CN112102350A - Secondary image segmentation method based on Otsu and Tsallis entropy - Google Patents

Secondary image segmentation method based on Otsu and Tsallis entropy Download PDF

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CN112102350A
CN112102350A CN202010885498.XA CN202010885498A CN112102350A CN 112102350 A CN112102350 A CN 112102350A CN 202010885498 A CN202010885498 A CN 202010885498A CN 112102350 A CN112102350 A CN 112102350A
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李云红
姚兰
穆兴
李传真
罗雪敏
朱绵云
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Abstract

The invention discloses a quadratic image segmentation method of Otsu and Tsallis entropies, which is implemented in the following way: step 1, carrying out contrast expansion transformation preprocessing on an input original image I, wherein the gray scale dynamic range of the processed image is 0,255](ii) a Step 2, calculating a threshold value K of the original image by adopting an Otsu algorithm, and performing primary segmentation on the image according to the threshold value K to obtain a segmented image I1(ii) a Step 3, creating a segmentation image I1Calculating a segmented image I1The Tsallis entropy of (1); step 4, obtaining (u ', v') which maximizes the entropy of the two-dimensional Tsallis as an optimal threshold value, and using the optimal threshold valueFor the segmented image I1Performing secondary segmentation to obtain a final re-segmented image I2. The invention solves the problem of wrong segmentation caused by Otsu without considering the distribution condition of target and background pixels, and improves the segmentation accuracy.

Description

Secondary image segmentation method based on Otsu and Tsallis entropy
Technical Field
The invention belongs to the technical field of image processing, and relates to a secondary image segmentation method based on Otsu and Tsallis entropy.
Background
Image segmentation is a key technology in image processing, is also a classical problem, and a general segmentation method is not found until now. Image segmentation has important effects on feature extraction, object recognition, etc., and the quality of segmentation determines the quality of the subsequent image processing. Therefore, it is very important to research the image segmentation technology. The current common segmentation methods include a threshold segmentation method, an edge detection method, a region segmentation method, a segmentation method based on a specific theory, and the like. Among image segmentation techniques, a threshold segmentation method is a relatively common method, and is favored because of its simplicity of implementation and ease of operation.
The maximum inter-class variance method is one of the classical algorithms in threshold segmentation, and is widely applied due to simple calculation and strong adaptability. The maximum inter-class variance method takes the maximum inter-class variance between the target and the background of the image as a criterion, and has a better segmentation effect in most cases. However, the inter-maximum-class variance method does not take into consideration the distribution of pixels inside the target and the background, and in this case, the adoption of the inter-maximum-class variance method easily causes erroneous segmentation of the image. One threshold segmentation method that is similar to the maximum inter-class variance method is the maximum entropy segmentation method, which uses the image entropy criterion for segmentation. However, the entropy threshold method has a problem of too large amount of calculation and slow operation speed due to a large amount of logarithmic calculation. Therefore, there is a problem in directly using both of these common threshold segmentation methods.
Disclosure of Invention
The invention aims to provide a quadratic image segmentation method based on Otsu and Tsallis entropy, which solves the problem of wrong segmentation caused by the fact that image pixel distribution is not considered in the traditional Otsu algorithm.
The technical scheme adopted by the invention is that a secondary image segmentation method based on Otsu and Tsallis entropy is implemented according to the following steps:
step 1, carrying out contrast expansion transformation pretreatment on an input original image I, and obtaining a gray level image after the pretreatment, wherein the gray level dynamic range of the gray level image is [0,255 ];
step 2, calculating a threshold value K of the gray-scale image by adopting an Otsu algorithm, and performing primary segmentation on the gray-scale image according to the threshold value K to obtain a segmented image I1；
Step 3, creating a segmentation image I1Calculating a segmented image I1The Tsallis entropy of (1);
step 4, obtaining (u ', v') with the maximum entropy of the two-dimensional Tsallis, taking (u ', v') as an optimal threshold value, and using the optimal threshold value (u ', v') to segment the image I1Performing secondary segmentation to obtain a final re-segmented image I2。
The invention is also characterized in that:
the primary segmentation in step 2 is represented as:
C0from the grey scale value in the grey scale map at 0, K]All image compositions within the range, C1The gray scale value in the gray scale map is [ K +1, L-1 ]]All pixels in the range;
C0and C1The variance between the two classes is calculated as shown in equation (4):
σ2＝ω0(μ0-μ)2+ω1(μ1-μ)2 (4)
by applying gray scale values [0, L-1 ] to the entire gray scale map]Traversing, calculating the inter-class probability of the target background under the current gray value, and calculating the gray image C0And C1The value with the largest inter-class variance between the two classes is the optimal threshold K, and the calculation of the maximum inter-class variance is shown in formula (5):
Figure BDA0002655444690000021
ω in the formula (4)0Is C in the gray scale map0Total probability of class occurrence, ω1Is C in the gray scale map1Total probability of class occurrence, μ0Is represented by C0Mean value of the gray levels of classes, mu1Is represented by C1The mean value of the gray levels of the classes, μ, represents the mean value of the gray levels of the whole image, and the calculation formula is as follows:
Figure BDA0002655444690000031
Figure BDA0002655444690000032
Figure BDA0002655444690000033
Figure BDA0002655444690000034
Figure BDA0002655444690000035
in the formula:
Figure BDA0002655444690000036
representing the probability of the occurrence of a pixel with a grey value i in a grey scale map, where niThe number of pixels having a gradation value i in the gradation map is indicated, and n indicates the total number of pixels in the gradation map.
And 3, performing threshold segmentation by using a Tsallis entropy, wherein the Tsallis entropy calculation process comprises the following steps:
for input segmentation image I1The (x, y) size is M × N, and the calculation of the gray value in the l × l region centered on the point (x, y) is as shown in equation (11):
Figure BDA0002655444690000037
wherein f (x, y) represents the gray value of the point (x, y),
Figure BDA0002655444690000038
denotes the probability of occurrence of (f (x, y), g (x, y)) by rounding
Figure BDA0002655444690000039
SfgThe (f (x, y), g (x, y)) in the divided image I1Number of occurrences in, PfgForm a divided image I1The threshold (u, v) divides the histogram into a background a region and a target B region, an edge C region, and a noise D region.
The background a region and target B region probability calculations are shown in equations (12) (13):
Figure BDA00026554446900000310
Figure BDA00026554446900000311
the maximum two-dimensional Tsallis entropy calculation process in the step 4 is as follows:
the two-dimensional Tsallis entropy calculation is obtained by pseudo-additivity, as shown in equation (14):
Figure BDA00026554446900000312
the tsalis entropy algorithm considers both the gray value distribution of a pixel and the average gray value distribution of its neighboring pixels, so that the segmented threshold is a two-dimensional vector, and the optimal threshold (u ', v') is obtained by maximizing the two-dimensional tsalis entropy, as shown in equation (15):
Figure BDA0002655444690000041
the invention has the beneficial effects that:
1. the method carries out contrast expansion preprocessing on the input image, is beneficial to improving the contrast of the image, better distinguishes the target and the background and is convenient for subsequent image segmentation;
2. the method adopts the one-dimensional Otsu method to obtain the global threshold value, and performs primary segmentation, so that the image can be rapidly divided into a target part and a background part, the operation speed is high, and the subsequent secondary image segmentation processing is facilitated.
3. According to the method, the Tsallis entropy is adopted to perform secondary segmentation of the image, the problem of wrong segmentation caused by the relation between image pixel points is not considered in the process of performing image segmentation by the Otsu method, the influence of noise on image segmentation can be reduced according to the Tsallis entropy, the relation between probability distribution of a target and the background is further considered, the phenomenon of wrong segmentation of the image can be effectively improved, and the segmentation precision is improved.
Drawings
FIG. 1 is a schematic flow chart of a quadratic image segmentation method based on Otsu and Tsallis entropy according to the present invention;
fig. 2 is a two-dimensional histogram region division diagram of the Tsallis entropy image segmentation in the quadratic image segmentation method based on Otsu and Tsallis entropy according to the present invention.
Fig. 3 is a comparison graph of the segmentation effect of the quadratic image segmentation method based on Otsu and tsalis entropy in embodiment 1 and other threshold segmentation methods.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
Real-time example 1
The invention relates to a quadratic image segmentation method based on Otsu and Tsallis entropy, which is implemented according to the following steps as shown in FIG. 1:
step 1, carrying out contrast expansion transformation pretreatment on an input original image I, and obtaining a gray level image after the pretreatment, wherein the gray level dynamic range of the gray level image is [0,255 ];
in step 1, an input original image I is set to be an image with a size of M × N and a gray level of L, and an image gray value at a point (x, y) is set to be f (x, y), contrast of the original image I is expanded, and the wider the gray dynamic range is, the higher the contrast of the image is, and the sharper the corresponding image is. The pretreatment process is as follows:
A＝min[f(x，y)] (1)
B＝max[f(x，y)] (2)
Figure BDA0002655444690000051
where a is the minimum gray scale value of the original image I, B is the maximum gray scale value of the original image I, g (x, y) is the gray scale of the gray scale image after the contrast expansion transformation, and the gray scale dynamic range is [0,255 ].
Step 2, calculating a threshold value K of the gray-scale image by adopting an Otsu algorithm, and performing primary segmentation on the gray-scale image according to the threshold value K to obtain a segmented image I1；
In the step 2, an Otsu algorithm is adopted to solve a threshold value K, the gray-scale image is subjected to primary segmentation, and the gray-scale image is rapidly divided into C0And C1Two kinds, wherein C0From the grey scale value in the grey scale map at 0, K]All image compositions within the range, C1The gray scale value in the gray scale map is [ K +1, L-1 ]]All pixels in the range.
C0And C1The variance between the two classes is calculated as shown in equation (4):
σ2＝ω0(μ0-μ)2+ω1(μ1-μ)2 (4)
by applying gray scale values [0, L-1 ] to the entire gray scale map]Traversing, calculating the inter-class probability of the target background under the current gray value, and calculating the gray image C0And C1The value with the largest inter-class variance between the two classes is the optimal threshold K, and the calculation of the maximum inter-class variance is shown in formula (5):
Figure BDA0002655444690000061
ω in the formula (4)0Is C in the gray scale map0Total probability of class occurrence, ω1Is C in the gray scale map1Total probability of class occurrence, μ0Is represented by C0Mean value of the gray levels of classes, mu1Is represented by C1The mean value of the gray levels of the classes, μ, represents the mean value of the gray levels of the whole image, and the calculation formula is as follows:
Figure BDA0002655444690000062
Figure BDA0002655444690000063
Figure BDA0002655444690000064
Figure BDA0002655444690000065
Figure BDA0002655444690000066
in the formula:
Figure BDA0002655444690000067
representing the probability of the occurrence of a pixel with a grey value i in a grey scale map, where niThe number of pixels having a gradation value i in the gradation map is indicated, and n indicates the total number of pixels in the gradation map.
Step 3, creating a segmentation image I1Calculating a segmented image I1The Tsallis entropy of (1);
wherein step 3, a segmentation image I is created1The two-dimensional histogram adopts Tsallis entropy to carry out secondary segmentation on the wrongly segmented pixels, so that the wrongly segmented phenomenon of the image can be effectively improved, and the image segmentation precision is improved. For input segmentation image I1(x, y) size M N, centered on point (x, y)The gray value calculation in the l × l region is shown in equation (11):
Figure BDA0002655444690000068
wherein f (x, y) represents the gray value of the point (x, y),
Figure BDA0002655444690000069
denotes the probability of occurrence of (f (x, y), g (x, y)) by rounding
Figure BDA00026554446900000610
SfgDenotes the number of times (f (x, y), g (x, y)) appears in the image, PfgForm a divided image I1The threshold (u, v) divides the histogram into a background a region and a target B region, an edge C region, and a noise D region. The proportion of the background A area and the target B area is large, and the edge C area and the noise D area, namely P, can be ignoredC+PD0, then the background A and target B region probabilities are calculated as shown in equation (12) (13):
Figure BDA0002655444690000071
Figure BDA0002655444690000072
step 4, obtaining (u ', v') with the maximum entropy of the two-dimensional Tsallis, taking (u ', v') as an optimal threshold value, and using the optimal threshold value (u ', v') to segment the image I1Performing secondary segmentation to obtain a final re-segmented image I2。
In step 4, the two-dimensional Tsallis entropy S is obtained by traversing the whole two-dimensional histogramq(u, v) is maximized to obtain the maximum (u, v) as the optimum threshold, and the segmentation image I is subjected to1The secondary segmentation is carried out, the problem of pixel distribution in the target area and the background area is fully considered, and the problem of wrong segmentation caused by Otsu segmentation can be effectively solvedCutting problems. Q in the formulas (12) and (13) represents a measurement parameter of an entropy index non-extensive tissue, and a two-dimensional Tsallis entropy calculation can be obtained through pseudo-additivity, as shown in a formula (14):
Figure BDA0002655444690000073
the tsalis entropy algorithm considers both the gray value distribution of a pixel and the average gray value distribution of its neighboring pixels, so that the segmented threshold is a two-dimensional vector, and the optimal threshold (u ', v') can be obtained by maximizing the two-dimensional tsalis entropy, as shown in equation (15):
Figure BDA0002655444690000074
the principle of the quadratic image segmentation method based on Otsu and Tsallis entropies is that the image is secondarily segmented by adopting an Otsu and Tsallis entropy combination method, and the Otsu method can rapidly divide the image into a target and a background during primary image segmentation; the Tsallis entropy can find the maximum two-dimensional Tsallis entropy, namely the optimal threshold value, by traversing the two-dimensional histogram of the image by using the pixel information of the image, and can effectively improve the wrong segmentation phenomenon caused by Otsu by performing secondary segmentation by using the threshold value.
Fig. 2 is a two-dimensional histogram region division diagram of an image subjected to primary segmentation, and thresholds (u, v) divide the histogram into a background a region and a target B region, an edge C region, and a noise D region. Because the ratio of the background A area to the target B area is relatively large, the edge C area and the noise D area can be ignored, and therefore the influence of noise on image segmentation can be reduced. Fig. 3 is a diagram of the segmentation effect of embodiment 1 using the method of the present invention and other threshold segmentation methods, and it can be seen from fig. 3 that both the Otsu algorithm and the maximum entropy algorithm have the phenomenon of wrong segmentation of the background and the target.
The method for segmenting the secondary image based on Otsu and Tsallis entropy has the advantages that the image is segmented twice by utilizing the global threshold and the two-dimensional maximum Tsallis entropy of the Otsu method, the relationship between pixels inside a target and a background is considered, the defects of Otsu can be overcome, and a good segmentation effect is achieved.

Claims (6)

1. A quadratic image segmentation method based on Otsu and Tsallis entropy is characterized by comprising the following steps:
step 1, carrying out contrast expansion transformation pretreatment on an input original image I, and obtaining a gray level image after the pretreatment, wherein the gray level dynamic range of the gray level image is [0,255 ];
step 2, calculating a threshold value K of the gray-scale image by adopting an Otsu algorithm, and performing primary segmentation on the gray-scale image according to the threshold value K to obtain a segmented image I1；
Step 3, creating a segmentation image I1Calculating a segmented image I1The Tsallis entropy of (1);
step 4, obtaining (u ', v') with the maximum entropy of the two-dimensional Tsallis, wherein the (u ', v') is the optimal threshold value, and using the optimal threshold value (u ', v') to segment the image I1Performing secondary segmentation to obtain a final re-segmented image I2。
2. The method for segmenting the secondary image based on Otsu and Tsallis entropy as claimed in claim 1, wherein the primary segmentation in the step 2 is represented as:
C0from the grey scale value in the image at 0, K]All image compositions within the range, C1From the grey value in the image at [ K +1, L-1]All pixels in the range;
said C is0And said C1The variance between the two classes is calculated as shown in equation (4):
σ2＝ω0(μ0-μ)2+ω1(μ1-μ)2 (4)
by applying gray scale values [0, L-1 ] to the entire image]Go through the traversal and calculateCalculating the inter-class probability of the target background under the front gray value to obtain an image C0And C1The value with the largest inter-class variance between the two classes is the optimal threshold K, and the calculation of the maximum inter-class variance is shown in formula (5):
Figure FDA0002655444680000011
3. a quadratic image segmentation method based on Otsu and tsalis entropy as claimed in claim 2, wherein ω in the formula (4)0Is C in the image0Total probability of class occurrence, ω1Is C in the image1Total probability of class occurrence, μ0Is represented by C0Mean value of the gray levels of classes, mu1Is represented by C1The mean value of the gray levels of the classes, μ, represents the mean value of the gray levels of the whole image, and the calculation formula is as follows:
Figure FDA0002655444680000021
Figure FDA0002655444680000022
Figure FDA0002655444680000023
Figure FDA0002655444680000024
Figure FDA0002655444680000025
in the formula:
Figure FDA0002655444680000026
representing the probability of the occurrence of a pixel with a grey value i in a grey image, where niThe number of pixels having a gradation value i in the image is indicated, and n indicates the total number of pixels in the image.
4. The method for segmenting the secondary image based on Otsu and Tsallis entropy as claimed in claim 1, wherein Tsallis entropy is adopted for threshold segmentation in the step 3, and the Tsallis entropy calculation process is as follows:
for input segmentation image I1The (x, y) size is M × N, and the calculation of the gray value in the l × l region centered on the point (x, y) is as shown in equation (11):
Figure FDA0002655444680000027
wherein f (x, y) represents the gray value of the point (x, y),
Figure FDA0002655444680000028
denotes the probability of occurrence of (f (x, y), g (x, y)) by rounding
Figure FDA0002655444680000029
SfgDenotes the number of times (f (x, y), g (x, y)) appears in the image, PfgForm a divided image I1The threshold (u, v) divides the histogram into a background a region and a target B region, an edge C region, and a noise D region.
5. The method for quadratic image segmentation based on Otsu and Tsallis entropy as claimed in claim 4, wherein the probability calculation of the background A region and the target B region is as shown in formula (12) (13):
Figure FDA00026554446800000210
Figure FDA0002655444680000031
6. the method for segmenting the secondary image based on Otsu and Tsallis entropy as claimed in claim 1, wherein the maximum two-dimensional Tsallis entropy calculation process in the step 4 is as follows:
the two-dimensional Tsallis entropy calculation is obtained by pseudo-additivity, as shown in equation (14):
Figure FDA0002655444680000032
the tsalis entropy algorithm considers both the gray value distribution of a pixel and the average gray value distribution of its neighboring pixels, so that the segmented threshold is a two-dimensional vector, and the optimal threshold (u ', v') is obtained by maximizing the two-dimensional tsalis entropy, as shown in equation (15):
Figure FDA0002655444680000033
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