CN102163321B - Image segmentation method based on lattice Boltzman model - Google Patents

Image segmentation method based on lattice Boltzman model Download PDF

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CN102163321B
CN102163321B CN 201110060920 CN201110060920A CN102163321B CN 102163321 B CN102163321 B CN 102163321B CN 201110060920 CN201110060920 CN 201110060920 CN 201110060920 A CN201110060920 A CN 201110060920A CN 102163321 B CN102163321 B CN 102163321B
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CN102163321A (en
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刘玮
严壮志
张蕊
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University of Shanghai for Science and Technology
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Abstract

The invention discloses an image segmentation method based on a lattice Boltzman model, which comprises the following steps: performing the segmentation process to an image based on a microscopic lattice Boltzman model, and then realizing the solution to a macroscopic partial differential equation of the image segmentation so as to realize the automatic segmentation of the image. Compared with a typical image segmentation based on a partial differential equation method, the image segmentation method can realize an iterative computation in large step so as to effectively improve the efficiency of image segmentation with rapid segmentation speed and good segmentation effect.

Description

Image partition method based on grid Boltzmann model
Technical field
The present invention relates to that a kind of (Lattice Boltzmann Model, image partition method LBM) belongs to image processing field based on grid Boltzmann model.
Technical background
Image is cut apart technology and the process that finger is divided into the zone of each tool characteristic to image and proposes interesting target, and it is a kind of important images analytical technology.Four ten years in the past, Study of Image Segmentation are subjected to the attention of people's height always.It is major issue during image is handled and analyzed that image is cut apart, and also is a classic problem in the computer vision research.
The Partial Differential Equation method that image is handled developed rapidly from the nineties in 20th century, had demonstrated the performance that is better than the traditional images disposal route [1]In the image processing field based on Partial Differential Equation method, because movable contour model has high efficiency, the simplicity of calculating and is specially adapted to modeling and the advantages such as deformable contour of extraction arbitrary shape, over nearly 20 years, movable contour model has had in rim detection, medical image segmentation and motion tracking to be used and very big development widely.Active contour during image is cut apart or " snake " (snake) model are at first proposed by M. Kass etc., its basic thought image segmentation problem is summed up as minimize a closed curve C(p) " energy " functional, realize that minimizing of " energy " functional namely lacked as far as possible and the closed curve of fairing as far as possible.But the major defect that the method exists is that it not only depends on geometric configuration and the position of curve C, also depends on the parameter p of curve.In order to overcome this defective, V. Caselles, R. Sapiro proposed not contain free parameter geodesic line active contour (GAC) model in 1997, had eliminated the defective that classical snake model relies on free parameter.But the defective that GAC exists is curve can not be close to the border that dark depression is arranged in the image.And for both there not being limbus also to lack the image of obvious textural characteristics, the GAC model is difficult to realize successful cutting apart.Based on this, T. Chan and L. Vese have proposed non-flanged active contour (C-V) model, have realized preferably segmentation effect automatically.
Digital picture is discontinuous, must be by numerical evaluation to obtain the approximate solution of partial differential equation.Many partial differential equation all are to disperse by explicit finite difference.Partial differential equation is found the solution complexity on the one hand, even does not exist; On the other hand, be subjected to the restriction of stability, the algorithm iteration step-length is very little, needs iteration many times just can produce a desired effect, and algorithm implementation procedure efficient is low.Along with developing rapidly of field robotization such as industry, agricultural, medical science, military affairs and intelligent demand, the requirement of image processing techniques is also improved day by day, therefore needing efficiently, implementation algorithm applies to the image real-time processing domain.
Grid Boltzmann model has physical thought clearly, the advantage of simple boundary treatment and fast parallel calculating, and it is the spatial model that disperses, and is particularly suitable for Digital Image Processing.From grid Boltzmann's microvisual model, design grid Boltzmann EVOLUTION EQUATION, can be met macroscopical partial differential equation of image processing requirements at last.Therefore grid Boltzmann method rapidly and efficiently provides the realization approach with accuracy for what the realization image was handled.
Summary of the invention
The objective of the invention is to the technical matters at the prior art existence, propose a kind of image partition method based on grid Boltzmann model, this method can not only improve image cuts apart quality, and can improve counting yield, is particularly useful for image and handles in real time.
In order to achieve the above object, design of the present invention is:
Image partition method based on grid Boltzmann model of the present invention comprises: set up two-dimensional lattice Boltzmann model, it is made of the computing grid of discretize, and the node of each grid is equivalent to a cellular, and the value of cellular is by the distribution function of particle With the diffusion vector
Figure 646780DEST_PATH_IMAGE002
Determine.
Finding the solution the EVOLUTION EQUATION that nonlinear diffusion equations realizes that gray level image is cut apart based on the method for grid Boltzmann model is:
Figure 2011100609209100002DEST_PATH_IMAGE003
Wherein
Figure 514461DEST_PATH_IMAGE004
Be the vector of diffusion,
Figure 2011100609209100002DEST_PATH_IMAGE005
For iterations is nIn time, be positioned at xThe place has speed
Figure 647502DEST_PATH_IMAGE004
The particle density distribution function, formula
Figure 700908DEST_PATH_IMAGE006
Be relaxation factor,
Figure 2011100609209100002DEST_PATH_IMAGE007
Be the equilibrium state distribution function,
Figure 603005DEST_PATH_IMAGE008
Be the Heaviside function derivative, its variable uBe distance function, c 1, c 2Be respectively to cut apart the inside and outside average gray of evolution curve,
Figure 2011100609209100002DEST_PATH_IMAGE009
Be constant.
Based on the flow process of the image partition method of grid Boltzmann model as shown in Figure 4, the method that the present invention proposes adopts the variation level diversity method, introduce the Heaviside function, its derivative function is embedded in the relaxation factor of grid Boltzmann EVOLUTION EQUATION, find grid Boltzmann EVOLUTION EQUATION and macroscopical equation corresponding relation to find the solution nonlinear diffusion equations and cut apart to realize image.
According to the foregoing invention design, the present invention adopts following technical proposals:
A kind of image partition method based on grid Boltzmann model is characterized in that operation steps is as follows:
(1) input initial pictures
Figure 145982DEST_PATH_IMAGE010
, the value of node is made as the gray-scale value of respective pixel;
(2) use two-dimensional lattice Boltzmann model, the initial balance state function of each action direction in the grid Boltzmann EVOLUTION EQUATION is set
Figure 2011100609209100002DEST_PATH_IMAGE011
(3) determine the iterations of grid Boltzmann EVOLUTION EQUATION NAdopt the variation level diversity method, draw the Heaviside function, the initialization distance function
Figure 2205DEST_PATH_IMAGE012
As the initial segmentation curve C;
(4) calculate the Heavside function
Figure 2011100609209100002DEST_PATH_IMAGE013
, parameter wherein
Figure 859303DEST_PATH_IMAGE014
Control function rises to 1 speed from 0;
(5) the inside and outside average gray value of computed segmentation curve c 1With c 2:
Figure 2011100609209100002DEST_PATH_IMAGE015
，
Figure 615906DEST_PATH_IMAGE016
(6) calculating parameter
Figure 2011100609209100002DEST_PATH_IMAGE017
Derivative , the relaxation factor in the traversal image calculation grid Boltzmann EVOLUTION EQUATION
Figure 375100DEST_PATH_IMAGE006
(7) establish nBe iterations, according to two-dimensional lattice Boltzmann model modification balanced distribution function be
Figure 396408DEST_PATH_IMAGE018
(8) transition process of calculating two-dimensional lattice Boltzmann model:
Figure 2011100609209100002DEST_PATH_IMAGE019
(9) mechanism of calculating two-dimensional lattice Boltzmann model:
Figure 945201DEST_PATH_IMAGE020
Wherein
Figure 95560DEST_PATH_IMAGE009
Be constant;
(10) upgrade particle distribution function
Figure 2011100609209100002DEST_PATH_IMAGE021
Obtain embedding the distanceization function
Figure 424910DEST_PATH_IMAGE022
, get its zero level collection and be the new curve of cutting apart;
(11) judge whether to reach iterations N, if reach NWhen inferior, then output uZero level assemble fruit and be segmentation contour; If do not reach NInferior, then change step (4), repeating step (4)-(10) are up to reaching iteration NZero level after output is handled behind the number of times is assembled fruit, is last segmentation result.
According to diffusion vector discrete in the two-dimensional lattice Boltzmann model
Figure 623810DEST_PATH_IMAGE004
Direction number qDifference, can be divided into D2Q5 and D2Q9 two classes to two-dimensional lattice Boltzmann model.
When the two-dimensional lattice Boltzmann's model in the above-mentioned steps (2) is the D2Q5 model, the initial balance state function
Figure 27110DEST_PATH_IMAGE011
For:
Figure 2011100609209100002DEST_PATH_IMAGE023
The relaxation factor of being correlated with in the above-mentioned steps (6)
Figure 348370DEST_PATH_IMAGE006
For:
Wherein
Figure DEST_PATH_IMAGE025
Be parameter of curve, determine the smoothness of evolution curve.
New distribution function more in the above-mentioned steps (7)
Figure 403493DEST_PATH_IMAGE018
For:
Figure 989195DEST_PATH_IMAGE026
， n=1,2…, N
When two-dimensional lattice Boltzmann model is the D2Q9 model in the above-mentioned steps (2), the initial balance state function
Figure 419039DEST_PATH_IMAGE011
For:
Figure DEST_PATH_IMAGE027
The relaxation factor of being correlated with in the above-mentioned steps (6)
Figure 457402DEST_PATH_IMAGE006
For:
Figure 998105DEST_PATH_IMAGE028
Wherein
Figure 703893DEST_PATH_IMAGE025
Be parameter of curve, determine the smoothness of evolution curve.
New distribution function more in the above-mentioned steps (7)
Figure 39059DEST_PATH_IMAGE018
For:
Figure DEST_PATH_IMAGE029
， n=1,2…, N
The present invention compared with prior art, have following apparent outstanding substantive distinguishing features and remarkable advantage: above-mentioned image partition method based on grid Boltzmann model can not only be realized cutting apart automatically of image, obtain high-quality image segmentation effect, and guaranteeing to carry out the computing of big step-length under the stable situation of algorithm, thereby improve the efficient of calculating effectively.Being particularly useful for image handles in real time.
Description of drawings
Fig. 1 is two-dimensional lattice Boltzmann's model structure synoptic diagram that the computational grid by discretize constitutes.
Fig. 2 is based on the grid Boltzmann model structure synoptic diagram of D2Q5 among Fig. 1.
Fig. 3 is based on the grid Boltzmann model structure synoptic diagram of D2Q9 among Fig. 1.
Fig. 4 is the process flow diagram of the image partition method based on grid Boltzmann model of the present invention.
Fig. 5 is the former figure of gray level image to be split.
Fig. 6 is the initial curve figure of image local being cut apart setting.
Fig. 7 is based on the image segmentation effect figure of the grid Boltzmann model of D2Q5.
Fig. 8 is the initial curve figure of image overall being cut apart setting.
Fig. 9 is based on the image segmentation effect figure of the grid Boltzmann model of D2Q5.
Embodiment
Embodiment to the image partition method based on grid Boltzmann model of the present invention elaborates below: present embodiment is to implement under the prerequisite with technical scheme of the present invention; provided detailed embodiment, but protection scope of the present invention is not limited to following embodiment.
Embodiments of the invention are described with reference to the accompanying drawings as follows:
Shown in Fig. 1,2 and 3, set up two-dimensional lattice Boltzmann model, it is made of the computing grid of discretize, and the node of each grid is equivalent to a cellular, and its value is by the distribution function of particle
Figure 325903DEST_PATH_IMAGE001
With the diffusion vector
Figure 404718DEST_PATH_IMAGE002
Determine.Each renewal (iteration) of nodal value can be divided into two stages: migration phase and effect stage.Migration phase is transmitted particle by the field node to Centroid, and the effect stage then determines the quantity transmitted.Use grid Boltzmann model to handle M* NDigital picture the time, each pixel and computing node can be mapped naturally, the gray-scale value of pixel is the population on the corresponding node then.Each pixel of node among Fig. 1 (round dot) representative image, arrow has shown migration and the action direction of model.
According to discrete diffusion vector
Figure 965012DEST_PATH_IMAGE004
Direction number qDifference, can be two-dimensional lattice Boltzmann D nQ q( nDimension qDirection) be divided into two classes:
The D2Q5 model, as shown in Figure 2, it has 5 discrete speed:
Figure 471080DEST_PATH_IMAGE030
The D2Q9 model, as shown in Figure 3, it has 9 discrete speed:
Figure DEST_PATH_IMAGE031
Based on the flow process of the image partition method of grid Boltzmann model as shown in Figure 4, the method that the present invention proposes embeds the Heaveside function derivative of image in the relaxation factor of grid Boltzmann EVOLUTION EQUATION, has found grid Boltzmann EVOLUTION EQUATION and macroscopical corresponding relation to find the solution nonlinear diffusion equations and has cut apart to realize image.
Embodiment 1: image local is cut apart
The segmentation effect of gray level image is shown in Fig. 5,6 and 7, and Fig. 5 is head mri image to be split, and size is 388 * 388; Fig. 6 is for cutting apart the initial curve figure of setting to image, wherein white marking is initial circular curve; Fig. 7 is the image segmentation effect figure based on the grid Boltzmann model of D2Q5.
Be example with the dividing method based on D2Q5 grid Boltzmann model, its step is as follows:
(1) input initial pictures
Figure 811931DEST_PATH_IMAGE010
, the value of node is made as the gray-scale value of respective pixel;
(2) use two-dimensional lattice Boltzmann model, the initial balance state function of each action direction in the grid Boltzmann EVOLUTION EQUATION is set
Figure 694437DEST_PATH_IMAGE011
:
Figure 610702DEST_PATH_IMAGE023
(3) determine iterations NBe 80, and initial curve C is set is:
Figure 553250DEST_PATH_IMAGE032
(4) calculate the Heavside function
Figure 53502DEST_PATH_IMAGE013
, parameter wherein
Figure 474119DEST_PATH_IMAGE014
=1.0;
(5) the inside and outside average gray value c of computed segmentation curve 1And c 2:
Figure 9005DEST_PATH_IMAGE015
，
(6) calculating parameter
Figure 844423DEST_PATH_IMAGE017
Derivative
Figure 68731DEST_PATH_IMAGE008
, the traversal image calculation is based on the relaxation factor in the grid Boltzmann EVOLUTION EQUATION of D2Q5
Figure 395807DEST_PATH_IMAGE024
, wherein
Figure 243940DEST_PATH_IMAGE025
=3;
(7) establish nBe iterations, according to two-dimensional lattice Boltzmann model modification balanced distribution function be
Figure 656467DEST_PATH_IMAGE018
(8) transition process of calculating two-dimensional lattice Boltzmann model:
Figure 481203DEST_PATH_IMAGE019
(9) mechanism of calculating two-dimensional lattice Boltzmann model:
Figure DEST_PATH_IMAGE033
Wherein
Figure 725103DEST_PATH_IMAGE009
=0.004;
(10) upgrade particle distribution function
Figure 180355DEST_PATH_IMAGE021
Obtain embedding the distanceization function , get its zero level collection and be the new curve of cutting apart;
(11) judge whether to reach iterations 80, if when reaching 80 times, then output uZero level assemble fruit and be segmentation contour; If do not reach NInferior, then change step (4), fruit is assembled up to the zero level that reaches after 80 number back output of iteration is handled in repeating step (4)-(10), is last segmentation result such as Fig. 7.At HP notebook (AMD Turion 64,2.01GHz CPU, 2G RAM), running environment is 5.98s for working time on the MATLAB 2008a.
Embodiment 2: image overall is cut apart
The initial curve figure of cutting apart setting as Fig. 8 for head mri image to be split; Fig. 9 is the image segmentation effect figure based on the grid Boltzmann model of D2Q5.Be example with the dividing method based on D2Q5 grid Boltzmann model, its step is identical with embodiment one, and wherein the parameter setting changes to some extent: the initial curve of setting as shown in Figure 8; Iterations NIt is 4 times.Last segmentation effect such as Fig. 9, be 1.28s working time.
Experiment shows, based on the image partition method of grid Boltzmann model, by different initial curves is set, can carries out target effectively and cut apart.For global segmentation, can cut apart fast automatically, segmentation result is good.

Claims (7)

1. image partition method based on grid Boltzmann model is characterized in that operation steps is as follows:
(1). the input initial pictures
Figure 2011100609209100001DEST_PATH_IMAGE001
, the value of node is made as the gray-scale value of respective pixel;
(2) use two-dimensional lattice Boltzmann model, the initial balance state function of each action direction in the grid Boltzmann EVOLUTION EQUATION is set
Figure 615323DEST_PATH_IMAGE002
(3) determine the iterations of grid Boltzmann EVOLUTION EQUATION NAdopt the variation level diversity method, introduce the Heaviside function, the initialization distance function
Figure 2011100609209100001DEST_PATH_IMAGE003
As initial curve C;
(4) calculate the Heavside function
Figure 346518DEST_PATH_IMAGE004
, parameter wherein Control function rises to 1 speed from 0;
(5) the inside and outside average gray value of computed segmentation curve c 1With c 2:
Figure 903664DEST_PATH_IMAGE006
，
Figure 2011100609209100001DEST_PATH_IMAGE007
(6) calculating parameter
Figure 844944DEST_PATH_IMAGE008
Derivative
Figure 2011100609209100001DEST_PATH_IMAGE009
, the relaxation factor in the traversal image calculation grid Boltzmann EVOLUTION EQUATION
Figure 145737DEST_PATH_IMAGE010
(7) establish nBe iterations, according to two-dimensional lattice Boltzmann model modification balance function be
Figure 2011100609209100001DEST_PATH_IMAGE011
(8) transition process of calculating two-dimensional lattice Boltzmann model: , wherein
Figure 417425DEST_PATH_IMAGE004
Be speed,
Figure 684458DEST_PATH_IMAGE006
Be positioned at the x place for iterations during for n and have speed
Figure 883358DEST_PATH_IMAGE008
The particle density distribution function, Be direction number;
(9) mechanism of calculating two-dimensional lattice Boltzmann model:
Figure 483284DEST_PATH_IMAGE012
Wherein
Figure 161284DEST_PATH_IMAGE014
Be constant;
(10) upgrade particle distribution function
Figure 175297DEST_PATH_IMAGE014
Obtain distance function
Figure 912308DEST_PATH_IMAGE016
, get its zero level collection and be the new curve of cutting apart;
(11) judge whether to reach iterations N, if reach NWhen inferior, then output uZero level is assembled fruit and is segmentation contour; If do not reach NInferior, then change step (4), repeating step (4)-(10) are up to reaching iteration NZero level after output is handled behind the number of times is assembled fruit, is last segmentation result.
2. the image partition method based on grid Boltzmann model according to claim 1 is characterized in that:
When the two-dimensional lattice Boltzmann's model in the above-mentioned steps (2) is the D2Q5 model, the initial balance state function
Figure 802667DEST_PATH_IMAGE002
For:
Figure DEST_PATH_IMAGE017
。
3. the image partition method based on grid Boltzmann model according to claim 1 is characterized in that:
When two-dimensional lattice Boltzmann model is the D2Q9 model in the above-mentioned steps (2), the initial balance state function
Figure 446138DEST_PATH_IMAGE002
For:
Figure 339226DEST_PATH_IMAGE018
。
4. the image partition method based on grid Boltzmann model according to claim 1 is characterized in that:
When the two-dimensional lattice Boltzmann's model in the above-mentioned steps (6) is the D2Q5 model, relevant relaxation factor
Figure 68148DEST_PATH_IMAGE010
For:
Figure DEST_PATH_IMAGE019
，
Wherein
Figure 209279DEST_PATH_IMAGE020
Be parameter of curve, determine the smoothness of evolution curve.
5. the image partition method based on grid Boltzmann model according to claim 1 is characterized in that:
When two-dimensional lattice Boltzmann model is the D2Q9 model in the above-mentioned steps (6), relevant relaxation factor For:
Figure DEST_PATH_IMAGE021
，
Wherein
Figure 541221DEST_PATH_IMAGE020
Be parameter of curve, determine the smoothness of evolution curve.
6. the image partition method based on grid Boltzmann model according to claim 1 is characterized in that:
When the two-dimensional lattice Boltzmann's model in the above-mentioned steps (9) is the D2Q5 model, upgrade the equilibrium state function For:
Figure 436681DEST_PATH_IMAGE022
， n=1,2…, N?。
7. the image partition method based on grid Boltzmann model according to claim 1 is characterized in that:
When two-dimensional lattice Boltzmann model is the D2Q9 model in the above-mentioned steps (9), upgrade the equilibrium state function
Figure 789165DEST_PATH_IMAGE011
For:
Figure DEST_PATH_IMAGE023
， n=1,2…, N?。
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CN103337097A (en) * 2013-07-02 2013-10-02 上海大学 Multiple Cartesian grid generation method applicable to LBM)
CN104867110A (en) * 2014-12-08 2015-08-26 上海大学 Lattice Boltzmann model-based video image defect repairing method
CN105241911B (en) * 2015-09-23 2017-07-21 中国石油大学(北京) The method and device that low-field nuclear magnetic resonance analyzes fluid is simulated based on LBM
CN106404730B (en) * 2016-08-30 2019-10-11 上海大学 The description method that light based on Lattice Boltzmann method model is propagated in the medium
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