CN101751695A - Estimating method of main curvature and main direction of point cloud data - Google Patents
Estimating method of main curvature and main direction of point cloud data Download PDFInfo
- Publication number
- CN101751695A CN101751695A CN200810239327A CN200810239327A CN101751695A CN 101751695 A CN101751695 A CN 101751695A CN 200810239327 A CN200810239327 A CN 200810239327A CN 200810239327 A CN200810239327 A CN 200810239327A CN 101751695 A CN101751695 A CN 101751695A
- Authority
- CN
- China
- Prior art keywords
- point
- neighbour
- cloud data
- coordinate system
- vector
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 238000000034 method Methods 0.000 title claims abstract description 110
- 239000013598 vector Substances 0.000 claims abstract description 103
- 239000011159 matrix material Substances 0.000 claims abstract description 30
- 238000004422 calculation algorithm Methods 0.000 claims abstract description 13
- 238000005457 optimization Methods 0.000 claims description 14
- 230000009466 transformation Effects 0.000 claims description 6
- 238000012937 correction Methods 0.000 claims description 3
- 230000000295 complement effect Effects 0.000 claims description 2
- 238000000354 decomposition reaction Methods 0.000 claims description 2
- 230000001419 dependent effect Effects 0.000 claims description 2
- 238000013144 data compression Methods 0.000 abstract description 5
- 238000013461 design Methods 0.000 abstract description 5
- 238000000605 extraction Methods 0.000 abstract description 5
- 238000004088 simulation Methods 0.000 abstract description 3
- 238000007781 pre-processing Methods 0.000 abstract 1
- 238000004364 calculation method Methods 0.000 description 12
- 238000002474 experimental method Methods 0.000 description 12
- 241000406668 Loxodonta cyclotis Species 0.000 description 6
- 230000000694 effects Effects 0.000 description 4
- 238000005516 engineering process Methods 0.000 description 3
- 238000005070 sampling Methods 0.000 description 3
- 230000008901 benefit Effects 0.000 description 2
- 238000009826 distribution Methods 0.000 description 2
- 230000004807 localization Effects 0.000 description 2
- 230000008569 process Effects 0.000 description 2
- 238000003860 storage Methods 0.000 description 2
- 238000012360 testing method Methods 0.000 description 2
- 239000000654 additive Substances 0.000 description 1
- 230000000996 additive effect Effects 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 238000004040 coloring Methods 0.000 description 1
- 238000007796 conventional method Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 230000002708 enhancing effect Effects 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 238000012417 linear regression Methods 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 230000007246 mechanism Effects 0.000 description 1
- 238000012797 qualification Methods 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 210000003813 thumb Anatomy 0.000 description 1
- 238000013519 translation Methods 0.000 description 1
Images
Abstract
The invention relates to an estimating method of the main curvature and the main direction of point cloud data, which comprises the following steps of: preprocessing, estimating a normal transversal curvature, fitting a Weingarten matrix, computing the characteristic value and the characteristic vector of the Weingarten matrix and computing the main curvature and the main direction. In the method, the main curvature and the main direction faithful to an original object are obtained only by utilizing the scanning data and the estimated normal vector of a laser scanner. The main curvature and the main direction are computed by the method through least square linear fitting and the characteristic value and the characteristic vector of the matrix, the algorithm is simple, the computing result is accurate, and the time complexity is highly effective. The method is called as a normal transversal fitting method, and the computing result thereof has important application value in the fields of virtual reality, computer games, natural scene simulation, urban landscape design, data compression, characteristic extraction, object 3D reconstruction and the like.
Description
Technical field
What the present invention relates to infinitesimal geometry, computational mathematics, computer graphics and technical field of computer vision a kind ofly utilizes three-dimensional laser scanner to carry out material object to measure cloud data, and carries out principal curvatures and principal direction Calculation Method according to cloud data.Have important use is worth in fields such as virtual reality, computer game, natural scene simulation, city landscape design, data compression, feature extraction, 3D in kind reconstructions.
Background technology
Along with the raising of laser scanner precision, the information that scanning obtains is more and more abundanter, and the model data that scanning obtains is more and more huger.People utilize these huge data to carry out feature extraction, data compression or carry out three-dimensional reconstruction.But the realization of these work often needs some infinitesimal geometry amounts are estimated that wherein most important estimation comprises the estimation of principal curvatures and principal direction.
The method of estimation of principal curvatures and principal direction roughly can be divided into three major types at present:
The first kind is to carry out local surface fitting, obtains secondary or cubic surface, obtains principal curvatures and principal direction according to differential geometric theory again, as the cubic surface approximating method of Goldfeather proposition in 2004;
Second class is earlier cloud data to be carried out gridding, and neighbours' point of getting again in one or two rings carries out the estimation of principal curvatures or principal direction, the method based on grid data that proposes as nineteen ninety-five Taubin;
The third-largest class is directly cloud data to be carried out the calculating of differential character amount.Effect was fine during in the past some of preceding two class methods were used, but along with the raising of scanner precision, the increase day by day of data scale, the time and space expense of these two class methods is bigger, and their application just has been subjected to restriction.So people attempt directly to carry out the calculating of differential character from cloud data, just the 3rd class methods.For present achievement, directly when a cloud calculated, some method was just utilized the positional information of point, did not utilize the normal vector information of each point, can make that like this robustness of method is relatively poor; Certain methods normal vector information is also arranged, but they are often in conjunction with first kind method, and normal vector is used as a constraint condition, have increased the computing time of principal curvatures and principal direction model solution and the expense of storage space.
Summary of the invention
The technical matters that desire of the present invention solves is the accurate calculating of the principal curvatures and the principal direction of discrete point cloud data, the objective of the invention is to, at the discrete point cloud data that obtains by laser scanning in the real world, provide one to principal curvatures and principal direction carry out accurately, the fast principal curvatures and the principal direction method of estimation of cloud data that calculate, robust.
For achieving the above object, technical solution of the present invention provides a kind of principal curvatures of cloud data and the method for estimation of principal direction, is called method transversal fitting process, and this principal curvatures and principal direction estimating step comprise:
Step 1: utilize laser scanner scans directly to gather cloud data and to the cloud data pre-service, coordinate according to each point in the cloud data carries out spatial division, realizes that the data store organisation of three-dimensional binary chop tree is called kd tree (k-dimensional tree); The coordinate of described each point all is the original coordinates that adopts laser scanner to produce.
Step 2: for each point of cloud data, utilize the kd tree of cloud data to search 15 or 30 neighbour's points, according to least square method these neighbour's points are simulated a plane, with the normal vector on this plane as an initial estimate of cloud normal vector, passing through the normal vector of each point of weighted mean algorithm correction cloud data then estimates, be so that each puts the inverse of the Euclidean distance of ordering with the neighbour as weights in the cloud data, the inverse of described Euclidean distance, if distance value is 0, then do not calculate this neighbour's point.Described these neighbours being put according to least square method simulates a plane, wherein need construct the cum rights least square problem during fit Plane, this least square problem is the absolute value that these neighbours put the residual error of fit Plane, multiply by again the long-pending of weight coefficient and minimum problems.Described weight coefficient is so that each puts the inverse of the Euclidean distance of ordering with the neighbour as weights in the cloud data.
Step 3:, utilize its normal vector, section structure partial 3 d rectangular coordinate system for each point of cloud data; Described partial 3 d rectangular coordinate system, its building method are, for some p in the cloud data, are N=(n if put the normal vector of p
X, p, n
Y, p, n
Z, p), then this p is exactly the initial point of local coordinate system, X, and Y, three coordinate axis of Z are respectively
Z=N=(n
X, p, n
Y, p, n
Z, p), wherein
The first direction angle of representation vector N, ψ=arccos (n
Z, p) complementary angle at third direction angle of representation vector.
Step 4:, utilize the kd tree of cloud data to search 15 or 30 neighbour's points for each point of cloud data;
Step 5: for the neighbour's point that finds, pass through three-dimensional coordinate transformation, the normal vector that the original coordinates that these neighbours are ordered and these neighbours are ordered all is converted into the coordinate of local coordinate system, be to be exactly the coordinate that the coordinate that these neighbours are ordered deducts the local coordinate system initial point coordinates of these neighbours' points in local coordinate system, three coordinate axis of normal vector coordinate that these neighbours are ordered and local coordinate system are made scalar product respectively, calculate the coordinate of normal vector in local coordinate system that these neighbours are ordered.
Step 6: the normal vector structure that utilizes each point of cloud data and normal vector thereof, neighbour's point, a neighbour to order is subtriangular, provides the approximate expression of normal curvature of the method transversal of a cloud according to sine; Described structure is subtriangular, and this triangle is determined by angle arm of angle theorem: the point of the normal curvature to be calculated in the cloud of setting up an office is p, and its neighbour's point is q
iPoint p and q
iNormal vector be respectively N and M
i, vectorial N and M
iAngle be β, vectorial N and vector
Angle be α, line segment | pq
i| be the limit, angle β then, angle α, the limit | pq
i| determined this triangle.The approximate expression of the normal curvature of the described method transversal that provides a cloud with sine is
K wherein
n iRepresent that the i neighbour puts the normal curvature of pairing method transversal, β puts the angle of normal vector and local coordinate system Z axle for the neighbour, the location vector that α is ordered for the neighbour and the supplementary angle at Z axle clamp angle, and the initial point of local coordinate system is p, neighbour's point is q
i, | pq
i| expression point q
iEuclidean distance with a p.Described
This expression formula adopts the approximate treatment form in actual computation
Wherein,
n
z=n
Z, i, the neighbour puts q
iLocal coordinate be (x
i, y
i, z
i), the neighbour puts q
iThe local coordinate of normal vector be (n
X, i, n
Y, i, n
Z, i).
Step 7: in local coordinate system, utilize normal curvature, according to Euler's formula (Euler Equation) structure nonlinear optimization problem, carry out identical transformation by Triangle Formula, this nonlinear optimization problem is converted into linear fit, obtains each element of Wei Enjiating matrix (Weingarten matrix); Described according to Euler's formula (Euler Equation) structure nonlinear optimization problem, establish principal curvatures and the principal direction that need ask a point in the cloud data, then
Be the nonlinear optimization problem of structure, wherein k
1, k
2Be principal curvatures to be asked, unknown number θ is the angle of the X-axis principal direction corresponding with maximum principal curvatures in the local coordinate system, θ
iFor the neighbour puts q
iThe angle of X-axis in the location vector of the subpoint of xOy face and the local coordinate system in local coordinate system.Described this nonlinear optimization problem is converted into linear fit, be exactly that normal curvature that all neighbours are ordered is as the dependent variable observed reading, the cosine value of all neighbours point and the deflection of the x axle of local coordinate system square, square the observed reading of the sine value of 2 times sine value of deflection, deflection as independent variable, make the ternary linear fit.Three fitting coefficient values are successively as three elements of the last triangle of second order symmetric matrix Weingarten matrix.
Step 8: utilize the svd (SVD decomposition) of matrix to obtain the eigenwert and the proper vector of Weingarten matrix;
Step 9: utilize the eigenwert of Weingarten matrix and proper vector to obtain principal curvatures and principal direction.Described eigenwert and the proper vector of obtaining the Weingarten matrix, if two eigenwerts equate that then this is an omphalion, proper vector is taken as (1,0) and (0,1).The eigenwert of the described Weingarten of utilization matrix is obtained principal curvatures, is as principal curvatures with two eigenwerts.The proper vector of the described Weingarten of utilization matrix is asked principal direction, is to use two components of two proper vectors as combination coefficient respectively, does the linear combination of the X-axis and the Y-axis of local coordinate system, as two principal directions.
The invention has the beneficial effects as follows proposition to the improved new method of three types of technology, is directly to calculate principal curvatures and principal direction on cloud data.Utilize the normal vector information of the coordinate information and the some cloud of some cloud.The difference of the present invention and forefathers' method is mainly reflected in, normal vector is directly used to determine the method transversal, carrying out principal curvatures by the normal curvature of method transversal estimates, rather than as the constraint condition of nonlinear programming problem, the present invention also finds the solution a linear system to nonlinear optimization the question resolves itself in addition.Therefore, time and space performance that the present invention calculates are also superior than previous methods, and experiment shows that the result of calculation of principal direction is also accurate than additive method.We utilize three-dimensional laser scanner to obtain surface information in kind, and utilize conventional method to calculate the normal vector of each point according to scan-data, provide the normal curvature estimator of method transversal again, pass through linear fit and Wei Enjiating (Weingarten) matrix computations at last and obtain principal curvatures and principal direction.The result of calculation that the present invention obtained can be used for each application of computer graphics, comprises that fields such as feature enhancing, surperficial simplification, grid optimization, feature extraction, data compression, skeletal extraction and 3D reconstruction in kind, virtual reality, computer game, natural scene simulation, city landscape design, data compression have important use and are worth.Utilize the present invention, can calculate the principal curvatures and the principal direction of cloud data fast, easily and accurately.
Description of drawings
Fig. 1 algorithm flow chart
Fig. 2 neighbour point and the determined triangle of normal vector thereof
Fig. 3 local space rectangular coordinate system and method transversal synoptic diagram
Design sketch after Fig. 4 anchor ring figure and the interpolation noise thereof
The error ratio of Fig. 5 anchor ring principal curvatures estimated result
The principal direction estimated result of Fig. 6 noiseless fingerprint type
Fig. 7 has the principal direction estimated result of noise fingerprint type
The principal direction estimated result of Fig. 8 noiseless elephant model
Fig. 9 has the principal direction estimated result of noise elephant model
Figure 10 branch model point cloud data
The principal direction of Figure 11 branch model point cloud data
The principal direction of Figure 12 branch model point cloud data trunk surface
The principal direction of Figure 13 branch model point cloud data trunk crotch
The principal direction of Figure 14 branch model point cloud data trunk recess
Embodiment
Describe each related detailed problem in the technical solution of the present invention in detail below in conjunction with accompanying drawing.Be to be noted that described embodiment only is intended to be convenient to the understanding of the present invention, and it is not played any qualification effect.
1, method general introduction (overview of approach)
As Fig. 1 the flow process of whole algorithm of the present invention is shown, the key step of algorithm of the present invention comprises:
1), the data pre-service, create the kd tree, calculate the normal vector of each point of cloud data;
2), pointwise calculates principal curvatures and principal direction, comprises 7 sub-steps: (a) set up normal curvature, (e) linear fit that local coordinate system, (b) search neighbour point, (c) neighbour point coordinate localization, (d) calculate the method transversal of the correspondence that each neighbour orders and go out Wei Enjiating (Weingarten) entry of a matrix element, (f) and obtain eigenwert and proper vector, (g) of Weingarten matrix and obtain principal curvatures and principal direction.
3), export result of calculation, the principal curvatures of memory point and principal direction, the principal direction of display dot.
2, data pre-service
The coordinate information that three dimensional point cloud is generally only had a few.Estimate principal curvatures and principal direction, should estimate the normal vector of each point earlier.And ask normal vector and principal curvatures, principal direction all to need to use neighbour's point, can learn from the computational geometry theory, one of quick method of searching that the neighbour orders is exactly the binary chop tree of setting up 3 dimension spaces of cloud data, abbreviate kd tree (k-dimensional tree) as, this is the very high data store organisation of search efficiency.So pretreatment stage need be finished the foundation of kd tree and the calculating of normal vector.
At first, set up the kd tree.In computational geometry, kd tree is one of data structure the most efficiently of the certified neighbour of searching.The kd tree is divided three dimensions based on the spatial positional information of point by the dichotomy iteration, realizes optimal storage.On the kd tree, the time complexity that carries out the k neighbor searching is O (log
2N), n is the number of the point of cloud data here.
Secondly, calculate the normal vector of each point.Each point for cloud data, utilize the kd tree of cloud data to search 15 or 30 neighbour's points, suppose that these neighbour's points come from same plane, so can put the absolute value of the residual error of fit Plane with these neighbours, multiply by the long-pending and structure least square problem of weight coefficient again, determining of power wherein is that the inverse of the Euclidean distance of ordering with each point in the cloud data and neighbour is as weights.Utilize least square method to simulate this plane, with the normal vector on this plane initial estimate as the normal vector of a cloud, estimate by the normal vector of weighted mean algorithm adjusting point cloud that then weights equal so that each puts the inverse of the Euclidean distance of ordering with the neighbour in the cloud data.
Principal curvatures and principal direction are calculated in 3 pointwises
Calculate the principal curvatures of each point in the cloud data that obtains of scanning and principal direction fast and exactly and be the main target among the present invention.Calculation Method is that pointwise iteration carries out.Principal curvatures and the principal direction of calculating a point (being designated as p) comprise following seven steps:
3.1 set up local coordinate system
Set up local coordinate system, shown this local space rectangular coordinate system as Fig. 3: partial 3 d rectangular coordinate system, the normal vector of the p that sets up an office are N=(n
X, p, n
Y, p, n
Z, p), then this p point is exactly the initial point of local coordinate system, X, and Y, three coordinate axis of Z are respectively
Z=N=(n
X, p, n
Y, p, n
Z, p), ψ=arccos (n wherein
Z, p),
3.2 search neighbour point
Because pretreatment stage has been set up the kd tree, with a p is query point, search the k neighbour based on Euclidean distance, such as k=15 neighbour or k=30 neighbour, determine the number that the neighbour orders according to the data scanning precision, scanning accuracy is low then gets 15 neighbour's points, otherwise gets 30 neighbour's points, the error threshold that the neighbour is searched in setting is 0.0, remembers q here
i(i=1,2 ..., m) m the neighbour's point that obtains for inquiry.
3.3 neighbour's point coordinate localization
Obtain the coordinate of all neighbour's points at local coordinate system.Method of the present invention can be described as following several steps.Suppose to wait that asking the point of principal curvatures is p, neighbour's point is q
i, with location vector
Coordinate as a q
iLocal coordinate, the essence of coordinate transformation is neighbour point have been done the translation transformation of a point here.
The normal vector that the neighbour is ordered is converted into the coordinate of local coordinate system.Method of the present invention is that the normal vector that each neighbour that pretreatment stage is obtained is ordered (is designated as M
i) direction cosine in local coordinate system are as the coordinate in local coordinate system of normal vector.
3.4 calculate the normal curvature that each neighbour puts corresponding method transversal
Suppose that the point, the neighbour that wait to ask principal curvatures and principal direction put and their normal vector has been determined a method transversal, estimate the normal curvature of this method transversal now at a p.
Wait to ask some p, the neighbour of principal curvatures and principal direction to put q
iAnd their normal vector N and M
iDetermine one subtriangular, put O, p, q by the neighbour shown in Fig. 2
iAnd normal vector N and M
iDetermined triangle.The method of determining is according to angle arm of angle theorem, and β puts the angle of normal vector and local coordinate system Z axle, the location vector pq that α is ordered for the neighbour for the neighbour
iWith the supplementary angle at Z axle clamp angle, line segment pq
iBe the limit.Subtriangular at this, follow the example of curvature according to sine and be
K wherein
n iRepresent that the i neighbour puts the normal curvature of pairing method transversal, | pq
i| expression point q
iEuclidean distance with a p.For the ease of calculating, formula above the coordinate substitution
The utilization triangle formula can be converted into following formula to this formula, as the estimator of normal curvature
Wherein,
The neighbour puts q
iLocal coordinate be (x
i, y
i, z
i), the neighbour puts q
iThe local coordinate of normal vector be (n
X, i, n
Y, i, n
Z, i).
3.5 the Weingarten matrix is obtained in linear regression
According to Euler's formula (Euler Equation) structure nonlinear optimization problem, establish principal curvatures and the principal direction that to ask a some p in the cloud data
Then
Be structure nonlinear optimization problem, wherein k
1, k
2Be to be asked and principal direction
Corresponding principal curvatures, θ is a unknown number, is the X-axis principal direction e corresponding with maximum principal curvatures in the local coordinate system
1Angle, the some Q
iBe that the neighbour puts q
iThe subpoint on the S of section, θ
iBe vectorial pQ
iAngle with X-axis in the local coordinate system.Fig. 3 illustrates method transversal and principal direction and q
i, Q
i, these points of p, angle θ
i, θ.
The present invention is above-mentioned nonlinear programming problem
Be converted into and find the solution following least square problem,
Wherein,
μ＝(A，B，C)
T，A＝k
1cos
2θ+k
2sin
2θ，B＝(k
2-k
1)cosθsinθ，C＝k
1sin
2θ+k
2cos
2θ
The finding the solution to be converted into of this step found the solution overdetermination system of linear equations M μ=R.Then, use the A that obtains, B, the value of C is constructed the Weingarten matrix
3.6 calculate the eigenwert and the proper vector of Weingarten matrix
Obtain the eigenwert and the proper vector of the Weingarten matrix of previous step, the size of eigenwert is sorted, big eigenwert is designated as k
1, it also is the maximum curvature of this point, and the proper vector of corresponding unit length is called big eigenwert characteristic of correspondence vector, and another less proper vector is designated as k
2, its value is the minimum curvature of this point, the proper vector of corresponding unit length is called less eigenwert characteristic of correspondence vector.
If this two eigenwerts equate that represent that promptly this point is an omphalion, and the principal direction of omphalion is any direction that is parallel to the section, direction is not only.The present invention is to get orthonormal basis (1,0) and (0,1) as proper vector to the disposal route of this particular point.
Obtain principal curvatures and principal direction 3.7 utilize eigenwert and proper vector
The proper vector that previous step calculates is two-dimentional, is with respect to the vector on the xOy face in the local coordinate system.Need be transformed into global coordinate system to them.The method that transforms be each component of maximum curvature characteristic of correspondence vector as combination coefficient, obtain the principal direction of the linear combination of the X-axis of local coordinate system and Y-axis as the maximum curvature correspondence, be principal direction e
1Similarly, each component of minimum curvature characteristic of correspondence vector as combination coefficient, is obtained the principal direction of the linear combination of the X-axis of local coordinate system and Y-axis as the minimum curvature correspondence, be e
2
Choosing of the value of principal curvatures and coordinate system is irrelevant, does not need to transform, and is the eigenwert k that previous step is calculated
1And k
2
4 results output
For result calculated, the invention provides two kinds of form outputs.First kind of mode shown by professional software for coordinate, normal vector, principal direction, the principal curvatures put are stored with document form again.The second way is for to be converted into Vector Message or colouring information to principal direction, principal curvature information, and binding site cloud data presentation is come out.
5 experimental results and conclusion
We are applied to the data of the different complexities that resolution data and actual scanning obtain with the method, compare with before two kinds of main principal curvatures principal direction methods of estimation.Proof by experiment, more accurately and reliably, robustness is also stronger to the estimation of principal curvatures and principal direction in the present invention.
5.1 the contrast experiment of analytic surface simulated data
The experiment of resolution data is used for illustrating that the new method that the present invention proposes compares the whole bag of tricks before more accurately and reliably.Resolution data is from an annulus analytic surface, and its analytic expression is known, and the anchor ring equation that the present invention uses is:
r(u，v)＝((R+rcosu)cos?v，(R+rcosu)sin?v，rsinu)
(0≤u≤2π，0≤v≤2π)
Parameters R=2 wherein, r=1.From this analytic surface, obtain 5000 stochastic sampling points according to even distribution of two dimension, can calculate the principal curvatures and the principal direction (the actual principal curvatures and the actual principal direction that are called sampled point) of each point according to the infinitesimal geometry formula.Then, these 5000 sampled points are regarded as the cloud data that scanning obtains.To each some p, add noise along the normal vector direction
Here
Be the normal vector of a p, a obeys the even distribution of [mh, mh], and m is the median of the distance between any 2, and h is a noise level, and the noise level with mistake in the experiment is h=0.1, and 0.2 ..., 1.0.Fig. 4 has shown the design sketch after anchor ring figure and the interpolation noise thereof, and wherein Fig. 4 (a) is initial annulus, and Fig. 4 (b) is for adding the anchor ring of noise.
The method that compares experiment with the present invention is Goldfeather cube of curved surface fitting method and Taubin method.The Goldfeather that published in 2004 cube curved surface fitting method is the accurate method of announcing at present, this method is different on mechanism with method transversal approximating method of the present invention, it is actually the part for the treatment of the point of asking principal curvatures and carries out the cubic surface match, obtain principal curvatures and principal direction according to analytic method then, this method takes in normal vector as constraint condition, therefore all more accurate than all methods of estimation in the past, robustness is also better.The Taubin method that nineteen ninety-five is openly issued then utilizes the neighbour to put structure polygon calculating curvature tensor, obtains principal curvatures and principal direction.This method is the typical algorithm of Curvature Estimation, and how much are improvement algorithm that its effect was announced before unlike 2003 or new algorithm difference, and these algorithms not usage vector march rate estimate that the accuracy of result of calculation is relatively poor.Therefore, the present invention is with the representative of Taubin method as these algorithms.
The contrast experiment carries out on the personal desktop computer, computer be configured to Intel (R) Core (TM) 2CPU, 4400@2G, 1.99GHz, 2.0G internal memory.Programming language is C++ and Opengl glut3.7.
What experiment showed is the geometric sense of two principal curvatures structures, i.e. mean curvature and Gaussian curvature.The error ratio that Fig. 5 has shown curvature Gaussian curvature and average Curvature Estimation result.
From Fig. 5 (a) Gaussian curvature evaluated error and Fig. 5 (b) mean curvature evaluated error as can be seen, estimated result of the present invention is little more many than Taubin method error, and noise level is high more, and superiority is remarkable more.More approaching from the estimated result of the estimated result of figure method of the present invention and Goldfeath method, therefore as follows the data list of experimental result.
Table 1 mean curvature is estimated the absolute error contrast table
As can be seen from Table 1, the present invention compares with the Goldfeath method, and except mean curvature error when noise level is low was bigger, all the other situation errors were littler, illustrated that calculating is more accurate.For the bigger situation of noise, advantage of the present invention is more obvious.
5.2 the contrast experiment of cloud data
The present invention and Goldfeath method are applied to the actual scanning data, have used two models to test.
First model is the data of " hand ".The height of this model is 202 long measures, and 6258 stochastic sampling points are arranged, and data itself have normal vector more accurately.Fig. 6 is the principal direction estimated result of noiseless fingerprint type, shows the principal direction estimated result of primary data figure and the present invention and Goldfeath method.Add noise along the normal vector direction for data point, noise level is 2.0 units, and then the positional information of normal vector and point is not entirely true, and it is the principal direction estimated result that noise fingerprint type is arranged that the principal direction of obtaining is presented at Fig. 7.Fig. 6 (a) is a raw data, and Fig. 6 (b) is experimental calculation result of the present invention, and Fig. 6 (c) is the result of calculation of Goldfeath method; Fig. 7 (a) is a raw data; Fig. 7 (b) is a result of calculation of the present invention, and Fig. 7 (c) is the calculation result data of Goldfeath method.From these figure as can be seen, when noise level is low, method of the present invention and Goldfeath method all have result preferably, method of the present invention is more not remarkable especially than the advantage of Goldfeath method, but when noise level strengthened, the principal direction that the Goldfeath method is estimated obviously became messy.In Fig. 7, the back of thumb, method of the present invention still embody former orderliness, and the Goldfeath method is more in disorder with being more or less the same among Fig. 6.The present invention is more accurate than Goldfeath method for this description of test, and robustness is also better.
Another model data is " elephant ".This point cloud model height is 75 long measures, comprises 6859 stochastic sampling points.Experimental technique is with " hand " model.Fig. 8 is noiseless elephant model and the principal direction estimated result that obtains under distinct methods thereof, and Fig. 9 is the principal direction estimated result that noise elephant model is arranged and obtain under distinct methods, and it is 2.0 data for noise level.Observe the back of elephant among Fig. 9, as can be seen, method of the present invention is more or less the same with muting situation, still embody original direction, and the Goldfeath method is more in disorder.It is more accurate than Goldfeath method that this experiment further specifies the present invention, more robust.Fig. 8 (a) is a raw data; Fig. 8 (b) is data of the present invention, and Fig. 8 (c) is the data of Goldfeath method, and Fig. 9 (a) is a raw data; Fig. 9 (b) is data of the present invention, and Fig. 9 (c) is the data of Goldfeath method.
5.3 the application of the present invention in complicated cloud data (branch model)
The point cloud model complexity that the texture ratio of tree is general is many, is mainly reflected in following 3 points: owing to block, the skewness of point, agglomerating sometimes, become line sometimes, sometimes cluster; The surface changes bigger, and the thickness of trunk changes greatly; The growth change of branch is abundant, causes the annexation complexity.Therefore, the principal direction of branch is estimated very difficult.
The branch point cloud model that the present invention uses is 12 meters of the height of trees, also has four branches except major branch.These point cloud model data have 6950 points.Experiment effect such as Figure 10 to Figure 14.Figure 10 is the original cloud data of branch model.Figure 11 is the principal direction figure of each point of branch model point cloud data.Figure 12 has shown the principal direction of each point of branch model point cloud data trunk surface, it is characterized in that the principal direction of principal curvatures the greater correspondence has embodied the cross-sectional direction of trunk, and the direction of growth that the principal direction of principal curvatures smaller correspondence has been portrayed trunk.Figure 13 has shown the principal direction feature at branch model point cloud data branch bifurcation place.Figure 14 has shown the principal direction feature of branch model point cloud data trunk surface recess, and the principal direction of these principal curvatures the greater correspondences is pointed to the center of depression.
Principal curvatures that the present invention proposes and principal direction computing method are characterised in that the principal curvatures and the principal direction of the normal vector calculation level that utilizes cloud data and each point.
Above-mentioned experimental result and utilize cloud data to ask for the method for principal direction and principal curvatures can be used for each application of computer graphics, has high confidence level, simple to operate, characteristics that application prospect is wide.
The above; only be the embodiment among the present invention; but protection scope of the present invention is not limited thereto; anyly be familiar with the people of this technology in the disclosed technical scope of the present invention; can understand conversion or the replacement expected; all should be encompassed in of the present invention comprising within the scope, therefore, protection scope of the present invention should be as the criterion with the protection domain of claims.
Claims (15)
1. the principal curvatures of a cloud data and principal direction method of estimation is characterized in that, this principal curvatures and principal direction estimating step comprise:
Step 1: utilize laser scanner scans directly to gather cloud data and to the cloud data pre-service, coordinate according to each point in the cloud data carries out spatial division, realizes that the data store organisation of three-dimensional binary chop tree is called kd tree (k-dimensional tree);
Step 2: for each point of cloud data, utilize the kd tree of cloud data to search 15 or 30 neighbour's points, according to least square method these neighbour's points are simulated a plane, as an initial estimate of cloud normal vector, the normal vector of each point by weighted mean algorithm correction cloud data is estimated then with the normal vector on this plane;
Step 3:, utilize its normal vector, section structure partial 3 d rectangular coordinate system for each point of cloud data;
Step 4:, utilize the kd tree of cloud data to search 15 or 30 neighbour's points for each point of cloud data;
Step 5: for the neighbour's point that finds, by three-dimensional coordinate transformation, the normal vector that the original coordinates that these neighbours are ordered and these neighbours are ordered all is converted into the coordinate of local coordinate system;
Step 6: the normal vector structure that utilizes each point of cloud data and normal vector thereof, neighbour's point, a neighbour to order is subtriangular, provides the approximate expression of normal curvature of the method transversal of a cloud according to sine;
Step 7: in local coordinate system, utilize normal curvature, according to Euler's formula (Euler Equation) structure nonlinear optimization problem.Carry out identical transformation by Triangle Formula, this nonlinear optimization problem is converted into linear fit, obtain each element of Wei Enjiating matrix (Weingarten matrix);
Step 8: utilize the svd (SVD decomposition) of matrix to obtain the eigenwert and the proper vector of Weingarten matrix;
Step 9: utilize the eigenwert of Weingarten matrix and proper vector to obtain principal curvatures and principal direction.
2. by the described method of claim 1, it is characterized in that the coordinate of described each point all is the original coordinates that adopts laser scanner to produce.
3. by the described method of claim 1, it is characterized in that, the normal vector of each point of described weighted mean algorithm correction cloud data is estimated, be so that each puts the inverse of the Euclidean distance of ordering with the neighbour as weights in the cloud data, the inverse of described Euclidean distance, if distance value is 0, then do not calculate this neighbour's point.
4. by the described method of claim 1, it is characterized in that, described these neighbours being put according to least square method simulates a plane, wherein need construct the cum rights least square problem during fit Plane, this least square problem is the absolute value that these neighbours put the residual error of fit Plane, multiply by again the long-pending of weight coefficient and minimum problems.
5. by the described method of claim 4, it is characterized in that described weight coefficient is so that each puts the inverse of the Euclidean distance of ordering with the neighbour as weights in the cloud data.
6. by the described method of claim 1, it is characterized in that, described partial 3 d rectangular coordinate system, its building method is, for some p in the cloud data, if the normal vector of some p is N=(n
X, p, n
Y, p, n
Z, p), then this p is exactly the initial point of local coordinate system, X, and Y, three coordinate axis of Z are respectively
Z=N=(n
X, p, n
Y, p, n
Z, p), wherein
The first direction angle of representation vector N, ψ=arccos (n
Z, p) complementary angle at third direction angle of representation vector.
7. by the described method of claim 1, it is characterized in that, the normal vector that the described original coordinates that these neighbours are ordered and these neighbours are ordered all is converted into the coordinate of local coordinate system, be to be exactly the coordinate that the coordinate that these neighbours are ordered deducts the local coordinate system initial point coordinates of these neighbours' points in local coordinate system, three coordinate axis of normal vector coordinate that these neighbours are ordered and local coordinate system are made scalar product respectively, calculate the coordinate of normal vector in local coordinate system that these neighbours are ordered.
8. by the described method of claim 1, it is characterized in that described structure is subtriangular, this triangle is determined by angle arm of angle theorem: the point of the normal curvature to be calculated in the cloud of setting up an office is p, and its neighbour's point is q
iPoint p and q
iNormal vector be respectively N and M
i, vectorial N and M
iAngle be β, vectorial N and vector
Angle be α, line segment | pq
i| be the limit, angle β then, angle α, the limit | pq
i| determined this triangle.
9. by the described method of claim 1, it is characterized in that the approximate expression of the normal curvature of the described method transversal that provides a cloud with sine is
K wherein
n iRepresent that the i neighbour puts the normal curvature of pairing method transversal, β puts the angle of normal vector and local coordinate system Z axle for the neighbour, the location vector that α is ordered for the neighbour and the supplementary angle at Z axle clamp angle, and the initial point of local coordinate system is p, neighbour's point is q
i, | pq
i| expression point q
iEuclidean distance with a p.
10. by the described method of claim 9, it is characterized in that described approximate expression
In actual computation, adopt the approximate treatment form
Wherein,
The neighbour puts q
iLocal coordinate be (x
i, y
i, z
i), the neighbour puts q
iThe local coordinate of normal vector be (n
X, i, n
Y, i, n
Z, i).
11. by the described method of claim 1, it is characterized in that, described according to Euler's formula (EulerEquation) structure nonlinear optimization problem, establish principal curvatures and the principal direction that need ask a point in the cloud data, then
Be the nonlinear optimization problem of structure, wherein k
1, k
2Be principal curvatures to be asked, unknown number θ is the angle of the X-axis principal direction corresponding with maximum principal curvatures in the local coordinate system, θ
iFor the neighbour puts q
iThe angle of X-axis in the location vector of the subpoint of xOy face and the local coordinate system in local coordinate system.
12. by the described method of claim 1, it is characterized in that, described this nonlinear optimization problem is converted into linear fit, be exactly that normal curvature that all neighbours are ordered is as the dependent variable observed reading, the cosine value of all neighbours point and the deflection of the x axle of local coordinate system square, square the observed reading of the sine value of 2 times sine value of deflection, deflection as independent variable, make the ternary linear fit.Three fitting coefficient values are successively as three elements of the last triangle of second order symmetric matrix Weingarten matrix.
13. by the described method of claim 1, it is characterized in that, described eigenwert and the proper vector of obtaining the Weingarten matrix, if two eigenwerts equate that then this is an omphalion, proper vector is taken as (1,0) and (0,1).
14., it is characterized in that the eigenwert of the described Weingarten of utilization matrix is obtained principal curvatures, be as principal curvatures with two eigenwerts by the described method of claim 1.
15. by the described method of claim 1, it is characterized in that the proper vector of the described Weingarten of utilization matrix is asked principal direction, is to use two components of two proper vectors as combination coefficient respectively, do the linear combination of the X-axis and the Y-axis of local coordinate system, as two principal directions.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN2008102393279A CN101751695B (en) | 2008-12-10 | 2008-12-10 | Estimating method of main curvature and main direction of point cloud data |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN2008102393279A CN101751695B (en) | 2008-12-10 | 2008-12-10 | Estimating method of main curvature and main direction of point cloud data |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN101751695A true CN101751695A (en) | 2010-06-23 |
| CN101751695B CN101751695B (en) | 2012-05-23 |
Family
ID=42478633
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN2008102393279A Expired - Fee Related CN101751695B (en) | 2008-12-10 | 2008-12-10 | Estimating method of main curvature and main direction of point cloud data |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN101751695B (en) |
Cited By (25)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102306397A (en) * | 2011-07-08 | 2012-01-04 | 中国科学院自动化研究所 | Method for meshing point cloud data |
| CN102750730A (en) * | 2012-06-15 | 2012-10-24 | 北京理工大学 | Characteristic-maintained point cloud data compacting method |
| CN102750449A (en) * | 2012-06-20 | 2012-10-24 | 北京航空航天大学 | Point cloud linear feature extraction method based on substep three-dimensional space and feature dimension mapping |
| CN102799763A (en) * | 2012-06-20 | 2012-11-28 | 北京航空航天大学 | Point cloud posture standardization-based method for extracting linear characteristic of point cloud |
| CN102945551A (en) * | 2012-10-16 | 2013-02-27 | 同济大学 | Graph theory based three-dimensional point cloud data plane extracting method |
| CN103593874A (en) * | 2013-11-08 | 2014-02-19 | 浙江工业大学 | Point cloud normal vector redirection method and device based on uniform grid local focusing |
| CN104063499A (en) * | 2014-07-04 | 2014-09-24 | 纵横皆景（北京)信息技术有限公司 | Space vector POI extracting method based on vehicle-mounted space information collection |
| CN104123746A (en) * | 2014-07-10 | 2014-10-29 | 上海大学 | Calculating method for three-dimension scanning point cloud real-time normal vectors |
| CN105067276A (en) * | 2015-07-31 | 2015-11-18 | 中国人民解放军信息工程大学 | Engine thrust line measurement method |
| CN105115441A (en) * | 2015-04-23 | 2015-12-02 | 北京理工大学 | Feature point extraction automatic segmenting method for profile of revolution solid part |
| CN105117508A (en) * | 2015-05-15 | 2015-12-02 | 重庆大学 | Scan path generating method based on selective laser fusing technology |
| CN105157597A (en) * | 2015-10-23 | 2015-12-16 | 西安近代化学研究所 | Method for measuring deformation of effect target with laser |
| CN105629278A (en) * | 2014-11-21 | 2016-06-01 | 桂林电子科技大学 | GNSS pseudo-range single-point positioning-based high-precision mutual difference value median weighted positioning method |
| CN106056659A (en) * | 2016-05-27 | 2016-10-26 | 山东科技大学 | Building corner space position automatic extraction method in vehicle laser scanning point cloud |
| CN106441155A (en) * | 2016-11-14 | 2017-02-22 | 绍兴文理学院 | Structural plane contour line sampling accuracy determining method |
| CN106934853A (en) * | 2017-03-13 | 2017-07-07 | 浙江优迈德智能装备有限公司 | A kind of acquiring method of the automobile workpiece surface normal vector based on point cloud model |
| CN107248966A (en) * | 2017-06-08 | 2017-10-13 | 黑龙江大学 | Single node dynamically receives sensor noise analysis model and analysis method |
| CN108171761A (en) * | 2017-12-13 | 2018-06-15 | 北京大学 | A kind of point cloud inner frame coding method and device that transformation is schemed based on Fourier |
| CN109035153A (en) * | 2018-06-06 | 2018-12-18 | 链家网（北京）科技有限公司 | A kind of modification method and device of point cloud data |
| CN111311576A (en) * | 2020-02-14 | 2020-06-19 | 易思维（杭州）科技有限公司 | Point cloud information-based defect detection method |
| CN112184869A (en) * | 2020-10-09 | 2021-01-05 | 北京理工大学 | Point cloud simplification method for keeping geometric features based on absolute Gaussian curvature estimation |
| CN112561984A (en) * | 2020-12-16 | 2021-03-26 | 南京邮电大学 | Point cloud principal curvature direction calculation method and process |
| CN112767512A (en) * | 2020-12-31 | 2021-05-07 | 广州小鹏自动驾驶科技有限公司 | Environment linear element generation method and device, electronic equipment and storage medium |
| CN113465552A (en) * | 2021-06-29 | 2021-10-01 | 湖北中烟工业有限责任公司 | Surface flatness detection method and device for packaging box |
| CN114880332A (en) * | 2022-07-08 | 2022-08-09 | 深圳市信润富联数字科技有限公司 | Point cloud data storage method and device, electronic equipment and storage medium |
Family Cites Families (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB0225716D0 (en) * | 2002-11-05 | 2002-12-11 | Univ Edinburgh | Virtual models |
| CN1885349A (en) * | 2006-07-05 | 2006-12-27 | 东南大学 | Point cloud hole repairing method for three-dimensional scanning |
| CN1928921A (en) * | 2006-09-22 | 2007-03-14 | 东南大学 | Automatic searching method for characteristic points cloud band in three-dimensional scanning system |
| CN101067858A (en) * | 2006-09-28 | 2007-11-07 | 腾讯科技（深圳）有限公司 | Network advertisment realizing method and device |
-
2008
- 2008-12-10 CN CN2008102393279A patent/CN101751695B/en not_active Expired - Fee Related
Cited By (42)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102306397A (en) * | 2011-07-08 | 2012-01-04 | 中国科学院自动化研究所 | Method for meshing point cloud data |
| CN102750730A (en) * | 2012-06-15 | 2012-10-24 | 北京理工大学 | Characteristic-maintained point cloud data compacting method |
| CN102750449B (en) * | 2012-06-20 | 2015-05-20 | 北京航空航天大学 | Point cloud linear feature extraction method based on substep three-dimensional space and feature dimension mapping |
| CN102799763A (en) * | 2012-06-20 | 2012-11-28 | 北京航空航天大学 | Point cloud posture standardization-based method for extracting linear characteristic of point cloud |
| CN102799763B (en) * | 2012-06-20 | 2015-09-02 | 北京航空航天大学 | A kind of based on a cloud attitude standardized some cloud line feature extraction method |
| CN102750449A (en) * | 2012-06-20 | 2012-10-24 | 北京航空航天大学 | Point cloud linear feature extraction method based on substep three-dimensional space and feature dimension mapping |
| CN102945551A (en) * | 2012-10-16 | 2013-02-27 | 同济大学 | Graph theory based three-dimensional point cloud data plane extracting method |
| CN102945551B (en) * | 2012-10-16 | 2015-02-18 | 同济大学 | Graph theory based three-dimensional point cloud data plane extracting method |
| CN103593874A (en) * | 2013-11-08 | 2014-02-19 | 浙江工业大学 | Point cloud normal vector redirection method and device based on uniform grid local focusing |
| CN103593874B (en) * | 2013-11-08 | 2016-07-27 | 浙江工业大学 | Point cloud normal vector reorientation method and device based on uniform grid local focal |
| CN104063499A (en) * | 2014-07-04 | 2014-09-24 | 纵横皆景（北京)信息技术有限公司 | Space vector POI extracting method based on vehicle-mounted space information collection |
| CN104123746A (en) * | 2014-07-10 | 2014-10-29 | 上海大学 | Calculating method for three-dimension scanning point cloud real-time normal vectors |
| CN104123746B (en) * | 2014-07-10 | 2017-07-25 | 上海大学 | The computational methods of real-time normal vector in a kind of 3-D scanning point cloud |
| CN105629278A (en) * | 2014-11-21 | 2016-06-01 | 桂林电子科技大学 | GNSS pseudo-range single-point positioning-based high-precision mutual difference value median weighted positioning method |
| CN105629278B (en) * | 2014-11-21 | 2017-12-12 | 桂林电子科技大学 | A kind of mutual deviation intermediate value weighting localization method of high-precision GNSS pseudorange One-Point Location |
| CN105115441A (en) * | 2015-04-23 | 2015-12-02 | 北京理工大学 | Feature point extraction automatic segmenting method for profile of revolution solid part |
| CN105117508A (en) * | 2015-05-15 | 2015-12-02 | 重庆大学 | Scan path generating method based on selective laser fusing technology |
| CN105117508B (en) * | 2015-05-15 | 2018-05-22 | 重庆大学 | Scan path generation method based on selective laser melting technology |
| CN105067276B (en) * | 2015-07-31 | 2017-06-06 | 中国人民解放军信息工程大学 | A kind of motor power line measuring method |
| CN105067276A (en) * | 2015-07-31 | 2015-11-18 | 中国人民解放军信息工程大学 | Engine thrust line measurement method |
| CN105157597A (en) * | 2015-10-23 | 2015-12-16 | 西安近代化学研究所 | Method for measuring deformation of effect target with laser |
| CN105157597B (en) * | 2015-10-23 | 2017-09-29 | 西安近代化学研究所 | A kind of method of laser measurement effect target deformation |
| CN106056659A (en) * | 2016-05-27 | 2016-10-26 | 山东科技大学 | Building corner space position automatic extraction method in vehicle laser scanning point cloud |
| CN106056659B (en) * | 2016-05-27 | 2018-09-21 | 山东科技大学 | Building angle point spatial position extraction method in Vehicle-borne Laser Scanning point cloud |
| CN106441155A (en) * | 2016-11-14 | 2017-02-22 | 绍兴文理学院 | Structural plane contour line sampling accuracy determining method |
| CN106441155B (en) * | 2016-11-14 | 2018-11-30 | 绍兴文理学院 | A kind of determination method of structural plane contour line sampling precision |
| CN106934853A (en) * | 2017-03-13 | 2017-07-07 | 浙江优迈德智能装备有限公司 | A kind of acquiring method of the automobile workpiece surface normal vector based on point cloud model |
| CN107248966B (en) * | 2017-06-08 | 2020-02-28 | 黑龙江大学 | Single-node dynamic receiving sensor noise analysis system and analysis method |
| CN107248966A (en) * | 2017-06-08 | 2017-10-13 | 黑龙江大学 | Single node dynamically receives sensor noise analysis model and analysis method |
| CN108171761B (en) * | 2017-12-13 | 2020-10-16 | 北京大学 | Point cloud intra-frame coding method and device based on Fourier image transformation |
| CN108171761A (en) * | 2017-12-13 | 2018-06-15 | 北京大学 | A kind of point cloud inner frame coding method and device that transformation is schemed based on Fourier |
| CN109035153B (en) * | 2018-06-06 | 2019-07-09 | 贝壳找房(北京)科技有限公司 | A kind of modification method and device of point cloud data |
| CN109035153A (en) * | 2018-06-06 | 2018-12-18 | 链家网（北京）科技有限公司 | A kind of modification method and device of point cloud data |
| CN111311576A (en) * | 2020-02-14 | 2020-06-19 | 易思维（杭州）科技有限公司 | Point cloud information-based defect detection method |
| CN112184869A (en) * | 2020-10-09 | 2021-01-05 | 北京理工大学 | Point cloud simplification method for keeping geometric features based on absolute Gaussian curvature estimation |
| CN112561984A (en) * | 2020-12-16 | 2021-03-26 | 南京邮电大学 | Point cloud principal curvature direction calculation method and process |
| CN112561984B (en) * | 2020-12-16 | 2022-09-13 | 南京邮电大学 | Point cloud principal curvature direction calculation method and process |
| CN112767512A (en) * | 2020-12-31 | 2021-05-07 | 广州小鹏自动驾驶科技有限公司 | Environment linear element generation method and device, electronic equipment and storage medium |
| CN112767512B (en) * | 2020-12-31 | 2024-04-19 | 广州小鹏自动驾驶科技有限公司 | Method and device for generating environment linear element, electronic equipment and storage medium |
| CN113465552A (en) * | 2021-06-29 | 2021-10-01 | 湖北中烟工业有限责任公司 | Surface flatness detection method and device for packaging box |
| CN114880332A (en) * | 2022-07-08 | 2022-08-09 | 深圳市信润富联数字科技有限公司 | Point cloud data storage method and device, electronic equipment and storage medium |
| CN114880332B (en) * | 2022-07-08 | 2022-09-16 | 深圳市信润富联数字科技有限公司 | Point cloud data storage method and device, electronic equipment and storage medium |
Also Published As
| Publication number | Publication date |
|---|---|
| CN101751695B (en) | 2012-05-23 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN101751695B (en) | Estimating method of main curvature and main direction of point cloud data | |
| DeHaemer Jr et al. | Simplification of objects rendered by polygonal approximations | |
| CN104616349B (en) | Scattered point cloud data based on local surface changed factor simplifies processing method | |
| Ji et al. | A novel simplification method for 3D geometric point cloud based on the importance of point | |
| CN101021954A (en) | Three-dimensional scanning point cloud compressing method | |
| CN104835202A (en) | Quick three-dimensional virtual scene constructing method | |
| CN104616345A (en) | Octree forest compression based three-dimensional voxel access method | |
| CN105654483A (en) | Three-dimensional point cloud full-automatic registration method | |
| CN108053483A (en) | A kind of Wei Nuotu three-dimensional grid reconstructing methods accelerated based on GPU | |
| Patrikalakis et al. | Representation of piecewise continuous algebraic surfaces in terms of B-splines | |
| US8736608B2 (en) | System and method for rendering surface materials | |
| CN103700135B (en) | A kind of three-dimensional model local spherical mediation feature extracting method | |
| Zhang et al. | Efficient and accurate Hausdorff distance computation based on diffusion search | |
| CN108230452A (en) | A kind of model filling-up hole method based on textures synthesis | |
| CN109345571A (en) | A kind of point cloud registration method based on extension Gaussian image | |
| Gorman et al. | A systematic approach to unstructured mesh generation for ocean modelling using GMT and Terreno | |
| Tymków et al. | 3D GIS for flood modelling in river valleys | |
| CN107818578B (en) | Rapid face model reconstruction algorithm and system based on registration method | |
| CN115760954A (en) | Method for rapidly calculating surface area of complex surface based on point cloud data | |
| Lee et al. | Shrinking: Another method for surface reconstruction | |
| Su et al. | 3D reconstruction of submarine landscape ecological security pattern based on virtual reality | |
| Shu et al. | Research on spatial interpolation of meteorological elements in Anhui Province based on ANUSPLIN | |
| Szombara | Comparison of methods used in cartography for the skeletonisation of areal objects | |
| Cao et al. | Design of developable surface via CSA-based modification of boundary curves | |
| CN106504325A (en) | A kind of DEM feature point extraction parallel methods based on CUDA |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| C14 | Grant of patent or utility model | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20120523 Termination date: 20211210 |