CN114693682A - Spine feature identification method based on image processing - Google Patents
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Abstract
The invention relates to the field of image processing, in particular to a spine feature identification method based on image processing.
Description
Technical Field
The application relates to the field of image processing, in particular to a spine feature identification method based on image processing.
Background
For the spondylopathy, the medical image is needed to be shot to diagnose the disease condition, and usually, due to the different sizes of the medical equipment, most of the shot spondylopathy image is a line film, and only the spondylopathy of a local section can be observed. The standing type full spine image can be used for shooting a complete spine image, but the larger the image is, the more complex the information is, the limited dynamic range of the photosensitive element is, the limited contrast of some key details is, and the image is not easy to observe manually.
Therefore, in order to observe a complete spine image more clearly, the invention optimizes and enhances the spine image characteristics in the spine medical image by using an image processing technology on the basis of machine vision to obtain an image with clear contrast of spine and bone textures and muscle contours, and image detail information is also kept, and the method is intelligent and accurate.
Disclosure of Invention
The invention provides a spine feature identification method based on image processing, which solves the problem of unsharpness in a whole spine image in a medical image and adopts the following technical scheme:
acquiring a full spine lateral image map, and performing semantic segmentation on the full spine lateral image map to obtain a full spine image map;
detecting the whole spine image map by using a sobel operator to obtain gradient edge pixel points of the whole spine image map;
carrying out frequency division filtering on the whole spine image map to obtain high-frequency pixel points and low-frequency pixel points of the whole spine image map;
determining spine edge high-frequency pixel points and non-spine edge high-frequency pixel points in the high-frequency pixel points by utilizing the gradient edge pixel points;
taking the corresponding gray levels of the spine edge high-frequency pixel points, the non-spine edge high-frequency pixel points and the low-frequency pixel points as the gray level of the spine edge high-frequency pixel points, the gray level of the non-spine edge high-frequency pixel points and the gray level of the low-frequency pixel points;
obtaining a gray level histogram according to the gray level of the vertebra edge high-frequency pixel points, the gray level of the non-vertebra edge high-frequency pixel points and the frequency of the gray level of the low-frequency pixel points appearing in the whole vertebra image map;
acquiring the average frequency of the gray levels of all low-frequency pixel points in the gray histogram and the frequency of the gray level of each high-frequency pixel point at the edge of the vertebra;
obtaining the weight ratio of the gray levels of all the low-frequency pixel points and the gray level of each spine edge high-frequency pixel point according to the average frequency of the gray levels of all the low-frequency pixel points and the frequency of the gray level of each spine edge high-frequency pixel point;
determining the gray levels of the low-frequency pixel points, the gray levels of the spine edge high-frequency pixel points and the weights of the gray levels of the non-spine edge high-frequency pixel points according to the gray levels of all the low-frequency pixel points and the weight ratio of the gray levels of each spine edge high-frequency pixel point;
and constructing an accumulation mapping function according to the gray levels of the low-frequency pixel points, the gray levels of the high-frequency pixel points at the spine edge and the gray levels of the high-frequency pixel points at the non-spine edge, and performing histogram equalization on the full spine image map by using the accumulation mapping function to obtain the processed full spine image map.
The method for determining the spine edge high-frequency pixel points and the non-spine edge high-frequency pixel points in the high-frequency pixel points comprises the following steps:
taking gradient edge pixel points of the whole spine image as spine edge high-frequency pixel points in the high-frequency pixel points;
and other pixels except the high-frequency pixels at the edge of the spine in the high-frequency pixels are non-high-frequency pixels at the edge of the spine.
The method for obtaining the weight ratio of the gray levels of all the low-frequency pixel points to the gray level of each high-frequency pixel point at the edge of the spine comprises the following steps:
calculating the average frequency of the gray levels of all low-frequency pixel points in the gray histogram;
obtaining the average value of the entropies of the gray levels of all the low-frequency pixel points according to the average frequency of the gray levels of all the low-frequency pixel points;
acquiring the frequency of the gray level of each high-frequency pixel point at the edge of each vertebra;
and taking the ratio of the frequency of the gray level of each spine edge high-frequency pixel point to the average value of the entropies of the gray levels of all low-frequency pixel points as the weight ratio of the gray level of each low-frequency pixel point to the gray level of each spine edge high-frequency pixel point.
The method for determining the weight of the gray level of the low-frequency pixel point, the gray level of the high-frequency pixel point at the edge of the spine and the gray level of the high-frequency pixel point at the edge of the non-spine comprises the following steps:
calculating a weight average value of the gray levels of the high-frequency pixel points at the edge of the spine according to the weight ratio of the gray levels of the low-frequency pixel points to the gray level of each high-frequency pixel point at the edge of the spine;
setting the ratio of the weight average value of the gray level of the spine edge high-frequency pixel points to the gray level weight of all non-spine edge high-frequency pixel points as 1: 2;
and calculating the gray level of the low-frequency pixel, the gray level of the spine edge high-frequency pixel and the weight of the gray level of the non-spine edge high-frequency pixel according to the gray level of the low-frequency pixel and the weight ratio of the gray level of each spine edge high-frequency pixel, the weight average value of the gray level of the spine edge high-frequency pixel and the gray level weight ratio of all non-spine edge high-frequency pixels.
The cumulative mapping function is as follows:
in the formula (I), the compound is shown in the specification,
the weight of the gray level of the high-frequency pixel point at the edge of the vertebra,
the weight of the gray level of the non-vertebral edge high-frequency pixel point,
is the weight of the gray level of the low-frequency pixel,
for the gray scale cumulative distribution function of the histogram equalized image,
is shown as
The mapping function of the original image and the equalized image at each gray level,
is shown in the original image
The frequency with which the individual gray levels occur,
is the total number of pixel points and is the gray level of the original image
，
As is the number of grey levels in the original image,
for the purpose of the normalized gray scale level,
，
, 
，
respectively representing gray levels in the original image as
，
，
，
The number of the pixel points.
The invention has the beneficial effects that: based on image processing, detecting the whole spine image map by using sobel operator to obtain a gradient edge image of the whole spine image map, frequency division filtering is carried out on the whole spine image map to obtain high-frequency pixel points and low-frequency pixel points in the whole spine image map, dividing the high-frequency pixel points into spine edge high-frequency pixel points and non-spine edge high-frequency pixel points according to the high-frequency pixel points and the gradient edge pixel points of the whole spine image map, according to the frequency of the gray level distribution of the spine edge high-frequency pixel points, the non-spine edge high-frequency pixel points and the low-frequency pixel points in the gray level histogram, the gray levels of the high-frequency pixel points at the spinal edge, the high-frequency pixel points at the non-spinal edge and the low-frequency pixel points are subjected to weight distribution, the mapping accumulation function is obtained through weight distribution, histogram equalization is carried out on the whole spine image to obtain the whole spine image with clear contrast and complete details, and the method improves the identification degree of the spine medical image.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
Fig. 1 is a schematic flow chart of a spine feature identification method based on image processing according to the present invention;
FIG. 2a is a schematic view of a full spine image of a spine feature recognition method based on image processing according to the present invention;
fig. 2b is a schematic diagram of a full spine image after histogram equalization in a spine feature identification method based on image processing according to the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
An embodiment of a spine feature identification method based on image processing according to the present invention is shown in fig. 1, and includes:
the method comprises the following steps: acquiring a lateral image map of the whole spine, and performing semantic segmentation to obtain the image map of the whole spine;
the purpose of this step is, gather the whole backbone image in the medical image, extract the backbone part image among them, as the basis of the subsequent data analysis.
It should be noted that: the whole spinal column film is obtained from a database of a hospital, comprises all bones from cervical vertebra to femoral shaft, and is formed by splicing a chest film and a waist film. But not a single chest film and a single waist film, because of multiple imaging, focal distance is difficult to align and coincide, vertebral body images of the two films cannot be connected, and angle measurement is inaccurate.
The semantic segmentation method comprises the following steps:
for the processing of the whole spine image map, the influence of non-target areas is removed as much as possible, and CNN semantic segmentation is adopted:
(1) CNN is an Encoder-Decoder network, and the CNN is calculated according to the following ratio of 7: a scale of 3 divides the data set into a training set and a test set.
(2) The spine region is labeled 1 and all other regions are labeled 0.
(3) The loss function used by the network is a cross entropy loss function.
The whole spine image and the background image can be obtained through semantic segmentation.
Step two: detecting the whole spine image map by using a sobel operator to obtain gradient edge pixel points of the whole spine image map; carrying out frequency division filtering on the whole spine image map to obtain high-frequency pixel points and low-frequency pixel points of the whole spine image map;
the purpose of this step is to carry out edge detection and frequency division on the image and classify the pixel points in the image.
It should be noted that, to improve the recognition effect of the spine image, the edge and texture details of the spine need to be enhanced, but a large amount of detail information of the spine is lost by directly performing histogram equalization processing on a complete full spine medical image, for example, fig. 2a is a full spine image, and fig. 2b is an image after histogram equalization of fig. 2a, it can be seen that a large amount of detail information is lost in the image, for example, contour information of excessively high brightness at the end of the lumbar vertebra is lost, the cervical vertebra is dark, the texture of the bony spur is lost, the bone edge becomes rough and unsmooth, and the like, because many pixels distributed less in the image are easily submerged, and because when the original image is mapped to the output image in the histogram equalization process, a small number of gray levels approximate to the accumulation result are rounded and combined, the gray scale range is compressed and therefore the detail features can be preserved as long as these low distributed gray levels are preserved.
In the embodiment, the detail information is processed by using a frequency division filter, the enhancement of the spine image is realized by preventing the gray levels of the parts from being combined and then equalizing, so that the contrast is enlarged and the details of key parts are kept as much as possible. The detailed characteristics of the spine can be well reserved so as to facilitate the recognition and extraction of the machine.
The method for acquiring the gradient edge pixel points of the whole spine image map comprises the following steps:
calculating each pixel point of the target area by using sobel operator
Direction and
gradient of direction
Counting all edge pixel point sets with gray gradient on vertebra
。
The method for acquiring the high-frequency pixel points and the low-frequency pixel points in the whole spine image map comprises the following steps:
splitting an image into low frequency portions using a crossover filter
And high frequency
Because a large amount of noise is generated in the process of medical image shooting, the types of the noise are various, some noises can blur images, some noises can gather to become dead points to destroy details of the images, and the noises in the images can be amplified during histogram equalization, the embodiment mainly protects the edge contour and detail information of the images, so that the problem of blurring the details by other linear filtering can be solved by adopting a median filtering algorithm.
Step three: determining spine edge high-frequency pixel points and non-spine edge high-frequency pixel points in the high-frequency pixel points by utilizing the gradient edge pixel points;
the purpose of the step is to classify the pixel points in the high-frequency information of the image, store the detail characteristics in the image,
the method for dividing the high-frequency pixel points into the spine edge high-frequency pixel points and the non-spine edge high-frequency pixel points comprises the following steps:
gradient edge pixel point set using a full spine image map
To eliminate high frequency part
Of non-spinal edge parts
Namely:
wherein the content of the first and second substances,
is a high-frequency pixel point at the edge of the vertebra,
is a high-frequency pixel point at the edge of non-vertebra,
are high frequency pixels.
Step four: taking the gray levels corresponding to the vertebra edge high-frequency pixel points, the non-vertebra edge high-frequency pixel points and the low-frequency pixel points as the gray levels of the vertebra edge high-frequency pixel points, the non-vertebra edge high-frequency pixel points and the low-frequency pixel points respectively; obtaining a gray level histogram according to the gray level of the vertebra edge high-frequency pixel points, the gray level of the non-vertebra edge high-frequency pixel points and the frequency of the gray level of the low-frequency pixel points appearing in the whole vertebra image map; acquiring the average frequency of the gray levels of all low-frequency pixel points in the gray histogram and the frequency of the gray level of each high-frequency pixel point at the edge of the vertebra; obtaining the weight ratio of the gray levels of all the low-frequency pixel points and the gray level of each spine edge high-frequency pixel point according to the average frequency of the gray levels of all the low-frequency pixel points and the frequency of the gray level of each spine edge high-frequency pixel point; determining the gray levels of the low-frequency pixel points, the gray levels of the spine edge high-frequency pixel points and the weights of the gray levels of the non-spine edge high-frequency pixel points according to the gray levels of all the low-frequency pixel points and the weight ratio of the gray levels of each spine edge high-frequency pixel point;
the purpose of this step is to calculate the weight of the grey level according to the frequency of the grey level corresponding to the different kinds of pixel points in the histogram.
The gray levels of the spine edge high-frequency pixel points, the non-spine edge high-frequency pixel points and the low-frequency pixel points are gray levels corresponding to the gray values of the spine edge high-frequency pixel points, the gray levels corresponding to the gray values of the non-spine edge high-frequency pixel points and the gray levels corresponding to the gray values of the low-frequency pixel points, and the gray levels of the spine edge high-frequency pixel points, the non-spine edge high-frequency pixel points and the low-frequency pixel points are determined according to the gray levels of the spine edge high-frequency pixel points, the gray levels of the non-spine edge high-frequency pixel points and the gray levels of the low-frequency pixel pointsThe frequency of the level appearing in the whole spine image map is obtained to obtain a gray histogram, and the gray level of the high-frequency pixel point at the edge of the spine is given weight
Weighting the gray level of the high-frequency pixel point at the edge of non-vertebra
Weighting the gray level of the low-frequency pixel
。
The method for acquiring the weight ratio of the gray levels of all the low-frequency pixel points to the gray level of each high-frequency pixel point at the edge of the spine comprises the following steps:
(1) obtaining the frequency of each high-frequency vertebra gray level appearing in the gray histogram
And the average frequency of the gray levels of all low-frequency pixel points appearing in the gray histogram
；
(3) Obtaining the average value of the entropies of the gray levels of all the low-frequency pixel points according to the average frequency of the gray levels of all the low-frequency pixel points appearing in the gray histogram
；
(3) Entropy average value according to gray level of low-frequency pixel point
The ratio of the gray level of each high-frequency pixel point at the edge of the vertebra to the gray level of each high-frequency pixel point at the edge of the vertebra is obtained
And low frequency pixel gray scale
The weight ratio of (A):
in the formula, the first step is that,
for each vertebra edge high frequency pixel gray level
And low frequency pixel gray scale
The weight ratio of (a) to (b),
entropy average of gray levels of low-frequency pixel points
The ratio of the gray level of the high-frequency pixel point at the edge of each vertebra,
is the frequency with which the grey levels occur,
the frequency of the gray level of the high-frequency pixel points at the edge of the spine,
the average frequency of the gray levels of the low-frequency pixels is equal to the frequency of the gray levels of the high-frequency pixels at the edge of the spineLow frequency grey scale average frequencies, they can be retained as much as the low frequency information.
It should be noted that, first, for the high-frequency edge portion with the highest importance degree, the histogram equalization is the most ideal state when the frequency of occurrence of each gray level is equal. However, the total number of the pixels is fixed, and many low-distributed gray levels will inevitably disappear due to combination during histogram equalization, so that the gray levels combined in the low-frequency information do not need to be considered, and only the high-frequency information is subjected to
And
the remaining processing is performed, only the frequency is adjusted, which inevitably causes the uncertainty of gray level combination, if the average frequency of the gray levels of the low-frequency pixels is too large, in order to make the average frequency larger
=
More low-profile gray levels are merged, which ignores the richness of the gray levels. The invention introduces entropy to optimize the defect, the entropy describes the disorder degree of the system, the larger the entropy is, the larger the uncertainty of the system is, so that the larger the image information amount is, and after each easily swallowed high-frequency low-distribution gray level is endowed with a weight value, the entropy is equal to the average value of the gray level entropy of the low-frequency pixel points, and the high-frequency gray levels can be reserved.
The method for obtaining the weights of the gray level of the low-frequency pixel point, the gray level of the spine edge high-frequency pixel point and the gray level of the non-spine edge high-frequency pixel point comprises the following steps:
(1) this embodiment is directed to non-spinal edge high frequency pixel
Corresponding non-spine edge high frequency pixel gray scaleStage
Endowing a uniform weight value
Calculating the weight mean value of the gray levels of all the vertebra edge high-frequency pixel points, and weighting the gray levels of the non-vertebra edge high-frequency pixel points
And the weight mean value of the gray levels of all the high-frequency pixel points at the edge of the spine
Is set to
；
Because for
It contains not only high-frequency information on the spine but also high-frequency information on muscle texture, organs, and the like. And therefore less important than the spine edge, a portion of the gray levels may be "sacrificed" to ensure preservation of the spine edge gray levels during histogram equalization.
(2) According to the weight ratio of the gray levels of all low-frequency pixel points and the gray level of each high-frequency pixel point at the edge of the vertebra, namely
And
the ratio, the proportional relation between the gray level weight of the non-spinal edge high-frequency pixel and the weight mean value of the gray levels of all spinal edge high-frequency pixels
And
the ratio of the gray scale to the gray scale of the high-frequency pixels at the edge of the spine to the gray scale of the low-frequency pixels and the gray scale of the high-frequency pixels at the edge of the non-spine
、
、
And carrying out weight distribution according to the proportional relation.
For example, the calculation method of the gray level weight of the high-frequency pixel point at the edge of the spine, the gray level weight of the low-frequency pixel point and the gray level weight of the high-frequency pixel point at the edge of the non-spine is illustrated as follows:
(1) suppose the gray level of the high-frequency pixel point at the edge of the vertebra is
、
The gray level of the non-vertebral edge high-frequency pixel point is
、
Low frequency pixel point gray scale of
;
(2) According to the method for obtaining the weight ratio of the gray levels of all the low-frequency pixel points to the gray level of each spine edge high-frequency pixel point, the weight ratio of the gray levels of all the low-frequency pixel points to the gray level of each spine edge high-frequency pixel point is obtained as
, 
Then, then
=
, 
=
;
(3) Obtaining the proportion of the gray level weight of the non-vertebra edge high-frequency pixel points to the weight average value of the gray levels of all vertebra edge high-frequency pixel points according to the step:
；
wherein
=
Then, then
，
；
(4) Then obtain
Obtaining the gray level of the high-frequency pixel point at the edge of the vertebra according to the proportional relation
、
High frequency gray scale of non-vertebral edge pixel
、
Gray level of low frequency pixel
The weight of (c):
Step five: and constructing an accumulation mapping function according to the gray level of the low-frequency pixel point, the gray level of the spine edge high-frequency pixel point and the weight of the gray level of the non-spine edge high-frequency pixel point, and performing histogram equalization on the whole spine image map by using the accumulation mapping function to obtain the processed whole spine image map.
The purpose of the step is to modify the mapping accumulation function of histogram equalization according to the gray level weight of the non-vertebra edge high-frequency pixel point, the gray level weight of the vertebra edge high-frequency pixel point and the gray level weight of the low-frequency pixel point, perform histogram equalization and enhance the image.
The cumulative mapping function after adding weight distribution during histogram equalization is as follows:
in the formula, the first step is that,
for the gray scale cumulative distribution function of the histogram equalized image,
is shown as
The mapping function of the original image and the equalized image at each gray level,
is shown in the original image
The frequency with which the individual gray levels occur,
the total number of the pixel points is,
for grey levels of the original image
，
As is the number of grey levels in the original image,
for the purpose of the normalized gray scale level,
，
, 
，
respectively representing the gray levels of the original image as
，
，
，
The number of the pixel points.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the scope of the present invention, which is intended to cover any modifications, equivalents, improvements, etc. within the spirit and scope of the present invention.
Claims (5)
1. A spine feature identification method based on image processing is characterized by comprising the following steps:
acquiring a full spine lateral image map, and performing semantic segmentation on the full spine lateral image map to obtain a full spine image map;
detecting the whole spine image map by using a sobel operator to obtain gradient edge pixel points of the whole spine image map;
carrying out frequency division filtering on the whole spine image map to obtain high-frequency pixel points and low-frequency pixel points of the whole spine image map;
determining spine edge high-frequency pixel points and non-spine edge high-frequency pixel points in the high-frequency pixel points by utilizing the gradient edge pixel points;
taking the gray levels corresponding to the vertebra edge high-frequency pixel points, the non-vertebra edge high-frequency pixel points and the low-frequency pixel points as the gray levels of the vertebra edge high-frequency pixel points, the non-vertebra edge high-frequency pixel points and the low-frequency pixel points respectively;
obtaining a gray level histogram according to the gray level of the vertebra edge high-frequency pixel points, the gray level of the non-vertebra edge high-frequency pixel points and the frequency of the gray level of the low-frequency pixel points appearing in the whole vertebra image map;
acquiring the average frequency of the gray levels of all low-frequency pixel points in the gray histogram and the frequency of the gray level of each high-frequency pixel point at the edge of the vertebra;
obtaining the weight ratio of the gray levels of all the low-frequency pixel points and the gray level of each spine edge high-frequency pixel point according to the average frequency of the gray levels of all the low-frequency pixel points and the frequency of the gray level of each spine edge high-frequency pixel point;
determining the gray levels of the low-frequency pixel points, the gray levels of the spine edge high-frequency pixel points and the weights of the gray levels of the non-spine edge high-frequency pixel points according to the gray levels of all the low-frequency pixel points and the weight ratio of the gray levels of each spine edge high-frequency pixel point;
and constructing an accumulation mapping function according to the gray levels of the low-frequency pixel points, the gray levels of the high-frequency pixel points at the spine edge and the gray levels of the high-frequency pixel points at the non-spine edge, and performing histogram equalization on the full spine image map by using the accumulation mapping function to obtain the processed full spine image map.
2. The spine feature identification method based on image processing according to claim 1, wherein the method for determining spine edge high frequency pixel points and non-spine edge high frequency pixel points among the high frequency pixel points comprises:
taking gradient edge pixel points of the full spine image map as spine edge high-frequency pixel points in the high-frequency pixel points;
and other pixels except the high-frequency pixels at the edge of the spine in the high-frequency pixels are non-high-frequency pixels at the edge of the spine.
3. The spine feature identification method based on image processing according to claim 1, wherein the method for obtaining the weight ratio of the gray levels of all the low-frequency pixel points to the gray level of each spine edge high-frequency pixel point comprises:
calculating the average frequency of the gray levels of all low-frequency pixel points in the gray histogram;
obtaining the average value of the entropies of the gray levels of all the low-frequency pixel points according to the average frequency of the gray levels of all the low-frequency pixel points;
acquiring the frequency of the gray level of each high-frequency pixel point at the edge of each vertebra;
and taking the ratio of the frequency of the gray level of each spine edge high-frequency pixel point to the average value of the entropies of the gray levels of all low-frequency pixel points as the weight ratio of the gray level of each low-frequency pixel point to the gray level of each spine edge high-frequency pixel point.
4. The spine feature identification method based on image processing according to claim 3, wherein the method for determining the weight of the gray level of the low-frequency pixel, the gray level of the spine edge high-frequency pixel and the gray level of the non-spine edge high-frequency pixel comprises the following steps:
calculating a weight average value of the gray levels of the high-frequency pixel points at the edge of the spine according to the weight ratio of the gray levels of the low-frequency pixel points to the gray level of each high-frequency pixel point at the edge of the spine;
gray scale of high-frequency pixel point at spine edgeThe proportion of the weight mean value of the levels to the gray level weight of all the non-vertebral edge high-frequency pixel points is set as
；
Obtaining the proportional relation of the gray level of the low-frequency pixel point, the gray level of the spine edge high-frequency pixel point and the gray level of the non-spine edge high-frequency pixel point according to the weight ratio of the gray level of the low-frequency pixel point to the gray level of each spine edge high-frequency pixel point, the weight average value of the gray level of the spine edge high-frequency pixel point and the weight proportion of the gray levels of all non-spine edge high-frequency pixel points;
and carrying out weight distribution according to the proportional relation of the gray level of the low-frequency pixel point, the gray level of the high-frequency pixel point at the edge of the spine and the gray level of the high-frequency pixel point at the edge of the non-spine.
5. A spine feature identification method based on image processing according to claim 4, characterized in that the cumulative mapping function is as follows:
in the formula (I), the compound is shown in the specification,
the weight of the gray level of the high-frequency pixel point at the edge of the vertebra,
the weight of the gray level of the non-vertebral edge high-frequency pixel point,
is the weight of the gray level of the low-frequency pixel,
for the gray scale cumulative distribution function of the histogram equalized image,
is shown as
The mapping function of the original image and the equalized image at each gray level,
is shown in the original image
The frequency with which the individual gray levels occur,
the total number of the pixel points is,
for grey levels of the original image
，
As is the number of grey levels in the original image,
for the purpose of the normalized gray scale level,
，
, 
，
respectively representing the gray levels of the original image as
，
，
，
The number of the pixel points.
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