CN106201995B - A kind of image boundary member processing method - Google Patents
A kind of image boundary member processing method Download PDFInfo
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- CN106201995B CN106201995B CN201610526189.7A CN201610526189A CN106201995B CN 106201995 B CN106201995 B CN 106201995B CN 201610526189 A CN201610526189 A CN 201610526189A CN 106201995 B CN106201995 B CN 106201995B
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/17—Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method
- G06F17/175—Function evaluation by approximation methods, e.g. inter- or extrapolation, smoothing, least mean square method of multidimensional data
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
- G06T17/30—Polynomial surface description
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2210/00—Indexing scheme for image generation or computer graphics
- G06T2210/56—Particle system, point based geometry or rendering
Abstract
The invention discloses a kind of image boundary member processing methods, include the following steps, S01: converting multidimensional image to from physical space and calculate space；The following steps are included: S011 in step S01: differentiating that multidimensional image whether there is singularity boundary, and if it exists, then enter step S012；If it does not exist, then S013 is entered step；S012: singularity boundary is eliminated using smooth particle, enters step S013；S013: carrying out mesh generation for multidimensional image, is converted to and calculates space；S02: divided net boundary is solved using boundary integral equation；S03: acceleration convergence is carried out to net boundary using extrapolation；S04: the fields inside and external field of net boundary are constructed.The present invention utilizes smooth particle hydrodynamic, and the physical space of image is converted to and calculates space, and the calculating space converted is suitable for extrapolation to increase computational accuracy, and reduces grid and handle quantity.
Description
Technical field
The present invention relates to image boundary process field, especially a kind of image boundary member processing method.
Background technique
Smoothed Particle Hydrodynamics Method is a kind of Lagrangian mesh free particle method.It carries out physical problem using kernel function approximate
Processing, described with discrete particle macroscopic view it is continuously distributed it is microcosmic be still particle fluid, and each particle then carries its institute
In the various properties of the fluid of position, such as quality, density, speed, energy.Smoothed Particle Hydrodynamics Method by Lucy (1977) and
Gingold&Monaghan (1977) is proposed independently of each other, for handling astrophysics problem.Later, Smoothed Particle Hydrodynamics Method extends
It is applied to the fields such as aerodynamics, incompressible, explosion, Solid Mechanics and elastomer.
It often will appear singularity boundary in image, in the processing on singularity boundary, there are many processing for conventional method at present
Mode, for example use multipole Element BEM.However, will increase a large amount of auxiliary when using multistage Element BEM and calculate, and
And extrapolation is not available to improve accuracy.Meanwhile the matrix that multistage Element BEM generates, conditional number is very big,
It can be led to the problem of in matrix inversion new.Also, on processing Singular Boundary Value Problems, especially the problems such as handling most difficult crack
On, precision is not high, and consumes very much machine time.
Summary of the invention
In view of the above-mentioned problems, using smooth particle hydrodynamic, will scheme the present invention provides a kind of image boundary member processing method
The physical space of picture, which is converted to, calculates space, and the calculating space converted is suitable for extrapolation to increase computational accuracy, and reduces
Grid handles quantity.
The technical scheme is that a kind of image boundary member processing method, includes the following steps,
S01: it converts multidimensional image to from physical space and calculates space；
In step S01 the following steps are included:
S011: differentiate that multidimensional image whether there is singularity boundary, and if it exists, then enter step S012；If it does not exist, then into
Enter step S013；
S012: singularity boundary is eliminated using smooth particle, enters step S013；
S013: carrying out mesh generation for multidimensional image, is converted to and calculates space；
S02: divided net boundary is solved using boundary integral equation；
S03: acceleration convergence is carried out to net boundary using extrapolation；
S04: the fields inside and external field of net boundary are constructed.
Further, in the step S02 the following steps are included:
S021: in calculating space, it is discrete that integral equation is carried out to the net boundary divided；
S022: judge whether it is singularity boundary, if so, entering step S023；If it is not, then entering step S024；
S023: it is converted using smooth particle, reconfigures integral equation discrete form；
S024: calculating solution is carried out to discrete integral equation.
Further, in the step S03 the following steps are included:
S031: any one grid of subdivision sets the subdivision characteristic parameter under different low precision；
S032: the solution of net boundary corresponding to subdivision characteristic parameter different under low precision is found out；
S033: by the solution of the net boundary under low precision, the solution of the net boundary under higher precision is extrapolated.
Further, in the step S031, the subdivision characteristic parameter include h,In the step S032, no
The solution of net boundary corresponding to same subdivision characteristic parameter are as follows: S1, S2；Ginseng in the step S033, under higher precision
Amount includesWherein, a > 1.
Further, in the step S012 the following steps are included:
S0121: the function class of the smooth particle transformation of Selection utilization, this class function meet: in singular point, functional value 0；In surprise
Near point, functional value is intended to 0；And derivative is non-zero.
Further, in the step S0121, the function class using the transformation of smooth particle is sim function class, double power letters
One kind in several classes of.
Further, in the step S013 the following steps are included:
S0131: when directly converting calculating space from physical space for the multidimensional image on no singularity boundary, physics is empty
Between with calculate space it is consistent；
S0132: when will there is the multidimensional image on singularity boundary to be converted into calculating space from physical space, physical space and meter
It is inconsistent to calculate space.
The invention has the advantages that image boundary member processing method of the invention, has used special smooth particle processing side
Method and can not increase and calculate with the processing as common boundary so that when the problem of handling the strong singularity such as crack
Amount；And in post-processing, suitable for extrapolation to increase computational accuracy, and reduces grid and handle quantity；Processing can be reduced
It is consumed when the machines such as crack, while precision can be improved, improved efficiency of research and development, reduce cost.
Detailed description of the invention
The invention will be further described with reference to the accompanying drawings and examples.
Fig. 1 is the step flow chart of the image boundary member processing method of inventive embodiments.
Fig. 2 is the listed representative singularity angle point schematic diagram of inventive embodiments.
Specific embodiment
Embodiment: as shown in Figure 1, a kind of image boundary member processing method, includes the following steps.
S01: it converts multidimensional image to from physical space and calculates space.
Specifically, including the following steps in step S01.
S011: differentiate that multidimensional image whether there is singularity boundary, and if it exists, then enter step S012；If it does not exist, then into
Enter step S013.
S012: singularity boundary is eliminated using smooth particle, enters step S013.
Further, include the following steps in the step S012.
S0121: the function class of the smooth particle transformation of Selection utilization, this class function meet: in singular point, functional value 0；In surprise
Near point, functional value is intended to 0；And derivative is non-zero.
Further, in the step S0121, the function class using the transformation of smooth particle is sim function class, double power letters
One kind in several classes of.
S013: carrying out mesh generation for multidimensional image, is converted to and calculates space.
Further, include the following steps in the step S013.
S0131: when directly converting calculating space from physical space for the multidimensional image on no singularity boundary, physics is empty
Between with calculate space it is consistent.
S0132: when will there is the multidimensional image on singularity boundary to be converted into calculating space from physical space, physical space and meter
It is inconsistent to calculate space.
It is mainly after boundary model establishes completion, to do primary differentiation for CAD image in industry mapping personnel, differentiating should
Whether model has very strong singularity (being exactly to have some angle points as shown in Figure 2).
Fig. 2 lists the singularity angle point of Three Represents, and in Fig. 2, (a) indicates angle of the angle less than 30 °；(b) phase is indicated
The angle cut；(c) it indicates crack, is just entirely the boundary at 0 ° of angle.Firstly, to judge the singularity angle point of such two and three dimensions is
No presence.If it does not exist, then we will convert without smooth particle, and mesh generation is directly carried out, directly generates calculating
Space lattice (in the case of this, physical space is consistent with space is calculated).If it is present being converted using smooth particle, by object
Reason space is converted into calculating space, and grid is redistributed in calculating space, generates and calculates space lattice.
When being converted using smooth particle, selection designs a kind of smooth particle function class (sim function class, double power letters first
It is several classes of etc.), this class function meets, and is equal to 0 in singular point functional value, is oriented in 0 near its singularity functional value, but derivative is non-zero, institute
To be canonical as transformation.Original physical space is transformed in new parameter space, is exactly using the contact transformation
The calculating space that we say.Our available calculating spaces under new parameter in this way.
S02: divided net boundary is solved using boundary integral equation.
Further, include the following steps in the step S02.
S021: in calculating space, it is discrete that integral equation is carried out to the net boundary divided.
S022: judge whether it is singularity boundary, if so, entering step S023；If it is not, then entering step S024.
S023: it is converted using smooth particle, reconfigures integral equation discrete form.
S024: calculating solution is carried out to discrete integral equation.
S03: acceleration convergence is carried out to net boundary using extrapolation.
In traditional boundary element processing, the problem of for no singularity, extrapolation convergence can be used, but due to above-mentioned
The appearance for the singularity mentioned, so that extrapolation is not available, the reason is that obtained solution is unable to get Taylor in physical space
Expansion.And since we used smooth particles, the calculating of physical space is converted to the conversion for calculating space, is calculating space
It is interior, it can be unfolded to obtain approximate rank by taylor, extrapolation is carried out.
Such as.
S031: any one grid of subdivision sets the subdivision characteristic parameter under different low precision, and subdivision characteristic parameter includes
h、
S032: finding out the solution of net boundary corresponding to subdivision characteristic parameter different under low precision, solution be respectively as follows: S1,
S2。
S033: by the solution of the net boundary under low precision, the solution of the net boundary under higher precision is extrapolated.It is more high-precision
Degree under parameter includeWherein, a > 1.Solve obtained in utilizing: S1 and S2 obtains extrapolated value.Usual level-one extrapolation,
Using h and h/2 grid, the computational accuracy of the grid search-engine of available h/4.
S04: the fields inside and external field of net boundary are constructed.
It should be pointed out that can also have the embodiment of a variety of transformation and remodeling for the present invention through absolutely proving,
It is not limited to the specific embodiment of above embodiment.Above-described embodiment as just explanation of the invention, rather than to this
The limitation of invention.In short, protection scope of the present invention should include that those are apparent to those skilled in the art
Transformation or substitution and remodeling.
Claims (6)
1. a kind of image boundary member processing method, which is characterized in that include the following steps,
S01: it converts multidimensional image to from physical space and calculates space；
In step S01 the following steps are included:
S011: differentiate that multidimensional image whether there is singularity boundary, and if it exists, then enter step S012；If it does not exist, then enter step
Rapid S013；
S012: singularity boundary is eliminated using smooth particle, enters step S013；
S013: carrying out mesh generation for multidimensional image, is converted to and calculates space；
S02: divided net boundary is solved using boundary integral equation；
S03: acceleration convergence is carried out to net boundary using extrapolation；
In the step S03 the following steps are included:
S031: any one grid of subdivision sets the subdivision characteristic parameter under different low precision；
S032: the solution of net boundary corresponding to subdivision characteristic parameter different under low precision is found out；
S033: by the solution of the net boundary under low precision, the solution of the net boundary under higher precision is extrapolated；
S04: the fields inside and external field of net boundary are constructed.
2. image boundary member processing method according to claim 1, which is characterized in that in the step S02 include with
Lower step:
S021: in calculating space, it is discrete that integral equation is carried out to the net boundary divided；
S022: judge whether it is singularity boundary, if so, entering step S023；If it is not, then entering step S024；
S023: it is converted using smooth particle, reconfigures integral equation discrete form；
S024: calculating solution is carried out to discrete integral equation.
3. image boundary member processing method according to claim 1, which is characterized in that described in the step S031
Subdivision characteristic parameter include h,In the step S032, the solution of net boundary corresponding to different subdivision characteristic parameters
Are as follows: S1, S2；In the step S033, the parameter under higher precision includesWherein, a > 1.
4. image boundary member processing method according to claim 1, which is characterized in that include following in the step S012
Step:
S0121: the function class of the smooth particle transformation of Selection utilization, this class function meet: in singular point, functional value 0；It is attached in singular point
Closely, functional value is intended to 0；And derivative is non-zero.
5. image boundary member processing method according to claim 4, which is characterized in that in the step S0121, utilize
The function class of smooth particle transformation is sim function class, one kind in double power function classes.
6. image boundary member processing method according to claim 4, which is characterized in that in the step S013 include with
Lower step:
S0131: by the multidimensional image on no singularity boundary directly from physical space be converted into calculate space when, physical space with
It is consistent to calculate space；
S0132: when will have the multidimensional image on singularity boundary to be converted into calculating space from physical space, physical space and calculating are empty
Between it is inconsistent.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102609988A (en) * | 2012-01-18 | 2012-07-25 | 浙江大学 | Method for extracting fluid surface based on anisotropic screen-space smoothed particle hydrodynamics |
| CN104268322A (en) * | 2014-06-27 | 2015-01-07 | 北京航空航天大学 | Boundary processing technology of WENO difference method |
| CN104574503A (en) * | 2014-12-25 | 2015-04-29 | 中国科学院深圳先进技术研究院 | Method and device for simulating diffusion process of contrast agent |
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| GB0305315D0 (en) * | 2003-03-07 | 2003-04-09 | Weber Martin | Image processing system |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102609988A (en) * | 2012-01-18 | 2012-07-25 | 浙江大学 | Method for extracting fluid surface based on anisotropic screen-space smoothed particle hydrodynamics |
| CN104268322A (en) * | 2014-06-27 | 2015-01-07 | 北京航空航天大学 | Boundary processing technology of WENO difference method |
| CN104574503A (en) * | 2014-12-25 | 2015-04-29 | 中国科学院深圳先进技术研究院 | Method and device for simulating diffusion process of contrast agent |
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