CN109472792B - Local energy functional and non-convex regular term image segmentation method combining local entropy - Google Patents

Local energy functional and non-convex regular term image segmentation method combining local entropy Download PDF

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CN109472792B
CN109472792B CN201811328521.4A CN201811328521A CN109472792B CN 109472792 B CN109472792 B CN 109472792B CN 201811328521 A CN201811328521 A CN 201811328521A CN 109472792 B CN109472792 B CN 109472792B
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韩明
王敬涛
孟军英
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Shijiazhuang University
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Abstract

The invention discloses an image segmentation method of a local energy functional and a non-convex regular term by combining local entropy, which comprises the following steps: (1) reading in an image I (x, y); (2) initializing each parameter in an image segmentation model of a local energy functional based on local entropy and a non-convex regular term; (3) computing the local entropy h of an image I (x, y)x(ii) a (4) Segmenting the image I (x, y) on the basis of the initialized parameters in the step (2), segmenting the image I (x, y) by adopting an image segmentation model of a local energy functional based on local entropy and a non-convex regular term, and updating a level set function phi in the segmentation process; (5) evolving the level set function phi according to an equation, judging whether the level set function phi is converged, if so, stopping the evolution of the level set function phi, and outputting a segmentation image; otherwise, returning to the step (4) for continuing. The invention can efficiently and accurately segment the image with uneven gray scale.

Description

Local energy functional and non-convex regular term image segmentation method combining local entropy
Technical Field
The invention belongs to the technical field of image processing, and particularly relates to an image segmentation method.
Background
Image segmentation is used as a key technology in the fields of pattern recognition, computer vision, artificial intelligence and the like, and the main purpose is to separate a specific foreground target from a background. However, the gray levels of the region of interest and the background region in the image may have a gray level non-uniformity phenomenon, which brings certain difficulty to the accurate segmentation of the image. At present, in a plurality of image segmentation technologies, as a variational level set model has the characteristic of free topological transformation, a complex target boundary can be effectively extracted, and the variational level set model is paid more and more attention to and applied.
The level set method comprises a region-based method and an edge-based method, wherein the CV model is a typical level set method based on region statistics, and the model utilizes global region information of an image, utilizes a global binary piecewise constant to carry out fitting of a level set function, and drives an active contour to evolve to a target edge. But the model assumes that the gray levels in each target region in the image are homogeneous and only utilizes the global information of the image, ignoring the local information, resulting in difficulty in segmenting images with uneven gray levels.
In order to realize the segmentation of the uneven image, scholars at home and abroad propose a plurality of models based on local image characteristics, such as an LBF model, a LIF model, an LGD model, an LAW model and the like, wherein Li et al propose an LBF (local Binary fitting) model using local Binary fitting as a most typical model. The LBF model utilizes local region information and uses local neighborhood information of pixel points to carry out energy functional of binary fitting, the model well overcomes the characteristic of uneven image gray scale, but is sensitive to an initial contour and is easy to fall into a local minimum value. Although these models implement segmentation of an image with uneven gray scale, they only consider statistical information of local gray scale conditions, and therefore, the segmentation result of the image with uneven gray scale distribution is not accurate enough, and the robustness of the initial contour is not enough.
The documents WANG XiaOfeng, Huang DeShuang, XU Huang.an effective local Chan-Vese model for image segmentation [ J ]. Pattern Recognition, 2010, 43 (3): 603-618, a Local Chan-Vese model is disclosed, which combines the global region information with the Local region information to realize image segmentation, but the model is only a simple combination of Local and global, and the segmentation of the image with uneven gray scale still fails.
Disclosure of Invention
The invention aims to provide an image segmentation method combining a local energy functional of local entropy and a non-convex regular term aiming at the defects of poor segmentation effect and the like of the gray-scale non-uniform image in the prior art so as to ensure that a satisfactory segmentation effect is obtained when the gray-scale non-uniform image is segmented.
The technical solution of the invention is as follows:
an image segmentation method combining a local energy functional of local entropy and a non-convex regular term comprises the following steps:
(1) reading in an image I (x, y);
(2) image segmentation model for initializing local energy functional based on local entropy and non-convex regular term
The parameters in type phi, alpha, beta, mu, v and sigma, the model is as follows:
Figure GSB0000178399420000021
wherein: phi is a level set function, alpha is a global energy term adjusting parameter, beta is a local energy term adjusting parameter, mu is a length term coefficient, v is an energy penalty term coefficient, mu and v are constants larger than 0, and sigma is a Gaussian kernel function gσ(x) Standard deviation of (d); c. C1And c2Mean gray values E inside and outside the closed active contour curve C, respectivelygAs a global energy functional, ElFor introducing local entropy, local energy functional, El′Length penalty term based on non-convex regular term, E, for keeping contours smoothpEnergy penalty term, f, for the level set function to remain as a symbol distance function during evolution1(x) And f2(x) Mean fitting function, h, inside and outside the evolution curve of the x neighborhood, respectivelyxIs the local entropy of pixel x;
(3) computing the local entropy h of an image I (x, y)x；
(4) Segmenting the image I (x, y) on the basis of the initialized parameters in the step (2), segmenting the image I (x, y) by adopting an image segmentation model of a local energy functional based on local entropy and a non-convex regular term, and updating a level set function phi in the segmentation process;
(5) evolving the level set function phi according to the following equation, judging whether the level set function phi is converged, if so, stopping the evolution of the level set function phi, and outputting a segmentation image; otherwise, returning to the step (4) for continuing; the evolution equation is as follows:
Figure GSB0000178399420000031
wherein:
phi is a level set function (phi > 0 indicates inside the zero level set, phi < 0 indicates outside the zero level set, and phi ═ 0 indicates the zero level set);
alpha is a global energy term adjusting parameter;
beta is a local energy term adjusting parameter;
mu is a length term coefficient and v is an energy penalty term coefficient (both mu and v are constants greater than 0);
δεis a Driac function;
i is an input image;
c1and c2The average gray values of the inside and the outside of the closed active contour curve C are respectively;
eta is
Figure GSB0000178399420000032
The boundary stopping function of (1);
e1and e2The method comprises the following steps of (1) performing substitution expression in the calculation process of a local energy functional evolution equation;
Figure GSB0000178399420000033
is a gradient operator.
The invention provides an image segmentation model of an energy functional and a non-convex regular term based on local entropy, which comprises four parts, namely a global energy functional E in a traditional CV modelgLocal energy functional E in LBF model introducing local entropylA length penalty term E based on a non-convex regular term for keeping the contour smoothl′And the level set function remains as the energy penalty E of the symbol distance function during the evolution processp。
Global energy functional EgAnd local energy functional ElCan ensure the homogeneity of the curve inside (or outside) in the evolution process, and utilizes the global energy functional EgObtaining a rough contour of curve evolution by using a local energy functional ElObtaining a fine contour of curve evolution; length penalty term El′While the curve keeps smooth, the model is made to have robustness to noise images, and image edges are protectedA rim; energy penalty term EpIs another driving force for curve evolution, so that the curve evolution speed is accelerated.
When the evolution curve is far away from the boundary of the target to be segmented, the global energy functional EgPlays a main role; local energy functional E as the curve evolves near the target boundary to be segmentedlPlays a leading role through the local energy functional ElThe evolution curve is attracted to the target contour. When the evolution curve is far away from the target, the global energy functional EgThe method plays a leading role to obtain a rough segmentation model, and utilizes a local energy functional E on the basis of rough segmentation when the distance to a target boundary is closelThe exact segmentation is performed so that the global energy functional E is for the entire imagegAnd local energy functional ElThe precise evolution of the level set curve is realized under the combined action, so that the image segmentation effect is ensured.
In the curve evolution process, the iteration process of the level set function value is unstable, the periodic oscillation occurs, the periodic reinitialization is necessary, the level set function is changed into a symbol distance function again, and in order to avoid the reinitialization, an energy penalty term E is adoptedpAvoids complex re-initialization and energy penalty term E when level set function shrinks during evolutionpTaking the value as positive, keeping the total energy item unchanged, and making the global energy functional EgAnd local energy functional ElAs small as possible; on the contrary, when the evolution curve is enlarged, the energy penalty term EpTaking a negative value, keeping the total energy term unchanged, and making the global energy functional EgAnd local energy functional ElThe iteration efficiency of each calculation is improved as much as possible, the iteration times are reduced, and the curve evolution speed is improved. Continuous and stable evolution of the level set function is realized, so that the segmentation precision and efficiency of the model on the image with uneven gray scale are improved.
The local entropy hxThe calculation formula of (a) is as follows:
Figure GSB0000178399420000041
wherein: h isxIs the local entropy of the pixel x,
Figure GSB0000178399420000042
for the probability density estimation of the gray level y in the neighborhood Ω, nyThe number of pixels having a gray level y in the neighborhood Ω.
In image processing, the image entropy is used for counting the gray information of an image and representing the gray distribution of the image. The calculation formula of the local entropy of a pixel x is as the above formula when a gray level image I with the size of M × N is set, the gray level y of the image satisfies that y is more than or equal to 0 and less than or equal to L, a pixel x is defined in an image space, and the size of the neighborhood omega with the pixel as the center is M × N. Therefore, if the gray level change of the image is relatively strong, the local entropy at the position is small, otherwise, when the gray level distribution of the image is relatively uniform, the local entropy of the image is large, and the local entropy can be used for reflecting the spatial information among the pixels of the image to a certain extent, so that the edge with large gray level discreteness and sudden change in the image can be detected by using the local entropy, and the accuracy of image detection and the robustness to noise are realized by introducing the local entropy.
C is mentioned1And c2The calculation formula of (a) is as follows:
Figure GSB0000178399420000051
wherein:
i (x, y) represents an input image;
Hεrepresenting a regularized smoothing function Heaviside function;
epsilon is a regularization parameter;
phi is a level set function (phi > 0 indicates inside the zero level set, phi < 0 indicates outside the zero level set, and phi ═ 0 indicates the zero level set);
Ω is a grayscale image space of the input image I (x, y).
F is1(x) And f2(x) The calculation formula of (a) is as follows:
Figure GSB0000178399420000052
wherein:
gσ(x) Is a Gaussian kernel function;
sigma is a Gaussian kernel function gσ(x) Standard deviation of (d);
i (x) represents the x value of the input image I (x, y);
h () represents the regularizing smoothing function Heaviside function;
phi is a level set function (phi > 0 indicates inside the zero level set, phi < 0 indicates outside the zero level set, and phi ═ 0 indicates the zero level set).
Said e1And e2The calculation formula of (a) is as follows:
Figure GSB0000178399420000053
wherein:
hxis the local entropy of pixel x;
i (y) the gray-scale value of the input image.
The invention has the following beneficial effects:
in order to overcome the influence of uneven gray level on image segmentation, the invention provides an image segmentation method combining a local energy functional of local entropy and a non-convex regular term. Firstly, obtaining an approximate evolution outline of an image by adopting a global energy functional; and realizing accurate segmentation of the image by constructing a local energy functional with local entropy information. Then, a non-convex regular term is used as a driving force for driving curve evolution and edge protection of a zero level set approximation target in an image evolution process. The method minimizes the newly constructed energy functional by using a variational level set method, and completes curve evolution by updating a level set function iteratively. The invention can efficiently and accurately segment the image with uneven gray scale.
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FIG. 1 is a flow chart of the overall implementation of the present invention;
FIG. 2 is a graph showing the effect of segmenting three artificially synthesized images according to the present invention in example 1;
FIG. 3 is a graph comparing the segmentation effect of the image by using the present invention, CV model and LBF model in example 2;
FIG. 4 is the final level set function of the present invention, CV model, LBF model in example 2;
FIG. 5 is a graph comparing the segmentation effect on images using the invention, CV model, LBF model and GLP model in example 3.
Detailed Description
The following examples are given for the detailed implementation and specific operation of the present invention, but the scope of the present invention is not limited to the following examples.
As shown in fig. 1, the segmentation of the image by the present invention comprises the following steps:
(1) reading in an image I (x, y);
(2) initializing each parameter in an image segmentation model of a local energy functional based on local entropy and a non-convex regular term, wherein the parameters are phi, alpha, beta, mu, v and sigma, and the model is as follows:
Figure GSB0000178399420000071
wherein: phi is a level set function, alpha is a global energy term adjusting parameter, beta is a local energy term adjusting parameter, mu is a length term coefficient, v is an energy penalty term coefficient, mu and v are constants larger than 0, and sigma is a Gaussian kernel function gσ(x) Standard deviation of (d); c. C1And c2Mean gray values E inside and outside the closed active contour curve C, respectivelygAs a global energy functional, ElFor introducing local entropy, local energy functional, El′Length penalty term based on non-convex regular term, E, for keeping contours smoothpEnergy penalty term, f, for the level set function to remain as a symbol distance function during evolution1(x) And f2(x) Mean values inside and outside the evolution curve of the x neighborhood, respectivelyFitting function, hxIs the local entropy of pixel x;
(3) computing the local entropy h of an image I (x, y)x；
(4) Segmenting the image I (x, y) on the basis of the initialized parameters in the step (2), segmenting the image I (x, y) by adopting an image segmentation model of a local energy functional based on local entropy and a non-convex regular term, and updating a level set function phi in the segmentation process;
(5) evolving the level set function phi according to the following equation, judging whether the level set function phi is converged, if so, stopping the evolution of the level set function phi, and outputting a segmentation image; otherwise, returning to the step (4) for continuing; the evolution equation is as follows:
Figure GSB0000178399420000072
wherein:
phi is a level set function (phi > 0 indicates inside the zero level set, phi < 0 indicates outside the zero level set, and phi ═ 0 indicates the zero level set);
alpha is a global energy term adjusting parameter;
beta is a local energy term adjusting parameter;
mu is a length term coefficient and v is an energy penalty term coefficient (both mu and v are constants greater than 0);
δεis a Driac function;
i is an input image;
c1and c2The average gray values of the inside and the outside of the closed active contour curve C are respectively;
eta is
Figure GSB0000178399420000081
The boundary stopping function of (1);
e1and e2The method comprises the following steps of (1) performing substitution expression in the calculation process of a local energy functional evolution equation;
Figure GSB0000178399420000083
is a gradient operator.
In order to verify the effect of the present invention, different images were selected to perform segmentation contrast experiments.
The experimental environment was as follows: the experiment adopts Matlab2016a as a simulation environment, and the experiment computer is configured with: a win 1064-bit operating system, a CPU Intel i 7-67003.40 GHz and a memory 32 GB.
Compared with the present invention, the experiment is carried out by the traditional CV model, LBF model and GLP model, wherein the GLP model is the abbreviation of Image segmentation by combining the global and local properties, which is detailed in the literature WANG Zhenzhou. 30-40.
The general settings of the parameters of the invention are: step Δ t of time equal to 0.1, HεThe regularization parameter epsilon of (phi) is 1, and other parameters are set correspondingly for different images.
In order to realize the comparison between the invention and other algorithms, two quantitative methods are adopted for comparison, and the two evaluation methods are respectively as follows: jaccard family (JS) and Dice Coefficient (DC), see in detail ZHAO Yuqian, WANG Xiao Ofang, SHIH Frank Y, et al.A level-set method based on global and local regions for image segmentation [ J ]. International Journal of Pattern Recognition and architecture insight, 2012, 26 (1): 61-70.
The definition is as follows:
Figure GSB0000178399420000082
wherein S is1And S2Respectively representing a standard segmentation result and an image segmentation algorithm segmentation result. N (-) represents the number of pixels in the closed set. The larger the values of JS and DC, the better the segmentation effect.
Example 1:
the invention is used for segmenting three artificially synthesized images, as shown in figure 2(a), which are three persons with uneven gray levelsThe image is synthesized, wherein 1 st, 2 nd image contains a plurality of grey levels, and 3 rd image is from top to bottom grey level inhomogeneous, and parameter setting is respectively: α ═ 0.9, β ═ 0.1, and σ ═ 3 μ ═ 0.002 × 2552. As can be seen from fig. 2(b), the present invention can achieve effective segmentation for all three images with uneven gray scale.
Example 2:
in order to verify the effectiveness of the invention, three images with uneven gray levels are adopted for comparison experiments, and the comparison experiments are respectively a CV model and an LBF model.
The present embodiment adopts the sensitivity of the initial contour verification algorithm of three different shapes to the initial contour and the processing of different quality areas. The parameters of the algorithm are selected as follows: α is 0.1, β is 1, and the length control parameter is respectively selected as μ 0.001 × 2552，μ＝0.003*2552And μ ═ 0.01 × 2552Variance σ1＝3，σ2＝5，σ3＝2。
The superiority of the algorithm of the present invention can be seen from fig. 3 and 4, in which the columns of fig. 4 correspond to those of fig. 3, by the final level set function diagram and the curve evolution result. The method can adapt to different initial contours of the image, and can better realize target segmentation for the image with uneven gray scale and the image with shadow. From the segmentation result, it can be known that the CV model does not finally obtain a satisfactory result for the image with uneven gray scale, and the phenomenon of segmentation failure occurs. The LBF model can also be used for segmenting the image with uneven gray scale in the first two images, but the segmentation inaccuracy is caused, when a white cup in the third image is similar to the background, the segmentation failure phenomenon is caused, and the LBF model can segment the image with uneven gray scale but is sensitive to the profile.
Example 3:
in this embodiment, the present invention is compared with a CV model, an LBF model and a GLP model, respectively, and the image segmentation effects of the four methods are considered.
The specific parameters are set as follows: the 1 st and 2 nd images α ═ 0.25, β ═ 0.75, and μ ═ 0.001 ×.2552σ is 4, α is 0.1, β is 0.9, and μ is 0.002 × 255 in the 3 rd image2，σ＝2。
As shown in fig. 5, column 1 is the image curve initialization position, column 2 is the CV model segmentation result, column 3 is the LBF model segmentation result, column 4 is the GLP model segmentation result, and column 5 is the segmentation result of the present invention. Table 1 shows the iteration times and processing times of different algorithms in the comparison experiment, and table 2 shows the comparison results of JS coefficients and DC coefficients of different algorithms.
Figure GSB0000178399420000091
Figure GSB0000178399420000101
TABLE 1
Figure GSB0000178399420000102
TABLE 2
Therefore, for an image with large gray scale change, the 2 nd column of segmentation results show that the CV model is purely dependent on the global energy functional, and the segmentation effect is not ideal; for the LBF model, the influence of gradient information is received, the initial contour is sensitive, the time consumption is long, for the GLP model, the rapid evolution can be realized in a region with uniform gray scale, but when the GLP model is close to a target boundary, the constraint performance of a distance regular term on a distance term and an energy term is poor, the smoothness and the stability of a curve are poor, the segmentation failure is caused in the 2 nd graph, the smoothness of the curve is poor in the 3 rd graph, but the segmentation can be reluctant, but the algorithm time consumption is long due to the fact that the local fitting is carried out by using the gradient information as the LBF model. The invention can obtain satisfactory segmentation effect, and is shorter than GLP model in time consumption.
It should be noted that, although the invention has been described in terms of the above-mentioned embodiments, there are many other embodiments of the invention. It will be apparent to those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention, and it is intended that all such changes and modifications be covered by the appended claims and their equivalents.

Claims (4)

1. An image segmentation method combining a local energy functional of local entropy and a non-convex regular term is characterized by comprising the following steps:
(1) reading in an image I (x, y);
(2) initializing each parameter in an image segmentation model of a local energy functional based on local entropy and a non-convex regular term, wherein the parameters are phi, alpha, beta, mu, v and sigma, and the model comprises the following steps:
Figure FDA0003156211410000011
wherein: phi is a level set function, alpha is a global energy term adjusting parameter, beta is a local energy term adjusting parameter, mu is a length term coefficient, and v is an energy penalty term coefficient, mu and v are constants larger than 0, and sigma is a Gaussian kernel function gσ(x) Standard deviation of (d); c. C1And c2Mean gray values E inside and outside the closed active contour curve C, respectivelygAs a global energy functional, ElFor introducing local entropy, local energy functional, El′Length penalty term based on non-convex regular term, E, for keeping contours smoothPEnergy penalty term, f, for the level set function to remain as a symbol distance function during evolution1(x) And f2(x) Mean fitting function, h, inside and outside the evolution curve of the x neighborhood, respectivelyxIs the local entropy of pixel x; Ω is a grayscale image space of the input image I (x, y);
f is1(x) And f2(x) The calculation formula of (a) is as follows:
Figure FDA0003156211410000012
wherein:
gσ(x) Is a Gaussian kernel function;
sigma is a Gaussian kernel function gσ(x) Standard deviation of (d);
i (x) represents the x value of the input image I (x, y);
h () represents the Heaviside function;
phi is a level set function, phi > 0 is represented in the zero level set, phi < 0 is represented in the zero level set, and phi-0 is represented in the zero level set;
(3) computing the local entropy h of an image I (x, y)x；
(4) Segmenting the image I (x, y) on the basis of the initialized parameters in the step (2), segmenting the image I (x, y) by adopting an image segmentation model of a local energy functional based on local entropy and a non-convex regular term, and updating a level set function phi in the segmentation process;
(5) evolving the level set function phi according to the following equation, judging whether the level set function phi is converged, if so, stopping the evolution of the level set function phi, and outputting a segmentation image; otherwise, returning to the step (4) for continuing; the evolution equation is as follows:
Figure FDA0003156211410000021
wherein:
phi is a level set function, phi > 0 is represented in the zero level set, phi < 0 is represented in the zero level set, and phi-0 is represented in the zero level set;
alpha is a global energy term adjusting parameter;
beta is a local energy term adjusting parameter;
mu is a length coefficient, v is an energy penalty coefficient, and both mu and v are constants larger than 0;
δεis a Driac function;
i is an input image;
c1and c2Respectively in a closed active contour curve CAverage gray scale values of the portions and the outside;
η is the boundary stop function;
e1and e2The method comprises the following steps of (1) performing substitution expression in the calculation process of a local energy functional evolution equation;
Figure FDA0003156211410000031
is a gradient operator.
2. The method for image segmentation of local energy functional and non-convex regularization terms in combination with local entropy as claimed in claim 1, characterized in that said local entropy hxThe calculation formula of (a) is as follows:
Figure FDA0003156211410000032
wherein: h isxIs the local entropy of the pixel x,
Figure FDA0003156211410000033
for the probability density estimation of the gray level y in the neighborhood Ω, nyThe number of pixels having a gray level y in the neighborhood Ω.
3. The method of image segmentation in combination with local entropy local energy functional and non-convex regularization term according to claim 1, wherein c is1And c2The calculation formula of (a) is as follows:
Figure FDA0003156211410000034
wherein:
i (x, y) represents an input image;
Hεa regularization function representing a Heaviside function;
epsilon is a regularization parameter;
phi is a level set function, phi > 0 is represented in the zero level set, phi < 0 is represented in the zero level set, and phi-0 is represented in the zero level set;
Ω is a grayscale image space of the input image I (x, y).
4. The method of image segmentation in combination with local entropy local energy functional and non-convex regularization term according to claim 1 wherein e is1And e2The calculation formula of (a) is as follows:
Figure FDA0003156211410000035
wherein:
hxis the local entropy of pixel x;
i (y) the gray-scale value of the input image.
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