CN1885349A - Point cloud hole repairing method for three-dimensional scanning - Google Patents

Abstract

The invention relates to a point hole filling method for supplying curvature polymerizing accuracy, wherein the invention comprises: selecting the coordinate point Ps needed to initially polymerize curvature at the periphery of point hole; using least square method to polymerize the selected coordinate Ps; to obtain the initial polymerized curvature S (u, v, w); based on approach method with the Newton iterate method, optimizing the polymerized curvature, to improve the polymerized accuracy; said curvature is based on the constant-parameter curvature to select line and select point on the line, to calculate the point needed to be filled, to realize smooth polymerizing filling. The invention can confirm smooth and conformal property.

Description

The method for filling dot cloud hole of 3-D scanning

Technical field

The present invention relates to a kind of method for repairing and mending, relate in particular to a kind of method for filling dot cloud hole of 3-D scanning three-dimensional picture.

Background technology

Reverse-engineering (Reverse Engineering, RE) technology is the later stage eighties 20th century to appear at the new technology in the advanced manufacturing field, it generally comprises four basic links: three-dimensional body detects and conversion (acquisition of physical data), data pre-service (put cloud processing, identification, look splicing more), the foundation of cad model (surface reconstruction), the moulding of CAM product, its basic flow sheet as shown in Figure 1.In the process that three-dimensional body detects and changes, by the three-dimensional digital scanner three-dimensional scanning survey is fast carried out on the mock-up surface, under the prerequisite that satisfies the discrete sampling speed and the quality of data, obtain the 3 d-dem data of product, the appearance of dot cloud hole has caused the imperfect of these data, therefore hole is compensated that promptly data to be carried out pre-service be a ring of forming a connecting link very crucial in the reverse-engineering, directly influence the quality of reconstruct success or not and cad model, its follow-up link is played very crucial restrictive function.The present invention mainly relates in the digitized process of reverse-engineering, a kind of automatic compensating method when obtaining the product point cloud model and hole occurs with 3 D scanning system (accompanying drawing 2).

In recent years, the algorithm of filling up of dot cloud hole has all been obtained very big progress at home and abroad, delivered a considerable amount of documents, the some of them algorithm has obtained to use comparatively widely, as the algorithm of filling up based on hole in energy-optimised and segmentation, triangle grid model, the mesh surface model.The point cloud model that these algorithms need earlier 3-D scanning directly to be obtained is done certain processing in early stage or dot cloud hole is carried out Boundary Recognition, and real-time is not strong, and complexity is also than higher.In application of practical project, should be able in time solve the problem that occurs.

Document " Minimal energy surfaces using parametric splines. " (Gregory E.Fasshauer, LarryL.Schumarker.Computer Aided Geometric Design, 1996,13:45～79) by finding the solution optimization aim function based on " strain energy of distortion function ", realization is filled up hole, guaranteed certain fairness, yet these class methods need subdivision curved surface mostly, and a plurality of subsurface sheets are spliced, therefore the continuity of surface boundary is had relatively high expectations, be difficult to reach the Second Order Continuous between curved surface usually.Because the related algorithm comparative maturity of existing triangle grid model, existing algorithm all is based on this model mostly, document " A study of stereolithography file errors and repair " (Leong K F for example, ChuaC K, Ng Y M.International Journal of Advanced Manufacturing, 1996,12:415～422) hole repairing is summed up as the triangulation problem of a space polygon.But only adopt original hole polygon vertex mostly when the new triangular plate of structure, do not increase new triangular plate summit, thereby be difficult to obtain to be used to preferably fill up the triangular plate shape of hole, it is not ideal enough to fill up effect.And it is bigger that this class algorithm is set up the triangle grid model operand for the cloud data programming of complexity, in filling up the process of hole, also need to change the topological structure of triangle gridding, therefore have triangle grid model is revised and the shortcoming of designed capacity deficiency again, complexity height, these shortcomings have all limited its application in practice.Filling algorithm to a class polygon hole is not suitable for general point cloud model.Filling algorithm for general surface mesh all needs to obtain the hole boundary information accurately, and difficulty is big, is difficult for realizing.Compensate in the algorithmic procedure of hole by scattered point set around the dot cloud hole is carried out surface fitting, the parametrization of point at random is essential.Even parametrization, entad parametrization and accumulation Chord Length Parameterization method are arranged usually, and these methods are primarily aimed at the data point that is topological rectangular array, to the cloud data of random distribution, need sort to it, difficulty is also bigger.

Traditional triangular surface interpolation algorithm has also obtained using comparatively widely, has also obtained effect preferably simultaneously.Document " An Adaptive Method for Smooth Surface Approximation to Scattered 3D Points. " (Park H for example, KimK.ComputerAided Design, 1995,27 (12): the adaptive-interpolation algorithm of the structure smooth surface match point at random that proposes 929～939).Though this class interpolation algorithm velocity ratio is very fast, and its fatal shortcoming is arranged, that is: the 1 non-occluding surface that can only handle monodrome; 2 will suppose that the local derviation arrow is linear distribution on the boundary curve of territory; The curved surface of 3 reconstruct depends on the local derviation that estimates and vows, thus the surface interpolation method to discrete point approach effect and bad, and the big efficient of calculated amount is low.

In the application process of reality, the some cloud master pattern that normally has magnanimity point at random that obtains with 3 D scanning system.Just inevitably have the hole phenomenon this moment, it is crucial that these holes are filled up timely.For this reason, use a kind of new algorithm that hole is compensated among the present invention.Be difficult point in this type of algorithm how at random some parametrization and the fitting precision that improves curved surface.What propose among the present invention carries out parameterized method and can reach the iterative approach optimization method of curved surface the smooth match of hole is filled to point at random.

Summary of the invention

The invention provides a kind of method for filling dot cloud hole that the 3-D scanning of surface fitting degree of accuracy can be provided.

The present invention adopts following technical scheme:

A kind of method for filling dot cloud hole of the 3-D scanning based on the triangular domain bezier surface:

The first step: around dot cloud hole and in the screen coordinate plane, set a triangle ABC, the regional extent of this triangle ABC can make dot cloud hole and the projection of point on every side to the screen coordinate plane thereof fall in the triangle ABC, and the some P of fitting surface when projection fallen into point in the triangle ABC as perforations adding _s(s=0,1 ..., m-1), according to the some P of fitting surface _sProjection P on triangle ABC plane _s' its curved surface parametrization coordinate of position calculation (u _s, v _s, w _s), u _s=(Δ AP _s' the B area)/(Δ ABC area), v _s=(Δ AP _s' the C area)/(Δ ABC area), w _s=(Δ BP _s' the C area)/(Δ ABC area), with the some P of fitting surface _s(s=0,1 ..., coordinate m-1) and curved surface parametrization coordinate (u thereof _s, v _s, w _s) n Bezier surface equation of substitution and obtain the reference mark of n Bezier curved surface with least square method, thereby obtain initial fitting curved surface S (u, v, w);

Second step: the some P that obtains each fitting surface _s(s=0,1 ..., m-1) to the distance vector d of curved surface (u, v, w) and curved surface respectively to the partial differential S of corresponding point parametric direction _u(u, v, w), S _v(u, v, w), S _w(u, v, w), order:

$\left\{\begin{array}{c}f(u,v,w)=d(u,v,w)\·S_u(u,v,w)=0\\ g(u,v,w)=d(u,v,w)\·S_v(u,v,w)=0\\ h(u,v,w)=d(u,v,w)\·S_w(u,v,w)=0\end{array}\right.$

The point P of fitting surface _sThe parametrization coordinate be (u _s, v _s, w _s), with (u _s, v _s, w _s) be initial estimate, find the solution above system of equations according to Newton iteration method, have:

Hσ ^T＝κ ^T

In the formula:

σ=(δ u, δ v, δ w), wherein, δ u, δ v, δ w are curved surface u, v, the iteration step length on three directions of w.

κ＝-(f(u _s，v _s，w _s)，g(u _s，v _s，w _s)，h(u _s，v _s，w _s))

$H=\left[\begin{array}{ccc}{f}_u& f_v& f_w\\ g_u& g_v& g_w\\ h_u& h_v& h_w\end{array}\right]=\left[\begin{array}{ccc}{\left|\right|S_u\left|\right|}^2+d\·S_{\mathrm{uu}}& S_v\·S_u+d\·S_{\mathrm{uv}}& S_w\·S_u+d\·S_{\mathrm{uw}}\\ S_u\·S_v+d\·S_{\mathrm{vu}}& {\left|\right|S_v\left|\right|}^2+d\·S_{\mathrm{vv}}& S_w\·S_v+d\·S_{\mathrm{vw}}\\ S_u\·S_w+d\·S_{\mathrm{wu}}& S_v\·S_w+d\·S_{\mathrm{wv}}& {\left|\right|S_w\left|\right|}^2+d\·S_{\mathrm{ww}}\end{array}\right]$

In the formula, d=d (u _s, v _s, w _s); f _u, f _v, f _w, g _u, g _v, g _w, h _u, h _v, h _wBe illustrated respectively in point (u _s, v _s, w _s) locate corresponding vector to u, v, the single order partial derivative of w; S _Uu, S _Uv, S _Uw, S _Vv, S _Vu, S _Vw, S _Ww, S _Wu, S _WvBe that (u, v is w) at point (u for curved surface S _s, v _s, w _s) locate respectively to u v, the second-order partial differential coefficient of w.

Then can get:

$\left[\begin{array}{ccc}{\left|\right|S_u\left|\right|}^2+d\·S_{\mathrm{uu}}& S_v\·S_u+d\·S_{\mathrm{uv}}& S_w\·S_u+d\·S_{\mathrm{uw}}\\ S_u\·S_v+d\·S_{\mathrm{vu}}& {\left|\right|S_v\left|\right|}^2+d\·S_{\mathrm{vv}}& S_w\·S_v+d\·S_{\mathrm{vw}}\\ S_u\·S_w+d\·S_{\mathrm{wu}}& S_v\·S_w+d\·S_{\mathrm{wv}}& {\left|\right|S_w\left|\right|}^2+d\·S_{\mathrm{ww}}\end{array}\right]\left[\begin{array}{c}\mathrm{\δu}\\ \mathrm{\δv}\\ \mathrm{\δw}\end{array}\right]=-\left[\begin{array}{c}f(u_s,v_s,w_s)\\ g(u_s,v_s,w_s)\\ h(u_s,v_s,w_s)\end{array}\right]$

According to the definition of triangle Bezier curved surface δ u+ δ v+ δ w=0 as can be known, i.e. therefore δ w=-δ u-δ v obtains following iterative equation group:

$\left[\begin{array}{cc}{\left|\right|S_u\left|\right|}^2-S_w\·S_u+d\·(S_{\mathrm{uu}}-S_{\mathrm{uw}})& S_v\·S_u-S_w\·S_u+d(S_{\mathrm{uv}}-S_{\mathrm{uw}})\\ S_u\·S_v-S_w\·S_v+d(S_{\mathrm{vu}}-S_{\mathrm{vw}})& {\left|\right|S_v\left|\right|}^2-S_w\·S_v+d\·(S_{\mathrm{vv}}-S_{\mathrm{vw}})\\ S_u\·S_w-{\left|\right|S_u\left|\right|}^2+d\·(S_{\mathrm{wu}}-S_{\mathrm{ww}})& S_v\·S_w-{\left|\right|S_w\left|\right|}^2+d\·(S_{\mathrm{wv}}-S_{\mathrm{ww}})\end{array}\right]\left[\begin{array}{c}\mathrm{\δu}\\ \mathrm{\δv}\end{array}\right]=-\left[\begin{array}{c}f(u_s,v_s,w_s)\\ g(u_s,v_s,w_s)\\ h(u_s,v_s,w_s)\end{array}\right]$

Wherein, δ u, δ v are u, the iteration step length on the v both direction.S _Uu, S _Uv, S _Uw, S _Vv, S _Vu, S _Vw, S _Ww, S _Wu, S _WvBe that (u, v is w) at point (u for curved surface S _s, v _s, w _s) locate respectively u, v, the second-order partial differential coefficient of w, iterative up to $1/m\underset{s=0}{\overset{m-1}{\mathrm{\Σ}}}\left|\right|d(u_s+\mathrm{\δu},v_s+\mathrm{\δv},w_s+\mathrm{\δw})-d(u_s,v_s,w_s)\left|\right|\≤\mathrm{\ϵ},$ ε is for presetting the surface fitting precision, thus the triangle Bezier curved surface S ' that obtains finally determining (u, v, w);

The 3rd step: at described triangle Bezier curved surface S ' (u, v, w) go up based on curvature etc. the parameter line taking, online more first-class parameter is got a little, be used to fill up dot cloud hole, needing at first that in asking the process of curvature three-dimensional point cloud is deleted lattice divides, this deletes the minimum external square that lattice are divided into a cloud data of structure, its 3 limits perpendicular to each other are parallel with 3 coordinate axis of Cartesian coordinates respectively, being divided into the length of side along three change in coordinate axis direction is that L space hexahedron cube is deleted lattice, secondly at the some P of fitting surface _s27 sub-bounding boxs of vicinity in obtain its k neighbor point, establish the some P of fitting surface then _sForm set K (P with its k neighbor point _s), S (P _s) be the some P of fitting surface _sK neighbor point least square fitting plane, make that P is the some P of fitting surface _sK neighbor point set K (P _s) the centre of form, be called the some P of fitting surface _sCentral point, this central point is:

$\stackrel{\‾}{P}=\frac{1}{(k+1)}\underset{P_s\∈K\left(P_s\right)}{\mathrm{\Σ}}{P}_s$

If the some P of fitting surface _sJ neighbor point to least square plane S (P _s) distance be d _j, be λ to the distance of P _j, so to the some P of fitting surface _sJ point have a function f _j(P _s), this function f _j(P _s) be:

$f_j\left(P_s\right)=\frac{d_j}{{\mathrm{\λ}}_j}$

The point P of fitting surface so _sCurvature function can be expressed as

$f\left(P_s\right)=\frac{1}{k}\underset{j=1}{\overset{k}{\mathrm{\Σ}}}{f}_j\left(P_s\right)$

According to curvature function f (P _s) obtain the some P of fitting surface _sMean curvature ρ _s, in like manner obtain the mean curvature ρ of whole some cloud ₀Make that d is the equalization point distance of whole some cloud, then get an interval delta ω=ρ ₀* d/ ρ _s, when on the Bezier patch, getting, at first on parametric direction of curved surface, parametric line such as uniformly-spaced get with Δ ω, again parametric lines such as each bar are uniformly-spaced got a little with Δ ω on another parametric direction, try to achieve the point of filling up hole.

The present invention is mainly used in the application scenario that hole in the various some cloud master patterns with complex-curved shape in the 3 D scanning system is filled up.Utilize the Algorithm for Surface Fitting among the present invention, can obtain one and accurately approach the hole curved surface of point at random on every side, get according to the variation of curvature on the whole subsequently and a little can realize the smooth of hole filled up.This method mainly contains following advantage:

(1) since traditional surface interpolation method to discrete point approach effect and bad, the present invention adopts surface fitting method can obtain the curved surface of scattered point set around the accurate match hole.

(2) adopt based on the curved surface fitting method on the triangular domain, the random surface of the easier performance of curved surface than territory, four limits can guarantee certain fairness and conformality.

(3) gridding of comparing in the But most of algorithms is handled, and the present invention is primarily aimed at the original point cloud model that 3 D scanning system obtains, without any need for gridding handle, applicability is wide, speed is fast.

(4) during fitting surface, choose the point at random around the hole alternately, so when hole boundary shape more complicated, suitable too.

During (5) at random some parametrization, need not the boundary curve of match hole, owing to avoided the Boundary Recognition of hole, therefore the hole that has an arbitrary shape for the overwhelming majority is suitable for too.

(6) adopted initial fitting and iterative approach to optimize two-stage process because point at random is carried out surface fitting, can make the curved surface of match obtain higher precision.

(7) can be according to actual needs, the number of times of artificial control curved surface and the precision of match have been avoided unnecessary calculating redundancy in the surface fitting process.

When (8) getting on the whole, consider curved transition, can realize the smooth compensation to hole, generally in a cloud, put the big place of cloud density, curved transition is also bigger, therefore, based on curvature etc. parameter get an energy smooth fill up hole.

(9) operating process is fairly simple, as long as the discrete point around the mutual selected hole, ensuing step all can be finished automatically, and speed is fast.And this method has very strong versatility.

Be noted that in addition when choosing at random, around hole, choose on a large scale as far as possible, can avoid self-adaptation to increase number of spots at random, with the efficient of further raising algorithm.

Description of drawings

Fig. 1 is the reverse-engineering process flow diagram.

Fig. 2 is a grating style three-dimension scanning system composition diagram.

Fig. 3 is algorithm overall flow figure.

Fig. 4 is near the point set example schematic the hole of choosing in the dome point cloud.

At random some parametrization process flow diagram of Fig. 5.

Fig. 6 is a curved surface initial fitting process flow diagram.。

Fig. 7 is near the point set fitting surface example schematic the hole in the dome point cloud.

Fig. 8 is that the curved surface iterative approach is optimized process flow diagram

Fig. 9 is to the hole repairing example schematic in the dome point cloud.

Figure 10 deletes the figure that formats.

Figure 11 is that curvature function is found the solution figure.

Figure 12 gets on the face a little to fill up the hole process flow diagram.

Embodiment

A kind of method for filling dot cloud hole of the 3-D scanning based on the triangular domain bezier surface:

The first step: around dot cloud hole and in the screen coordinate plane, set a triangle ABC, the regional extent of this triangle ABC can make dot cloud hole and the projection of point on every side to the screen coordinate plane thereof fall in the triangle ABC, and the some P of fitting surface when projection fallen into point in the triangle ABC as perforations adding _s(s=0,1 ..., m-1), according to the some P of fitting surface _sProjection P on triangle ABC plane _s' its curved surface parametrization coordinate of position calculation (u _s, v _s, w _s), u _s=(Δ AP _s' the B area)/(Δ ABC area), v _s=(Δ AP _s' the C area)/(Δ ABC area), w _s=(Δ BP _s' the C area)/(Δ ABC area), with the some P of fitting surface _s(s=0,1 ..., coordinate m-1) and curved surface parametrization coordinate (u thereof _s, v _s, w _s) n Bezier surface equation of substitution and obtain the reference mark of n Bezier curved surface with least square method, thereby obtain initial fitting curved surface S (u, v, w);

Second step: the some P that obtains each fitting surface _s(s=0,1 ..., m-1) to the distance vector d of curved surface (u, v, w) and curved surface respectively to the partial differential S of corresponding point parametric direction _u(u, v, w), S _v(u, v, w), S _w(u, v, w), order:

$\left\{\begin{array}{c}f(u,v,w)=d(u,v,w)\·S_u(u,v,w)=0\\ g(u,v,w)=d(u,v,w)\·S_v(u,v,w)=0\\ h(u,v,w)=d(u,v,w)\·S_w(u,v,w)=0\end{array}\right.$

The point P of fitting surface _sThe parametrization coordinate be (u _s, v _s, w _s), with (u _s, v _s, w _s) be initial estimate, find the solution above system of equations according to Newton iteration method, have:

Hσ ^T＝κ ^T

In the formula:

σ=(δ u, δ v, δ w), wherein, δ u, δ v, δ w are curved surface u, v, the iteration step length on three directions of w.

κ＝-(f(u _s，v _s，w _s)，g(u _s，v _s，w _s)，h(u _s，v _s，w _s))

$H=\left[\begin{array}{ccc}{f}_u& f_v& f_w\\ g_u& g_v& g_w\\ h_u& h_v& h_w\end{array}\right]=\left[\begin{array}{ccc}{\left|\right|S_u\left|\right|}^2+d\·S_{\mathrm{uu}}& S_v\·S_u+d\·S_{\mathrm{uv}}& S_w\·S_u+d\·S_{\mathrm{uw}}\\ S_u\·S_v+d\·S_{\mathrm{vu}}& {\left|\right|S_v\left|\right|}^2+d\·S_{\mathrm{vv}}& S_w\·S_v+d\·S_{\mathrm{vw}}\\ S_u\·S_w+d\·S_{\mathrm{wu}}& S_v\·S_w+d\·S_{\mathrm{wv}}& {\left|\right|S_w\left|\right|}^2+d\·S_{\mathrm{ww}}\end{array}\right]$

In the formula, d=d (u _s, v _s, w _s); f _u, f _v, f _w, g _u, g _v, g _w, h _u, h _v, h _wBe illustrated respectively in point (u _s, v _s, w _s) locate corresponding vector to u, v, the single order partial derivative of w; S _Uu, S _Uv, S _Uw, S _Vv, S _Vu, S _Vw, S _Ww, S _Wu, S _WvBe that (u, v is w) at point (u for curved surface S _s, v _s, w _s) locate respectively to u v, the second-order partial differential coefficient of w.

Then can get:

$\left[\begin{array}{ccc}{\left|\right|S_u\left|\right|}^2+d\·S_{\mathrm{uu}}& S_v\·S_u+d\·S_{\mathrm{uv}}& S_w\·S_u+d\·S_{\mathrm{uw}}\\ S_u\·S_v+d\·S_{\mathrm{vu}}& {\left|\right|S_v\left|\right|}^2+d\·S_{\mathrm{vv}}& S_w\·S_v+d\·S_{\mathrm{vw}}\\ S_u\·S_w+d\·S_{\mathrm{wu}}& S_v\·S_w+d\·S_{\mathrm{wv}}& {\left|\right|S_w\left|\right|}^2+d\·S_{\mathrm{ww}}\end{array}\right]\left[\begin{array}{c}\mathrm{\δu}\\ \mathrm{\δv}\\ \mathrm{\δw}\end{array}\right]=-\left[\begin{array}{c}f(u_s,v_s,w_s)\\ g(u_s,v_s,w_s)\\ h(u_s,v_s,w_s)\end{array}\right]$

According to the definition of triangle Bezier curved surface δ u+ δ v+ δ w=0 as can be known, i.e. therefore δ w=-δ u-δ v obtains following iterative equation group:

$\left[\begin{array}{cc}{\left|\right|S_u\left|\right|}^2-S_w\·S_u+d\·(S_{\mathrm{uu}}-S_{\mathrm{uw}})& S_v\·S_u-S_w\·S_u+d(S_{\mathrm{uv}}-S_{\mathrm{uw}})\\ S_u\·S_v-S_w\·S_v+d(S_{\mathrm{vu}}-S_{\mathrm{vw}})& {\left|\right|S_v\left|\right|}^2-S_w\·S_v+d\·(S_{\mathrm{vv}}-S_{\mathrm{vw}})\\ S_u\·S_w-{\left|\right|S_u\left|\right|}^2+d\·(S_{\mathrm{wu}}-S_{\mathrm{ww}})& S_v\·S_w-{\left|\right|S_w\left|\right|}^2+d\·(S_{\mathrm{wv}}-S_{\mathrm{ww}})\end{array}\right]\left[\begin{array}{c}\mathrm{\δu}\\ \mathrm{\δv}\end{array}\right]=-\left[\begin{array}{c}f(u_s,v_s,w_s)\\ g(u_s,v_s,w_s)\\ h(u_s,v_s,w_s)\end{array}\right]$

Wherein, δ u, δ v are u, the iteration step length on the v both direction.S _Uu, S _Uv, S _Uw, S _Vv, S _Vu, S _Vw, S _Ww, S _Wu, S _WvBe that (u, v is w) at point (u for curved surface S _s, v _s, w _s) locate respectively u, v, the second-order partial differential coefficient of w, iterative up to $1/m\underset{s=0}{\overset{m-1}{\mathrm{\Σ}}}\left|\right|d(u_s+\mathrm{\δu},v_s+\mathrm{\δv},w_s+\mathrm{\δw})-d(u_s,v_s,w_s)\left|\right|\≤\mathrm{\ϵ},$ ε is for presetting the surface fitting precision, thus the triangle Bezier curved surface S ' that obtains finally determining (u, v, w);

The 3rd step: at described triangle Bezier curved surface S ' (u, v, w) go up based on curvature etc. the parameter line taking, online more first-class parameter is got a little, be used to fill up dot cloud hole, needing at first that in asking the process of curvature three-dimensional point cloud is deleted lattice divides, this deletes the minimum external square that lattice are divided into a cloud data of structure, its 3 limits perpendicular to each other are parallel with 3 coordinate axis of Cartesian coordinates respectively, being divided into the length of side along three change in coordinate axis direction is that L space hexahedron cube is deleted lattice, secondly at the some P of fitting surface _s27 sub-bounding boxs of vicinity in obtain its k neighbor point, establish the some P of fitting surface then _sForm set K (P with its k neighbor point _s), S (P _s) be the some P of fitting surface _sK neighbor point least square fitting plane, make that P is the some P of fitting surface _sK neighbor point set K (P _s) the centre of form, be called the some P of fitting surface _sCentral point, this central point is:

$\stackrel{\‾}{P}=\frac{1}{(k+1)}\underset{P_s\∈K\left(P_s\right)}{\mathrm{\Σ}}{P}_s$

If the some P of fitting surface _sJ neighbor point to least square plane S (P _s) distance be d _j, be λ to the distance of P _j, so to the some P of fitting surface _sJ point have a function f _j(P _s), this function f _j(P _s) be:

$f_j\left(P_s\right)=\frac{d_j}{{\mathrm{\λ}}_j}$

The point P of fitting surface so _sCurvature function can be expressed as

$f\left(P_s\right)=\frac{1}{k}\underset{j=1}{\overset{k}{\mathrm{\Σ}}}{f}_j\left(P_s\right)$

According to curvature function f (P _s) obtain the some P of fitting surface _sMean curvature ρ _s, in like manner obtain the mean curvature ρ of whole some cloud ₀Make that d is the equalization point distance of whole some cloud, then get an interval delta ω=ρ ₀* d/ ρ _s, when on the Bezier patch, getting, at first on parametric direction of curved surface, parametric line such as uniformly-spaced get with Δ ω, again parametric lines such as each bar are uniformly-spaced got a little with Δ ω on another parametric direction, try to achieve the point of filling up hole.

With reference to the accompanying drawings, the present invention is described in detail:

In reverse-engineering, what face is the intensive point random data that disperse like the clouds.During fitting surface, when if the object bounds of curved surface and shape are extremely complicated, general inconvenience is the conventional curved surface structure method of utilization directly, and the Bezier curved surface is because its structure is flexible, border adaptability is good, potentiality with complex structure shape, and itself has good properties: slickness, locality and conformality.Object based on the random profile of the most suitable performance of approximating method of triangular domain curved surface, people's face particularly, products such as natural forms such as landforms and toy, approximating method based on four limit field parameter curved surfaces, usually it is orderly requiring data point, this condition is relatively harsh, comprehensive more than, so the present invention adopts Bezier curved surface on the triangular domain that hole is partly carried out match to fill.Overall algorithm flow is seen accompanying drawing 3.

The present invention relates generally to the content of following four aspects:

1) the selected and parameterized procedure of point at random

Near dome dot cloud hole screen two-dimensional coordinate system, select not A, B, the C of conllinear at 3, constitute three angle points of the triangle Bezier patch that needs initial fitting, with the point around the hole to these 3 triangle projective planum projections that constituted, drop in the triangle projective planum required some P when then thinking fitting surface as fruit dot _s(s=0,1 ..., m-1), see accompanying drawing 4.

According to the some P that chooses _sProjected position on triangle ABC plane calculates its curved surface parametrization coordinate.If i.e. P _sCorresponding subpoint is P in triangle projective planum ABC _s', P so _sParametrization coordinate (u _s, v _s, w _s) be respectively u _s=area (Δ AP _s' B)/area (Δ ABC), v _s=area (Δ AP _s' C)/area (Δ ABC), w _s=area (Δ BP _s' C)/area (Δ ABC).Algorithm flow chart is seen accompanying drawing 5.

2) least square self-adapting preliminary match

The expression formula that triangular domain ABC goes up n Bezier curved surface is:

$S(u,v,w)=\underset{i=0}{\overset{n}{\mathrm{\Σ}}}\underset{j=0}{\overset{n-i}{\mathrm{\Σ}}}{B}_{\mathrm{ijk}}^n(u,v,w)b_{\mathrm{ijk}}$

In the formula $B_{\mathrm{ijk}}^n(u,v,w)=\frac{n!}{i!j!k!}{u}^i{v}^j{w}^k\≥0\left\{\begin{array}{c}0\≤u,v,w\≤1,u+v+w=1\\ 0\≤i,j,k\≤n,i+j+k=n\end{array}\right.$

On the triangular domain in the expression formula of n Bezier curved surface unknown quantity be P _sParametrization coordinate (u _s, v _s, w _s), and (n+1) (n+2)/2 control vertex, (u _s, v _s, w _s) known according to the last step, so as long as obtain (n+1) (n+2)/2 control vertex coordinate b _Ijk(k≤n i+j+k=n), can determine a triangle Bezier curved surface for 0≤i, j.

According to the character of triangle Bezier curved surface as can be known three angle points of triangle Bezier curved surface just in time be three control vertexs of its control polyhedron grid, so selected leg-of-mutton three summit A, B, C can be as three known control summit b _00n, b _0n0, b _N00, P _s(s=0,1 ..., coordinate substitution triangle Bezier surface equation m-1), constitute with (n+1) (n+2)/a 2-3 unknown control vertex is a m system of linear equations of unknown quantity.The three-dimensional coordinate of selected triangle inside count m generally greater than (n+1) (n+2)/2-3, when not satisfying this condition and promptly wait to ask the system of equations matrix of coefficients unusual, center of gravity with triangle ABC is a basic point, and the area of self-adaptation expansion triangle ABC increases the number of m.Adopt least square method to find the solution this at last and cross the equation of constraint group, determine other unknown control vertex of curved surface, obtain initial fitting curved surface S (u, v, w).Algorithm flow chart is seen accompanying drawing 6.

3) curved surface approaches optimization

After the least square initial fitting, scattered point set P _s(distance error w) is also bigger for u, v, therefore needs further Correction and Control summit, changes the polyhedral shape of control, thereby changes the shape of curved surface, makes curved surface approach point set with curved surface S.The present invention has adopted the iterative approach algorithm based on Newton iteration method, improves fitting precision, and (u, v w), see accompanying drawing 7 finally to determine curved surface S '.

Concrete steps are as follows:

(1) obtain each point to curved surface at random distance vector d (u, v, w) and curved surface respectively to the partial differential S of corresponding point parametric direction _u(u, v, w), S _v(u, v, w), S _w(u, v w), form and wait to ask system of equations as follows:

$\left\{\begin{array}{c}f(u,v,w)=d(u,v,w)\·S_u(u,v,w)=0\\ g(u,v,w)=d(u,v,w)\·S_v(u,v,w)=0\\ h(u,v,w)=d(u,v,w)\·S_w(u,v,w)=0\end{array}\right.$

(2) employing is found the solution this system of equations based on the method for Newton iteration method, and the iterative equation group that finally can try to achieve is:

$\left[\begin{array}{cc}{\left|\right|S_u\left|\right|}^2-S_w\·S_u+d\·(S_{\mathrm{uu}}-S_{\mathrm{uw}})& S_v\·S_u-S_w\·S_u+d\·(S_{\mathrm{uv}}-S_{\mathrm{uw}})\\ S_u\·S_v-S_w\·S_v+d\·(S_{\mathrm{vu}}-S_{\mathrm{vw}})& {\left|\right|S_v\left|\right|}^2-S_w\·S_v+d\·(S_{\mathrm{vv}}-S_{\mathrm{vw}})\\ S_u\·S_w-{\left|\right|S_w\left|\right|}^2+d\·(S_{\mathrm{wu}}-S_{\mathrm{ww}})& S_v\·S_w-{\left|\right|S_w\left|\right|}^2+d\·(S_{\mathrm{wv}}-S_{\mathrm{ww}})\end{array}\right]\left[\begin{array}{c}\mathrm{\δu}\\ \mathrm{\δv}\end{array}\right]=-\left[\begin{array}{c}f(u_s,v_s,w_s)\\ g(u_s,v_s,w_s)\\ h(u_s,v_s,w_s)\end{array}\right]$

(3) the above system of equations of iterative, when counting of fitting surface is less than the unknown number number of iterative equation group, and the system of equations coefficient is when unusual, and the center of gravity with triangle ABC is a basic point equally, the area of self-adaptation expansion triangle ABC increases the number of m, repeats (2).

Algorithm flow chart is seen accompanying drawing 8.

4) get a little on the face

Described triangle Bezier curved surface S ' (u, v, w) go up based on curvature etc. the parameter line taking, online more first-class parameter is got a little, is used to fill up dot cloud hole, sees accompanying drawing 9.Needing at first that in asking the process of curvature three-dimensional point cloud is deleted lattice divides, this deletes the minimum external square that lattice are divided into a cloud data of structure, its 3 limits perpendicular to each other are parallel with 3 coordinate axis of Cartesian coordinates respectively, being divided into the length of side along three change in coordinate axis direction is that L space hexahedron cube is deleted lattice, see accompanying drawing 10, next is at the some P of fitting surface _s27 sub-bounding boxs of vicinity in obtain its k neighbor point, establish the some P of fitting surface then _sForm set K (P with its k neighbor point _s), S (P _s) be the some P of fitting surface _sK neighbor point least square fitting plane, make that P is the some P of fitting surface _sK neighbor point set K (P _s) the centre of form, be called the some P of fitting surface _sCentral point, this central point is:

$\stackrel{\‾}{P}=\frac{1}{(k+1)}\underset{P_s\∈K\left(P_s\right)}{\mathrm{\Σ}}{P}_s$

If the some P of fitting surface _sJ neighbor point to least square plane S (P _s) distance be d _j, be λ to the distance of P _j, see accompanying drawing 11, so to the some P of fitting surface _sJ point have a function f _j(P _s), this function f _j(P _s) be:

$f_j\left(P_s\right)=\frac{d_j}{{\mathrm{\λ}}_j}$

The point P of fitting surface so _sCurvature function can be expressed as

$f\left(P_s\right)=\frac{1}{k}\underset{j=1}{\overset{k}{\mathrm{\Σ}}}{f}_j\left(P_s\right)$

According to curvature function f (P _s) obtain the some P of fitting surface _sMean curvature ρ _s, in like manner obtain the mean curvature ρ of whole some cloud ₀Make that d is the equalization point distance of whole some cloud, then get an interval delta ω=ρ ₀* d/ ρ _s, when on the Bezier patch, getting, at first on parametric direction of curved surface, parametric line such as uniformly-spaced get with Δ ω, again parametric lines such as each bar are uniformly-spaced got a little with Δ ω on another parametric direction, try to achieve the point of filling up hole.

Algorithm flow chart is seen accompanying drawing 12.

Claims (3)

1, a kind of method for filling dot cloud hole of 3-D scanning is characterized in that:

The first step: around dot cloud hole and in the screen coordinate plane, set a triangle ABC, the regional extent of this triangle ABC can make dot cloud hole and the projection of point on every side to the screen coordinate plane thereof fall in the triangle ABC, and the some P of fitting surface when projection fallen into point in the triangle ABC as perforations adding _s(s=0,1 ..., m-1), according to the some P of fitting surface _sProjection P on triangle ABC plane _s' its curved surface parametrization coordinate of position calculation (u _s, v _s, w _s), u _s=(Δ AP _s' the B area)/(Δ ABC area), v _s=(Δ AP _s' the C area)/(Δ ABC area), w _s=(Δ BP _s' the C area)/(Δ ABC area), with the some P of fitting surface _s(s=0,1 ..., coordinate m-1) and curved surface parametrization coordinate (u thereof _s, v _s, w _s) n Bezier surface equation of substitution and obtain the reference mark of n Bezier curved surface with least square method, thereby obtain initial fitting curved surface S (u, v, w);

Second step: the some P that obtains each fitting surface _s(s=0,1 ..., m-1) to the distance vector d of curved surface (u, v, w) and curved surface respectively to the partial differential S of corresponding point parametric direction _u(u, v, w), S _v(u, v, w), S _w(u, v, w), order:

$\left\{\begin{array}{c}f(u,v,w)=d(u,v,w)\·S_u(u,v,w)=0\\ g(u,v,w)=d(u,v,w)\·S_v(u,v,w)=0\\ h(u,v,w)=d(u,v,w)\·S_w(u,v,w)=0\end{array}\right.$

According to Newton iteration method, obtain following iterative equation group:

$\left[\begin{array}{c}{\left|\right|S_u\left|\right|}^2-S_w\·S_u+d\·(S_{\mathrm{uu}}-S_{\mathrm{uw}})S_v\·S_u-S_w\·S_u+d\·(S_{\mathrm{uv}}-S_{\mathrm{uw}})\\ S_u\·S_v-S_w\·S_v+d\·(S_{\mathrm{vu}}-S_{\mathrm{uw}}){\left|\right|S_v\left|\right|}^2-S_w\·S_v+d\·(S_{\mathrm{vv}}-S_{\mathrm{vw}})\\ S_u\·S_w-{\left|\right|S_w\left|\right|}^2+d\·(S_{\mathrm{wu}}-S_{\mathrm{ww}})S_v\·S_w-{\left|\right|S_w\left|\right|}^2+d\·(S_{\mathrm{wv}}-S_{\mathrm{ww}})\end{array}\right]\left[\begin{array}{c}\mathrm{\δu}\\ \mathrm{\δv}\end{array}\right]=-\left[\begin{array}{c}f(u_s,v_s,w_s)\\ g(u_s,v_s,w_s)\\ h(u_s,v_s,w_s)\end{array}\right]$

Wherein, δ u, δ v are u, the iteration step length on the v both direction, S _Uu, S _Uv, S _Uw, S _Vv, S _Vu, S _Vw, S _Ww, S _Wu, S _WvBe that (u, v is w) at point (u for curved surface S _s, v _s, w _s) locate respectively u, v, the second-order partial differential coefficient of w,

Iterative up to $1/m\underset{s=0}{\overset{m-1}{\mathrm{\Σ}}}\left|\right|d(u_s+\mathrm{\δu},v_s+\mathrm{\δv},w_s+\mathrm{\δw})-d(u_s,v_s,w_s)\left|\right|\≤\mathrm{\ϵ},$ ε is for presetting the surface fitting precision, thus the triangle Bezier curved surface S ' that obtains finally determining (u, v, w);

The 3rd step: at described triangle Bezier curved surface S ' (u, v, w) go up based on curvature etc. the parameter line taking, online more first-class parameter is got a little, be used to fill up dot cloud hole, needing at first that in asking the process of curvature three-dimensional point cloud is deleted lattice divides, this deletes the minimum external square that lattice are divided into a cloud data of structure, its 3 limits perpendicular to each other are parallel with 3 coordinate axis of Cartesian coordinates respectively, being divided into the length of side along three change in coordinate axis direction is that L space hexahedron cube is deleted lattice, secondly at the some P of fitting surface _s27 sub-bounding boxs of vicinity in obtain its k neighbor point, establish the some P of fitting surface then _sForm set K (P with its k neighbor point _s), S (P _s) be the some P of fitting surface _sK neighbor point least square fitting plane, make that P is the some P of fitting surface _sK neighbor point set K (P _s) the centre of form, be called the some P of fitting surface _sCentral point, this central point is:

$\stackrel{\‾}{P}=\frac{1}{(k+1)}\underset{P_s\∈K\left(P_s\right)}{\mathrm{\Σ}}{P}_s$

If the some P of fitting surface _sJ neighbor point to least square plane S (P _s) distance be d _j, be λ to the distance of P _j, so to the some P of fitting surface _sJ point have a function f _j(P _s), this function f _j(P _s) be:

$f_j\left(P_s\right)=\frac{d_j}{{\mathrm{\λ}}_j}$

The point P of fitting surface so _sCurvature function can be expressed as

$f\left(P_s\right)=\frac{1}{k}\underset{j=1}{\overset{k}{\mathrm{\Σ}}}{f}_j\left(P_s\right)$

According to curvature function f (P _s) obtain the some P of fitting surface _sMean curvature In like manner obtain the mean curvature of whole some cloud

Make that d is the equalization point distance of whole some cloud, then get an interval $\mathrm{\Δ\ω}=\stackrel{\‾}{{\mathrm{\ρ}}_0}\×\stackrel{\‾}{d}/\stackrel{\‾}{{\mathrm{\ρ}}_s},$ When on the Bezier patch, getting, at first on parametric direction of curved surface, parametric line such as uniformly-spaced get, again parametric lines such as each bar are uniformly-spaced got a little with Δ ω on another parametric direction, try to achieve the point of filling up hole with Δ ω.

2, the method for filling dot cloud hole of 3-D scanning according to claim 1 when it is characterized in that counting of fitting surface is less than the curved surface control vertex and counts, enlarges the area that sets triangle ABC, makes counting greater than curved surface control vertex number of fitting surface.

3, the method for filling dot cloud hole of 3-D scanning according to claim 1, when it is characterized in that counting of fitting surface is less than the unknown number number of iterative equation group, enlarge the area that sets triangle ABC, make counting of fitting surface more than or equal to the unknown number number of iterative equation group.

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