CN104268934B - Method for reconstructing three-dimensional curve face through point cloud - Google Patents
Method for reconstructing three-dimensional curve face through point cloud Download PDFInfo
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- CN104268934B CN104268934B CN201410479451.8A CN201410479451A CN104268934B CN 104268934 B CN104268934 B CN 104268934B CN 201410479451 A CN201410479451 A CN 201410479451A CN 104268934 B CN104268934 B CN 104268934B
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Abstract
The invention discloses a method for reconstructing a three-dimensional curve face through point cloud. The method comprises the steps of inputting point cloud data P possibly carrying noise and abnormal values and the number m of peaks of the curve face needed to be reconstructed; initializing a dictionary matrix V and a connection matrix B; updating the dictionary matrix V and the connection matrix B in an iteration mode till convergence; outputting a reconstructed triangular net to complete reconstruction of the three-dimensional curve face. By means of the method, the triangular net is directly reconstructed through the point cloud, the noise input into the point cloud can be removed well, non-uniform sampling is processed in a robust mode, and the characteristics in the point cloud can be recovered well. Compared with a conceal method, the triangular net is directly reconstructed through the point cloud so as to avoid accumulated errors caused by multi-step optimization in the conceal method. Compared with a combination method, the reconstruction errors serve as a target function, so that the reconstruction errors of the curve face reconstructed through the method are usually smaller than those reconstructed by the existing combination method.
Description
Technical field
The invention relates to a kind of method for directly reconstructing three-dimension curved surface by a cloud, the method can according to input point cloud and
The normal direction information that may carry directly reconstructs out high-quality three-dimension curved surface on point cloud, in three-dimensional scenic modeling, intelligent city, inverse
There is great using value to engineering and machine-building processing and other fields.
Background technology
Curve reestablishing is recent two decades occurring in computer-aided design, medical imaging, computer graphicss and intelligence
A hot issue in the fields such as city, its object is to find certain mathematical description or model, accurately, compactly represent institute
The cloud data (by laser scanner, or the feature detection of medical image is obtained etc.) of input, and based on this to point
The curve and surface that cloud data are located is analyzed, changes and draws.Curve reestablishing technology has a wide range of applications, wherein reverse work
Journey is one of those important application.In background introduction, will be launched to curved surface as application background with reverse-engineering
The discussion of reconstruction technique.Reverse Engineering Technology is the development with computer aided design and manufacture technology and ripe and data
Improving for e measurement technology and emerging a subject and technology developing rapidly.Its appearance, changes original computer
It is rapid research and development of product and rapid prototyping from drawing to Top-Down Design pattern in kind in Aided Design and manufacture system
There is provided brand-new approach.(see Fig. 1) in reverse-engineering system, the reconstruction of curved surface is undoubtedly most important and most difficult problem
One of.
Curved surface is rebuild according to the cloud data that scanning device is collected and plays core support in whole reverse-engineering
Effect, its object is to find certain mathematical description or model, accurate and compactly represent be input into scan data (also known as point
Cloud), and based on this curved surface that scan data is located is analyzed, changed and drawn, and require the table of this mathematics
Show and be consistent as far as possible with the mathematical notation of original entity or curved surface in CAD/CAM system.In general, curve reestablishing is asked
Topic can simply be divided into two stages：First stage reconstructs high-quality polygonal mesh from a cloud, and (triangle gridding is occupied
It is many)；Second stage, from polygonal mesh non-unified Rational B-splines NURBS (Non-Uniform Rational B- are reconstructed
Spline) curved surface；Second stage include parametrization, the burst of polygonal mesh, the feature extraction of polygonal mesh and
Burst fitting of polygonal mesh etc..
As shown in Fig. 2 providing one group of point cloud in space, they sample from a space curved surface (two dimension connection compact manifold
Or the two dimension connection compact manifold with border), in addition to knowing their three-dimensional coordinate, remaining information is known nothing how
One triangle mesh curved surface of construction carrys out interpolation or approaches this group point cloudUp to the present, be related to the theoretical research of this problem with
And algorithm is a lot, but it is broadly divided into following two types.
From the angle of fitting cloud data, with an implicit surface be input into cloud data is fitted.Due to hidden
Formula curved surface does not need parametrization, and in addition it can represent the curved surface of complicated shape, in curve reestablishing, the aspect of surface-rendering it compare
Explicit curved surface has more advantage.The general thinking of implicit surface fitting is such：First an implicit expression is constructed according to cloud data
Function, f (p)：R3- R, the curved surface representated by cloud data is approached with zero contour surface of the function, then by MC
(marching cube) method (or other similar methods) obtains grid surface.The good of cloud data is fitted with implicit function
Place has：The cloud data of noise can be processed, the cavity caused due to undersampling can be filled up, there is implicit function in addition,
CSG operations etc. can be carried out to cloud data.Its weak point：The equipotential surface of implicit function may produce unnecessary song
Face, this kind of method is processing complex boundary, and itself can have any problem when having the cloud data in cavity.
From the angle of interpolation cloud data, triangulation is carried out to cloud data, directly set up between points
Topological connection relation, so as to obtain a grid surface.Modal algorithm has dough sheet to reject algorithm and area in this kind of method
Domain growth algorithm.So-called dough sheet is rejected algorithm and is referred to, carries out triangulation to cloud data first (typically using Delaunay tri-
Angle subdivision), the set of a triangular plate is obtained, reject undesirable triangular plate, remaining triangle according to certain rule
Piece processes the reconstruction grid for obtaining a cloud through the appropriate later stage.This kind of interpolation algorithm is adapted to no noise or noise is smaller,
There is the cloud data of complex boundary.The method disadvantage of interpolation type is undesirable to the reconstruction of the cloud data with noise effect, separately
Outward for nonuniform sampling, and the situation that the point cloud of collection has disappearance can not be processed very well.
The content of the invention
(1) technical problem to be solved
In the application such as reverse-engineering and 3 D scene rebuilding, generally require to recover scene or the three-dimensional of model is bent
Face, and the data that existing collecting device is collected are that in the form of a cloud, this is accomplished by algorithm for reconstructing using a cloud as input
Three-dimension curved surface is reconstructed, and three-dimension curved surface is often what is represented in the form of triangular mesh.Triangular mesh is rebuild by a cloud
It is an inverse problem, noise, collection density and the sampling uniformity in cloud data etc. all have larger shadow to last reconstruction
Ring；In numerous applications, the feature that three-dimension curved surface comes on energy preferably reserving model rebuild is generally required；Existing many sides
Method is only capable of processing the model that topological structure is closing.
The present invention preferably resolves the following technical problem rebuild in triangular mesh problem by a cloud：
1st, the present invention can be processed with error, the cloud data of nonuniform sampling.
2nd, the present invention reconstructs the triangular mesh for coming and can be effectively maintained the feature of model.
3rd, the approximate error for reconstructing the triangular mesh and model for coming of the invention is little
4th, the present invention is not limited the topological structure of handled model.
In consideration of it, the main object of the present invention is to provide a kind of being directly reconstructed by a cloud for robustness based on dictionary learning
The method of three-dimension curved surface, according to the method, user can reconstruct guarantor from the three dimensional point cloud with noise and exceptional value
There is the curved surface of original geometry feature and details.
(2) technical scheme
To reach above-mentioned purpose, the invention provides a kind of method that three-dimension curved surface is directly reconstructed by a cloud, including：
Step A：Input may carry the cloud data P of noise and exceptional value and need to rebuild number of vertices m of curved surface；
Step B：Initialization dictionary matrix V and initialization connection matrix B；
Step C：Dictionary matrix V and connection matrix B are iteratively updated, until convergence；
Step D：The triangular mesh that output is rebuild, completes the reconstruction of three-dimension curved surface.
In such scheme, it is by input point cloud in existing Points Sample method that dictionary matrix V is initialized described in step B
Data P are sampled as m point, specifically include：Cloud data P to being input into carries out resampling so that it is m that cloud number is put after sampling,
In this, as initial dictionary matrix V.Existing Points Sample method described in step B is Poisson disk sampling method, variable density circle
The point cloud method for resampling that disk sampling method, stochastical sampling method or side perceive.
In such scheme, described in step B initialize connection matrix B be according to definition projection energy criterion and manifold about
Beam criterion, with the cloud data P construction triangle griddings after resampling, in this, as initial connection matrix B, specifically includes：Initially
Change a grid M, for cloud data P midpoint pi, find apart from its k nearest point to construct one in dictionary matrix V
Triangle sets T (pi), wherein 10≤k≤15, triangle sets T (pi) contain up toIndividual triangle；By the triangle
Set T (pi) in have minimum projection's energy triangle add in grid M, if update after grid M remain manifold,
Then the triangle is exactly sampled point piInitial correspondence triangle, otherwise continue to be chosen from remaining triangle there is minimum energy
The triangle of amount, repeats this operation until the triangle sets are that sky or the grid M after renewal remain manifold；Once choosing
Triangle, column vector b of connection matrix B are selectediWill be by solving as following formula carries out sub- initialization：
Here p 'i=α*vr+β*vs+γ*vtIt is piTo the subpoint of triangle f, (α*, β*, γ*) correspond to the center of gravity of f
Coordinate.
In such scheme, the projection energy criterion of the definition, is original sample point piTo the projection energy E of triangle f
(pi, f), described by following formula：
E(pi, f)=Eappr(pi, f)+ωeEedge(f)+ωnEnormal(f),
Original sample point p in formulaiTo apart from its nearest triangle f apart from Eappr(pi, f)=| d (pi, f) |qWeigh
L of the input point cloud to the distance for rebuilding curved surface2, qMould,It is regular terms so that triangle f is as far as possible
Close equilateral triangle, so that triangle gridding quality is as high as possible,Be normal direction just
Then item, in the case of normal direction information is carried on the point cloud of input f normal direction and input point cloud p are causediNormal directionIt is as consistent as possible,
Wherein eiIt is three sides of triangle f, npiIt is original sample point piNormal vector.
In such scheme, step C includes：
Step C1：Fixed dictionary matrix V, calculates the side e in current triangle griddingiThe sampling that corresponding triangle is included
Spot projection energy sum E (ei), a Priority Queues Q is constructed, deposit all pairing element (ei, E (ei))；
Step C2：If queue Q non-NULLs, E (e in Q are selectedi) maximum element, carry out side recurrence update algorithm；
Step C3：When queue Q is empty set, carries out triangle and delete detection, under conditions of manifold property is not destroyed, delete
Except the triangle for not corresponding to sampled point；
Step C4：Fixed connection matrix B, update dictionary element location matrix V, using alternating direction multiplier method, by correspondence
Optimization problem resolve into two sub- problem solvings.
In such scheme, the side recurrence update algorithm in step C2 also includes：
If eiIt is internal edges, edge flip detection is carried out to it, if E (e after exchangingi) value reduces, and the operation carries out it
Afterwards the grid remains manifold structure and then swaps operation；
If eiIt is boundary edge, virtual triangle is carried out to it and adds detection, if E (e after insertion trianglei) value reduction, then
Carry out adding triangle operation；
Above two operation then updates corresponding projection energy once occurring, and to eiAll neighbours pass when carrying out
Return update algorithm, otherwise termination algorithm.
(3) beneficial effect
The method that the kind that the present invention is provided directly reconstructs three-dimension curved surface by a cloud, by a cloud triangular mesh is directly reconstructed,
The noise in input point cloud can be well removed simultaneously, can recover to nonuniform sampling robust and well spy in a cloud
Levy.
Implicit method is compared, the present invention has advantages below：
1st, the present invention directly reconstructs triangular mesh by a cloud, it is to avoid the multistep optimization problem in implicit method is brought
Cumulative error.
2nd, the inventive method point cloud normal direction information is not required in that, and the normal direction information with direction is in implicit method
It is necessary, but to inherently one problem being difficult of the normal estimation with direction, and where feature is larger, normal direction
Estimation often have error, this may be brought than larger error to best curve reestablishing.
Combined method is compared, the present invention has advantages below：
1st, the present invention using reconstruction error as object function so that the present invention reconstruct come curved surface reconstruction error often
Can be little than existing combined method.
2nd, the cloud data for collecting is often with than larger noise, and sampled point non-uniform Distribution, energy of the present invention
This class data is processed well, and existing combined method is very sensitive to this kind of data.
Description of the drawings
Fig. 1, the implementation process schematic diagram of reverse-engineering in prior art；
Fig. 2, left figure is input point cloud, and right figure is the three-dimension curved surface after rebuilding；
Fig. 3, what the present invention was provided is directly reconstructed the method flow diagram of three-dimension curved surface by a cloud；
Fig. 4, according to the schematic diagram of the flow process of the curve reestablishing method of the embodiment of the present invention；
Fig. 5, according to the schematic diagram of the sparse coding algorithm flow of the embodiment of the present invention；
Fig. 6, according to the schematic diagram of the sparse coding algorithm flow of the embodiment of the present invention；
Fig. 7, according to the schematic diagram that the edge flip of the embodiment of the present invention is operated；
Fig. 8, the process of boundary edge：Left figure is the situation for needing to insert triangle, and right figure is need not to insert triangle
Situation；
Fig. 9, the example schematic on square body Model is acted on according to the sparse coding algorithm of the embodiment of the present invention；
Figure 10, according to the schematic diagram of the dictionary updating flow process based on alternating direction multiplier method of the embodiment of the present invention；
Figure 11, according to the curve reestablishing method of the embodiment of the present invention show by taking faceform as an example with iterationses increase
Many, reconstruction quality is gradually stepped up；
Figure 12, according to the curve reestablishing method of the embodiment of the present invention experimental result and with screened poisson methods
Contrast schematic diagram；
Figure 13, illustrates according to the experimental result of the curve reestablishing method of the embodiment of the present invention and with the contrast of additive method
Figure；
Figure 14, illustrates according to the experimental result of the curve reestablishing method of the embodiment of the present invention and with the contrast of additive method
Figure；
Figure 15, illustrates according to the experimental result of the curve reestablishing method of the embodiment of the present invention and with the contrast of additive method
Figure.
Specific embodiment
To make the object, technical solutions and advantages of the present invention become more apparent, below in conjunction with specific embodiment, and reference
Accompanying drawing, the present invention is described in more detail.
The technical thought of the present invention is such：Input needs the cloud data (may be with noise and exceptional value) rebuild
And number of vertices m of reconstruction curved surface, using existing cloud method for resampling, the point cloud to being input into carries out resampling so that
Point cloud number after sampling is m, in this, as initial dictionary matrix V, according to the criterion of definition, with the point cloud constructions after resampling
Triangle gridding, in this, as initial connection matrix B.
The present invention is defined as curved surface is rebuild with the error for being originally inputted a cloud：Original point cloud to 3 dictionary elements are constituted
Triangle minimum projection's distance, in order that the error is minimum, the present invention is proposed based on the Optimized model of dictionary learning,
Dictionary element (rebuild curved surface vertex position) and annexation (triangle gridding) are iteratively updated, meanwhile, in order to noise and different
Constant value data robust, the present invention adopts l2, qThe range error tolerance of (0 ＜ q ＜ 1) mould.Finally, for the triangle of outputting high quality
Grid, the present invention adds related constraint in Optimized model.During annexation is updated, the present inventor introduces one kind
It is main by three kinds of operations based on the sparse coding algorithm that side updates：Exchange side, delete triangle, addition triangle to update
Annexation, while the triangle gridding for ensureing output is manifold structure.
As shown in figure 3, the method flow diagram that three-dimension curved surface is directly reconstructed by a cloud that Fig. 3 is the present invention to be provided, the method
Comprise the following steps：
Step 31：Input may carry the cloud data P of noise and exceptional value and need to rebuild number of vertices m of curved surface.
Step 32：Initialization dictionary matrix V and initialization connection matrix B；
In this step, using existing Points Sample method, resampling is carried out to input point cloud so that cloud is put after sampling
Number is m, in this, as initial dictionary V, according to the projection energy and manifold constraint criterion of definition, with the point cloud structure after resampling
Triangle gridding is made, in this, as initial connection matrix B.
Step 321：Initialization dictionary matrix V, is to be sampled as m by cloud data P is input in existing Points Sample method
It is individual, specifically include：Cloud data P to being input into carries out resampling so that it is m that cloud number is put after sampling, in this, as initial
Dictionary matrix V.Existing Points Sample method described in step B is Poisson disk sampling method, variable density disk sampling method, random
Point cloud method for resampling or other method for resampling that sampling method, side perceive.
Step 322：Initialization connection matrix B：It is the projection energy criterion and manifold constraint criterion according to definition, to adopt again
Cloud data P construction triangle griddings after sample, in this, as initial connection matrix B, specifically include：One grid M of initialization is right
In cloud data P midpoint pi, find apart from its k nearest point to construct a triangle sets T (p in dictionary matrix Vi),
Wherein 10≤k≤15, triangle sets T (pi) contain up toIndividual triangle；By triangle sets T (pi) in have most
The triangle of little projection energy is added in grid M, if the grid M after updating remains manifold, the triangle is exactly to adopt
Sampling point piInitial correspondence triangle, otherwise continue to choose the triangle with least energy from remaining triangle, repeat
This operation is that sky or the grid M after renewal remain manifold until the triangle sets；Once choosing triangle, connect
Column vector b of matrix BiWill be by solving as following formula carries out sub- initialization：
Here p 'i=α*vr+β*vs+γ*vtIt is piTo the subpoint of triangle f, (α*, β*, γ*) correspond to the center of gravity of f
Coordinate.
Wherein, the projection energy criterion of the definition, is original sample point piTo the projection energy E (p of triangle fi, f),
Described by following formula：
E(pi, f)=Eappr(pi, f)+ωeEedge(f)+ωnEnormal(f),
Original sample point p in formulaiTo apart from its nearest triangle f apart from Eappr(pi, f)=| d (pi, f) |qWeigh
L of the input point cloud to the distance for rebuilding curved surface2, qMould,It is regular terms so that triangle f is as far as possible
Close equilateral triangle, so that triangle gridding quality is as high as possible,Be normal direction just
Then item, in the case of normal direction information is carried on the point cloud of input f normal direction and input point cloud p are causediNormal directionIt is as consistent as possible,
Wherein eiIt is three sides of triangle f, npiIt is original sample point piNormal vector.
Step 33：Dictionary matrix V and connection matrix B are iteratively updated, until convergence；
Step 331：Fixed dictionary matrix V, calculates the side e in current triangle griddingiWhat corresponding triangle was included adopts
Sampling point projection energy sum E (ei), a Priority Queues Q is constructed, deposit all pairing element (ei, E (ei))。
Step 332：If queue Q non-NULLs, E (e in Q are selectedi) maximum element, carry out side recurrence update algorithm；
Step 332-1：If eiIt is internal edges, edge flip detection is carried out to it, if E (e after exchangingi) value reduces, and be somebody's turn to do
Operate the grid after carrying out to remain manifold structure and then swap operation；If eiIt is boundary edge, virtual three is carried out to it
It is angular to add detection, if E (e after insertion trianglei) value reduction, then carry out adding triangle operation；Above two is operated once
Occur, then update corresponding projection energy, and to eiAll neighbours when carrying out recurrence update algorithm, otherwise termination algorithm.
Step 333：When queue Q is empty set, carries out triangle and delete detection, under conditions of manifold property is not destroyed,
Delete the triangle for not corresponding to sampled point.
Step 334：Fixed connection matrix B, update dictionary element location matrix V, using alternating direction multiplier method, by correspondence
Optimization problem resolve into two sub- problem solvings.
Step 34：The triangular mesh that output is rebuild, completes the reconstruction of three-dimension curved surface.
Using the such scheme of the present invention, can be reconstructed and be possessed spy by three dimensional point cloud (with noise and exceptional value)
The high-quality triangle mesh curved surface of details of seeking peace.
Based on the technical scheme that the invention described above is provided, it is described in greater detail below in conjunction with specific embodiment.This
It is bright that a kind of robustness curve reestablishing method based on dictionary learning is provided, according to the method, can be by with noise and exceptional value
Three dimensional point cloud in, reconstruct the curved surface with initial data feature and details.
As shown in figure 4, input three-dimensional point cloud P (with noise and exceptional value), using existing Points Sample method, by P
Resampling is m point, in this, as initial dictionary V, projection energy according to the definition of the present invention and manifold constraint criterion, to sample
Point cloud afterwards, i.e., initial dictionary V constructs triangle gridding, used as initial connection matrix B.
The approximate error of curved surface and original point cloud is rebuild according to defined in the present invention：
It is minimum projection's distance of the triangle that original point cloud is constituted to 3 dictionary elements, and corresponding sparse constraint is：
||bi||0≤ 3, | | bi||1=1, bi≥0
Wherein biFor the column vector of connection matrix B.
B should meet manifold constraint：B∈MT
In order that the error is minimum, the present invention proposes robustness song Optimized model (formula (1)) based on dictionary learning：
s.t.||bi||0≤ 3, | | bi||1=1, bi≥0
B∈MT
WhereinIt is regular terms, high-quality three is obtained by regularization triangle
Angle grid surface, here, eiThe side of triangle gridding M is represented, 1 is the number on side, and E is the matrix for storing side information.
If the three-dimensional point cloud P of input carries reliable normal direction information, the present invention can also add normal direction regularization term：
So that triangle f normal direction and corresponding input point cloud piNormal directionIt is as consistent as possible.
Based on above Optimized model, the present invention iteratively updates dictionary element (point cloud position) and the annexation (triangulation network
Lattice) until convergence, the high-quality triangle gridding of initial data feature and details is possessed in finally output.
When dictionary V is fixed, the present invention updates corresponding connection matrix B using the sparse coding algorithm based on side, such as Fig. 5 institutes
Show, with the side e of current grid MiAnd its corresponding projection energy and valueTo match element, set up
Queue Q, and deposit all pairing element (ei, E (ei)), each iteration deletes with maximal projection energy first in Q
Element, according to the side e of the elementiType, carry out recurrence side renewal and process, as shown in Figure 4：For eiIt is the situation of internal edges,
If E is (ei) reduce after edge flip is carried out, and the grid after edge flip remains manifold structure, then to eiSwap
Operation is shown in (such as Fig. 5)；For eiIt is the situation of boundary edge, by eiTwo boundary edges adjacent with its are respectively connected with, and obtain two
Virtual triangle (as shown in Figure 6), if corresponding comprising eiTriangle sampled point, virtual triangle can be projected to
On, and projection energy reduction, then the virtual triangle with less projection energy is added to into current net as new triangle
In lattice M, meanwhile, the corresponding pairing element in newly-generated side is added in queue Q.For both of these case, as E (ei) when, it is right
The projection energy of sampled point, side and the triangle answered is required for updating, side eiNeighbours side also according to the drop of new projection energy
Sequence is updated (as shown in Fig. 7 left figures and Fig. 8 left figures).
As shown in figure 9, these can reduce the target energy of Optimized model of the present invention based on the operation on side, passed by this
Return strategy, these partial operations can be spread to other regions of grid.
When queue Q is empty set, algorithm carries out triangle and deletes detection, under conditions of manifold property is not destroyed, deletes that
A little trianglees for not corresponding to sampled point.
Sparse coding algorithm based on side proposed by the present invention has following property：
1. manifold.Because edge flip and edge triangles insertion can't affect to be input into the manifold property of grid, so working as
Front grid is always manifold in whole algorithmic procedure.
2. energy reduces.Correspond to comprising the sampled point when triangle in front because the operation in algorithm only can reduce
Projection energy, and other point projection energies be to maintain it is constant, so the total energy of Optimized model (formula (1)) is under dullness
(such as Fig. 7) of drop.
3. amount of calculation effectiveness.Experiment shows, while the recursive algorithm for updating complexity be with while number linearly close
System, this is faster than common greedy algorithm.
When annexation B is fixed, dictionary updating is exactly to optimize vertex position V, is equivalent to seek following problem (formula (2))：
Directly optimization (2) is highly difficult, due to EapprL containing non-differentiability2, qMould, the present invention replaces E with matrix Zappr
In P-VB, dictionary updating is changed into (formula (3))：
S.t.h (V, Z)=0
Here, F (V, Z)=Eappr+EregAnd h (V, Z)=Z-P+VB.
The Augmented Lagrangian Functions of formula (3) are：
Wherein D is Lagrange multiplier.
The problems referred to above can be solved by alternating direction multiplier method, and as shown in Figure 10, wherein Z- subproblems are (formulas
(4))：
Wherein, ziBe matrix Z i-th row, xiIt isI-th row.(4) n minor issue can be decomposed into, often
Individual minor issue can be reduced to a scalar problem：
Optimal valueCan be tried to achieve by a few step iteration.
V- subproblems are：
This is a quadratic problem, can be by solving a linear system solution.The present invention utilizes incomplete cholesky
The conjugate gradient method of decomposition is solved.
As shown in figure 11, the optimization method of alternating direction proposed by the present invention can iteratively optimized reconstruction grid triangle
Change and vertex position.
As shown in Figure 12 to Figure 15, robustness curve reestablishing method proposed by the present invention, not only to noise and exceptional value Shandong
Rod, and can also export and the less high-quality triangulation network of original point cloud error in the case where data characteristicses and details are possessed
Lattice.
Particular embodiments described above, has been carried out further in detail to the purpose of the present invention, technical scheme and beneficial effect
Describe in detail it is bright, should be understood that the foregoing is only the present invention specific embodiment, be not limited to the present invention, it is all
Within the spirit and principles in the present invention, any modification, equivalent substitution and improvements done etc., should be included in the guarantor of the present invention
Within the scope of shield.
Claims (6)
1. a kind of method that three-dimension curved surface is directly reconstructed by a cloud, it is characterised in that include：
Step A：Input may carry the cloud data P of noise and exceptional value and need to rebuild number of vertices m of curved surface；
Step B：Initialization dictionary matrix V and initialization connection matrix B；
Step C：Dictionary matrix V and connection matrix B are iteratively updated, until convergence：
Step D：The triangular mesh that output is rebuild, completes the reconstruction of three-dimension curved surface；
Wherein, it is the projection energy criterion and manifold constraint criterion according to definition that connection matrix B is initialized described in step B, with
Cloud data P construction triangle griddings after resampling, in this, as initial connection matrix B, specifically include：
One grid M of initialization, for input sample point p in cloud data Pi, find in dictionary matrix V apart from its nearest k
Individual point is constructing a triangle sets T (pi), wherein 10≤k≤15, triangle sets T (pi) contain up toIndividual triangle
Shape；By triangle sets T (pi) in have minimum projection's energy triangle add in grid M, if update after net
Lattice M remains manifold, then the triangle is exactly input sample point piInitial correspondence triangle, otherwise continue from remaining triangle
Triangle of the selection with least energy in shape, repeats this operation until the triangle sets are sky or the grid after renewal
M remains manifold；Once triangle f is chosen, column vector b of connection matrix BiWill be by solving as following formula is initialized：
Wherein, vr,vs,vtIt is three summits of selected triangle, α, beta, gamma represents summit pi' under three above summit
Combination coefficient, here p 'i=α*νr+β*νs+γ*νtIt is piTo the subpoint of triangle f, (α*,β*,γ*) correspond to the center of gravity of f
Coordinate.
2. the method that three-dimension curved surface is directly reconstructed by a cloud according to claim 1, it is characterised in that described in step B
Initialization dictionary matrix V is to be sampled as m point by cloud data P is input in existing Points Sample method, is specifically included：To defeated
The cloud data P for entering carries out resampling so that it is m that cloud number is put after sampling, in this, as initial dictionary matrix V.
3. the method that three-dimension curved surface is directly reconstructed by a cloud according to claim 2, it is characterised in that described in step B
Existing Points Sample method is the point cloud that Poisson disk sampling method, variable density disk sampling method, stochastical sampling method or side perceive
Method for resampling.
4. the method that three-dimension curved surface is directly reconstructed by a cloud according to claim 1, it is characterised in that the throwing of the definition
Shadow energy criteria, is input sample point piTo the projection energy E (p of triangle fi, f), described by following formula：
E(pi, f)=Eappr(pi,f)+ωeEedge(f)+ωnEnormal(f),
Input sample point p in formulaiTo apart from its nearest triangle f apart from Eappr(pi, f)=| d (pi,f)|qWeigh input
L of the point cloud to the distance for rebuilding curved surface2,qMould,Regular terms so that triangle f as close possible to etc.
Side triangle, so that triangle gridding quality is as high as possible,It is normal direction regular terms,
F normal direction and input sample point p are caused in the case of normal direction information is carried on the point cloud of inputiNormal directionIt is as consistent as possible, wherein
eiIt is three sides of triangle f,It is input sample point piNormal vector.
5. the method that three-dimension curved surface is directly reconstructed by a cloud according to claim 1, it is characterised in that the step C bag
Include：
Step C1：Fixed dictionary matrix V, calculates the side e in current triangle griddingiThe sampled point that corresponding triangle is included is thrown
Shadow energy sum E (ei), a Priority Queues Q is constructed, deposit all pairing element (ei,E(ei))；
Step C2：If queue Q non-NULLs, E (e in Q are selectedi) maximum element, carry out side recurrence update algorithm：
Step C3：When queue Q is empty set, carries out triangle and delete detection, under conditions of manifold property is not destroyed, deletion does not have
There is the triangle of corresponding sampled point；
Step C4：Fixed connection matrix B, update dictionary matrix V, using alternating direction multiplier method, by corresponding optimization problem point
Solution is into two sub- problem solvings.
6. the method that three-dimension curved surface is directly reconstructed by a cloud according to claim 5, it is characterised in that in step C2
Side recurrence update algorithm also include：
If eiIt is internal edges, edge flip detection is carried out to it, if E (e after exchangingi) value reduces, and be somebody's turn to do after the operation is carried out
Grid remains manifold structure and then swaps operation；
If eiIt is boundary edge, virtual triangle is carried out to it and adds detection, if E (e after insertion trianglei) value reduction, then carry out
Add triangle operation；
Aforesaid operations then update corresponding projection energy once occurring, and to eiAll neighbours when carrying out recurrence update calculate
Method, otherwise termination algorithm.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105279705A (en) * | 2015-09-30 | 2016-01-27 | 国网智能电网研究院 | Sparse representation method for on-line data collection of power |
| CN106485676B (en) * | 2016-09-29 | 2019-10-11 | 天津大学 | A kind of LiDAR point cloud data recovery method based on sparse coding |
| CN107958489B (en) * | 2016-10-17 | 2021-04-02 | 杭州海康威视数字技术股份有限公司 | Curved surface reconstruction method and device |
| CN106485783A (en) * | 2016-10-18 | 2017-03-08 | 合肥阿巴赛信息科技有限公司 | One kind is based on rarefaction representation and parameterized curved surface fitting method |
| CN106780751A (en) * | 2017-01-19 | 2017-05-31 | 桂林电子科技大学 | Three-dimensional point cloud method for reconstructing based on improved shielding Poisson algorithm |
| CN106952339A (en) * | 2017-03-15 | 2017-07-14 | 重庆邮电大学 | A kind of Points Sample method theoretical based on optimal transmission |
| CN108665548B (en) * | 2017-04-01 | 2022-01-07 | 上海宏桐实业有限公司 | Quick point cloud progressive reconstruction method based on star hypothesis |
| CN107610228A (en) * | 2017-07-05 | 2018-01-19 | 山东理工大学 | Curved surface increment topology rebuilding method based on massive point cloud |
| CN108765434B (en) * | 2018-01-15 | 2022-05-24 | 中国人民解放军陆军装甲兵学院 | Contour extraction method based on additive remanufacturing point cloud model |
| CN108257213B (en) * | 2018-01-17 | 2021-08-24 | 视缘(上海)智能科技有限公司 | Point cloud lightweight polygonal curved surface reconstruction method |
| CN109360272B (en) * | 2018-09-21 | 2023-08-29 | 浙江理工大学 | Grid curved surface curve design method based on distance constraint |
| CN109636915B (en) * | 2018-12-19 | 2020-11-20 | 哈尔滨理工大学 | Medical image three-dimensional reconstruction isosurface grid extraction method based on edge growth |
| CN111486864B (en) * | 2019-01-28 | 2022-04-08 | 北京工商大学 | Multi-source sensor combined calibration method based on three-dimensional regular octagon structure |
| CN111801707A (en) * | 2019-02-02 | 2020-10-20 | 深圳市大疆创新科技有限公司 | Method, device and system for point cloud resampling |
| CN109961517B (en) * | 2019-03-01 | 2021-05-07 | 浙江大学 | Triangular mesh reparameterization method for parametric surface fitting |
| CN112184840B (en) | 2020-09-22 | 2022-09-02 | 上海交通大学 | 3D point cloud compression system based on multi-scale structured dictionary learning |
| CN116468767B (en) * | 2023-03-28 | 2023-10-13 | 南京航空航天大学 | Airplane surface reconstruction method based on local geometric features and implicit distance field |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103853840A (en) * | 2014-03-18 | 2014-06-11 | 中国矿业大学(北京) | Filter method of nonuniform unorganized-point cloud data |
| CN103886625A (en) * | 2014-01-09 | 2014-06-25 | 北京工业大学 | Point cloud data sparse representation method based on compressed sensing |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20140198097A1 (en) * | 2013-01-16 | 2014-07-17 | Microsoft Corporation | Continuous and dynamic level of detail for efficient point cloud object rendering |
-
2014
- 2014-09-18 CN CN201410479451.8A patent/CN104268934B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103886625A (en) * | 2014-01-09 | 2014-06-25 | 北京工业大学 | Point cloud data sparse representation method based on compressed sensing |
| CN103853840A (en) * | 2014-03-18 | 2014-06-11 | 中国矿业大学(北京) | Filter method of nonuniform unorganized-point cloud data |
Non-Patent Citations (4)
| Title |
|---|
| l1Sparse Reconstruction of Sharp Point Set Surfaces;Haim Avron et al.;《ACM TRANSACTIONS ON GRAPHICS》;20101031;第29卷(第5期);第1-20页 * |
| 基于变分网格的曲面简化高效算法;金勇 等;《软件学报》;20110531;第22卷(第5期);第1097-1105页 * |
| 基于扫描数据的三维人脸表情合成;林裕旭;《中国博士学位论文全文数据库 信息科技辑》;20110815(第8期);第I138-67页 * |
| 网格曲面特征的稀疏性优化检测算法;王伟明 等;《计算机辅助设计与图形学学报》;20130831;第25卷(第8期);第1128-1136页 * |
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