CN110335275A - A kind of space-time vectorization method of the flow surface based on ternary biharmonic B-spline - Google Patents
A kind of space-time vectorization method of the flow surface based on ternary biharmonic B-spline Download PDFInfo
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Abstract
The present invention provides a kind of space-time vectorization method of flow surface based on ternary biharmonic B-spline, comprising: the streaming video height field reduction based on SFS；Fluid velocity field reduction based on shallow water equation；Data fitting based on ternary biharmonic B-spline；The three dimensional fluid indicated based on particle is reappeared.The present invention only needs to use monocular streaming video as input, automatically analyze the geometry and velocity information of fluid in video, and utilize ternary biharmonic B-spline, realize the serialization of flow surface geometry and speed on time and Spatial Dimension, using serialization result, it can be achieved that flow surface is restored in the super-resolution of time and Spatial Dimension；In addition, a possibility that streaming video is reduced to three dimensional fluid the present invention is based on the emulation again that particle realizes fluid, further demonstrates the physical simulation for realizing the driving of video fluid motion feature.
Description
Technical field
The present invention relates to computer vision, computer computational geometry, fluid emulation technical fields.
Background technique
In recent years, with the fast development of field of virtual reality, to complex object in natural environment and large scale scene
Emulation demand increasingly increases.In many natural scenes, fluid and class fluid behavior are generally existing one of phenomenons, such as sea
The large scale scenes such as wave, river, waterfall, flood, floating clouds, haze, smog, fire and dewdrop, water droplet, bubble, boiling water, greasy dirt,
The small-scale scene such as watercolor, oil painting, burning, blood flow has fluid or class fluid to participate in, and shows gorgeous changeable vision effect
Fruit.Therefore, to the modeling and simulation of fluid and class fluid behavior, the concern of a large amount of outstanding researchers has been obtained, void is increasingly becoming
One of the emphasis direction of quasi- field of reality research.
In addition, as fluid emulation technology is in production of film and TV, 3D game making, natural phenomena displaying, medical surgery teaching
The extensive use of (interaction, the phenomenon of bleeding etc. of simulation blood blood vessel) etc., it is contemplated that the computing capability and scene of computer
Modeling and cost of manufacture limitation, how as far as possible guarantee fluid physics rule correctness under the premise of improve simulation efficiency,
The technical issues of how guaranteeing the whole high visual vivid degree in details of fluid scene, becoming urgent need to resolve, also and then promotes
The development of fluid emulation technology.
In computer industry, both direction, computational fluid dynamics are broadly divided into the research of fluid emulation technology
(Computer Fluid Dynamics, CFD) and graphics fluid emulation (Fluid Animation).Wherein, fluid is calculated
Dynamics, in a manner of scientific and precise, the physics law of Study of Fluid movement carries out accurate numerical solution, main purpose,
It is the fluid modeling and model solution solved the problems, such as under the pinpoint accuracy simulation requirements environment such as industry fluid associated scenario.Its
Afterwards, with the promotion of the progress of computer graphics techniques and computer generated image effect, to pursue simulated effect visual vivid degree
For the purpose of graphics fluid emulation enter Rapid development stage.It 1996, is realized for the first time based on Navier-Stokes equation
Graphics fluid emulation, it is this that accurate hydrodynamic equations not asked to solve, but can guarantee that visual vivid is imitated again simultaneously
The fluid simulation method of fruit has catered to the development need of the show businesses such as video display, game making, and meets medical domain religion simultaneously
Learn emulation demand.
Although having possessed more than 20 years developing histories, fluid emulation is still a challenging computer graphic
Shape knowledge topic, this is as caused by the complexity of fluid phenomenon.Basic emulation mode, although can be to better simply natural phenomena
It is preferably emulated, but for the accurate simulation of complexity natural phenomena present in nature and extensive fluid scene, it is existing
The method of depositing can't carry out accurate description.Simple physical modeling is difficult to meet emulation demand, and therefore, a large amount of scholars drive data
Dynamic method has been introduced into fluid emulation technology, it is desirable to the progress of the motion state driving fluid emulation of real fluid.But
Since fluid does not have fixed geometry, the acquisition and analysis of fluid data, and become difficulty new in data-driven thinking
Point.
For the wilderness demand of scientific research and casino market, fluid modeling and emulation mode for high-accuracy high-efficiency rate are ground
Study carefully and be of great significance and be worth, research achievement will be used widely in real life.
Summary of the invention
In order to overcome the above-mentioned deficiencies of the prior art, the present invention is based on the flow surface of ternary biharmonic B-spline when
Blank vector method, this method extract the elevation information and velocity information of fluid by the analysis to streaming video, and by poly-
The methods of class, data fitting, sort out fluid information and are simplified, and as driving, realize the emulation of new fluid scene.
To complete goal of the invention, the technical solution adopted by the present invention is that: a kind of fluid based on ternary biharmonic B-spline
The space-time vectorization method on surface, the specific steps of which are as follows:
A kind of space-time vectorization method of the flow surface based on ternary biharmonic B-spline comprising the steps of:
(1) the streaming video height field reduction based on SFS: Shape From Shading method reconstitution fluid surface is utilized
Height field in an iterative process denoises height field using Gaussian Filter and Guided Filter, carries out
Retain the smooth optimization on boundary, restores flow surface geometry；
(2) based on shallow water equation fluid velocity field reduction: using shallow water equation and smooth item establish fluid level field and
The associated optimization method of velocity field solves the optimization, obtains the velocity field of flow surface in the horizontal plane；
(3) the data fitting based on ternary biharmonic B-spline: by the height field information and velocity field information of flow surface
It is regarded as three-dimensional data, carries out super voxel segmentation, Knot point is chosen using segmentation result, constructs ternary biharmonic B-spline base
Bottom carries out vectorization to flow surface information, realizes the mapping of space-time discrete data to continuous data；
(4) three dimensional fluid indicated based on particle is reappeared: being indicated the basic unit of fluid using particle, is utilized serialization knot
Fruit constructs three dimensional fluid, reappears the movement of fluid.
Further, in step (1), using Shape From Shading method, based on to image radiation equation
Iterative fitting is iterated analysis to the height field of each frame of streaming video, uses Gaussian Filter and Guided
The method that Filter is combined is filtered denoising to the height field that analysis obtains, removal is analyzed in result in each iteration step
Noise spot and exceptional value.
Further, in step (2), using shallow water equation as basic physical model, analysis obtains fluid level field and speed
The descriptive equation for spending field relationship adds the smooth item of Weight based on the equation, and building minimizes objective function, solves
The Euler-Lagrange equation of objective function, using iterative solution method, the minimum of function to achieve the objective uses step
(1) the flow surface elevation information that analysis obtains in, can obtain the two-dimension speed field information of flow surface.
It further, is x, y with the transverse and longitudinal coordinate of video frame by the velocity field visualization of information of fluid in step (3)
Axis carries out super voxel segmentation to the volume data, and calculate velocity vector in super voxel using the time as the three-dimensional data of z-axis
Average vector, and super voxel center is moved into coordinate origin, it calculates and obtains several groups of ternary biharmonic B-spline bases, to each
Speed data in a super voxel is fitted, and obtains fitting coefficient Vector Groups, realizes the vectorization to flow surface information.
Further, in step (4), the basic unit of fluid is indicated using particle.
Further, the Guided Filter in step (1), for the purpose of denoising and establish better iteration basis
It is used in former step iterative process, the Gaussian Filter for the purpose of denoising and is smooth is in rear a few step iterative process
It uses, the access times of Guided Filter and Gaussian Filter can be determined by user.
Compared with prior art, the advantages and positive effects of the present invention are:
1, the present invention divides the fluid level field in monocular streaming video by Shape From Shading method
Analysis, and give Gaussian Filter and Guided filter and the extraction process of height field is optimized.Meanwhile the present invention
The algorithm optimization based on CUDA is realized, realizes the real-time analysis to video fluid height field using GPU.
2, the present invention realizes the fluid meter based on fluid level field by shallow water equation and Euler-Lagrange equation
Face velocity field analysis realizes comprehensive description to flow surface movement；
3, the present invention passes through the discrete sampling by the fluid motion information based on video acquisition depending on doing fluid Evolution process, benefit
The discrete data is fitted with ternary biharmonic B-spline, fluid motion is realized and develops in the serialization in space-time direction
It indicates.
4, the present invention is based on fluid vectorization as a result, realizing the reuse to data, and it is corresponding to construct streaming video
Three dimensional fluid scene.
Detailed description of the invention
Fig. 1 is space-time vectorization method the method stream the present invention is based on the flow surface of ternary biharmonic B-spline
Cheng Tu；
Fig. 2 is the streaming video height field reduction result figure of based on SFS and not homogeneous filter denoising of the invention；
Fig. 3 is the streaming video height field reduction process of the invention based on SFS and the fluid velocity based on shallow water equation
The time statistical chart of different the number of iterations in the reduction process of field；
Fig. 4 is the data fitting result schematic diagram of the invention based on ternary biharmonic B-spline；
Fig. 5 is that the particle of the three dimensional fluid replay method of the invention indicated based on particle initializes schematic diagram；
Fig. 6 is the data fitting front and back of the invention based on ternary biharmonic B-spline, the time-derivative between consecutive frame
Schematic diagram；
Fig. 7 is the super voxelization result of space-time of the data fitting of the invention based on ternary biharmonic B-spline；
Fig. 8 is the super voxelization result in space of the data fitting of the invention based on ternary biharmonic B-spline；
Fig. 9 is that the three dimensional fluid of the invention indicated based on particle reappears rendering result (small ripple scene)；
Figure 10 is that the three dimensional fluid of the invention indicated based on particle reappears rendering result (wave scene).
Specific embodiment
The present invention provides a kind of space-time vectorization method of flow surface based on ternary biharmonic B-spline, comprising: defeated
Enter fluid sample video, reconstitution fluid apparent height field restores fluid geometry；It is right using diving equation and smoothness constraint
The surface velocity field of fluid is fitted；By the geometry and velocity information of flow surface, it is regarded as the volume data of space-time three-dimensional, is used
Ternary biharmonic B-spline is fitted the geometry and speed data of fluid as space-time substrate respectively, realizes discrete space to continuously
The mapping in space；Based on space and time continuous as a result, basic unit using particle as fluid, carries out weight to the movement of fluid
It is existing, and extract flow surface and rendered, obtain the fluid emulation result of fluid motion mode in similar input video.
Below with reference to specific method step, the principle of the invention is introduced.
Step 1: it the streaming video height field reduction based on SFS: is regarded by fluid of the ocean video in DynTex database
Frequency source, using Shape From Shading method, based on the iterative fitting to image radiation equation, to the every of streaming video
The height field of one frame is iterated analysis.The method combined using Gaussian Filter and Guided Filter, each
In iteration step, denoising is filtered to the height field that analysis obtains, noise spot and exceptional value in removal analysis result.Wherein,
Fluid level field analysis based on Shape From Shading is realized by iteration, to denoise and establish better iteration
Guided Filter for the purpose of basis is used in former step iterative process, the Gaussian for the purpose of denoising and is smooth
Filter is used in rear a few step iterative process, the access times of Guided Filter and Gaussian Filter can by with
Family determines.
Step 2: the fluid velocity field reduction based on shallow water equation: using shallow water equation as basic physical model, analysis is obtained
The descriptive equation of fluid level field and velocity field relationship adds the smooth item of Weight based on the equation, and building minimizes
Objective function solves the Euler-Lagrange equation (Euler-Lagrangian Equation) of objective function, uses iteration
Method for solving, the minimum of function to achieve the objective obtain the two-dimension speed field information of flow surface.Wherein, " shallow water equation " is
The two-dimentional approximate form of the three dimensional N-S equation of fluid motion is described, Euler-Lagrange equation is the classical energy in the calculus of variations
Measure the method for solving of minimization.
Step 3: the data fitting based on ternary biharmonic B-spline: the velocity field visualization of information of fluid is with video frame
Transverse and longitudinal coordinate be x, y-axis, using the time as the three-dimensional data of z-axis, super voxel segmentation carried out to the volume data, and calculate super body
The average vector of velocity vector in element, and super voxel center is moved into coordinate origin.It calculates and obtains several groups of ternary biharmonic B
Spline Basis surpasses the speed data in voxel to each and is fitted, and obtains fitting coefficient Vector Groups.Wherein, ternary is double adjusts
It is the base of one group of three-dimensional space with B-spline, ternary biharmonic B-spline has localization property, can be realized Partition of Unity, and
With certain robustness and stability.
Step 4: the three dimensional fluid indicated based on particle is reappeared: the basic unit of fluid is indicated using particle, using continuous
Change as a result, building three dimensional fluid, reappears the movement of fluid.
The present invention only needs to use monocular streaming video as input, automatically analyzes the geometry of fluid and speed letter in video
Breath, and ternary biharmonic B-spline is utilized, it is continuous on time and Spatial Dimension to realize flow surface geometry and speed
Change, using serialization result, it can be achieved that flow surface is restored in the super-resolution of time and Spatial Dimension；In addition, the present invention is based on
Particle realizes the emulation again of fluid, and streaming video is reduced to three dimensional fluid, further demonstrates and realizes video fluid motion
A possibility that physical simulation of character-driven.
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawing, to of the invention
Method is explained in detail explanation.It should be appreciated that specific example described herein is only used to explain the present invention, it is not used to limit
The fixed present invention.
The invention proposes a kind of frames to extract the elevation information and speed letter of fluid by the analysis to streaming video
Breath, and by the methods of cluster, data fitting, fluid information is sorted out and is simplified, and as driving, realizes fluid
The reconstruction and emulation of three-dimensional scenic.
The present invention provides a kind of space-time vectorization method of flow surface based on ternary biharmonic B-spline, references
Shown in Fig. 1 holistic approach flow chart, specific embodiment is as follows:
Step 1: the streaming video height field reduction based on SFS:
The essence of Shape From Shading method is the radiosity equation (formula (1)) according to image, establishes image
Relationship between brightness value and position height value, and then by the brightness value of image, calculate the height value of each location of pixels.It is public
In formula (1), R (n (x))=ω n (x) indicates that radiation equation, ω are incident direction of illumination, and n (x) indicates surface normal, calculates
Shown in method such as formula (3-2), p (x) and q (x) respectively indicate the space derivation of height field in the x and y direction.
R (n (x))=I (x) (1)
With reference to the method for the Tsai and Shah direct fitting radiosity equation proposed, finite difference method, approximation meter are used
The space derivation p (x) of calculated altitude field in the x and y direction and q (x), therefore, if by the radiation member of equation in formula (1), writing
In the form of p (x) and q (x) is independent variable, then formula (3) can be obtained.Wherein, subscript i, j indicate respective physical amount in the picture
Position coordinates be (i, j).
r(pi,j,qi,j)=r (ui,j-ui-1,j,ui,j-ui,j-1)=Ii,j (3)
Height field, u are indicated using u in this sectioni,jIt indicates the height value of the position (i, j), usesIndicate that current iteration step is opened
To the assay value of height field before beginning, useIndicate assay value (more accurate point after current iteration step calculates to height field
Analysis value).Formula (3) is an one-dimensional nonlinear equation, and Newton iteration method (Newton-Raphson Method) can be used to think
Think, the iteration function (such as shown in formula (4)) of constructive formula (3), for realizing to height field ui,jSolution.
Wherein, footmark is increased to function fIt indicates to increase corresponding footmark to the independent variable of f, it may be assumed thatBut it should be noted that formula (4) are not that stringent Newton iteration method provides
Iteration function, because of ui-1,jAnd ui,j-1It can change after each iteration step, therefore, formula (4) is simply by reference
What the solution thought and solution form of Newton iteration method obtained, whether such iterative solution is strictly restrained, is not had also at present
There is pervasive proof.The iterative equation for being write iteration function (i.e. formula (4)) as display can obtain following formula (formula (5)):
Since not pervasive proof guarantees formula (5) convergence, Tsai and Shah et al. propose following improved iteration side
Journey form, as shown in formula (6).In formulaIt should meetClose to initial value when non-zero, otherwise for
0, therefore, use auxiliary quantityIt willIt is expressed as the form as shown in formula (3-7), the W value in formula is 0.01, is used for
Guarantee that denominator is not 0, auxiliary quantityIterative calculation method such as formula (3-8) shown in.
According to above-mentioned analysis, the iterative calculation algorithm of height field can be obtained, as follows.
In order to eliminate the vertical translation of each frame height field of video, after iterating to calculate fluid level field, need to height value
It is normalized, the average value of the height field of the every frame of video is normalized to 0.
Step 1 experimental result is as shown in Figure 2.Scene is rebuild to indicate the height of fluid using gray level image and 3D in figure
?.As in Fig. 2 without shown in Guassian Filter and the position irised out without the box in Guided Filter subgraph, height
The reconstruction process of field can generate cumulative errors and slight error.In order to eliminate significant cumulative errors and similar to the small of noise spot
Error optimizes iteration result each time using Guided Filter and Gaussian Filter.Fig. 2, which is illustrated, to be made
The experimental result optimized with Guided Filter and the Gaussian Filter of different numbers.Without using Guided
When Filter, cumulative errors are difficult to be effectively eliminated, and when being not suitable for Gaussian Filter, slight error has been difficult to
Effect is eliminated.
The time statistical result of step 1 is as shown in Figure 3.Four scenes (ripple, raindrop, waterfall, fountains are given in figure
Scene) run time statistics under different the number of iterations.It can be seen from the figure that the method that step 1 proposes can be realized reality
Shi Yunhang.
Step 2: the fluid velocity field reduction based on shallow water equation；
In order to obtain the velocity field that flow surface can be driven to move, using the method for models fitting, according to above-mentioned height
, using shallow water equation, velocity field is restored.
In the Basic equation group of shallow water equation, it is able to reflect equation such as formula (9) institute of height field and velocity field relationship
Show.Wherein, z indicates that height field, u=(u, v) indicate unknown velocity field.
zt=-u ▽ z-z (ux+vy) (9)
Formula (9) is expanded into more generally form, as shown in formula (10).
zt+zxu+zyv+z(ux+vy)=0 (10)
The physical meaning of intuitivism apprehension above-mentioned formula, the evolution z of flow surface height field at any timetCan by two subitems into
Row modeling, firstly, height field carries out under the advection conveying of the velocity field on horizontal plane (surface vertical with height field direction)
It updates, by subitem-(zxu+zyV) it expresses；Secondly, the variation ratio of the two-dimentional Divergence Field of the variation and velocity field of height field is related,
By subitem-z (ux+vy) expression.
Other than physical control item, in order to guarantee the flatness of the velocity field obtained, it should also add in optimization object function
Enter smooth item (| ▽ u |2+|▽v|2), by adjusting smooth item full weight, obtain expected velocity field extraction effect.To sum up institute
It states, shown in the form of optimization object function such as formula (11).
E=∫ ∫ [(zt+zxu+zyv+z(ux+vy))2+α2(|▽u|2+|▽v|2)]dxdy (11)
The optimization of formula (11) can be realized by solving the corresponding Euler-Lagrange equation of the optimization method.Euler-
Lagrange's equation can be expressed by following linear system: AuBT=Cu, AvBT=Cv, wherein B=(u, v), indicates speed to be solved
Spend field, AuAnd AvExpanded form such as formula (12) and (13) shown in, CuAnd Cv.Expanded form such as formula (14) and (15) institute
Show；If w={ u, v },WithW is respectively indicated at (x, y) along the average value in the direction x and y, calculation formula
As shown in formula (15) and (16).
Pass through formulaIt can obtainAccordingly, using iteration
Method gradually approaching to reality solution, obtains following iterative formula (formula (3-17) and formula (3-18)):
Using above-mentioned iterative formula, fluid meter face velocity field can be fitted according to flow surface height field, meanwhile,
Using high speed filtering method, the exceptional value and noise spot in above-mentioned fitting result are removed.
Step 2 experimental period statistical result is as shown in Figure 3.Four scenes (ripple, raindrop, waterfall, sprays are given in figure
Spring scene) run time statistics under different the number of iterations.It can be seen from the figure that the method that step 2 proposes can be realized
Real time execution.
Step 3: the data fitting based on ternary biharmonic B-spline；
Firstly, by the velocity field visualization of information of fluid be with the transverse and longitudinal coordinate of video frame be x, y-axis, using the time as z-axis
Three-dimensional data, and the data of each position (x, y, t) should be a bivector (u, v).It is clustered with reference to based on linear iteraction
Image superpixel partitioning algorithm, super voxel segmentation is carried out to velocity field volume data.
Traditional image superpixel partitioning algorithm based on linear iteraction cluster, uses Lab color space coordinate and two dimension
The Euclidean distance on quintuple space that coordinate is constituted, to measure the distance between pixel.It is similar, herein using velocity field and
The quintuple space of three-dimensional position compositionEach tissue points are portrayed, as shown in formula (19).It usesOn Euclidean distance, come
Measure the distance between voxel, distance DsIt can be obtained by formula (20).In formula, (m is got over compactedness of the m for controlling super voxel
Greatly, super voxel is compacter),Indicate the grid interval of super voxel, wherein N indicates tissue points total number, and K indicates super
The substantially number of voxel.
The expected results of current procedures are the super voxel divided as a result, its visualization result is probably super similar to two dimensional image
Voxel segmentation result, the difference is that the segmentation of super voxel corresponds to three-dimensional voxel data, and super-pixel segmentation corresponds to two-dimensional pixel
Data.
After the completion of super voxel segmentation, the selection of Knot point is carried out according to the position of super voxel.In each super voxel, using with
The machine method of sampling chooses the Knot point of M fixation, if the number of the super voxel of K expression, from the point of view of the overall situation, shares KM Knot
Point, ifIt indicates Knot point set, that is, has
Calculate the ternary biharmonic B-spline basic function at all Knot points position.Biharmonic B-spline basic function it is discrete
Shown in form such as formula (21), wherein p (x) indicates Green's function, and basic function is by the set of weights of the Green's function of Knot point
Composition is closed, shown in the method for solving of coefficient such as formula (3-22), each column of H are the coefficient of Green's function.
In formula (22),Indicate Knot point set,Indicate the adjacent Knot point of a ring of j-th of Knot point (i.e.
The neighbours Knot point of direct neighbor),Indicate Green's function set.
Using M fixed basic function, velocity field value (u, v) is fitted.Indicate each with the fitting vector that 2M is tieed up
Voxel value, for characterizing velocity field.I-th point of coefficient vectorFollowing optimization method (formula can be passed through
(23)) it acquires, wherein
The experimental result of step 3 is as shown in Figure 4.The first row of Fig. 4 is the exemplary frames intercepted from former input video.It is right
In each exemplary frames, Fig. 4 furthermore presents the height field of step 1 reconstruction as a result, the velocity field result that step 2 is rebuild
Gray scale schematic diagram and 3D reconstructed results schematic diagram, subsequent column give super voxel segmentation result, based on step 3 method in succession
Highly, velocity field rebuilding result (grayscale image, 3D schematic diagram and regression criterion signal).
Data based on ternary biharmonic B-spline are fitted front and back, the time-derivative between consecutive frame as shown in Fig. 6, from
As can be seen that the result after fitting eliminates temporal discontinuous noise to a certain extent in figure；The super voxelization knot of space-time
Fruit is as shown in fig. 7, Fig. 7 by taking small ripple as an example, gives the super voxel spatialization reconstructed results of time and Spatial Dimension, in figure
Number represent the time-derivative value of adjacent two interframe, which reflects step 3 method and is capable of relatively continuous reconstitution fluid
Height field and velocity field；The super voxelization result in space is as shown in figure 8, the resolution ratio of reconstruction image is listed in image surface, space
Step 3 method can rebuild continuous fluid space under the premise of keeping fluid details as the result is shown for super voxelization.
Step 4: the three dimensional fluid indicated based on particle is reappeared；
In order to reuse the data after fluid motion evolutionary process vectorization, the present invention uses the base that fluid is indicated using particle
This unit, the three-dimensional emulation again of the progress to fluid, wherein height field and velocity field using flow surface are the stream of vectorization
The guide that the super-resolution result of body evolution result is moved as fluid particles.Three dimensional fluid replay method based on particle expression
Particle initialization result is as shown in Figure 5.Surface is carried out using fluid motion result of the Marching Cube algorithm to each frame to mention
It takes, and carries out flow surface rendering using Blender software, obtain such as Fig. 9 of the present invention and rendering result shown in Fig. 10 and illustrate
Figure.
The above described is only a preferred embodiment of the present invention, being not that the invention has other forms of limitations, appoint
What those skilled in the art changed or be modified as possibly also with the technology contents of the disclosure above equivalent variations etc.
It imitates embodiment and is applied to other fields, but without departing from the technical solutions of the present invention, according to the technical essence of the invention
Any simple modification, equivalent variations and remodeling to the above embodiments, still fall within the protection scope of technical solution of the present invention.
Claims (6)
1. a kind of space-time vectorization method of the flow surface based on ternary biharmonic B-spline, it is characterised in that comprising following
Step:
(1) the streaming video height field reduction based on SFS: Shape From Shading method reconstitution fluid apparent height is utilized
, in an iterative process, height field is denoised using Gaussian Filter and Guided Filter, carries out reservation side
The smooth optimization on boundary restores flow surface geometry；
(2) fluid level field and speed the fluid velocity field reduction based on shallow water equation: are established using shallow water equation and smooth item
The associated optimization method in field, solves the optimization, obtains the velocity field of flow surface in the horizontal plane；
(3) the data fitting based on ternary biharmonic B-spline: the height field information of flow surface and velocity field information are regarded as
Three-dimensional data carries out super voxel segmentation, chooses Knot point using segmentation result, constructs ternary biharmonic B-spline substrate, right
Flow surface information carries out vectorization, realizes the mapping of space-time discrete data to continuous data；
(4) based on particle indicate three dimensional fluid reappear: using particle indicate fluid basic unit, using serialization as a result,
Three dimensional fluid is constructed, the movement of fluid is reappeared.
2. a kind of space-time vectorization method of flow surface based on ternary biharmonic B-spline according to claim 1,
It is characterized by: in step (1), it is quasi- based on the iteration to image radiation equation using Shape From Shading method
It closes, analysis is iterated to the height field of each frame of streaming video；Use Gaussian Filter and Guided Filter
In conjunction with method denoising is filtered to the obtained height field of analysis, the noise in result is analyzed in removal in each iteration step
Point and exceptional value.
3. a kind of space-time vectorization method of flow surface based on ternary biharmonic B-spline according to claim 1,
It is characterized by: using shallow water equation as basic physical model, analysis obtains fluid level field and velocity field is closed in step (2)
The descriptive equation of system adds the smooth item of Weight based on the equation, and building minimizes objective function, solves target letter
Several Euler-Lagrange equations, using iterative solution method, the minimum of function to achieve the objective uses analysis in step (1)
The flow surface elevation information of acquisition can obtain the two-dimension speed field information of flow surface.
4. a kind of space-time vectorization method of flow surface based on ternary biharmonic B-spline according to claim 1,
By the velocity field visualization of information of fluid be with the transverse and longitudinal coordinate of video frame be x, y-axis it is characterized by: in step (3), with when
Between be z-axis three-dimensional data, super voxel segmentation carried out to the volume data, and calculate velocity vector in super voxel be averaged to
Amount, and super voxel center is moved into coordinate origin, it calculates and obtains several groups of ternary biharmonic B-spline bases, body is surpassed to each
Speed data in element is fitted, and obtains fitting coefficient Vector Groups, realizes the vectorization to flow surface information.
5. a kind of space-time vectorization method of flow surface based on ternary biharmonic B-spline according to claim 1,
It is characterized by: indicating the basic unit of fluid using particle in step (4).
6. a kind of space-time vectorization method of flow surface based on ternary biharmonic B-spline according to claim 2,
It is characterized by: the Guided Filter for the purpose of denoising and establish better iteration basis is former in step (1)
It being used in step iterative process, the Gaussian Filter for the purpose of denoising and is smooth is used in rear a few step iterative process,
The access times of Guided Filter and Gaussian Filter are determined by user.
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