CN112330698B - Improved image segmentation method for geometric active contour - Google Patents

Improved image segmentation method for geometric active contour Download PDF

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CN112330698B
CN112330698B CN202011214403.8A CN202011214403A CN112330698B CN 112330698 B CN112330698 B CN 112330698B CN 202011214403 A CN202011214403 A CN 202011214403A CN 112330698 B CN112330698 B CN 112330698B
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CN112330698A (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

The invention discloses an improved image segmentation method of a geometric active contour, which comprises the following steps of 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 the 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 the 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. Compared with the traditional scheme, the method provided by the invention has obvious advantages and obtains a better segmentation effect.

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, typically involve complex motions and deformations. To accomplish this challenging task, an Active Contour (AC) method initiates an evolutionary curve near the object boundary, then matches the evolutionary curve to the true contour, and finally resides on the contour. Geometric Active Contour (GAC) captures the position of the 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 the sequence, so 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 steps are as follows:
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.
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 GDA0002845108300000021
in the formula:
Figure GDA0002845108300000022
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, λ 1 And λ 2 Is to satisfy lambda 1 +λ 2 A positive coefficient of 1;
obtaining a regular equation by solving partial derivatives in an energy equation
Figure GDA0002845108300000023
And solving by using ridge regression to obtain advection vector field
Figure GDA0002845108300000024
Comprises the following steps:
Figure GDA0002845108300000025
wherein U ═ D T D+λ 1 L T L) -1 D T 。
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 GDA0002845108300000026
In the formula, the level set phi represents the image space
Figure GDA0002845108300000027
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 GDA0002845108300000028
The advection velocity in (1); on the right side of the equation, the first term
Figure GDA0002845108300000029
Denotes an unrestricted diffusion of phi; second item
Figure GDA00028451083000000210
Representing a motion driven by the edges and the gradient of the advection vector field, which motion is activated if the intensity is significant; the third item retains the heterogeneityConservation of 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 GDA00028451083000000313
The divergence operation of (a) can also be decomposed into:
Figure GDA0002845108300000031
when a singular point having a large curvature is present near the vector field X,
Figure GDA0002845108300000032
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 GDA0002845108300000033
in addition, the gradient direction of the curve C
Figure GDA0002845108300000034
At a speed value of
Figure GDA0002845108300000035
Tangential direction of the vector field X
Figure GDA0002845108300000036
At a speed value of
Figure GDA0002845108300000037
Then, the velocity vector is projected to the gradient direction
Figure GDA0002845108300000038
The evolution equation for the level set function is formulated as:
Figure GDA0002845108300000039
computing constraint functions
Figure GDA00028451083000000310
And
Figure GDA00028451083000000311
the level set φ for elapsed time t is updated as:
Figure GDA00028451083000000312
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.
The beneficial effects of the invention are: 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 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.
Further, Step1 can be set to refer to inputting the image to be processed, and simultaneously inputting a vector field X:
Figure GDA0002845108300000041
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 GDA0002845108300000042
sampling is carried out; sampling to obtain an observation set
Figure GDA0002845108300000043
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 obtaining the advection vector field by realizing the ridge regression after smoothing and modifying the elastic net. Because of the adverse effects of the smoothing term, ridge regression tends to activate vectors for almost every location. 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 GDA0002845108300000044
Wherein
Figure GDA0002845108300000045
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, λ 1 And λ 2 Is to satisfy lambda 1 +λ 2 A positive coefficient of 1. Obtaining a regular equation by solving partial derivatives in the equation
Figure GDA0002845108300000046
And solving by using ridge regression to obtain advection vector field
Figure GDA0002845108300000047
Comprises the following steps:
Figure GDA0002845108300000048
U＝(D T D+λ 1 L T L) -1 D T
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 GDA0002845108300000051
in the formula, the level set phi represents the image space
Figure GDA0002845108300000052
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 GDA0002845108300000053
The advection velocity in (2). On the right side of the equation, the first term
Figure GDA0002845108300000054
Denotes an unrestricted diffusion of phi; second item
Figure GDA0002845108300000055
Representing a motion driven by the edges and the gradient of the advection vector field, 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 GDA0002845108300000056
The divergence operation of (d) can also be decomposed into:
Figure GDA0002845108300000057
when a singular point having a large curvature is present near the vector field X,
Figure GDA0002845108300000058
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 GDA0002845108300000059
in addition, the method can be used for producing a composite materialGradient direction of curve C
Figure GDA00028451083000000510
At a speed value of
Figure GDA00028451083000000511
Tangential direction of the vector field X
Figure GDA00028451083000000512
At a speed value of
Figure GDA00028451083000000513
Then, the velocity vector is projected to the gradient direction
Figure GDA00028451083000000514
The evolution equation of the function of the level set is formulated as
Figure GDA00028451083000000515
Computing constraint functions
Figure GDA00028451083000000516
and
Figure GDA00028451083000000517
We can update the level set φ of the elapsed time t to
Figure GDA00028451083000000518
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 accurate complex motion 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 an initial frame of the current moment t, the initial frame moves towards the segmentation contour, the dark gray circle represents a final segmentation result, and the initial frame is closer to the final segmentation result under the action of an advection vector field and a 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. The experimental results prove that the method of the invention is superior to the traditional method based on the Active Contour (AC), and especially has more advantages under the condition of obvious global motion.
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 (2)

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 the 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;
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 FDA0003690250090000011
in the formula, the level set phi represents the image space
Figure FDA0003690250090000012
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 FDA0003690250090000013
The advection velocity in (1); on the right side of the equation, the first term
Figure FDA0003690250090000014
Denotes an unrestricted diffusion of phi; second item
Figure FDA0003690250090000015
Representing a motion driven by the edges and the gradient of the advection vector field, 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 quantity;
the level set formula is expanded to be embedded in the tangential direction of the flat flow field, and the tangential direction is
Figure FDA0003690250090000016
The divergence operation of (a) can also be decomposed into:
Figure FDA0003690250090000017
when a singular point having a large curvature is present near the vector field X,
Figure FDA0003690250090000018
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 FDA0003690250090000019
In addition, the gradient direction of the curve C
Figure FDA0003690250090000021
At a speed value of
Figure FDA0003690250090000022
Tangential direction of the vector field X
Figure FDA0003690250090000023
At a speed value of
Figure FDA0003690250090000024
Then, the velocity vector is projected to the gradient direction
Figure FDA0003690250090000025
The evolution equation for the level set function is formulated as:
Figure FDA0003690250090000026
computing constraint functions
Figure FDA0003690250090000027
And
Figure FDA0003690250090000028
the level set φ for elapsed time t is updated as:
Figure FDA0003690250090000029
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.
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 FDA00036902500900000210
in the formula:
Figure FDA00036902500900000211
is a column vector ordering the conventional grid matrix in dictionary order, L is the vector field X by Laplace's operator for each elementA matrix subjected to smoothing processing, D is a matrix insertion observation point b i Nearby 4 grid points pointing in a bilinear manner to their own position, λ 1 And λ 2 Is to satisfy lambda 1 +λ 2 A positive coefficient of 1;
obtaining a regular equation by solving partial derivatives in an energy equation
Figure FDA00036902500900000212
And solving by using ridge regression to obtain advection vector field
Figure FDA00036902500900000213
Comprises the following steps:
Figure FDA00036902500900000214
Wherein U is (D) T D+λ 1 L T L) -1 D T 。
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