CN110378924B - Level set image segmentation method based on local entropy - Google Patents

Level set image segmentation method based on local entropy Download PDF

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CN110378924B
CN110378924B CN201910654340.9A CN201910654340A CN110378924B CN 110378924 B CN110378924 B CN 110378924B CN 201910654340 A CN201910654340 A CN 201910654340A CN 110378924 B CN110378924 B CN 110378924B
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local entropy
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邹乐
王晓峰
周琼
肖连军
唐超
黄前静
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Hefei University
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Abstract

The invention discloses a level set image segmentation method based on local entropy, which relates to the technical field of image processing and comprises the steps of selecting an original image, calculating the local entropy of the original image to obtain a preprocessed image, carrying out thresholding processing on the preprocessed image to obtain coarse segmentation of the preprocessed image, and taking the obtained result as an initial level set contour; constructing an image segmentation energy functional by combining Local entropy with a Local Binary Fitting (LBF) model, and linearly combining the image segmentation energy functional with a Local Chan-Vese (LCV) model to obtain global and Local active contour models based on the Local entropy so as to obtain an evolution equation; and solving an evolution equation by using a Hermite differential operator, and finely dividing the roughly divided image. The method can effectively eliminate the influence of noise on image segmentation by introducing the local entropy, and has the advantages of a CV model and an LBF model.

Description

Level set image segmentation method based on local entropy
Technical Field
The invention relates to the technical field of image processing, in particular to a level set image segmentation method based on local entropy.
Background
With the development of internet technology, image processing, image analysis, and image understanding have been intensive in various research and application fields. Image processing in a complex scene is an important basic research problem in the field of computer vision, is a key technology in many related applications of artificial intelligence, has a very wide application prospect, and therefore has important research value. In the image analysis and understanding process, people are generally interested in not the whole image but certain area or areas (called foreground) in the image, which usually have different characteristic features from the background and belong to different things. In order to identify and analyze the targets, they need to be extracted from the image. Image segmentation is one of the most basic and difficult problems in the field of computer recognition, as the basis for image analysis and image understanding. Complex scene image segmentation remains a challenging task.
Image segmentation is the basis of image processing techniques, whose main purpose is to separate the region of interest image from the background. This makes processing more difficult, as there may be a lot of noise in the image and uneven grey scale distribution, while objects in the image may be affected by factors such as hardware conditions, viewing angle, lighting conditions, complex background, occlusion, etc. It is difficult for people to extract information related to object recognition from the image. Even if useful information can be extracted, the solving process has unreliability.
Disclosure of Invention
In order to solve the problem that the processing difficulty is increased due to the fact that the noise in an image is large, the gray distribution is uneven and the representation of a target in the image is influenced by various factors during image segmentation, the invention provides a coarse-fine improved Chan-Vese level set image segmentation method based on local entropy.
The method for segmenting the level set image based on the local entropy comprises the following steps:
step 1: selecting an original image;
step 2: calculating the local entropy of an original image to obtain a preprocessed image, performing thresholding processing on the preprocessed image to obtain coarse segmentation of the preprocessed image, and taking the obtained result as an initial level set contour;
and step 3: constructing an image segmentation energy functional by combining local entropy with an LBF (local binary matrix function) model, and linearly combining the image segmentation energy functional with an LCV (local computer vision) model to obtain a global and local active contour model based on the local entropy so as to obtain an evolution equation;
and 4, step 4: and solving an evolution equation by using a Hermite differential operator, and finely segmenting the roughly segmented image.
2. The local entropy-based level set image segmentation method of claim 1, wherein the step of roughly segmenting is:
step 1: calculating a local entropy matrix E of the original image by taking the neighborhood with each pixel i as the center as 9 multiplied by 9;
step 2: detecting motion of the upper left corner and the upper right corner of the local entropy matrix E, and then removing the motion to enable E (i) ═ C to be vignetted in a vignetted area, wherein C is a constant;
and 3, step 3: converting the local entropy matrix E into a gray level image, generating a local entropy image Eim, wherein the value E (i) is linearly transformed between 0 and 255;
and 4, step 4: and (4) segmenting the local entropy image Eim by using an OTSU threshold method to obtain a coarse segmentation result.
3. The local entropy-based level set image segmentation method of claim 1, wherein the step of finely segmenting is:
step 1: obtaining an initialization contour by using a rough segmentation result, and taking the initialization contour as a level set function phi;
step 2: initializing each parameter in a level set evolution equation, wherein the parameters are sigma, r, delta t, epsilon, mu and upsilon; the level set evolution equation is:
Figure BDA0002136356630000031
in the formula:
Figure BDA0002136356630000032
Figure BDA0002136356630000033
wherein σ is the standard deviation of the kernel function; r is the window size of the entropy function; Δ t is the division time; omega is weight, omega is more than or equal to 0 and less than or equal to 1; δ is a Dirac function; a regularization parameter with ε being δ; mu is lambda multiplied by 2552, lambda belongs to [0,1 ]](ii) a V is positiveA weighting constant of (d); k σ Is a Gaussian kernel function; e r Is the local entropy; lambda [ alpha ] 1 And λ 2 Is a constant taking a positive value; c. C 1 And c 2 Respectively obtaining the average gray value of the original image areas inside and outside the evolution curve; g k Representing an average convolution kernel used for local information detection, and k represents a window size and is used for controlling the sensitivity control of local items to noise; i is an image to be segmented; d 1 ,d 2 Representing gray values inside and outside the curve C after the original image and the convolution image are operated;
and step 3: on the basis of the step 2, evolving a level set function phi according to a level set evolution equation;
and 4, step 4: analyzing the evolution process of the level set function phi, if the evolution difference of the level set function phi is smaller than a given threshold value, terminating the evolution, extracting a zero level set of the function phi (x) as a final segmentation result, and outputting to obtain a segmentation image; otherwise, returning to the step 3 to continue to evolve the level set function phi.
The invention has the beneficial effects that: compared with the prior art, the image segmentation method based on the local entropy has the advantages that the image segmentation result is obtained through the local entropy, a formula similar to an energy formula of the LBF model is redefined according to the local entropy, and the image segmentation method based on the local entropy is combined with the LCV model to obtain the image segmentation method from coarse to fine. The new and improved model can not only process images with uneven gray levels, but also enhance the robustness of the model to noise. The local entropy is used as an initial contour, so that the position of a target object, namely the approximate contour of the object can be pre-judged, the interference of background information on the target is avoided, the number of times of contour evolution is greatly reduced, and the effect and efficiency of a traditional active contour model are improved.
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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 embodiments or the prior art descriptions will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a flow chart of a model implementation of the present invention;
FIG. 2 is a graph showing the segmentation result of an uneven gray scale image;
FIG. 3 is a graph of segmentation results for noisy images;
FIG. 4 is a graph of the segmentation results compared to LBF with noisy images;
FIG. 5 is a graph of the segmentation result compared with CV for an image with non-uniform gray scale;
fig. 6 is a graph showing the result of segmentation of the real image.
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.
As shown in fig. 1, an embodiment of the present invention provides a level set image segmentation method based on local entropy, including:
step 1: selecting an original image;
step 2: calculating the local entropy of an original image to obtain a preprocessed image, performing thresholding processing on the preprocessed image to obtain coarse segmentation of the preprocessed image, and taking the obtained result as an initial level set contour;
and 3, step 3: constructing an image segmentation energy functional by combining local entropy with an LBF (local binary distortion) model, and linearly combining the image segmentation energy functional with the LCV (local computer vision) model to obtain a global and local active contour model based on the local entropy so as to obtain an evolution equation;
and 4, step 4: and solving an evolution equation by using a Hermite differential operator, and finely segmenting the roughly segmented image.
Image rough segmentation
The image segmentation can be regarded as dividing all image pixels into different clusters with similar characteristics, firstly selecting an original image, and roughly segmenting the original image, wherein the roughly segmenting step is as follows:
step 1: calculating a local entropy matrix E of the given image by taking the neighborhood with each pixel i as the center as 9 multiplied by 9;
step 2: detecting motion of the upper left corner and the upper right corner of the local entropy matrix E, and then removing the motion to enable E (i) ═ C to be vignetted in a vignetted area, wherein C is a constant;
and step 3: converting the local entropy matrix E into a gray level image, generating a local entropy image Eim, wherein the value E (i) is linearly transformed between 0 and 255;
and 4, step 4: and (4) segmenting the local entropy image Eim by using an OTSU threshold method to obtain a coarse segmentation result.
Image fine segmentation
The image fine segmentation method comprises the following steps:
step 1: obtaining an initialized contour by using a rough segmentation result, and taking the initialized contour as a level set function;
step 2: initializing each parameter in the formula (1.20), wherein the parameters are sigma, r, delta t, epsilon, mu and upsilon;
and step 3: on the basis of the step 2, according to a formula (1.20) evolution level set function phi;
and 4, step 4: analyzing the evolution process of the level set function phi, if the evolution difference of the level set function phi is smaller than a given threshold value, terminating the evolution, extracting a zero level set of the function phi (x) as a final segmentation result, and outputting to obtain a segmentation image; otherwise, returning to the step 3 to continue to evolve the level set function phi.
The concrete steps are as follows:
using local entropy
Figure BDA0002136356630000061
Describing omega between one point x area x Redefining a new image segmentation energy functional, which is expressed as follows:
Figure BDA0002136356630000062
in the formula, omega 1 ＝inside(C)，Ω 2 ＝outside(C)，E r (x) E (x, W (x, r)) is the local entropy of x ∈ Ω.
W (x, r) is a rectangular window function, wherein W (x, r) is { y: | < x-y | ≦ r }, and r is greater than 0.
The energy formula for LCV is:
E LCV (c 1 ,c 2 ,φ)＝∫|u 0 (x,y)-c 1 | 2 H ε (φ(x,y))dxdy+∫|u 0 (x,y)-c 2 | 2 (1-H ε (φ(x,y)))dxdy
+∫|g k *u 0 (x,y)-u 0 (x,y)-d 1 | 2 )H ε (φ(x,y))dxdy+∫|g k *u 0 (x,y)-u 0 (x,y)-d 2 | 2 )(1-H ε (φ(x,y)))dxdy
(1.11)
wherein, g k Representing an average convolution kernel used for local information detection, and k represents a window size and is used for controlling the sensitivity control of local items to noise; d 1 ,d 2 And (4) representing the gray level mean value inside and outside the curve C after the original image and the convolution image are operated.
The energy model defined by the invention is as follows:
E(C,c 1 ,c 2 ,f 1 ,f 2 )＝(1-ω)E LCV (C,c 1 ,c 2 )+ωE NRSF (C,f 1 ,f 2 ) (1.12)
omega value range of 0-1, c 1 And c 2 The average gray values of the original image regions inside and outside the evolution curve respectively. f. of 1 And f 2 Is the fitted value of the image at point x. By using the Heaviside function H (Φ), equation (1.12) can be changed to:
Figure BDA0002136356630000071
in the formula, M 1 (φ)＝H(φ)，M 2 And (Φ) 1-H (Φ), and ν and μ are positive weighting constants. C in formula (1.13) 1 (x)，c 2 (x)，d 1 ，d 2 ，f 1 (x) And f 2 (x) Can be obtained by the relation:
Figure BDA0002136356630000081
Figure BDA0002136356630000082
Figure BDA0002136356630000083
Figure BDA0002136356630000084
Figure BDA0002136356630000085
Figure BDA0002136356630000086
using variational and gradient descent methods for equation (1.13) to obtain the level set evolution equation:
Figure BDA0002136356630000087
in the formula:
Figure BDA0002136356630000088
Figure BDA0002136356630000091
wherein σ is the standard deviation of the kernel function; r is the window size of the entropy function; Δ t is the split time; omega is weight, omega is more than or equal to 0 and less than or equal to 1; δ is a Dirac function; the regularization parameter with epsilon as delta is generally taken as 1; mu is lambda multiplied by 2552, lambda belongs to [0,1 ]](ii) a Upsilon is a positive weighting constant; k σ Is a Gaussian kernel function; e r Is the local entropy; lambda [ alpha ] 1 And λ 2 Is a constant taking a positive value, usually let λ 1 ＝λ 2 ＝1；c 1 And c 2 Respectively obtaining the average gray value of the original image areas inside and outside the evolution curve; and I is an image to be segmented.
Solving the level set evolution equation by using a Hermite differential operator as follows:
calculating to obtain the specific value of a differential operator:
d＝[0.083139007900672,-0.662858814766878,0.662858814766878,-0.083139007900672](1.23)
discrete differentiation of the image (represented in x-direction, same form in y-direction):
f x (x)＝0.083139007900672(f(x-2,y)-f(x+2,y))-0.662858814766878(f(x-1,y)-f(x+1,y))(1.24)
accordingly, the forward difference along the x-axis is changed to the Hermite difference at the (i +1, j) point, and the forward difference along the y-axis is changed to the Hermite difference at the (i, j +1) point in the image domain; the backward difference along the x-axis is changed to the Hermite difference at point (i-1, j), and the forward difference along the x-axis is changed to the Hermite difference at point (i, j-1), resulting in:
Figure BDA0002136356630000092
Figure BDA0002136356630000093
Figure BDA0002136356630000094
Figure BDA0002136356630000095
Figure BDA0002136356630000096
Figure BDA0002136356630000097
after the Hermite difference operator is used, when a function derivative is calculated, the second-order neighborhood difference of the pixel point is used, so that the robustness of the level set evolution process on noise is greatly improved.
Examples
To verify the validity of the present invention, the verification result of this embodiment is as follows:
the result of image segmentation with non-uniform gray scale is shown in fig. 2: graph (a) is an original image, graph (b) is a local entropy image, and graph (c) is a cut result; the segmentation results of graph (c) demonstrate the ability of the method to segment images with non-uniform gray scale.
Adding Gaussian noise and salt-pepper noise with different intensities to an unprocessed image, and segmenting the image with noise, as shown in FIG. 3: wherein (a) is a segmentation result of an original image which is not processed, (b) and (c) are segmentation results after gaussian noise with variances of 0.01 and 0.1 is added to the image, respectively, and (d) and (e) are segmentation results after salt and pepper noise with variances of 0.005 and 0.01 is added to the image, respectively. The method obtained from the segmentation result has good segmentation effect on the pictures processed by the Gaussian noise and salt and pepper noise with different intensities.
Comparing the segmentation result with the traditional LBF model, the invention selects two different pictures with noise, and respectively uses the LBF model and the method to segment, and the segmentation result is shown in figure 4: as can be seen from the segmentation result graph (c), the LBF model does not have a good effect on segmenting the noisy picture, and the segmentation method can be very accurate.
Compared with the traditional CV model, the invention adopts two images with different uneven gray levels for segmentation, and the segmentation result is shown in FIG. 5: the segmentation result graphs of the two models can clearly obtain that the method has a much better segmentation effect on the image with uneven gray levels than the traditional CV model segmentation.
A real image result is segmented, and in order to verify the segmentation effect of the method more accurately, a real image is selected for verification, as shown in fig. 6: the conventional LBF model has poor segmentation result, and the segmentation effect of the method is relatively ideal. Therefore, the realization method of the invention can not only segment the simulation image, but also segment simple real images.
According to the invention, the gray level map distribution of the image is firstly deduced through local entropy, a formula similar to an energy formula of an LBF model is redefined, and the formula is combined with the LCV model. The new and improved model not only can process images with uneven gray levels, but also enhances the robustness of the model to noise. The local entropy is used as an initial contour, so that the position of a target object, namely the approximate contour of the object can be pre-judged, the interference of background information on the target is avoided, the number of times of contour evolution is greatly reduced, and the effect and efficiency of a traditional active contour model are improved.
The above disclosure is only for the specific embodiment of the present invention, but the embodiment of the present invention is not limited thereto, and any variations that can be made by those skilled in the art should fall within the scope of the present invention.

Claims (3)

1. The method for segmenting the level set image based on the local entropy is characterized by comprising the following steps of:
step 1: selecting an original image;
step 2: calculating the local entropy of an original image to obtain a preprocessed image, performing thresholding processing on the preprocessed image to obtain coarse segmentation of the preprocessed image, and taking the obtained result as an initial level set contour;
and step 3: constructing an image segmentation energy functional by combining local entropy with an LBF (local binary distortion) model, and linearly combining the image segmentation energy functional with the LCV (local computer vision) model to obtain a global and local active contour model based on the local entropy so as to obtain an evolution equation;
and 4, step 4: and solving an evolution equation by using a Hermite differential operator, and finely segmenting the roughly segmented image.
2. The local entropy-based level set image segmentation method of claim 1, wherein the step of roughly segmenting is:
step 1: calculating a local entropy matrix E of the original image by taking the neighborhood with each pixel i as the center as 9 multiplied by 9;
step 2: detecting motion sickness in the upper left corner and the upper right corner of the local entropy matrix E, and then removing the motion sickness so that E (i) ═ C is vignetted in the vignetting region, wherein C is a constant;
and step 3: converting the local entropy matrix E into a gray level image, generating a local entropy image Eim, wherein the value E (i) is linearly transformed between 0 and 255;
and 4, step 4: and (4) segmenting the local entropy image Eim by using an OTSU threshold method to obtain a coarse segmentation result.
3. The local entropy-based level set image segmentation method of claim 1, wherein the step of finely segmenting is:
step 1: obtaining an initialization contour by using a rough segmentation result, and taking the initialization contour as a level set function phi;
step 2: initializing each parameter in a level set evolution equation, wherein the parameters are sigma, r, delta t, epsilon, mu and upsilon; the level set evolution equation is:
Figure FDA0002136356620000021
in the formula:
Figure FDA0002136356620000022
Figure FDA0002136356620000023
wherein σ is the standard deviation of the kernel function; r is the window size of the entropy function; Δ t is the division time; omega is weight, omega is more than or equal to 0 and less than or equal to 1; δ is a Dirac function; a regularization parameter with ε being δ; mu is lambda multiplied by 2552, lambda belongs to [0,1 ]](ii) a V is a positive weighting constant; k is σ Is a Gaussian kernel function; e r Is the local entropy; lambda [ alpha ] 1 And λ 2 Is a constant with a positive value; c. C 1 And c 2 Respectively obtaining the average gray value of the original image areas inside and outside the evolution curve; g is a radical of formula k An average convolution kernel used for local information detection is represented, k represents a window size and is used for controlling the sensitivity control of local items to noise; i is an image to be segmented; d 1 ,d 2 Representing gray values inside and outside the curve C after the original image and the convolution image are operated;
and step 3: on the basis of the step 2, a level set function phi is evolved according to a level set evolution equation;
and 4, step 4: analyzing the evolution process of the level set function phi, if the evolution difference of the level set function phi is smaller than a given threshold value, terminating the evolution, extracting a zero level set of the function phi (x) as a final segmentation result, and outputting to obtain a segmentation image; otherwise, returning to the step 3 to continue to evolve the level set function phi.
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