CN112184740B - Image segmentation method based on statistical active contour and texture dictionary - Google Patents

Image segmentation method based on statistical active contour and texture dictionary Download PDF

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CN112184740B
CN112184740B CN202011064617.1A CN202011064617A CN112184740B CN 112184740 B CN112184740 B CN 112184740B CN 202011064617 A CN202011064617 A CN 202011064617A CN 112184740 B CN112184740 B CN 112184740B
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高国伟
张志彦
吕菲亚
彭云峰
刘家磊
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Abstract

The invention provides an image segmentation method based on a statistical active contour and texture dictionary, which is used for solving the technical problems that an active contour model based on sparse texture cannot clearly represent the structure and texture of an image and the model calculation amount is large. The invention establishes a level set energy function and a level set updating equation based on Gaussian mixture distribution under a statistical framework. The method comprises the following steps: firstly, obtaining a binary sparse matrix by utilizing a dictionary learning algorithm; secondly, initializing a level set and obtaining a probability label through linear transformation of a binary sparse matrix; then, obtaining the statistical parameters of the current segmentation by utilizing the probability label; the current level set function, probability labels and statistical parameters are then combined to predict a new segmentation curve. The level set function evolves under the drive of the probabilistic tags, which are updated from the level set based binary tags by a line transformation. Compared with the traditional method, the method has the advantages that the calculation cost is greatly reduced, and meanwhile, the complex texture is effectively segmented.

Description

Image segmentation method based on statistical active contour and texture dictionary
Technical Field
The invention relates to the technical field of image processing, in particular to an image segmentation method based on a statistical active contour and a texture dictionary, which can efficiently complete complex texture image segmentation and can be widely applied to the field of image analysis.
Background
Active contour models are a class of methods for object segmentation in the field of computer vision and have irreplaceable positions in applications such as medical image analysis. The model is typically implemented by minimizing an energy function and evolving a level set function to a time dependent partial differential equation and constraining the boundaries of objects coupling the image data with a smoothness of zero level set. Most of the existing research focuses on designing a class of effective energy functional, and brings various constraints and constructions about images into the functional, and some effective methods are provided. In general, these methods can be divided into two categories: edge-based methods and region-based active contour methods, which have been receiving much attention because of their many advantages (e.g., closed and smooth contour, pixel-level accuracy, lower initial sensitivity).
The basic idea of the region-based active contour approach, in which the most common piecewise smoothing model is the Chan-Vese model, which is a simplified variant of the Mumford-Shah model and relies on global information to guide contour evolution, is to identify each region of interest by driving the evolution of the level set function using some region descriptor. The Chan-Vese model assumes that the image is statistically uniform, but this condition is difficult to achieve for an ideal case. Therefore, lie-pure-minds proposed a method driven by local binary fitting energy, defined by a kernel function with localized nature of variational formulas. But such models use only local intensity means to characterize the contour model and do not provide sufficient information. Most existing region-based methods use global or local intensity information as region descriptors to guide contour evolution, but cannot process natural images with rich texture features.
To improve the effectiveness of region-based active contours for complex natural images, researchers have proposed many texture descriptor models that introduce other types of information into the energy function for the purpose of formalizing and measuring differences between different objects. Some methods represent the texture image as a Beltrami framework of a two-dimensional Riemannian manifold and introduce a hybrid active contour model for segmentation of the texture image. Still others use texture detection operators to generate an enhanced image containing texture information, then use image segmentation methods to initially segment the image, and use adaptive active contour methods to improve the segmentation results. In the national Liuliu male professor, a local self-similarity-based texture description operator is introduced into a local Gaussian distribution-based active contour model fitting method, so that an evolution contour effectively captures a texture boundary. In addition to these texture detection operators, sparse representations are also introduced into the active contour model. There is an evolution of the active contours used to optimize the fidelity of the sparse representation of texture information provided by the object dictionary, and also sparse texture energy defined by using a weighted combination of texture and structural variation maps to enhance robustness to object boundary detection. Current sparse texture-based active contour models construct only complex energy functions and use edge-based active contours, which can result in high computational effort and often are not effective in characterizing structures and textures in images.
Disclosure of Invention
Aiming at the defects in the background technology, the invention provides an image segmentation method based on a statistical active contour and texture dictionary, and solves the technical problems that an active contour model based on sparse texture cannot clearly represent the structure and texture of an image and the model calculation amount is large.
The technical scheme of the invention is realized as follows:
an image segmentation method based on a statistical active contour and texture dictionary comprises the following steps:
the method comprises the following steps: modeling an observed value of each pixel in an original image by using a Gaussian mixture model;
step two: constructing dictionary elements according to the original image, and constructing a binary sparse matrix according to the dictionary elements;
step three: initializing a segmentation curve according to an original image, and initializing a level set function by using the segmentation curve;
step four: obtaining a probability label of each pixel in an original image belonging to a target and background region through a level set function through binary sparse matrix linear transformation;
step five: updating the statistical parameters of the target and the background area according to the probability label in the step four and the observed value of each pixel in the original image;
step six: according to the probability label of the step four, the level set function of the step three and the statistical parameter of the step five, a new level set function is obtained through a probabilistic level set evolution equation;
step seven: and returning to the step four to iteratively solve the level set function and the probability label until the change value of the new level set function is smaller than the threshold value T, and finishing image segmentation.
The method for modeling the observed value of each pixel in the original image by using the Gaussian mixture model comprises the following steps:
Figure BDA0002713392570000021
wherein the content of the first and second substances,
Figure BDA0002713392570000022
gaussian distribution function, x, representing the observed value of an imagejRepresenting an image observation value, { pi ═ pi }1,π2}，Θ＝{θ1,θ2}，πiRepresents the weight, p (x)j|θi) Representing a probability density function, thetaiStatistical parameters indicating a region i, where j ═ {1, 2., U × V }, U × V being an image size, i ∈ {1,2}, i ═ 1 indicating a target region, and i ═ 2 indicating a background region;
Figure BDA0002713392570000023
wherein, thetai＝{μi,∑iDenotes the statistical parameter of the probability space, ΣiIs a variance matrix, mu, of region i in probability spaceiIs the mean of the region i in probability space.
The method for constructing the dictionary elements according to the original image and constructing the binary sparse matrix according to the dictionary elements comprises the following steps:
s21, extracting N1 images with the size of
Figure BDA0002713392570000024
The image blocks are clustered by using a K-means algorithm, N1 image blocks are clustered to obtain N clustering centers, and the N clustering centers are used as dictionary elements D [ D ]1,D2,...,Dl,...,DN]，Dl∈RM，l＝{1,...,N}；
S22, pixel point xjThe centered image block is associated with a dictionary element:
Figure BDA0002713392570000031
wherein the content of the first and second substances,
Figure BDA0002713392570000032
is a pixel point xjIs a center of size
Figure BDA0002713392570000033
The image block of (a) is selected,
Figure BDA0002713392570000034
is an image block
Figure BDA0002713392570000035
J ═ 1, 2.., uxv }, uxv being the image size;
s23, defining a binary sparse matrix
Figure BDA0002713392570000036
Figure BDA0002713392570000037
Representing a pixel point xjAnd dictionary element DlMiddle pixel point
Figure BDA0002713392570000038
In which
Figure BDA0002713392570000039
Figure BDA00027133925700000310
Representing a dictionary element DlThe mth pixel point in (1);
Figure BDA00027133925700000311
the level set function is:
H(Φ)∈RUV×1
wherein phi is (phi)1,φ2,...,φU×V) H (-), is the Heaviside step function;
Figure BDA00027133925700000312
wherein phijRepresenting a pixel point xjThe corresponding level set function value.
The method for calculating the probability label of each pixel belonging to the target comprises the following steps:
P1Y＝diag(SI')-1SH(Φ)
P1X＝diag(STI”)-1STP1Y
wherein I 'represents a unit column vector of length UV, I' represents a unit column vector of length MN, P1YProbability labels, P, representing objects to which pixels in dictionary elements belong1XProbability labels representing that the pixels of the image to be segmented belong to the target;
Figure BDA00027133925700000313
Figure BDA00027133925700000314
wherein the content of the first and second substances,
Figure BDA00027133925700000315
representing pixels in dictionary elements
Figure BDA00027133925700000316
The probability of belonging to the object is,
Figure BDA00027133925700000317
representing a pixel point x in an original imagejProbability of belonging to the object, Ω1Representing a target area in the original image.
The statistical parameters include mean and variance matrices:
the calculation formula of the mean value is as follows:
Figure BDA0002713392570000041
the calculation formula of the variance matrix is as follows:
Figure BDA0002713392570000042
wherein the content of the first and second substances,
Figure BDA0002713392570000043
representing pixels x learned from a dictionaryjProbability labels, x, belonging to region ijIs the observed value of the image pixel.
The method for obtaining the new level set function through the probabilistic level set evolution equation comprises the following steps:
Figure BDA0002713392570000044
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002713392570000045
pixel point x representing k iterationsjCorresponding level set functionThe value of the one or more of the one,
Figure BDA0002713392570000046
pixel point x representing k +1 iterationsjThe corresponding level set function value,. DELTA.t, denotes the step size,. epsilon.is the scale factor,
Figure BDA0002713392570000047
representing k iterations pixel x from dictionary learningjThe probability label belonging to the object is,
Figure BDA0002713392570000048
representing k iterations pixel x from dictionary learningjA probability label belonging to the background is assigned,
Figure BDA0002713392570000049
pixel x representing k timesjAbout statistical parameters
Figure BDA00027133925700000410
Beta represents the weight of the adjustment area term, div represents the curvature operator,
Figure BDA00027133925700000411
for gradient, γ represents the weight of the adjustment of the girth term.
The beneficial effect that this technical scheme can produce: firstly, acquiring a sparse dictionary by utilizing a dictionary learning algorithm; then initializing a level set and obtaining probability labels through linear transformation based on a learning dictionary; obtaining a statistical parameter of the current segmentation by using the probability label; and then predicting a new segmentation curve by combining the current level set function, the probability label and the statistical parameter. The level set function evolves under the drive of the probabilistic tags, which are updated from the level set based binary tags by a line transformation. Compared with the traditional method, the method has the advantages that the calculation cost is greatly reduced, and meanwhile, the complex texture is effectively segmented.
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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 description of the embodiments or the prior art will be briefly described below, 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 the drawings without creative efforts.
FIG. 1 is a flow chart of the present invention.
FIG. 2 is an initial profile image of the present invention.
Fig. 3 shows the GPAC model segmentation result.
FIG. 4 shows the results of the TACSMM model segmentation.
Fig. 5 shows the DSNAKE model segmentation results.
FIG. 6 shows the segmentation result of the proposed method.
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 obtained by a person skilled in the art based on the embodiments of the present invention without inventive step, are within the scope of the present invention.
The embodiment of the invention provides an image segmentation method based on a statistical active contour and a texture dictionary, which is used for solving the problems of accuracy and efficiency in texture segmentation. The method is carried out under the drive of a sparse dictionary, the target is carried out by probability label drive segmentation representing a texture target, and the method can be divided into two steps: 1) obtaining probability labels belonging to textures by a binary level set function; 2) and obtaining probability distribution of the target and the background by the probability label, and obtaining a new level set function. These two steps are alternated until a stop condition is met. The specific process is shown in fig. 1, and comprises the following steps:
the method comprises the following steps: describing an observed value of each pixel in an original image by using a Gaussian mixture model; the original image is expressed as omega E R2Wherein Ω ═ { Ω ═ Ωi}，i∈{1,2}，Ω1Representing objects in an original imageRegion, Ω2Representing the background area in the original image. d-dimensional random variable xjThe j-th pixel point in the original image is represented, j is {1, 2., U × V }, and U × V represents the number of pixels in the original image. The present invention utilizes a Gaussian Mixture Model (GMM) to model image data, let p (x)j|θi) Is a gaussian distribution function and is also an element in the GMM.
The method for describing the observed value of each pixel in the original image by using the Gaussian mixture model comprises the following steps:
Figure BDA0002713392570000051
wherein the content of the first and second substances,
Figure BDA0002713392570000052
gaussian distribution function, x, representing observed values of an imagejRepresenting an image observation value, { pi ═ pi }1,π2}，Θ＝{θ1,θ2}，πiRepresents the weight, p (x)j|θi) Representing the probability density, θiA statistical parameter indicating an area i, where j ═ 1, 2., U × V }, U × V is an image size, i ∈ {1,2}, i ═ 1 indicates a target area, and i ═ 2 indicates a background area;
Figure BDA0002713392570000053
wherein, thetai＝{μi,∑iDenotes the statistical parameter of the probability space, ΣiIs a variance matrix, mu, of region i in probability spaceiIs the mean of the region i in probability space. d is an observed value xjDimension of (a), sigmaiIs a positive definite matrix with size d x d.
Step two: constructing dictionary elements according to the original image, and constructing a binary sparse matrix according to the dictionary elements; the specific method comprises steps S21 to S23:
s21, extracting N1 images with the size of
Figure BDA0002713392570000061
The image blocks are clustered by using a K-means algorithm, N1 image blocks are obtained, and the N clustering centers are used as dictionary elements D ═ D1,D2,...,Dl,...,DN]，Dl∈RM1, ·, N }; in the embodiment, M is 9;
s22, dividing the pixel point x intojThe centered image block is associated with a dictionary element:
Figure BDA0002713392570000062
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002713392570000063
is a pixel point xjIs a center of size
Figure BDA0002713392570000064
The image block of (a) is selected,
Figure BDA0002713392570000065
is an image block
Figure BDA0002713392570000066
J ═ 1, 2.., uxv };
s23, defining a binary sparse matrix
Figure BDA0002713392570000067
Figure BDA0002713392570000068
Representing a pixel point xjAnd dictionary element DlMiddle pixel point
Figure BDA0002713392570000069
In which
Figure BDA00027133925700000610
Figure BDA00027133925700000611
Representing a dictionary element DlThe mth pixel point in (1);
Figure BDA00027133925700000612
the step two process is the most time-consuming step in the whole segmentation, but the step can be performed in advance, and the sparse matrix can be used for multiple times after calculation is carried out on one picture.
The above process has the following properties, each image block
Figure BDA00027133925700000613
All pointing to a single dictionary element DlBut due to image blocks
Figure BDA00027133925700000614
Are overlapping, i.e. each pixel point xjMay appear in different positions of different image blocks, each pixel being M ═ M2Dictionary pixels are related (image pixels are related to less than M dictionary pixels at the edge of width M-1). In other words, each assignment associates m elements in the image into m pixels in the dictionary. This binary relationship between image pixels and dictionary pixels is represented here using a sparse binary matrix S that extracts texture features by simultaneous dictionary assignment to each image block and spatial relationships between image blocks.
Step three: initializing a segmentation curve according to an original image, and initializing a level set function by using the segmentation curve;
level set function phijIs a signed distance function, defined herein as
Figure BDA00027133925700000615
Wherein ε is a scaleThe coefficients of which are such that,
Figure BDA00027133925700000616
representing a pixel point x in an original imagejThe probability of belonging to the target region is,
Figure BDA00027133925700000617
representing a pixel point x in an original imagejProbability of belonging to a background region.
The invention allows the level set function phi to be setjInitialized to an arbitrary shape. This is typically done by setting an identity matrix equal in size to the image and setting the values in the initial curve to zero, let phijRepresenting a pixel point xjCorresponding level set function value:
Figure BDA0002713392570000071
definition H (·) is the Heaviside step function:
Figure BDA0002713392570000072
through the operation of H (-), the target and the background of the current image can be obtained according to the level set function, namely H (-) > omega → {1,2 }. For each image block selected in the image
Figure BDA0002713392570000073
Corresponding to a label image patch in spatial position
Figure BDA0002713392570000074
Figure BDA0002713392570000075
Representing image blocks
Figure BDA0002713392570000076
The corresponding level set function. In turn, there are multiple D's in each dictionarylImage block pointing
Figure BDA0002713392570000077
The label of a dictionary cell can thus be calculated from H (Φ) ═ H1,φ2,...,φU×V)。
Step four: obtaining a probability label that each pixel in an original image belongs to a target region and a background region through a level set function through binary sparse matrix linear transformation;
the method for calculating the probability label of each pixel belonging to the target area comprises the following steps:
P1Y＝diag(SI')-1SH(Φ) (8)
wherein I' represents a unit column vector of length UV, P1YProbability labels representing pixels in dictionary elements, H (Φ) E RUV×1。
The label of the dictionary unit is obtained by the pixel-by-pixel average value of the label patch corresponding to the image block assigned to it. Dictionary labels can be computed by arranging the pixels in the label image H (Φ) into a binary vector and multiplying with a regularized matrix S that adds one for each row, noting that the label computation is a multiple label average and thus no longer binary. Probability map P1XIs achieved by means of averaging, each dictionary label being placed in the image space at the position of the image block assigned to the dictionary element in question. As patches overlap, up to M values need to be averaged to calculate the pixel probability.
The probability labels of the dictionary elements are defined by:
Figure BDA0002713392570000078
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002713392570000079
representing pixels in dictionary elements
Figure BDA00027133925700000710
Probability of belonging to an object。
The probability map is defined as follows:
Figure BDA00027133925700000711
wherein the content of the first and second substances,
Figure BDA00027133925700000712
representing pixels in dictionary elements
Figure BDA00027133925700000713
The probability of belonging to the object is,
Figure BDA00027133925700000714
representing a pixel point x in an original imagejProbability of belonging to the object, Ω1Representing a target area in the original image.
Figure BDA00027133925700000715
For the probability label belonging to the background,
Figure BDA00027133925700000716
the probability map is defined as follows:
P1X＝diag(STI”)-1STP1Y (11)
where I "represents a unit column vector of length MN, P1XProbability labels representing pixels of the image to be segmented.
P2YRepresenting pixels in dictionary elements
Figure BDA00027133925700000813
Probability of belonging to the background, P2XProbability labels for the pixels of the image to be segmented belonging to the background, and P1Y+P2Y＝1，P1X+P2X＝1。
Step five: updating the statistical parameters of the target area and the background area according to the probability label in the step four;
the invention uses the cost function of a probabilistic Chan-Vese model:
Figure BDA0002713392570000081
wherein, the first two terms on the right side of the equation of the formula (12) are data terms, the third term on the right side of the equation of the formula (12) is used for limiting the length of the segmentation contour, the fourth term on the right side of the equation of the formula (12) is used for limiting the area of the segmentation contour,
Figure BDA0002713392570000082
pixel x representing degree kjBased on parameters
Figure BDA0002713392570000083
The probability density function of the obtained Gaussian distribution,
Figure BDA0002713392570000084
representation is based on parameters
Figure BDA0002713392570000085
The obtained probability density function of Gaussian distribution, beta represents the weight of the adjusting area term,
Figure BDA0002713392570000086
gamma is a weight parameter for adjusting the perimeter term; beta and gamma are used to adjust the relationship between the terms. H (-) is defined by equation (7), is discrete and non-differentiable, and is approximated in practical applications using a regular expression:
Figure BDA0002713392570000087
the parameter update is realized by minimizing the energy function, and firstly, formula (5) is substituted for formula (13) to obtain a new approximate expression:
Figure BDA0002713392570000088
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0002713392570000089
denotes H (phi)j) In the approximation of (a) to (b),
Figure BDA00027133925700000810
to represent
Figure BDA00027133925700000811
The inverted image of (1);
rewriting the cost function equation (12) into a discrete form, and substituting equations (2) and (14) to obtain:
Figure BDA00027133925700000812
and minimizing the above equation for the mean and variance, respectively, first derivative of equation (15) with respect to the mean μ is first solved:
Figure BDA0002713392570000091
let equation (16) equal 0, then we get:
Figure BDA0002713392570000092
the same way can be found for the updated equation of variance:
Figure BDA0002713392570000093
unlike the traditional area-based active contour, the invention uses soft classification in parameter estimation, which can provide more information and accelerate muiAnd sigmaiSo that the results can be obtained in fewer iterations.
Step six: obtaining a new level set function through a probabilistic level set evolution equation according to the probability label in the step four, the level set function in the step three and the statistical parameter in the step five;
for a fixed θ, an updated equation for φ can be derived from the gradient descent method:
Figure BDA0002713392570000094
from equations (5) and (12):
Figure BDA0002713392570000095
substituting the above equation into equation (19) yields a probabilistic level set evolution equation:
Figure BDA0002713392570000096
wherein the content of the first and second substances,
Figure BDA0002713392570000097
pixel point x representing k iterationsjThe value of the corresponding level set function,
Figure BDA0002713392570000098
pixel point x representing k +1 iterationsjCorresponding level set function values, Δ t represents the step size, ε is the scale factor,
Figure BDA0002713392570000099
representing k iterations pixel x from dictionary learningjThe probability label belonging to the object is,
Figure BDA00027133925700000910
representing k iterations pixel x from dictionary learningjA probability label belonging to the background is assigned,
Figure BDA0002713392570000101
pixel x representing k timesjBeta represents the weight of the adjustment area term, div represents the curvature operator,
Figure BDA0002713392570000102
to be gradient, γ represents the weight of the adjustment perimeter term. Please note that the level set update formula given here is an expression under the probability framework, and it can be seen from the formula that the level set function is updated by the probability label and the statistical parameter
Figure BDA0002713392570000103
To be driven by
Figure BDA0002713392570000104
It is derived from the texture dictionary.
Step seven: returning to the step of four iterative solution level set functions phi and probability labels
Figure BDA0002713392570000105
And completing image segmentation until the change value of the new level set function is less than the threshold value T. The stop condition is a change in H (Φ) as a threshold, which can be set according to the image size. When H (Φ) does not change much (a specific value can be set according to the image size), the segmentation can be stopped.
Specific examples
To verify the performance of the proposed method, for an image generated by two textures with similar colors, the image with 473 × 473 resolution data set is compared with three algorithms as shown in fig. 2-6. Fig. 2 shows the initial contour, the same initial level set is used for the four algorithms, and fig. 6 shows the segmentation result of the method of the present invention. Three contrast algorithms include graph cut-based active contours (GPAC), student t-blending-based texture perception active contours (TACSM) and learning dictionary-based snake models (DSNAKE), and the segmentation results are respectively shown in FIGS. 3-5.
TABLE 1 comparison of several texture Activity Profile methods
GPAC TACSMM DSNAKE Ours
RI 0.5846 0.9428 0.9533 0.9637
GCE 0.3620 0.0392 0.0255 0.0178
VI 1.8726 0.5197 0.4570 0.3567
Table 1 gives the time taken for four algorithms to segment the image. Where RI represents a probability edge index, GCE represents a global consistency error, and VI represents change information. The higher the RI value, the better the segmentation, while the lower the GCE and VI values, the better. Experimental results show that the segmentation performance of the invention is better.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (6)

1. An image segmentation method based on a statistical active contour and texture dictionary is characterized by comprising the following steps:
the method comprises the following steps: modeling an observed value of each pixel in an original image by using a Gaussian mixture model;
step two: constructing dictionary elements according to the original image, and constructing a binary sparse matrix according to the dictionary elements;
step three: initializing a segmentation curve according to an original image, and initializing a level set function by using the segmentation curve;
step four: obtaining a probability label that each pixel in an original image belongs to a target and background region through a level set function through binary sparse matrix linear transformation;
step five: updating the statistical parameters of the target and the background area according to the probability label in the step four and the observed value of each pixel in the original image;
step six: according to the probability label of the step four, the level set function of the step three and the statistical parameter of the step five, a new level set function is obtained through a probabilistic level set evolution equation;
the method for obtaining the new level set function through the probabilistic level set evolution equation comprises the following steps:
Figure FDA0003596802720000011
wherein phi isj (k)Pixel x representing k iterationsjThe value of the corresponding level set function,
Figure FDA0003596802720000012
pixel point x representing k +1 iterationsjThe corresponding level set function value, at, represents the step size, epsilon is the scale factor,
Figure FDA0003596802720000013
representing k iterations of pixel x learned from a dictionaryjThe probability label belonging to the object is,
Figure FDA0003596802720000014
representing k iterations pixel x from dictionary learningjA probability label belonging to the background is assigned,
Figure FDA0003596802720000015
pixel point x representing k timesjAbout statistical parameters
Figure FDA0003596802720000016
Of the Gaussian distribution probability density function, thetaiStatistical parameters representing region i, i ∈ {1,2}, i ═ 1 representing the target region, i ═ 2 representing the background region, β representing the weight of the adjustment area term, div representing the curvature operator,
Figure FDA0003596802720000019
is a gradient, gamma represents the weight of the adjustment perimeter term;
step seven: and returning to the step four to iteratively solve the level set function and the probability label until the change value of the new level set function is smaller than the threshold value T, and finishing image segmentation.
2. The image segmentation method based on the statistical active contour and texture dictionary as claimed in claim 1, wherein the method for modeling the observed value of each pixel in the original image by using the gaussian mixture model is as follows:
Figure FDA0003596802720000017
wherein the content of the first and second substances,
Figure FDA0003596802720000018
gaussian distribution function, x, representing observed values of an imagejRepresenting an image observation value, { pi ═ pi }1,π2}，Θ＝{θ1,θ2}，πiRepresents a weight, p (x)j|θi) Representing a probability density function, thetaiStatistical parameters indicating a region i, where j ═ {1, 2., U × V }, U × V being an image size, i ∈ {1,2}, i ═ 1 indicating a target region, and i ═ 2 indicating a background region;
Figure FDA0003596802720000021
wherein, thetai＝{μi,ΣiDenotes statistical parameters of the probability space, sigmaiIs a variance matrix, μ, of region i in probability spaceiIs the mean of the region i in probability space.
3. The image segmentation method based on the statistical active contour and texture dictionary as claimed in claim 1, wherein the method for constructing dictionary elements from the original image and constructing the binary sparse matrix from the dictionary elements comprises:
s21, extracting N1 images with the size of
Figure FDA0003596802720000022
The image blocks are clustered by using a K-means algorithm, N1 image blocks are clustered to obtain N clustering centers, and the N clustering centers are used as dictionary elements D [ D ]1,D2,...,Dl,...,DN]，Dl∈RM，l＝{1,...,N}；
S22, dividing the pixel point x intojThe centered image block is associated with a dictionary element:
Figure FDA0003596802720000023
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003596802720000024
is a pixel point xjIs a center of size
Figure FDA0003596802720000025
The image block of (2) is selected,
Figure FDA0003596802720000026
is an image block
Figure FDA0003596802720000027
J ═ 1,2,., uxv }, uxv being the image size;
s23, defining a binary sparse matrix S ═ S1 T,S2 T,...,Sj T,...,SU×V T]∈RMN×UV，
Figure FDA0003596802720000028
Representing a pixel point xjAnd dictionary element DlMiddle pixel point
Figure FDA0003596802720000029
In which
Figure FDA00035968027200000210
Figure FDA00035968027200000211
Representing a dictionary element DlThe mth pixel point in (1);
Figure FDA00035968027200000212
4. the statistically active contours and texture dictionary-based image segmentation method of claim 3 wherein the level set function is:
H(Φ)∈RUV×1
wherein phi is (phi)1,φ2,...,φU×V) H (-), is the Heaviside step function;
Figure FDA00035968027200000213
wherein phijRepresenting a pixel point xjThe corresponding level set function value.
5. The image segmentation method based on the statistical active contour and texture dictionary as claimed in claim 4, wherein the probability label of each pixel belonging to the target is calculated by:
P1Y＝diag(SI')-1SH(Φ)
P1X＝diag(STI”)-1STP1Y
wherein I 'represents a unit column vector of length UV, I' represents a unit column vector of length MN, P1YProbability labels, P, representing objects to which pixels in dictionary elements belong1XProbability labels representing that the pixels of the image to be segmented belong to the target;
Figure FDA0003596802720000031
Figure FDA0003596802720000032
wherein the content of the first and second substances,
Figure FDA0003596802720000033
representing pixels in dictionary elements
Figure FDA0003596802720000034
The probability of belonging to the object is,
Figure FDA0003596802720000035
representing a pixel point x in an original imagejProbability of belonging to the object, Ω1Representing a target area in the original image.
6. The statistically active contours and texture dictionaries-based image segmentation method of claim 5 wherein the statistical parameters include mean and variance matrices:
the calculation formula of the mean value is as follows:
Figure FDA0003596802720000036
the calculation formula of the variance matrix is as follows:
Figure FDA0003596802720000037
wherein the content of the first and second substances,
Figure FDA0003596802720000038
representing pixels x learned from a dictionaryjProbability labels, x, belonging to region ijIs the observed value of the image pixel.
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