CN109727258B - Image segmentation method based on regional gray heterogeneous energy - Google Patents
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Abstract
The invention discloses an image segmentation method based on regional gray heterogeneous energy, which comprises the following steps: s10, inputting the original image to obtain the number of pixel points and the gray value of the gray image; s20, calculating a gray heterogeneous index and a gray heterogeneous factor of the image based on the number of pixel points and the gray value of the gray image to obtain a gray heterogeneous factor image corresponding to the initial image; s30, constructing an active contour model based on regional gray scale heterogeneous energy, wherein a total energy functional of the model comprises a regional gray scale heterogeneous energy functional item, an edge energy item and a local region fitting item; and S40, solving the total energy functional to obtain the segmentation result of the image. The energy functional of the invention not only uses the gray information of the original image, but also fuses the regional gray heterogeneous information. The two are combined and balanced with each other, and an image with extremely uneven gray scale can be effectively divided. Experiments show that when the method is used for segmenting two types of specific images, the segmentation result is superior to the segmentation result only based on the image gray scale information.
Description
Technical Field
The invention relates to the technical field of image processing, in particular to an image segmentation method.
Background
Image segmentation is a fundamental and important task in the field of image processing and computer vision, and the segmentation results will directly affect the performance of subsequent processing steps.
The uneven gray scale of the image is always a difficult problem for image segmentation. In recent decades, active contour model (active contour model) has become one of the most widely applied methods in the image segmentation field, and can be divided into two categories: boundary-based and region-based methods.
However, the existing active contour model cannot obtain ideal segmentation results in many times. The boundary-based active contour model makes such models sensitive to edge information in the image because the information of image gradients is utilized in the energy functional. Therefore, the performance of segmenting images with rich edge information, such as tigers and leopards in natural images and lesions with calcification and necrosis in medical images, is unsatisfactory. The region-based active contour model (e.g., C-V [1], RSF [2]) can solve the disadvantage of the boundary-based active contour model that is sensitive to edge information to some extent. Such models do not take into account the edge information of the image and can sometimes segment image objects with weak boundaries. But such models typically require that the object of the image be as homogenous as possible to the background. The RSF model of Li et al [2] utilizes inter-pixel spatial information by introducing a Gaussian kernel function, minimizes an energy functional based on local gray information, and can process images with non-uniform gray levels to a certain extent. But the degree of unevenness of the image gradation can only be slowly and smoothly varied. Zhang et al developed this model in [3], and proposed an LIF (local image shaping) model, which was segmented by minimizing the difference between the original image and the image obtained by 'RSF'. The main idea is to fit the original image with a 'RSF' image. Sandberg et al [4] propose to incorporate texture information into the active contour model to deal with the problem of uneven image gray scale. They chose Gabor filters to obtain the texture of the image. Kim et al [5] propose an active contour model based on significant boundary energy using significant boundaries in the image as a boundary indicative function in the active contour model. Zhang et al [6] propose a Local Statistical Active Contour Model (LSACM) for segmenting gray-scale heterogeneous images. Qi et al [7] propose an anisotropic data item that distinguishes between inside and outside regions based on local gray scale information along the contour direction. And a gradient down-flow regularization term based on the structure tensor is proposed. Recently, Zhi, Shen [8] proposed a level set-based approach that involved using saliency information and color intensity as the region-external energy to excite the evolution of the level set, but this saliency information seems not to be powerful enough to handle images of significantly inhomogeneous intensity. Wang, Chang et al [9] propose a hybrid image fitting energy segmentation method based on two different local fitting combinations. The methods in the above prior documents have a certain processing capability for images with non-uniform gray levels, but the above models also have difficulty in obtaining satisfactory segmentation results for images with very non-uniform target or background gray levels.
The cited references are as follows:
[1]T.Chan,L.Vese,Active contours without edges[J],IEEE Trans.ImageProcess.10(2),266-277,2001.
[2]C.Li,C.Kao,J.Gore,Z.Ding,Minimization of region-scalable fittingenergy for image segmentation[J],IEEE Trans.Image Process.vol.17,1940-1949,2008.
[3]K.Zhang,H.Song,L.Zhang,Active contours driven by local imagefitting energy[J],Pattern Recognition.2010,43(4):1199-1206.[163]
[4]B.Sandberg,T.Chan,L.Vese,A level-set and Gabor-based activecontour algorithm for segmenting textured images[C],UCLA CAM Report,2002.[164]
[5]W.Kim,C.Kim,Active contours driven by the salient edge energymodel[J],IEEE Transactions on Image Processing,2013,22(4):1667-1673.[160]
[6]K.Zhang,L.Zhang,K.M.Lam,and D.Zhang,A level set approach to imagesegmentation with intensity inhomogeneity[J],IEEE Trans.Cybernetics,46(2016),pp.546-557.
[7]Q.Ge,C.Li,W.Shao,et al.A hybrid active contour model withstructured feature for image segmentation[J].Signal Process.,108(2015),pp.147-158.
[8]X.H.Zhi,H.B.Shen.Saliency driven region-edge-based top down levelset evolution reveals the asynchronous focus in image segmentation[J].PatternRecognition,80(2018),pp.241-255.
[9]L.Wang,Y.Chang,H.Wang,et al.An active contour model based on localfitted images for image Segmentation[J].Information Sciences,418-419(2017),pp.61-73.
disclosure of Invention
The purpose of the invention is as follows: aiming at the defects of the prior art, the invention provides an image segmentation method based on regional gray heterogeneous energy, which can effectively segment images with extremely uneven gray levels.
The technical scheme is as follows: the invention discloses an image segmentation method based on regional gray heterogeneous energy, which comprises the following steps of:
s10, inputting the original image to obtain the number of pixel points and the gray value of the gray image;
s20, calculating a gray heterogeneous index d and a gray heterogeneous factor F (x) of the image based on the number of pixel points and the gray value of the gray image to obtain a gray heterogeneous factor image corresponding to the initial image;
s30, constructing an active contour model based on regional gray scale heterogeneous energy, wherein a total energy functional of the model comprises a regional gray scale heterogeneous energy functional item, an edge energy item and a local region fitting item;
and S40, solving the total energy functional to obtain the segmentation result of the image.
Preferably, in step S10, the original image includes a color image and a grayscale image, and when the original image is the color image, it is transformed into the grayscale image using the MATLAB self-contained program rgb2 gray.
Preferably, in step S20, the formula for calculating the gray level heterogeneity index d is:
wherein the content of the first and second substances,
omega represents a set of pixel points in the image, | omega | is the number of pixel points in the image, mean (I (N)k(x) ) is a neighborhood N)k(x) Mean value of gray levels of middle pixels, Nk(x)＝{y∈Ω:|xh-yh|≤k,|xv-yvI ≦ k, k denotes the size of the neighborhood, i (x) denotes any pixel point x ═ xh,xv) The gray value of (a);
the calculation formula of the area gray scale heterogeneous factor F (x) is as follows:
wherein the content of the first and second substances,
preferably, in step S30, the total energy functional is in the form of:
E＝λ1Erh+λ2Elocal+λ3Eedge+νLength(C)
wherein E isrhFor regional gray scale heterogeneous energy, ElocalAs local energy, EedgeIs the edge energy, λ1,λ2And λ3The weights of the three energies are length (C) represents a length constraint regular term, and v represents the weight of the length constraint regular term.
The area gray level heterogeneous energy calculation formula is as follows:
wherein the content of the first and second substances,
image representing regional gray scale difference factor, H(φ) is the regularization of the Heaviside function, φ is the level set function, P1And P2The average gray level heterogeneous factors inside and outside the contour C respectively have the following specific expressions:
the local energy calculation formula is as follows:
where W (x) is a neighborhood centered on pixel x, K is a Gauss kernel, t ═ m (x), s (x)]Is a simple texture description operator for describing the texture information in the original image, m (x), s (x) are the mean and variance of the image gray scale, tinAnd toutIndicating inside or outside of contoursAnd the texture description operator consists of the mean value and the variance of the image gray level.
The edge energy calculation formula is as follows:
wherein, FPMAnd (p) representing the grayscale heterogeneity factor of the denoised image Perona-Malik.
Preferably, the step S40 includes: embedding the contour C into a level set function phi, namely C is a zero level set of the function phi to obtain a specific form of the total energy functional, solving a first-order variation component related to phi by adopting a gradient descent method, and performing active contour evolution through iteration to obtain a target boundary.
Has the advantages that:
1. aiming at the segmentation of the image with very uneven gray scale, more image information needs to be combined, and the segmentation model is improved by considering the characteristics of the image. Based on the method, the concept of the regional gray heterogeneous index is introduced firstly, the regional gray heterogeneous index can measure the nonuniformity of the regional gray, and the pixel points in the region can be classified through the regional gray heterogeneous index. Secondly, an image of the heterogeneous energy functional of the defined region can be obtained according to the heterogeneous indexes of the regional gray scale. The energy functional of the invention not only uses the gray information of the original image, but also fuses the regional gray heterogeneous information. The two are combined and balanced with each other, and an image with extremely uneven gray scale can be effectively divided.
2. The invention provides a novel energy functional form based on regional gray heterogeneity, and the energy functional form is fused into a variation frame to obtain a regional gray heterogeneous energy functional. The heterogeneous energy functional of regional gray level can be regarded as the mark whether the gray level of a pixel point in an image is uniform or not, and the energy functional of the model mainly comprises three terms: the method comprises a region gray level heterogeneous energy spread function term, a local region fitting term and an edge energy term. By introducing the regional gray scale heterogeneous energy items, the method can effectively segment the target image with relatively uniform gray scale under the complex background and the target image with non-uniform gray scale under the homogeneous background.
Drawings
FIG. 1 is a flow diagram of a method according to an embodiment of the invention;
FIG. 2 is a plot of the square root of d obtained from an image laid out at different angles according to an embodiment of the present invention;
FIG. 3 is a heterogeneous factor image according to an embodiment of the invention;
FIG. 4 is a comparison of segmentation results according to different models for several images in a MSRA database, according to an embodiment of the present invention;
FIG. 5 is a comparison of different model segmentation results for two particular types of images, according to an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
Referring to fig. 1, the image segmentation method based on regional gray scale heterogeneous energy provided by the invention comprises the following steps:
and S10, inputting the original image to obtain the number of pixel points and the gray value of the gray image.
The original image may be a color image or a grayscale image, and if the original image is a color image, the MATLAB can be directly converted into a grayscale image from the band program rgb2 gray. The image is usually regarded as a matrix in the processing process (a gray image is an m × n × 1 matrix, and a color image is an m × n × 3 matrix), and in the process of reading the image by the MATLAB, the pixel value of each pixel point of the image is automatically dispersed into the value of the corresponding point in the matrix, and the number of the pixel points is the size of the matrix.
And S20, calculating a gray heterogeneous index d and a gray heterogeneous factor F (x) of the image based on the number of the pixels and the gray value of the gray image to obtain a gray heterogeneous factor image corresponding to the initial image.
One gray image can be seen as a function I: omega → R, and any pixel point x ═ xh,xv) The gray value is given as i (x). For any pixel point x, N in the imagek(x) Representing neighbors centred on the x pointDomain:
Nk(x)＝{y∈Ω:|xh-yh|≤k,|xv-yv|≤k}
k denotes the size of the neighborhood.
The gray level heterogeneous index d provided by the invention is defined as:
wherein
Where Ω represents the set of pixels in the image, | Ω | represents the number of pixels in the image, mean (I (N)k(x) ) is a neighborhood N)k(x) The mean value of the gray levels of the middle pixels. The gray level heterogeneity index d measures the mean square difference of the gray levels of the whole image, so that d can be used as an index of image gray level heterogeneity.
To check the robustness of the indicator, the square root of d is calculated by placing a stripe image (target is stripe and background is white) at different angles in the embodiment shown in fig. 2. This value was found to vary more slowly with the angle of the fringes in the image. This shows that using d as a measure of image gray level heterogeneity is very robust.
Further, the regional gray scale heterogeneity factor f (x) in step S20 is defined as follows:
wherein
From the definition of F (x), F (x) epsilon [0,1]N can be quantitatively characterized by F (x)k(x) Gray scale non-uniformity. For a fixed size Nk(x) F (x) the larger the gray value and phase of x pointThe gray values of the adjacent pixel points are highly inconsistent, and vice versa.
After the regional gray scale heterogeneous factor f (x) is defined, the regional gray scale heterogeneous factor of each point of an image can form a new image, and the new image is called a gray scale heterogeneous factor image.
As shown in fig. 3, the region heterogeneity factor defined in the present invention is displayed in the form of an image. Two cases of area gray scale heterogeneity factors are shown. (1) The first line is an image of leopard, in which the texture of the leopard body is rich, but the texture of the background is single. Therefore, in the gray scale heterogeneous factor image, the value of the regional gray scale heterogeneous factor is higher due to uneven gray scale among the regional regions with rich leopard body textures, namely the brighter part in the image. This is the case when the target is heterogeneous and the background is more homogeneous. (2) The second row is an image of a starfish, the gray level of part of the starfish changes smoothly, but the seabed part of the background has abundant textures and very uneven gray level. Therefore, in the grayscale heterogeneous factor image, the starfish portion is darker and the background portion is lighter. This is the case when the target gray is homogeneous and the background gray is heterogeneous.
S30, constructing an active contour model based on regional gray scale heterogeneous energy, wherein the total energy functional of the model comprises a regional gray scale heterogeneous energy universal function term, an edge energy term and a local region fitting term.
Find two P1And P2To approximate the regional gray scale heterogeneity factors inside and outside the contour C. In one aspect, the area gray scale heterogeneous energy of the present invention is defined as:
wherein
Image representing regional gray scale difference factor, H(φ) is the regularization of the Heaviside function, and the specific expression is as follows:
phi is a level set function, phi is iteratively updated according to an update function hereinafter, and a final segmentation contour is obtained by setting phi to 0.
P1And P2The average gray level heterogeneous factors inside and outside the contour C respectively have the following specific expressions:
in addition, the regional gray level heterogeneous factor can also give an effective way of depicting the edge. In order to reduce the influence of a nearby clutter region and maintain an important image structure, the method denoises an original image (a gray image or an image of a color image after passing through rgb2 gray) by using a Perona-Malik model, and then calculates a gray heterogeneous factor of the denoised image. The edge energy in the present invention is defined as:
wherein FPMAnd (p) representing the grayscale heterogeneity factor of the denoised image Perona-Malik. On the other hand, due to the complexity of the image, it is considered to use the local energy functional to fuse the gray information of the original image while considering the regional gray heterogeneity:
where w (x) is a neighborhood centered at x, the neighborhood being of variable size and selectable by the user from different images, 5x5, 3x3, 7x 7. K is a Gauss kernel, t ═ m (x), s (x) is a simple texture descriptor, which is used to describe the texture information in the original image. K has the following form:
m (x), s (x) are the mean and variance of the image gray scale. t is tinAnd toutTexture descriptor consisting of mean and variance of image gray levels inside and outside a contour, wherein
Combining the three energy functional functions together to obtain:
E＝λ1Erh+λ2Elocal+λ3Eedge+νLength(C)
λ1,λ2and λ3Is the weight of three energies, three normal numbers. Length (C) represents the length constraint regularization term of the contour C, and ν represents the weight of the length constraint regularization term, for determining the magnitude of the length constraint acting in the energy functional minimization process. The larger v the stronger the regular constraint, the smoother the contour, and vice versa.
Embedding C into a level set function, namely C is a zero level set of a function phi, so as to obtain the total energy functional of the invention:
and S40, solving the total energy functional to obtain the segmentation result of the image.
For the equation (#) in step S30, a gradient descent method is used to obtain a first order variation about Φ, and an update function of Φ is obtained as:
wherein(phi (x) is a function H(φ (x)) is a derivative, the specific expression being:
using identity
Rewrite the above equation to:
and (4) carrying out active contour evolution on the (×) mode to obtain a target boundary. The following iterative formula is used:
where l and Δ t denote the number of iterations and the time step, F (φ), respectivelyl(x) And R (phi)l(x) Numerical approximations of the first three terms and the last term on the right side of the (×) respectively.
The target boundary is continuously approximated by continuously iterating phi through the above equation. After a certain number of iterations or after an iteration termination condition (i.e. | phi) is reachedk+1-φk|＜，φkI.e., the level set function iterates k times) the level set function reaches the target boundary.
The following two specific examples are provided to demonstrate the effects of the present invention.
Example 1:
aiming at 40 natural images taken from an MSRA database, the image segmentation method based on regional gray heterogeneous energy is compared with segmentation results of models in C-V, RSF, LSACM, document [8] and document [9], and F-value is adopted to quantitatively compare segmentation performance, and the calculation formula is as follows:
where β is a parameter, P is accuracy (Precision), and R is Recall (Recall). Can know that FβThe results of P and R are combined, when FβHigher levels indicate more effective test methods. In the experiment, betaAll experiments were performed with Matlab R2011a on a CPU 2.5GHz, RAM 6000G computer. For the model proposed by the present invention, the following parameter k is taken as 5, λ2＝1，Δt＝0.1,＝0.1,σ＝10,λ1，λ3And v is used as a pending parameter and can be adjusted. Through a series of experiments, lambda is found1∈[3,14]，λ3∈[0.8,3],ν∈[0.5,1.3]The time division effect is good. All color images are converted into grayscale images and are uniformly resized to 180 x 240.
Fig. 4 is a comparison of the results of segmentation of a partial image according to different models, wherein the first column is the initial image, the second column is the manually labeled real object boundary, the third column is the result of the inventive model segmentation, the fourth column is the result of the RSF model segmentation, the fifth column is the result of the C-V model segmentation, the sixth column is the result of the LSACM model segmentation, the seventh column is the result of the model segmentation in document [8], and the last column is the result of the model segmentation in document [9 ]. It can be seen that the results obtained by using the model of the present invention are significantly better than those obtained by other methods.
Table 1 shows the F-values for the six different segmentation models for the 7 images in fig. 4, and the average F-values for the different segmentation models for the 40 images selected from the MSRA database.
TABLE 1F-values for each model segmentation in example 1
Example 2:
for two specific types of images: (1) the target gray level complex background gray level is relatively uniform, (2) the background gray level complex target gray level relatively uniform image gray level image, and other experimental conditions are the same as example 1.
Fig. 5 shows the segmentation results for two specific types of images according to different models, in fig. 5, the first column is the initial image, the second column is the segmentation result of the present invention, the third column is the C-V model segmentation result, the fourth column is the RSF model segmentation result, the fifth column is the LSACM model segmentation result, the sixth column is the model segmentation result in document [8], and the last column is the model segmentation result in document [9 ].
Table 2 is a comparison of the number of iterations and the segmentation time for the six segmentation models for the 5 images in fig. 5, where i represents the number of iterations and T represents the segmentation time in seconds.
Table 2 number of iterations and iteration time for each division model in example 2
Experiments show that when the model provided by the invention is used for segmenting two specific images, the segmentation result is superior to that of the traditional segmentation model only based on image gray information.
Claims (4)
1. An image segmentation method based on regional gray heterogeneous energy is characterized by comprising the following steps:
s10, inputting the original image to obtain the number of pixel points and the gray value of the gray image;
s20, calculating a gray heterogeneous index d and a gray heterogeneous factor F (x) of the image based on the number of pixel points and the gray value of the gray image to obtain a gray heterogeneous factor image corresponding to the initial image;
s30, constructing an active contour model based on regional gray scale heterogeneous energy, wherein the total energy functional of the model comprises a regional gray scale heterogeneous energy universal function term, an edge energy term and a local region fitting term, and the specific form is as follows:
wherein E isrhFor regional gray scale heterogeneous energy, ElocalAs local energy, EedgeIn order to be the edge energy,
and
the weights of the three energies are length (C) represents a length constraint regular term of the contour C, and v represents the weight of the length constraint regular term;
the area gray level heterogeneous energy calculation formula is as follows:
wherein the content of the first and second substances,
a set of pixel points in the image is represented,
an image representing a regional gray level difference factor,
is the regularization of the Heaviside function,
is a level set function, P1And P2The average gray level heterogeneous factors inside and outside the contour C respectively have the following specific expressions:
the local energy calculation formula is as follows:
wherein W (x) is a neighborhood centered on pixel x, K is a Gauss kernel, t = [ m (x), s (x)]For the texture description operator, used to describe the texture information in the original image, m (x), s (x) is the mean and variance of the image gray scale, tinAnd toutExpressing texture description operators consisting of image gray mean values and variances inside and outside the contours;
the edge energy calculation formula is as follows:
wherein, FPM(p) representing a gray scale heterogeneous factor of the denoised image Perona-Malik;
and S40, solving the total energy functional to obtain the segmentation result of the image.
2. The method for image segmentation based on regional gray heterogeneous energy according to claim 1, wherein in step S10, the original image comprises a color image and a gray image, and when the original image is the color image, the MATLAB self-band program rgb2gray is used to transform the original image into the gray image.
3. The image segmentation method based on regional gray heterogeneous energy as claimed in claim 1, wherein in step S20, the formula for the gray heterogeneous index d is:
wherein the content of the first and second substances,
the calculation formula of the area gray scale heterogeneous factor F (x) is as follows:
wherein the content of the first and second substances,
4. the image segmentation method based on regional gray heterogeneous energy according to claim 1, wherein the step S40 includes: embedding contour C into level set function
Obtaining a specific form of the total energy functional, and then solving a function related to a level set by adopting a gradient descent method
And then carrying out active contour evolution through iteration to obtain a target boundary, wherein the iteration formula is as follows:
whereinlAnd
respectively representing the number of iterations and the time step,
and
respectively, the numerical approximation of the level set function energy term and the length term after the first-order variation.
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