimal solution in the population is gradually concentrated in a certain local area, and at the moment, the CR value is gradually increased, so that the CR value is larger, and the population is beneficial to inheriting excellent individual vectors.
The invention applies a differential evolution algorithm (Differential Evolution Algorithm, DE) in combination with a maximum inter-class variance method (OTSU method) to image segmentation. Firstly initializing a population, randomly generating NP individual vectors in a D-dimensional space, and calculating the fitness value of the current individual vectors; and then randomly selecting 3 initialized cluster centers, dividing individual vectors in the population into 3 data sets by using a K-Means algorithm, and respectively performing mutation operation, cross operation and selection operation on the individuals in the population after the clustering is completed. If the iteration number of the current population reaches the maximum iteration number or reaches the optimal fitness value, outputting an optimal threshold value and an optimal segmentation image, and if the termination condition is not met, continuing the differential evolution operation.
The double mutation strategy adopted in the invention is adjusted according to the individual fitness value in the population. In the initial stage of algorithm evolution, the fitness value of individual vectors in the population is generally lower than the optimal fitness value, so as to maintain the diversity of the population and improve the global searching capability of the population, at the moment, a mutation strategy 1 is adopted, and 3 mutually different individual vectors are randomly selected for differential operation. With the increasing number of iterations, the fitness value of individual vectors in the population is mostly higher than the average fitness value, and most individuals converge near the optimal individuals. When the fitness value of the individual vector reaches the maximum, a mutation strategy 2 is adopted to focus on the development of the vicinity of the optimal individual, so that the local searching capability of the population is improved, and the convergence is quickened.
The mutation operator and the crossover operator are adaptively adjusted according to global searching capability and convergence of the population in an iterative process, so that the convergence characteristics of the population at different stages can be adapted to the maximum limit, blind searching and local optimum sinking of an algorithm in an evolution process are avoided, and the defects of high time complexity and low image segmentation precision caused by the fact that a traditional differential evolution algorithm (Differential Evolution Algorithm, DE) and a maximum inter-class variance method (OTSU method) are combined and applied to image segmentation are overcome.
The invention has the beneficial effects that: the invention combines the self-adaptive differential evolution algorithm based on cluster partition population and the maximum inter-class variance method (OTSU method) to image segmentation, adopts double mutation and self-adaptive adjustment mutation operator and crossover operator strategies, not only balances the global searching capability and convergence speed of the algorithm, but also improves the image segmentation precision, has better application value, and can be widely applied to medical image processing and canopy image processing.
Drawings
Fig. 1 is a flowchart of an image segmentation method of the differential evolution algorithm and the OTSU algorithm based on cluster division.
Fig. 2 is a graph of the variation of the adaptive control parameter F of the present invention.
Fig. 3 is a graph of the variation of the adaptive control parameter CR of the present invention.
Detailed Description
The following detailed description of the invention is presented in conjunction with the drawings and specific embodiments to enable one skilled in the art to better understand the invention, but the illustrated embodiments are not intended to limit the invention.
As shown in fig. 1, an image segmentation method based on a cluster division differential evolution algorithm and an OTSU algorithm includes the following steps:
step 1: the gray image information is read, the gray value of the input image is encoded, the range of the gray value of the image is 0-255, the encoded gray image is encoded by an 8-bit binary string, and the encoding range is 00000000-11111111.
Step 2: initializing an image threshold population, and randomly generating NP individual vectors in a D-dimensional space:
wherein each individual vector is made up of D variables,represents +.>Individual vector,/->、/>Respectively represent the first->Upper and lower bounds of the g generation of the individual,/->The fitness value of each individual vector is calculated using the OTSU algorithm, representing a uniformly distributed number randomly generated between (0, 1).
Step 3: according to the K-Means algorithm, 3 initialization cluster centers are randomly selected based on the fitness values of the individual vectors, distances from each individual vector to the 3 initialization cluster centers are calculated, iteration is conducted step by step until all the individual vectors cannot be updated to other data sets, and the original population is divided into 3 sub-populations. The method comprises the following specific steps:
(1) Firstly, randomly selecting 3 initialization cluster centers according to individual vector fitness values;
(2) Calculating the distance between each individual vector and the selected 3 initialization cluster centers, dividing the individual vectors into the data class closest to the cluster centers, and forming 3 data sets after all the individual vectors are divided;
(3) Then, calculating the average value of the data objects of each data set again, and taking the average value as a new clustering center;
(4) Finally, calculating the distance from each individual vector to the new 3 initialization cluster centers, and re-dividing;
(5) After each partition, the initial cluster center needs to be recalculated, and the process is repeated until all individual vectors cannot be updated to other data sets.
Step 4: iteratively updating the population, and implementing a double mutation strategy in the mutation operation:
，
wherein,representing the target variant vector, ">、/>And +.>Respectively representing three individual vectors randomly selected from 3 cluster populations, r 1 、r 2 And r 3 Is three mutually non-equal random integers. />For a global optimum individual vector,indicate->The individual vector, F, is a variation factor, representing the adaptive control variation rate adjustment parameter.
In the initial stage of algorithm evolution, the fitness value of individual vectors in the population is generally lower than the optimal fitness value, so as to ensure the diversity of the population and improve the global optimizing capability of the algorithm, at the moment, a mutation strategy 1 is adopted, 3 individual vectors which are different from each other are randomly selected from the divided population to be used as the base vectors of the mutation strategy, and the diversity of the population is ensured to the greatest extent. Along with the continuous increase of the iteration times, the fitness value of individual vectors in the population is continuously increased. When the fitness value of the individual vector reaches the maximum, a mutation strategy 2 is adopted, and the optimal individual vector is selected from the global as a base vector of the mutation strategy, so that the population is promoted to be mutated towards the individual direction of the optimal fitness value.
In the initial stage of the algorithm, the individual vectors in the population have larger difference, so as to ensure the diversity of the population and ensure the global searching capability of the population, and the value of the variation factor F should be larger.
Along with the increase of the iteration times, the fitness value of individual vectors in the population is gradually increased, the optimal solution of the algorithm is gradually concentrated in a local area, the convergence is accelerated at the moment, the local searching capability of the algorithm is improved, and therefore the value of F is gradually reduced along with the iteration times.
Step 5: and iteratively updating the population, and performing cross operation on the population. Through mutation operation, the target vector and the individual vector generated by mutation are subjected to binomial crossing to generate a final experimental vector, and the adaptive crossing factor CR is used for adjusting the size of the crossing probability.
In the cross operation, in the initial stage of the differential evolution algorithm, the cross factor CR value is smaller, which is beneficial to increasing the diversity of the population and ensuring the global searching capability of the population. Along with the continuous increase of the iteration times of the population, the fitness value of individual vectors in the population is continuously increased, the optimal solution in the population is gradually concentrated in a certain local area, and at the moment, the CR value is gradually increased, so that the CR value is larger, and the population is beneficial to inheriting excellent individual vectors.
Step 6: iteratively updating the population, selecting the population, comparing the fitness value of the current offspring individual vector with the fitness value of the parent individual vector, and selecting the fitness value larger into the next generation population; after the selection operation is finished, the differential evolution operation is finished once.
Step 7: judging whether the current iteration number reaches the maximum iteration number or the optimal fitness value, if so, entering a step 8, otherwise, adaptively updating control parameters F and CR, and performing mutation, crossover and selection operations of the population again to select the current optimal individual vector.
The method comprises the following steps: as shown in fig. 2, the adaptive update of the control parameter F is achieved by:
，
where gen is the algebra of the current population and generations is the total number of iterations. F (F) max Indicating the cause of mutationMaximum value of son, F min Representing the minimum value of the mutant factor. Above-mentionedExhibits a decreasing trend in dynamic changes of (c).
Further, set F max =0.8，F min =0.2。
According to the evolutionary characteristics of the differential evolutionary population, the difference of individual vectors in the population is larger at the initial stage of the algorithm, so as to ensure the diversity of the population and ensure the global searching capability of the population, and the value of the variation factor F is larger at the moment. Along with the increase of the iteration times, the fitness value of individual vectors in the population is gradually increased, the optimal solution of the algorithm is gradually concentrated in a local area, the convergence is accelerated at the moment, the local searching capability of the algorithm is improved, and therefore the value of F is gradually reduced along with the iteration times.
As shown in fig. 3, the adaptive update of the control parameter CR is achieved by:
，
where gen represents the algebra of the current population and generations represents the total number of iterations; CR (computed radiography) min Representing the minimum value of the crossover factor, which is described aboveThe variation of (2) exhibits a monotonically increasing trend; set CR min =0.2。
In the initial stage of the differential evolution algorithm, the CR value of the cross factor is smaller, which is favorable for increasing the diversity of the population and ensuring the global searching capability of the population. Along with the continuous increase of the iteration times of the population, the fitness value of individual vectors in the population is continuously increased, the optimal solution in the population is gradually concentrated in a certain local area, and at the moment, the CR value is gradually increased, so that the CR value is larger, and the population is beneficial to inheriting excellent individual vectors.
Step 8: and inversely mapping the optimal individual vectors into the population, and determining an optimal image segmentation threshold value by calculating the fitness value of the individual vectors in the population after a differential evolution algorithm.
Step 9: and outputting the segmented image according to the optimal image segmentation threshold.
When the traditional threshold image segmentation method is used for multi-threshold image segmentation, the time complexity is exponentially increased along with the increase of the threshold number, and the segmentation quality is reduced. The self-adaptive improved differential evolution algorithm is applied to image segmentation, so that convergence can be accelerated, an optimal threshold value of image segmentation can be obtained in a short time, and the method can be widely applied to medical image processing and forest canopy image processing.
The invention uses a clustering algorithm to divide the population, improves a differential evolution algorithm, adopts a double-variation strategy and adaptively updates control parameters F and CR values, and combines the control parameters F and CR values with an OTSU algorithm to be applied to image segmentation, thereby greatly improving the accuracy of image segmentation. The application of the algorithm to image segmentation effect is obvious and the robustness is strong as can be seen through peak signal to noise ratio (PSNR).
As shown in tables 1 and 2 below, tables 1 and 2 correspond, table 1 expresses that table 2 has an optimal segmentation threshold at a threshold of 5, table 2 only has 7 sets of optimal thresholds at a threshold of k=5, and it can be seen from PSNR values that the improved differential evolution algorithm is more robust for image segmentation. Meanwhile, five data of each group of data in table 1 represent the optimal image segmentation threshold when the threshold is 5, and the foreground and the background of the original image are segmented to achieve the optimal segmentation effect.
Table 1 optimal threshold for gray image segmentation at threshold 5
Table 2 PSNR values for gray scale image segmentation at threshold 5
The foregoing embodiments of the present invention are not intended to limit the scope of the present invention, and all changes in the structure or flow chart made by the content of the description and drawings of the present invention, or direct or indirect use of the present invention in other related fields, are within the scope of protection of the present invention.
Claims (7)
1. The image segmentation method based on the clustering division differential evolution algorithm and the OTSU algorithm is characterized by comprising the following steps of
The method comprises the following steps:
step 1: preprocessing an image to obtain a gray image;
step 2: initializing a population, and calculating the fitness value of individual vectors in the population according to an OTSU algorithm;
step 3: dividing the population cluster into a plurality of sub-populations by using a K-Means algorithm based on the fitness value of individual vectors in the population;
step 4: iteratively updating the population, and performing double mutation operation on the population, wherein the method specifically comprises the following steps: in the initial stage of algorithm evolution, the fitness value of individual vectors in a population is generally lower than the optimal fitness value, a mutation strategy 1 is adopted at the moment, and a plurality of individual vectors which are different from each other are randomly selected from the divided population to be used as base vectors of the mutation strategy; along with the continuous increase of the iteration times, the fitness value of the individual vectors in the population is continuously increased, and when the fitness value of the individual vectors reaches the maximum, a mutation strategy 2 is adopted, and the optimal individual vector is selected from the global as the base vector of the mutation strategy;
step 5: iteratively updating the population, and performing cross operation on the population, wherein in the initial stage of a differential evolution algorithm in the cross operation, the cross factor CR value is smaller, so that the population diversity is increased, and the global searching capability of the population is ensured; along with the continuous increase of the iteration times of the population, the fitness value of individual vectors in the population is continuously increased, the optimal solution in the population is gradually concentrated in a certain local area, the CR value is gradually increased at the moment, and the larger CR value is beneficial to the population to inherit excellent individual vectors;
step 6: iteratively updating the population, selecting the population, comparing the fitness value of the current offspring individual vector with the fitness value of the parent individual vector, and selecting the fitness value larger into the next generation population; after the selection operation is finished, finishing one differential evolution operation;
step 7: judging whether the current iteration number reaches the maximum iteration number or the optimal fitness value, if so, entering a step 8, otherwise, adaptively updating control parameters F and CR, and performing mutation, crossover and selection operations of the population again to select the current optimal individual vector;
step 8: inversely mapping the optimal individual vectors into the population, and determining an optimal image segmentation threshold value by calculating the fitness value of the individual vectors in the population after a differential evolution algorithm;
step 9: outputting the segmented image according to the optimal image segmentation threshold;
and step 7, adaptively updating the control parameter F, wherein the control parameter F is realized by the following steps:
，
where gen is the algebra of the current population and generations is the total iteration number; f (F) max Represents the maximum value of the mutant factor, F min Representing the minimum value of the mutant factor;
the adaptive updating of the control parameter CR is achieved by:
，
where gen represents algebra of the current population, generations represents total iteration number, CR min Representing the minimum value of the crossover factor,refers to random numbers in the (0, 1) range.
2. The image segmentation method based on the cluster division differential evolution algorithm and the OTSU algorithm according to claim 1, wherein in step 2, the specific step of initializing the population is: NP individual vectors are randomly generated in D-dimensional space:
wherein each individual vector is made up of D variables,represents +.>Individual vector,/->、/>Respectively represent the first->Upper and lower bounds of the g generation of the individual,/->Representing a number randomly generated between (0, 1) subject to a uniform distribution.
3. The image segmentation method based on the differential evolution algorithm and the OTSU algorithm of cluster division according to claim 1, wherein in step 3, the cluster of the population is divided into 3 sub-populations, and the specific steps are as follows:
(1) Firstly, randomly selecting 3 initialization cluster centers according to individual vector fitness values;
(2) Calculating the distance between each individual vector and the selected 3 initialization cluster centers, dividing the individual vectors into the data class closest to the cluster centers, and forming 3 data sets after all the individual vectors are divided;
(3) Then, calculating the average value of the data objects of each data set again, and taking the average value as a new clustering center;
(4) Finally, calculating the distance from each individual vector to the new 3 initialization cluster centers, and re-dividing;
(5) After each partition, the initial cluster center needs to be recalculated, and the process is repeated until all individual vectors cannot be updated to other data sets.
4. The image segmentation method based on the cluster division differential evolution algorithm and the OTSU algorithm according to claim 1, wherein in step 4, the double mutation operation is specifically:
，
wherein,representing the target variant vector, ">、/>And +.>Respectively representing three individual vectors randomly selected from 3 cluster populations, r 1 、r 2 And r 3 Is three mutually unequal random integers, < ->Is a globally optimal individual vector,>indicate->And each individual vector, F is a variation factor and represents an adaptive control variation rate adjustment parameter.
5. The method for image segmentation based on the clustering division differential evolution algorithm and the OTSU algorithm according to claim 1, wherein in step 5, through mutation operation, a final experimental vector is generated by performing binomial intersection on a target vector and an individual vector generated by mutation, and the adaptive intersection factor CR is used for adjusting the magnitude of the intersection probability.
6. The image segmentation method based on the clustering-partitioning differential evolution algorithm and the OTSU algorithm according to claim 1, wherein in step 7, F is set max =0.8，F min =0.2。
7. The image segmentation method based on the clustering-partitioning differential evolution algorithm and the OTSU algorithm according to claim 1, wherein in step 7, CR is set min =0.2。
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