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CN112330698A - An Improved Geometric Active Contour Image Segmentation Method - Google Patents

An Improved Geometric Active Contour Image Segmentation Method Download PDF

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CN112330698A
CN112330698A CN202011214403.8A CN202011214403A CN112330698A CN 112330698 A CN112330698 A CN 112330698A CN 202011214403 A CN202011214403 A CN 202011214403A CN 112330698 A CN112330698 A CN 112330698A
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vector field
level set
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active contour
image
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CN112330698B (en
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王蒙
马意
郭正兵
付佳伟
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Kunming University of Science and Technology
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Abstract

本发明公开了一种改进的几何活动轮廓的图像分割方法，包括Step1：输入待处理的图像和一个矢量场；Step2：通过矩形网格对矢量场进行采样，采样后得到观测集，嵌入迭代鲁棒估计器来消除观测集中观测值的误差和噪声；然后插入观测点，利用平滑化后的岭回归并约束弹性网以构造平流矢量场；Step3：将平流矢量场与扩散流嵌入到几何活动轮廓中，从而构建为一个统一的基于平流矢量场和扩散流改进的几何活动轮廓模型模型指导初始水平集的更新，更新后水平集将活动轮廓曲线演化到准确的目标轮廓上，从而完成对图像的分割。本发明提出的方法相较于传统方案具有明显的优势，取得了较好的分割效果。

Figure 202011214403

The invention discloses an improved image segmentation method of geometric active contour, including Step 1: inputting an image to be processed and a vector field; Step 2: sampling the vector field through a rectangular grid, obtaining an observation set after sampling, and embedding iteratively Rod estimator to eliminate the error and noise of the observations in the observation set; then insert the observation points, use the smoothed ridge regression and constrain the elastic net to construct the advection vector field; Step3: Embed the advection vector field and diffusion flow into the geometric active contour In this way, a unified geometric active contour model based on advection vector field and diffusion flow is constructed to guide the update of the initial level set, and the updated level set will evolve the active contour curve to the accurate target contour, thus completing the image analysis. segmentation. Compared with the traditional scheme, the method proposed by the present invention has obvious advantages and achieves a better segmentation effect.

Figure 202011214403

Description

Improved image segmentation method for geometric active contour
Technical Field
The invention relates to an improved image segmentation method of a geometric active contour, and belongs to the field of image processing.
Background
The contour captured from the image sequence has a rich spatial structure, and has been widely applied to video monitoring, medical analysis, motion recognition and the like. Features of interest in an image, whether rigid or non-rigid, are typically associated with complex motion and deformation. To accomplish this challenging task, an Active Contour (AC) method initiates an evolution curve near the object boundary, then matches the evolution curve to the true contour, and finally resides on the contour. Geometric Active Contour (GAC) captures the position of a parametric contour by minimizing the combination of smooth and gradient-driven energies.
The curve evolution of the GAC model is essentially a Diffusion, e.g., a level set Function, considered as a spatial scalar model, and the non-uniform Diffusion is constrained by a Diffusion Coefficient Function (DCF) driven by the spatial data of the image. Many DCFs have been proposed to obtain the desired curve evolution behavior. The DCF of the original GAC is proposed based on a gradient-based stopping function that leads to curve shrinkage and boundary residuals. DCF has detailed spatial resolution, but the results are still sensitive to the initial level set, since the limited coordination range of DCF usually leads to local convergence. When dynamic segmentation of time series is involved, the disadvantages of DCF are very prominent, often confusing the true contours and the salient background.
Many models assume that evolving contour-aligned moving objects are time-smooth in sequence, so that the evolving contour at the current time can be initialized by the corresponding contour at the previous time. However, considering the sampling interval, even if diffusion by gaussian smoothing has been previously achieved to the original image, the global motion between neighboring images may be so significant that the DCF is discontinuous in time. To overcome this problem, predictive methods are embedded into the GAC model to initialize the level set, otherwise local convergence per discrete time will accumulate, eventually losing object boundaries.
Disclosure of Invention
The invention provides an improved image segmentation method of a geometric active contour, which is used for realizing the segmentation of an image by constructing the improved geometric active contour.
The technical scheme of the invention is as follows: an improved image segmentation method of geometric active contour, the method comprises the following steps:
step 1: inputting an image to be processed and a vector field;
step 2: sampling a vector field through a rectangular grid, obtaining an observation set after sampling, and embedding an iterative robust estimator to eliminate errors and noises of an observed value in the observation set; then inserting observation points, and utilizing the smoothed ridge regression and constraining the elastic net to construct an advection vector field;
step 3: embedding the advection vector field and the diffusion flow into a geometric active contour, so as to construct a uniform geometric active contour model based on advection vector field and diffusion flow improvement to guide the updating of an initial level set, and the updated level set evolves an active contour curve to an accurate target contour, thereby completing the segmentation of the image; wherein an internal contour of an image is captured from a sequence of images by means of a conventional geometric active contour model and an initial level set is generated.
Step2, establishing an energy equation E of a vector field according to a Lagrangian method and concisely writing the energy equation E into a matrix form:
Figure BDA0002759865600000021
in the formula:
Figure BDA0002759865600000022
is a column vector ordering a conventional grid matrix in dictionary order, L is a matrix smoothing each element of a vector field X by a Laplacian, D is 4 grid points inserted near an observation point and pointing to the position of the matrix in a bilinear manner, and lambda is1And λ2Is to satisfy lambda1+λ2A positive coefficient of 1;
obtaining a regular equation by solving partial derivatives in an energy equation
Figure BDA0002759865600000023
And solving by using ridge regression to obtain advection vector field
Figure BDA0002759865600000024
Comprises the following steps:
Figure BDA0002759865600000025
wherein U ═ DTD+λ1LTL)-1DT。
The Step3 is specifically as follows:
let the evolution of the curve be unlimited, the level set equation can be generalized by transferring spatial intensity through two processes inside the closed system: diffusion and advection; the geometric active contour model combines the divergence of diffusion vectors and advection vectors and can be decomposed into a divergence operation of the product of scalar and vector functions:
Figure BDA0002759865600000026
in the formula, the level set phi represents the image space
Figure BDA0002759865600000027
The variable of interest, g represents a function mapping the image intensity matrix to the corresponding diffusion coefficient, and the vector field X represents a finite vector space
Figure BDA0002759865600000028
The advection velocity in (1); on the right side of the equation, the first term
Figure BDA0002759865600000029
Denotes an unrestricted diffusion of phi; second item
Figure BDA00027598656000000210
Representing motion driven by gradients of the edge and advection vector fields, if significant in intensityActivating the motion; the third term preserves the conservation of the non-uniform force field; the last term compensates for the change in amount;
the level set formula is expanded to be embedded in the tangential direction of the flat flow field, and the tangential direction is
Figure BDA0002759865600000031
The divergence operation of (a) can also be decomposed into:
Figure BDA0002759865600000032
when a singular point having a large curvature is present near the vector field X,
Figure BDA0002759865600000033
represents the curvature of the vector field X and is typically small;
the curvature compensation C is used to enhance the detection performance of the evolution curve C driven by the level set:
Figure BDA0002759865600000034
in addition, the gradient direction of the curve C
Figure BDA0002759865600000035
At a speed value of
Figure BDA0002759865600000036
Tangential direction of the vector field X
Figure BDA0002759865600000037
At a speed value of
Figure BDA0002759865600000038
Then, the velocity vector is projected to the gradient direction
Figure BDA0002759865600000039
The evolution equation for the level set function is formulated as:
Figure BDA00027598656000000310
computing constraint functions
Figure BDA00027598656000000311
And
Figure BDA00027598656000000312
the level set φ of the elapsed time t is updated as:
Figure BDA00027598656000000313
the updated level set continues to guide the curve evolution of the geometric active contour to capture a dynamic contour with complex motion accuracy and complete the segmentation of the image.
The invention has the beneficial effects that: the invention provides a regression algorithm to construct an advection vector field, and utilizes the advection vector field and a diffusion flow to guide the update of a level set, an initial level set generated by a geometric active contour evolves towards an accurate dynamic contour under the guide of the advection vector field and the diffusion flow, the image segmentation is realized, the dynamic shape of the contour can be more accurately captured through the updated level set, and the problem that the traditional active contour model cannot accurately segment the dynamic complex image is solved; experimental results show that compared with the traditional scheme, the method provided by the invention has obvious advantages and obtains a better segmentation effect.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph showing the results of the experiment according to the present invention.
Detailed Description
Example 1: 1-2, an improved method for image segmentation of geometric active contours, the method comprising the steps of:
step 1: inputting an image to be processed and a vector field;
step 2: sampling a vector field through a rectangular grid, obtaining an observation set after sampling, and embedding an iterative robust estimator to eliminate errors and noises of an observed value in the observation set; then inserting observation points, and utilizing the smoothed ridge regression and constraining the elastic net to construct an advection vector field;
step 3: embedding the advection vector field and the diffusion flow into a geometric active contour, so as to construct a uniform geometric active contour model based on advection vector field and diffusion flow improvement to guide the updating of an initial level set, and the updated level set evolves an active contour curve to an accurate target contour, thereby completing the segmentation of the image; wherein an internal contour of an image is captured from a sequence of images by means of a conventional geometric active contour model and an initial level set is generated.
Further, Step1 can be set to refer to inputting the image to be processed, and simultaneously inputting a vector field X:
Figure BDA0002759865600000041
further, Step2 may be specifically configured as follows:
first, with a rectangular grid P of length-width dimension H, W ═ H × W versus continuous vector field X:
Figure BDA0002759865600000042
sampling is carried out; sampling to obtain an observation set
Figure BDA0002759865600000043
And N is less than P, an iterative robust estimator is embedded to eliminate errors and noises of observed values in an observation set; and (4) obtaining a horizontal vector field by realizing the ridge regression after smoothing and modifying the elastic net. Ridge regression tends to activate vectors at almost every location, as adversely affected by the smoothing term. In order to obtain accurate and significant results, the energy equation of the vector field is established according to the Lagrangian method and concisely written in the form of a matrix:
Figure BDA0002759865600000044
wherein
Figure BDA0002759865600000045
Is a column vector ordering a conventional grid matrix X in dictionary order, L is a matrix smoothing each element of X by the Laplacian, and D is a matrix inserting 4 grid points near the observation point pointing to its own position in a bilinear manner, λ1And λ2Is to satisfy lambda1+λ2A positive coefficient of 1. Obtaining a regular equation by solving partial derivatives in the equation
Figure BDA0002759865600000046
And solving by using ridge regression to obtain a advection vector field
Figure BDA0002759865600000047
Comprises the following steps:
Figure BDA0002759865600000048
U＝(DTD+λ1LTL)-1DT
and finally, embedding the constructed advection vector field into a solution of a subsequent step.
Further, Step4 can be set, and the specific steps of constructing a unified geometric active contour model (AD-GAC) based on advection vector field and diffusion flow improvement are as follows:
let the evolution of the curve be unlimited, the level set equation can be generalized by transferring spatial intensity through two processes inside the closed system: diffusion and advection. AD-GAC combines the divergence of diffusion and advection vectors and can be decomposed into a divergence operation of the product of a scalar and a vector function:
Figure BDA0002759865600000051
in the formula, the level set phi represents the image space
Figure BDA0002759865600000052
The variable of interest, g represents a function mapping the image intensity matrix to the corresponding diffusion coefficient, and the vector field X represents a finite vector space
Figure BDA0002759865600000053
The advection velocity in (1). On the right side of the equation, the first term
Figure BDA0002759865600000054
Denotes an unrestricted diffusion of phi; second item
Figure BDA0002759865600000055
Representing a motion driven by the gradient of the edge and advection vector fields, which motion is activated if the intensity is significant; the third term preserves the conservation of the non-uniform force field; the last term compensates for the change in the amount.
The level set formula is expanded to be embedded in the tangential direction of the flat flow field, and the tangential direction is
Figure BDA0002759865600000056
The divergence operation of (d) can also be decomposed into:
Figure BDA0002759865600000057
when a singular point having a large curvature is present near the vector field X,
Figure BDA0002759865600000058
represents the curvature of the vector field X and is typically small.
The curvature compensation C is used to enhance the detection performance of the evolution curve C driven by the level set:
Figure BDA0002759865600000059
in addition, the gradient direction of the curve C
Figure BDA00027598656000000510
At a speed value of
Figure BDA00027598656000000511
Tangential direction of the vector field X
Figure BDA00027598656000000512
At a speed value of
Figure BDA00027598656000000513
Then, the velocity vector is projected to the gradient direction
Figure BDA00027598656000000514
The evolution equation of the function of the level set is formulated as
Figure BDA00027598656000000515
Computing constraint functions
Figure BDA00027598656000000516
We can update the level set φ of elapsed time t to
Figure BDA00027598656000000517
Wherein s represents a set tuning parameter;
the updated level set continues to guide the curve evolution of the geometric active contour to capture a dynamic contour with complex motion accuracy and complete the segmentation of the image.
By the method of the invention, the following experimental data are given:
as shown in fig. 2, the microbial sequence indicates that the microbes perform spontaneous activities in the nutrient solution, which involves overall rotation and detailed deformation. To initiate the segmentation, 3 individual sub-regions in the body of the microorganism are manually related to the representation. The light gray circle represents the initial frame of the current time t, the initial frame moves towards the segmentation contour, the dark gray circle represents the final segmentation result, and the initial frame is closer to the final segmentation result under the action of the advection vector field and the diffusion flow along with the increase of t.
In the experimental process of the invention, a system win10 is used, and a computer configured as an AMD R52600 processor, a 16G running memory and a GeForce RTX 1070(8GB) graphics card is adopted.
The working principle of the invention is as follows: in the invention, a uniform GAC model, namely an improved geometric active contour model (AD-GAC) based on advection vector field and diffusion flow, and an embedded algorithm for advection vector field regression between adjacent frames are provided. To segment dynamic objects between image sequences, the AD-GAC method extends the conventional diffusion scheme according to the generation advection diffusion equation. The advection term of the advection diffusion equation is represented by the transfer of the level set function of the time-varying vector field. Furthermore, a ridge regression of the constrained norm is implemented and the elastic mesh is modified to obtain the vector field. In addition, errors and noise of the observed values are eliminated by embedding an iterative robust estimator. Experimental results prove that the method is superior to the traditional method based on the Active Contour (AC), and particularly has advantages under the condition that the global motion is obvious.
While the present invention has been described in detail with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.

Claims (3)

1. An improved image segmentation method of geometric motion contour is characterized in that: the method comprises the following steps:
step 1: inputting an image to be processed and a vector field;
step 2: sampling a vector field through a rectangular grid, obtaining an observation set after sampling, and embedding an iterative robust estimator to eliminate errors and noises of an observed value in the observation set; then inserting observation points, and constructing an advection vector field by utilizing the smoothed ridge regression and constraining the elastic net;
step 3: embedding the advection vector field and the diffusion flow into a geometric active contour, so as to construct a uniform geometric active contour model based on advection vector field and diffusion flow improvement to guide the updating of an initial level set, and evolving an active contour curve to an accurate target contour by the updated level set, thereby completing the segmentation of the image; wherein an internal contour of an image is captured from a sequence of images by means of a conventional geometric active contour model and an initial level set is generated.
2. The improved image segmentation method of geometric active contour according to claim 1, characterized in that: step2, establishing an energy equation E of a vector field according to a Lagrange method and concisely writing the energy equation E into a matrix form:
Figure FDA0002759865590000011
in the formula:
Figure FDA0002759865590000012
is a column vector ordering a conventional grid matrix in dictionary order, L is a matrix smoothing each element of the vector field X by the Laplacian, D is 4 grid points near the observation point of the matrix insertion, pointing to its own position in a bilinear manner, λ1And λ2Is to satisfy lambda1+λ2A positive coefficient of 1;
obtaining a regular equation by solving partial derivatives in an energy equation
Figure FDA0002759865590000015
And solving by using ridge regression to obtain advection vector field
Figure FDA0002759865590000013
Comprises the following steps:
Figure FDA0002759865590000014
wherein U ═ DTD+λ1LTL)-1DT。
3. The improved image segmentation method of geometric active contour according to claim 1, characterized in that: the Step3 is specifically as follows:
let the evolution of the curve be unlimited, the level set equation can be generalized by transferring spatial intensity through two processes inside the closed system: diffusion and advection; the geometric active contour model combines the divergence of diffusion vectors and advection vectors and can be decomposed into a divergence operation of the product of scalar and vector functions:
Figure FDA0002759865590000021
in the formula, the level set phi represents the image space
Figure FDA0002759865590000022
The variable of interest, g represents a function mapping the image intensity matrix to the corresponding diffusion coefficient, and the vector field X represents a finite vector space
Figure FDA0002759865590000023
The advection velocity in (1); on the right side of the equation, the first term
Figure FDA0002759865590000024
Denotes an unrestricted diffusion of phi; second item
Figure FDA0002759865590000025
Representing a motion driven by the edges and the gradient of the advection vector field, which motion is activated if the intensity is significant; item IIIThe conservation of the non-uniform force field is kept; the last term compensates for the change in amount;
the level set formula is expanded to be embedded in the tangential direction of the flat flow field, and the tangential direction is
Figure FDA0002759865590000026
The divergence operation of (a) can also be decomposed into:
Figure FDA0002759865590000027
when a singular point having a large curvature is present near the vector field X,
Figure FDA0002759865590000028
represents the curvature of the vector field X and is typically small;
the curvature compensation C is used to enhance the detection performance of the evolution curve C driven by the level set:
Figure FDA0002759865590000029
in addition, the gradient direction of the curve C
Figure FDA00027598655900000210
At a speed value of
Figure FDA00027598655900000211
Tangential direction of the vector field X
Figure FDA00027598655900000212
At a speed value of
Figure FDA00027598655900000213
Then, the velocity vector is projected to the gradient direction
Figure FDA00027598655900000214
The evolution equation for the level set function is formulated as:
Figure FDA00027598655900000215
computing constraint functions
Figure FDA00027598655900000216
And
Figure FDA00027598655900000217
the level set φ for elapsed time t is updated as:
Figure FDA00027598655900000218
the updated level set continues to guide the curve evolution of the geometric active contour to capture a dynamic contour with accurate complex motion and complete the segmentation of the image.
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