CN114972674B - Three-dimensional volume reconstruction method for slice data - Google Patents
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Abstract
The invention discloses a three-dimensional volume reconstruction method for slice data, which uses a phase field model to represent model slice data and generate a data structure with space grid information; and simulating the evolution process of any two adjacent slices in the volume reconstruction process according to a data structure with space grid information by a control equation comprising a constraint term, calculating the difference area between the t-moment slice and the target slice and the t-moment slice area, further obtaining a first moment sequence and a second moment sequence, weighting the first moment sequence and the second moment sequence to obtain a new moment sequence, selecting slice data according to the new moment sequence, reconstructing a three-dimensional volume, and planning a wire laying path according to a three-dimensional volume reconstruction result. The three-dimensional reconstruction method has the advantages of smooth volume surface, accurate shape and capability of retaining more details. The invention can reconstruct the three-dimensional volume with lower calculation cost and faster speed.
Description
Technical Field
The invention belongs to the technical field of 3D printing, and relates to a three-dimensional volume reconstruction method for slice data.
Background
Three-dimensional reconstruction of objects is an important method and core technology in the fields of Computer Aided Design (CAD), computer Aided Engineering (CAE), computer Aided Geometric Design (CAGD), computer Graphics (CG), computer animation, computer vision, virtual reality, and the like. There are two main types of methods for generating three-dimensional representations of objects by computer. One is to use geometric modeling software to generate a three-dimensional geometric model of an object under human control through human-computer interaction, and the other is to obtain the geometric shape of a real object through a certain means. The former implementation technology is already mature, and several software supports exist, such as: 3DMAX, maya, autoCAD, UG, etc., which generally represent geometry using curved surfaces with mathematical expressions. The latter is generally called as a three-dimensional reconstruction process, and three-dimensional reconstruction refers to a mathematical process and a computer technology for recovering three-dimensional information (shape and the like) of an object by utilizing two-dimensional projection, and comprises the steps of data acquisition, preprocessing, point cloud splicing, feature analysis and the like. Reconstruction of three-dimensional volumes from two-dimensional serial slice data has received great attention today, and has found wide application in radiation therapy planning, medical image processing, surgical planning, and medical image rendering, among others.
In addition, in the automatic wire laying-based composite manufacturing process, wire laying path planning needs to be performed on a given mandrel surface, and therefore, the mandrel in the physical space needs to be reconstructed in the digital space. In order to achieve the object, on the one hand, how to fill in excessive data content in the middle of any two adjacent slices according to the data of the two adjacent slices is a key problem, because points between the adjacent slices do not have correspondence and link relation, and therefore, the three-dimensional object cannot be reconstructed simply by using a linear interpolation algorithm, and how to fill in the empty data based on a certain constraint or evolution rule is a key problem. On the other hand, the reconstruction is regarded as the problem that the deformation between two adjacent slices cannot completely solve the defect of slice direction information, namely different sampling rules in the continuous deformation process can cause different reconstruction results, and the deformation processes between different slices are different, so that how to determine the sampling rules according to the deformation process, and further realize efficient and accurate reconstruction, and become another key problem.
And the automatic wire laying equipment carries out the conveying and shearing of the wire bundles on the surface of the die according to the planned wire laying path in the wire laying process. Therefore, the efficiency, reliability, tension control accuracy and positioning accuracy of the hardware equipment have very important influence on the laying quality of the tows. The quality of the wire laying path also determines the final mechanical property and manufacturing quality of the component, and particularly for large-size complex components, the quality of the wire laying path can often play a decisive role in the efficiency, quality and forming structural property of wire laying forming. Therefore, the method has great significance in researching the planning of the wire laying path on the surface of the die.
Disclosure of Invention
In view of the problems in the prior art, it is an object of the present invention to provide a three-dimensional volume reconstruction method for slice data, which can quickly and accurately reconstruct a weighted three-dimensional (3D) volume from a series of slice data using a control equation including a constraint term, and perform a better and better wire laying path planning on a given mandrel surface.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
A three-dimensional volume reconstruction method facing slice data comprises the following steps:
1) Representing model slice data by using a phase field model to generate a data structure with space grid information;
2) Simulating the evolution process of any two adjacent slices in the volume reconstruction process according to a data structure with space grid information by a control equation comprising a constraint term, sampling at the time t, and calculating the phase difference area of the slice at the time t and the target slice and the area of the slice at the time t by using the phase field function of the shape of the source slice and the phase field function of the shape of the source slice;
3) Obtaining a first sequence according to the area of the difference between the t-moment slice and the target slice; obtaining a second sequence according to the area of the slice at the time t;
4) Generating a first time sequence according to the first sequence, generating a second time sequence according to the second sequence, weighting the first time sequence and the second time sequence to obtain a new time sequence, selecting slice data according to the new time sequence, reconstructing a three-dimensional volume, and planning a wire laying path according to a three-dimensional volume reconstruction result.
Further, the control equation including the constraint term is:
Where t >0, x ε Ω is the point on a given slice; f (Φ) =0.25 (Φ 2-1)2, e is a constant related to the interface width, α is a parameter of the control constraint, and Φ (x, t) and ψ (x) represent the phase field functions of the source slice shape and the target slice shape, respectively.
Further, the control equation is split into a diffusion term, a nonlinear term and a constraint term by an operator splitting method:
Computing diffusion terms using finite difference method Calculating nonlinear terms using variable separation Computing constraint termsThereby obtaining a numerical solution:
further, the area a (t) of the difference between the slice at time t and the target slice is calculated by the following equation:
further, the area B (t) of the slice at time t is calculated by the following equation:
Where N x、Ny is the number of grid points in x-direction and y-direction, h is the spatial step size, Ω 1 (t) is the area of the object shape contained in the slice, respectively.
Further, t=nΔt, Δt is a time step of a single iteration of the control equation, and n is a corresponding number of iterations.
Further, the slices include a source slice S 1 and a target slice S 2,S1＝{x|φ(x,t)≥0},S2 = { x|ψ (x) > 0}.
Further, the first sequence is as follows:
wherein N z is the number of slices to be inserted, A (0) is the initial area difference between the source slice shape and the target slice shape, a 1 is the number of iterations corresponding to the 1 st slice to be inserted, a 2 is the number of iterations corresponding to the 2 nd slice to be inserted, For the number of iterations corresponding to the nth z slices to be inserted, Δt is the time step of a single iteration of the control equation.
Further, the second sequence is as follows:
Wherein B (B 1 Deltat) is the area of the slice at the time of B 1 Deltat, B (B 2 Deltat) is the area of the slice at the time of B 2 Deltat, B TC (h) is the cross-sectional area of the cone at the height coordinate of h, B TC (2 h) is the cross-sectional area of the cone at the height coordinate of 2h, Is thatThe area of the time slice, B TC(Nz h) is the cross-sectional area of the cone at the height coordinate of N z h.
Further, the definition field Ω V of the three-dimensional reconstruction volume is as follows:
ΩV＝{(xi,yj,zk):xi＝a+hi,yj＝c+hj,zk＝hk,0≤i≤Nx,0≤j≤Ny,0≤k≤Nz+1}
Wherein, c is the boundary space coordinate in the x direction, N x、Ny、Nz is the grid number in the x, y and z directions, h is the space step length, i is the count of the space step length in the x direction, j is the count of the space step length in the y direction, and k is the count of the space step length in the z direction.
Compared with the prior art, the invention has the following beneficial effects:
according to the invention, the three-dimensional volume reconstruction facing the slice is performed by utilizing the control equation comprising the constraint term, so that the reconstruction efficiency is higher, the speed is faster, the method is simple and easy to realize, and the calculation speed in the wire laying path planning can be accelerated. The invention can also achieve accurate volume reconstruction and preserve details such as the contour of muscles and the texture of skin aiming at different numbers of slices with complex structures, thereby improving the accuracy and the reduction degree of the process, having stronger robustness, being capable of accurately reconstructing the model with complex topological structure and widening the manufacturing range of the process.
Drawings
FIG. 1 is a representation of given model slice data using a phase field model, where (a) is the source shape Ω 1 (0), (b) is the target shape S 2, (c) is the intermediate shape Ω 1 (t), t >0, (d) is (Ω 1(t)∪S2)\(Ω1(t)∩S2) at time t, (e) is the shape of stacked source, target and intermediate slices, and (f) is the zero-order volumetric reconstruction isosurface;
FIG. 2 is a schematic representation of the variation of a slice of arbitrary shape converted into a corresponding disk of equal area;
Fig. 3 is a schematic diagram of three-dimensional volume reconstruction, wherein (a) is the determination of intermediate slice data stored in discrete time using θ, and (B) is the time evolution of a (t) and B (t) with corresponding morphology.
Fig. 4 is a schematic diagram of the volume reconstruction result of the chinese dragon, wherein (a) is the original dragon model of the chinese dragon, (b) is the volume after parallel slice data used, and (c) is the reconstructed volume.
Fig. 5 is a schematic diagram of the volume reconstruction result of the XYZ dragon model, wherein (a) is the original dragon model of chinese dragon, (b) is the volume after parallel slice data used, and (c) is the reconstructed volume.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings.
Existing methods for slice correlation can be divided into two categories: topology-based methods and variable-based methods. The first is based on the assumption of topology, using parameterized or implicit functions to interpolate an exact surface, such as using projection-based methods to reconstruct a three-dimensional surface through a network of curves; surface reconstruction algorithms controlled by global topology, etc. The second type is from a variable perspective, by solving an optimization problem to obtain a surface, such as reconstructing the surface using constraint terms, using the Cahn-Hilliard equation as a control equation, performing accurate volume reconstruction, and so on. However, because Cahn-Hilliard uses a fourth order operator, which can bring about extremely high computational cost, it has been proposed to use a modified Allen-Cahn equation with motion of average curvature to solve the problem of having holes or uneven volumes due to missing voxels. Furthermore, even if the calculation is performed using the Allen-Cahn equation, unacceptable results are produced because it does not take into account the nonlinear variation of the slice area in some cases.
The three-dimensional volume reconstruction method facing slice data and based on a modified Allen-Cahn equation, provided by the invention, is used for reconstructing a model structure layer by layer according to required information (such as model slice data) to realize rapid and accurate three-dimensional volume reconstruction, and specifically comprises the following steps:
1) In a digital space, representing given model slice data by using a phase field model, and generating a data structure with space grid information, wherein the data structure comprises grid points and space step sizes;
2) Adding a constraint term to the classical Allen-Cahn equation As a control equation, simulating the evolution process of any two adjacent slices in the volume reconstruction process, and obtaining the change process of the evolution of the initial shape into the target shape.
For any two adjacent slices, set as a source slice and a target slice respectively, the control equation is specifically as follows:
where t >0, x ε Ω is the point on a given slice; f (Φ) =0.25 (Φ 2-1)2, e is a constant related to the interface width, α is a parameter of the control constraint term.
The control equation is discretized to find a numerical solution, as shown in fig. 3 (a) and (b). To calculate faster, the modified Allen-Cahn equation is split into diffusion terms, nonlinear terms, and constraint terms using an operator splitting method:
Computing diffusion terms using finite difference method Calculating nonlinear terms using variable separation Constraint itemIs a common differential equation, and can obtain a numerical solution:
the method is easy to implement and can converge rapidly, thereby reducing the time cost required for the manufacturing process.
3) Sampling is carried out in the evolution process obtained in the step 2). T=nΔt, Δt is the time step of a single iteration of the control equation, and n is the corresponding number of iterations. The region of the object shape contained in the slice is denoted as Ω 1 (t), the source slice is Ω 1(0)＝S1, and the target slice is S 2,S1＝{x|φ(x,t)≥0},S2 = { x|ψ (x) > 0}. Using the phase field function phi (x, t) of the source slice shape and the phase field function phi (x) of the target slice shape, the area a (t) of the t-slice from the target slice is calculated, and the area B (t) of the t-slice:
wherein N x、Ny is the grid number in the x direction and the y direction, and h is the space step size. A (t) represents the discrete area of the set (Ω 1(t)∪S2)\(Ω1(t)∩S2) at t=nΔt, and monotonically decreases with time; b (t) represents the discrete area of the set Ω 1 (t) when t=nΔt. In fig. 1, (a), (b), (c), and (d) represent S 1、S2、Ω1 (t) and a (t), respectively, and in fig. 1, (e) and (f) represent the isosurfaces of the intermediate slice shapes stacked between the source slice and the target slice shapes, respectively, and the zero-order volume reconstruction.
4) Two standards are formulated according to the area A (t) of the difference between the t-time slice and the target slice and the area B (t) of the t-time slice:
And selecting slice data to be inserted from the evolution process. Let N z Zhang Qiepian be inserted in common, the evolution time corresponding to the kth slice can be denoted by a k Δt, where Δt is the time step of a single iteration of the control equation and a k is the corresponding number of iterations. Then considering the phase difference area a (t) of the slice at time a k Δt from the target slice, a k is required to be the smallest integer satisfying the following condition:
Where a (0) = (S 1∪S2)\(S1∩S2) is the initial area difference of the source slice shape and the target slice shape.
The inequality is the first criterion;
the following first sequence is obtained from the above inequality:
5) As shown in fig. 2, the irregularly shaped slices are transformed into disks of the same area, and the disks are stacked in succession to give a truncated cone, defined in terms of the cross-sectional area B TC (z) of the cone:
Where h is the distance between two serial number consecutive slices, z is the height coordinate, R 1 is the radius of the disk formed by the source slice, R 2 is the target radius, and N z is the number of slices that one wishes to choose between two given slices.
The evolution time corresponding to the kth slice may be denoted by b k Δt, where Δt is the time step of a single iteration of the control equation and b k is the corresponding number of iterations. Considering the area B (B k Δt) of the slice at time B k Δt, it is required that B k be the minimum integer satisfying the following condition:
sig(R1-R2)B(bkΔt)≤sig(R1-R2)BTC(kh),k＝1,…,Nz.
Where sig (R) is a sign function, R 1-R2 is-1 when R 1-R2 is negative, R 1-R2 is positive, R 1-R2 is 1, otherwise 0.
The inequality is a second criterion;
the second sequence is derived from the above inequality:
6) Generating a corresponding first time sequence by using the sequences of the step 4) and the step 5) And a second time sequenceGiving a weighting parameter of 0-1, and weighting the time sequences a and b, wherein the weighting method is as follows:
nk＝round((1-θ)ak+θbk),0≤k≤Nz+1
where round (x) is a function of rounding the input value x to the nearest integer, thus yielding a new series. This new sequence is the sequence of moments required for reconstruction.
7) Using the new time sequence n k obtained in step 6), selecting slice data at a corresponding time from the evolution process, and performing three-dimensional volume reconstruction to obtain a three-dimensional reconstruction volume ψ ijk, which is defined as follows:
The three-dimensional reconstruction volume ψ ijk is defined as ΩV＝{(xi,yj,zk):xi＝a+hi,yj＝c+hj,zk＝hk,0≤i≤Nx,0≤j≤Ny,0≤k≤Nz+1},a as the boundary space coordinate in the x-direction, c as the boundary space coordinate in the y-direction, N x、Ny、Nz as the grid number in the x, y, z-direction, h as the space step, i as the count of the space step in the x-direction, j as the count of the space step in the y-direction, and k as the count of the space step in the z-direction.
In the manufacturing process of the composite material based on automatic wire laying, slice data are selected according to a new time sequence n k obtained after weighting, the three-dimensional volume ψ ijk is reconstructed, and better wire laying path planning is performed on the surface of a given core mold according to the reconstructed three-dimensional volume.
In the invention, only the second-order equation is needed to be solved, and compared with the existing fourth-order method, the method has lower calculation cost and greatly reduces the manufacturing cost. The control equation is corrected, so that the problems in the prior art are solved, slice data are selected more preferably and more uniformly, and the three-dimensional volume is reconstructed more accurately.
Simulation example:
The three-dimensional volume is reconstructed using complex slice data, i.e., slice data of chinese dragon and XYZ-dragon models. From left to right in fig. 4 (a), (b), (c), are the original dragon model, the parallel slice data used, and the reconstructed volume, respectively. In fig. 4, the process is performed at Ω= (0, 1) × (0, 420/410) × (0, 199/410), and the grid is 410×420×199. See fig. 5 (a), (b), and (c), where Ω= (0, 1) × (0, 344/238) × (0, 190/238), the grid is 238×344×190. In the test of the Chinese dragon and XYZ-dragon model, 67 and 64 sections were selected, respectively. Other parameters were chosen as θ=0, Δt=0.1h 2, e=3h, α=10000.
By comparing the original model, the slice data and the corresponding reconstruction results, it can be observed that the method can accurately reconstruct the volume and preserve details.
The three-dimensional reconstruction volume definition domain generated by the method is very suitable for additive manufacturing processes requiring simulation analysis of the three-dimensional structure of the object, can be applied to the manufacturing process of the composite material with automatic wire laying, can convert the two-dimensional slice data easy to collect into the three-dimensional structure data suitable for simulation analysis, and is an advanced technology for connecting a physical space and a digital space.
Claims (10)
1. The three-dimensional volume reconstruction method for slice data is characterized by comprising the following steps of:
1) Representing model slice data by using a phase field model to generate a data structure with space grid information;
2) Simulating the evolution process of any two adjacent slices in the volume reconstruction process according to a data structure with space grid information by a control equation comprising a constraint term, sampling at the time t, and calculating the phase difference area of the slice at the time t and the target slice and the area of the slice at the time t by using the phase field function of the shape of the source slice and the phase field function of the shape of the source slice;
3) Obtaining a first sequence according to the area of the difference between the t-moment slice and the target slice; obtaining a second sequence according to the area of the slice at the time t;
4) Generating a first time sequence according to the first sequence, generating a second time sequence according to the second sequence, weighting the first time sequence and the second time sequence to obtain a new time sequence, selecting slice data according to the new time sequence, reconstructing a three-dimensional volume, and planning a wire laying path according to a three-dimensional volume reconstruction result.
2. The three-dimensional volumetric reconstruction method for slice data according to claim 1, wherein the control equation including the constraint term is:
Where t >0, x ε Ω is the point on a given slice; f (Φ) =0.25 (Φ 2-1)2, e is a constant related to the interface width, α is a parameter of the control constraint, and Φ (x, t) and ψ (x) represent the phase field functions of the source slice shape and the target slice shape, respectively.
3. The three-dimensional volume reconstruction method for slice data according to claim 2, wherein the control equation is split into a diffusion term, a nonlinear term and a constraint term by an operator splitting method:
Computing diffusion terms using finite difference method Calculating nonlinear terms using variable separation Computing constraint termsThereby obtaining a numerical solution:
4. the three-dimensional volumetric reconstruction method for slice data according to claim 1, wherein the area a (t) of the slice at time t, which is different from the target slice, is calculated by the following formula:
5. The three-dimensional volumetric reconstruction method for slice data according to claim 1, wherein the area B (t) of the slice at time t is calculated by the following formula:
Where N x、Ny is the number of grid points in x-direction and y-direction, h is the spatial step size, Ω 1 () is the region of the object shape contained in the slice, respectively.
6. The method of claim 1, wherein t=nΔt, Δt is a time step of a single iteration of the control equation, and n is a corresponding number of iterations.
7. The three-dimensional volumetric reconstruction method for slice data according to claim 1, wherein the slices comprise a source slice and a target slice, the source slice is S 1, and the target slice is S 2,S1＝{x|φ(x,t)≥0},S2 = { x|ψ (x) > 0}.
8. A method of three-dimensional volumetric reconstruction of slice-oriented data according to claim 1, wherein the first sequence is as follows:
wherein N z is the number of slices to be inserted, A (0) is the initial area difference between the source slice shape and the target slice shape, a 1 is the number of iterations corresponding to the 1 st slice to be inserted, a 2 is the number of iterations corresponding to the 2 nd slice to be inserted, For the number of iterations corresponding to the nth z slices to be inserted, Δt is the time step of a single iteration of the control equation.
9. A method of three-dimensional volumetric reconstruction of slice-oriented data according to claim 1, wherein the second sequence is as follows:
Wherein B (B 1 Deltat) is the area of the slice at the time of B 1 Deltat, B (B 2 Deltat) is the area of the slice at the time of B 2 Deltat, B TC (h) is the cross-sectional area of the cone at the height coordinate of h, B TC (2 h) is the cross-sectional area of the cone at the height coordinate of 2h, Is thatThe area of the time slice, B TC(Nz h) is the cross-sectional area of the cone at the height coordinate of N z h.
10. The method of claim 1, wherein the three-dimensional reconstruction volume has a definition field Ω V as follows:
ΩV＝{(xi,yj,zk):xi＝a+hi,yj＝c+hj,zk＝hk,0≤i≤Nx,0≤j≤Ny,0≤k≤Nz+1}
Where a is the boundary space coordinate in the x direction, c is the boundary space coordinate in the y direction, N x、Ny、Nz is the number of grid points in the x, y and z directions, h is the space step size, i is the count of the space step size in the x direction, j is the count of the space step size in the y direction, and k is the count of the space step size in the z direction.
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