CN104063896B - A kind of three-dimensional building model structure based on transformation space finds method - Google Patents

Abstract

The present invention relates to a kind of model structure analysis method, the present invention first passes through transform analysis and initial threedimensional model space is transformed into a two-dimension translational transformation space, thus the test problems of upper for input regular texture is converted into the most anti-problem pushed away of grid regular pattern in two-dimensional space that first detects.For grid regular pattern test problems in two-dimensional space, the present invention utilizes energy minimization method to estimate its relevant parameter, and the method can not only detect intact regular pattern, equally applicable during for there is some abnormity point or missing point.Release its generation parameter of rule of correspondence structure on threedimensional model finally according to grid regular pattern is counter, and then extract corresponding repetitive construct unit.The method of the present invention can rapid extraction go out to translate the repetitive construct unit that repetitive structure is corresponding in BUILDINGS MODELS.

Description

A kind of three-dimensional building model structure based on transformation space finds method

Technical field

The present invention relates to a kind of model structure analysis method, belong to Computer Image Processing and computer graphics techniques neck Territory, a kind of three-dimensional building model structure based on transformation space finds method.

Background technology

Various building it is found everywhere, it is seen that each building all can exist rule knot more or less around us , as the structural units such as mutually isostructural window, or door can be there is in certain region in structure.And we a lot of in the case of just by this A little structural units repeated identify the design style of relevant building.If some ad hoc approach therefore can be used to detect building We will be appreciated and understood by existing BUILDINGS MODELS and provide help greatly by the repetitive structure included in model.Most common The BUILDINGS MODELS construction unit detection method manual interactive mode of many employings carry out the extraction of structural unit, such as document 1Merrell P.,Manocha D.Model synthesis:a general procedural modeling algorithm.IEEE Transactions on Visualization and Computer Graphics, 2011,17 (6): 715-728. and document 2Lin J.-J.,Cohen-Or D.,Zhang H.,Liang C.,Sharf A.,Deussen O., ChenB.Q.Structure-preserving retargeting of irregular3d architecture.ACM Transactions on Graphics, 2011,30 (6): 183. grades are introduced.But such method time and effort consuming, needs user There is deep understanding could obtain complete structural unit to model to be analyzed.Along with the development of technology, Recent study personnel By the symmetry included in model, translate, the geometric transformation characteristic such as rotation, the half mutual or automatic mode of employing achieves builds Build the detection of model construction unit.

Carry out the research process of model structure analysis from geometric transformation angle, be broadly divided into three phases: open most Its application of beginning mainly appears in figure, such as document 3Liu Y., Collins R., Tsin Y.A computational model for periodic pattern perception based on frieze and wallpaper groups.IEEE Transactions on pattern analysis and machine intelligence,2004,26 (3): 354-371. and document 4Tuytelaars T., Turina A., Gool L.V.Non-combinatorial detection of regular repetitions under perspective skew.IEEE Transactions on Pattern analysis and machine intelligence, the introductions such as 2003,25 (4): 418-432..Want straight Connect and be applied in the structural analysis of threedimensional model be relatively difficult by above-mentioned picture structure analysis method.Therefore, then not By using for reference picture structure analysis thought in disconnected research process, also occur in that many can complete the structure for threedimensional model The method analyzed, such as document 5Mitra N.J., Guinbas L.J., Pauly M.2006.Partial and approximate symmetry detection for3d geometry.ACM Transactions on Graphics,25 : 560-568. and document 6Pauly M., (3) Mitra N.J., Wallner J., Pottmann H., Guibas L.J.Discovering structural regularity in3d geometry.ACM Transactions on Graphics, the introductions such as 2008,27 (3): 43:1-43:11..The emphasis of said method is all repeat pattern detection, and they All to treat model structure relation from the perspective of a kind of plane.In recent years, it is thought that with more complicated structural unit Membership credentials express more rich model, thus occur in that Analysis of Hierarchy Structure method, such as document 7Wang Y., Xu K., Li J.,Zhang H.,Shamir A.,Liu L.,Cheng Z.,Xiong Y.Symmetry hierarchy of man-made Objects.Computer Graphics Forum (Eurographics), 2011,30 (2): 287 296. and document 8Zhang H.,Xu K.,Jiang W.,Lin J.-J.,Cohen-Or D.,Chen B.-Q.Layered analysis of irregular facades via symmetry maximization.ACM Trans.Graph.2013,32(4):121:1- 121:13. Deng introduction.By during structural analysis propose one " level " concept, the most no longer with plane from the point of view of Treat a model face, and regarded as and be made up of many levels, such method achieve to ordinary construction detection method without The deciphering of the irregular structure that method understands.

Summary of the invention

Goal of the invention: the technical problem to be solved is for the deficiencies in the prior art, it is provided that a kind of based on change The three-dimensional building model structure changing space finds method.

Technical scheme: in order to solve above-mentioned technical problem, the invention discloses a kind of three-dimensional building based on transformation space Model structure find method, the building sample that the method input for user, can with rapid extraction its structural unit comprised, wrap Include following steps:

Step (1), carries out transform analysis to the sample building of user's input, initial threedimensional model space is transformed into two dimension Translation transformation space；Wherein user inputs the triangle gridding that sample building is the triangle relation comprising three-dimensional coordinate and point a little Model；

Step (2), carries out model estimation in two-dimension translational transformation space, tries to achieve the grid in two-dimension translational transformation space Regular pattern；

Step (3), releases rule knot on initial threedimensional model according to grid regular pattern in two-dimension translational transformation space is counter The generation parameter of structure, recycles these parameter aggregations and obtains the repetitive construct unit of this regular texture.

Step of the present invention (1) concentrates putting down between any two points by estimation with analyzing possible similar point in input model Move transformation relation, initial threedimensional model space be transformed into two-dimension translational transformation space, concretely comprise the following steps:

Step (11), tentatively asks for similar collection, will may be divided into the set of a point by similar point in initial threedimensional model In, and determine that one of them initial similar collection carries out next step and operates:

Step (12), rejects the point of this similar concentration redundancy to initial similar centralized procurement local registration method；

Step (13), carries out transformed mappings to the similar collection after local registration, it is achieved initial threedimensional model space is to two dimension The conversion in translation transformation space.

Step of the present invention comprises the following steps in (2):

Step (21), uses average and variance method to cluster the point in two-dimension translational transformation space；

Step (22), two main shafts in using consistent random algorithm to determine cluster back plane；

Step (23), uses Gaussian weighting marks method to minimize a combined energy, estimates the net in two-dimensional space Lattice regular pattern.

Each item of described combined energy is respectively as follows:

E_X→C=∑_i∑_jα_ij ²||x_ij-c(i,j)||², measure all mesh points cluster centre nearest with it close to journey Degree；

Measure the degree of closeness of all cluster centres mesh point nearest with it；

E_α=∑_i∑_j(1-α_ij ²)², measure total number that all mesh points cluster centre nearest with it is effectively matched；

E_β=∑_k(1-β_k ²)², measure total number that all cluster centres mesh point nearest with it is effectively matched.

Final energy equation is:

E=γ (E_X→C+E_C→X)+(1-γ)(E_α+E_β),

Wherein, γ is a coordination parameter, γ be used for weighing every pair of mesh point and cluster centre degree of closeness energy term and Mesh point and cluster centre are effectively matched total number energy term, and γ span is 0～1, N₁And N₂For grid regular pattern often Dimension on individual direction, | C | represents total number of cluster centre, and (i j) is off-network lattice point x to c_ijNearest cluster centre, wherein i Span be 1 to N₁, the span of j is 1 to N₂, x (k) represents from kth cluster centre c_kNearest mesh point, its The span of middle k is 1 to arrive | C |, α_ijRepresent mesh point x_ijIt is mapped as the credibility of its nearest cluster centre, β_kRepresent cluster Center c_kIt is mapped as the credibility of its nearest mesh point.

In step of the present invention (3), pushed back initial threedimensional model by the grid regular pattern in two-dimension translational transformation space is counter Basic translation transformation group T of upper regular texture₁And T₂, then utilize basic translation transformation group T₁And T₂Polymerization obtains this rule knot The repetitive construct unit of structure, comprises the following steps:

Step (31), defines a set S being initially empty, and puts p on the basis of a point of optional similar concentration₀, add Set S；

Step (32), to any not point in set S, as long as one point of existence is setting with the distance of this point in set S In the range of Ding, set point value is 1000～3000, then this point is called the consecutive points p of S₁, to the consecutive points p gathering S₁, calculate Consecutive points are registrated to registration error ω brought during datum mark；

Described consecutive points if ω is less than given threshold value, is then added set S, otherwise refuse by step (33)；Return step (32) until no point does not adds again, repetitive construct unit is finally given；

In step (32), registration error computing formula is:

$\mathrm{\ω}={\mathrm{\Σ}}_{i=1}^{\left|\mathrm{\Ω}\right|}(p_1-((p_{i1}-p_{i0})+p_0)),$

Wherein, p₁Represent datum mark p₀Consecutive points, | Ω | represents total number of similar centrostigma, p_i0Represent datum mark p₀ By p₀After translating to the translational movement relation of similar concentration i-th point on initial threedimensional model with datum mark p₀Nearest point, p_i1Table Show a p₁By p₀After translating to the translational movement relation of similar concentration i-th point on initial threedimensional model with a p₁Nearest point, wherein Translational movement be basic translation transformation group T₁And T₂A linear combination.

Beneficial effect: the model structure analysis method of present invention advantage compared with existing model structure analysis method is: Three-dimensional grid model for input, it is possible to prior information at aspects such as repetitive construct cell configuration, size, positions is unknown Under premise, it is rapidly completed the analysis of its model structure.It addition, the method for the present invention can not only detect intact grid Regular pattern, equally applicable to the situation that there is exception or lack part.

Accompanying drawing explanation

Being the present invention with detailed description of the invention below in conjunction with the accompanying drawings and further illustrate, the present invention's is above-mentioned And/or otherwise advantage will become apparent.

Fig. 1 is broad flow diagram of the present invention.

Fig. 2 a and Fig. 2 b is the initial similar collection at datum mark and the datum mark place manually demarcated on initial model.

Fig. 3 a and Fig. 3 b is initial similar collection and the similar collection after local registration.

Fig. 4 is the three dimensions that translation vector is constituted.

Fig. 5 is that the spot projection in three dimensions is to two dimensional surface.

Fig. 6 a, Fig. 6 b, Fig. 6 c and Fig. 6 d cross two main shafts, initial mesh of initial point after being respectively translation transformation space clustering β in regular pattern, final grid regular pattern_kα in the situation of value and final grid regular pattern_ijThe situation schematic diagram of value.

Fig. 7 is that on initial model, regular texture structural unit extracts result.

Detailed description of the invention

As it is shown in figure 1, the present invention comprises the following steps:

Step (1), carries out transform analysis to the sample building of user's input, initial threedimensional model space is transformed into two dimension Translation transformation space；Wherein user inputs the triangle gridding that sample building is the triangle relation comprising three-dimensional coordinate and point a little Model；

Step (2), carries out model estimation in two-dimension translational transformation space, tries to achieve the grid regular pattern in this space；

Step (3), releases rule knot on initial threedimensional model according to grid regular pattern in two-dimension translational transformation space is counter The generation parameter of structure, recycles these parameter aggregations and obtains the repetitive construct unit of this regular texture.

More specifically, the present invention is in the priori of the aspects such as three-dimensional building model repetitive construct cell configuration, size, position On the premise of information the unknown, use and estimate repeat pattern and the structure analysis method of detection constitutional repeating unit simultaneously, the completeest Become the structural analysis of its model.First pass through transform analysis and initial threedimensional model space is transformed into a two-dimension translational change Change space, thus the problem of regular texture repeat pattern on input model of asking for is converted into and first asks in translation transformation space The most anti-problem pushed away of grid regular pattern.For grid regular pattern test problems in translation transformation space, the present invention utilizes Energy minimization method is made model and is estimated, finds out the grid regular pattern existed in which, can not only detect in this step Intact grid regular pattern, during for there is some abnormity point or missing point, equally finds therein Repeat pattern.The relevant ginseng of regular texture on threedimensional model is released finally according to grid regular pattern in translation transformation space is counter Number, extracts corresponding repetitive construct unit.

Embodiment

Each step of the present invention is described below according to embodiment.

Due to the particularity of the present invention, part accompanying drawing disclosed in this invention, it has to use attached with gradation effect Figure is indicated.

Step (1), carries out transform analysis to the sample building of user's input, initial threedimensional model space is transformed into two dimension Translation transformation space.

Step (11) tentatively asks for similar collection.

This step wishes to mark off possible similar point set in input model, is referred to as similar collection.Similar collection is three-dimensional The model space and translation transformation space carry out the tie changed, and ask for phase by similar concentration any two points is carried out pairing The translation transformation answered, it is possible to be transformed into the translation transformation space that similar collection is asked for from input model space.Specific practice is as follows: For the institute on initial threedimensional model a little, two principal curvatures k of each sample point are asked for₁、k₂, first according to H²/ K is to all Point does and once divides, and by the absolute value of this value difference, less than certain threshold value, (the general span of described threshold value is 0-0.005, this reality Execute example value 0.001) point be divided into one set in, wherein H=(k₁+k₂)/2 are average curvature, K=k₁k₂Bent for Gauss Rate, classifies to previous step division result further according to the size of H, K value the most respectively, and the criteria for classifying is by H, K value difference Absolute value is both less than certain threshold value, and (the general span of described threshold value is 10^-7-10^-5, the present embodiment value 10^-6) point divide In a set.Thus all initial points are divided.

But the similar collection quantity owing to asking for is too much, and in order to simplify subsequent operation, the present embodiment is asking for a class formation list During unit, the most manual demarcates a datum mark on input model, such as the point of mark in Fig. 2 a, then basis and this datum mark phase Determining the final similar collection participating in and calculating like situation, such as the point of mark in Fig. 2 b, subsequent algorithm is then to this initial similar collection Carry out operating.

The Main Function carrying out aforesaid operations has two, and one is, for relative initial data set, this step is significantly reduced The number of point, can effectively reduce the operating time of next step local registration；Two are, the some set so tried to achieve has one Individual feature, the point i.e. belonging to same regular pattern can be in same set, it can be ensured that finally can find and only comprise one The similar collection of regular pattern.

Step (12) local registration.

After previous step divides, simply having carried out tentatively solving to similar collection, now, initial similar concentration still can Containing the point of some redundancies, therefore the purpose of local registration rejects the incorrect point of initial similar concentration exactly, finally gives ratio Relatively reliable similar collection, meanwhile, moreover it is possible to correct the position of similar concentrated part point, so that next step translation required becomes It is more accurate to change.

The datum mark (point of circles mark in Fig. 3 a) demarcated firstly, for the initial similar user of concentration, asks for it just A little, in order to allow certain range of error, the present embodiment arranges three-dimensional mould in institute on the fettucelle represented in beginning threedimensional model As long as from point in the range of h of the distance of datum mark in type, the most finally on this fettucelle, the point tried to achieve being designated as { x₁, x₂,…,x_n}.Depending on wherein the setting of parameter h will be according to different model data features, the present embodiment value is 3000.

Secondly, for rejecting the redundant points of similar concentration, document 9Pottmann H., Huang Q.-X, Yang Y.-are used L,Hu S.-M.Geometry and convergence analysis of algorithms for registration Of3D shapes.Int.J.Computer Vision, the closest approach iteration (Iterative of 2006,67 (3): 277-296. Closest Point, ICP) algorithm to similar concentration in addition to datum mark each point operate.First by this point and benchmark Point coordinates subtracts each other tries to achieve translation transformation, moves as in closest approach iteration (Iterative Closest Point, ICP) algorithm Map the initial value of α, then utilize α to a little { x on datum mark dough sheet₁,x₂,…,x_nMove, right after this The closest approach of each point after asking on dough sheet moving should be put, be designated as { y₁,y₂,…,y_n}.Finally minimize object function:

$F=\underset{i}{\mathrm{\Σ}}{\left|\right|x_{i+}-y_i\left|\right|}^2---\left(1\right)$

Wherein x_i+=α₊·x_i, α₊In this object function, the unknown, is to α correction.Constantly repeat above-mentioned ICP behaviour (the general value of described scope is one and connects within the specific limits to make the absolute value until the result difference tried to achieve for twice before and after (1) formula The real number of nearly 0, the present embodiment value 1e-8).If the final error F tried to achieve after certain some closest approach iteration is in critical error scope In (the general value of described critical error be one close to 0 real number, the present embodiment value 0.3), then accept this point, and will wherein The α tried to achieve₊As the similarity transformation between this point and datum mark；Otherwise, this point is weeded out from this similar concentration.Local registration After result as shown in Figure 3 b.

Step (13) transformed mappings.

After previous step, the present embodiment obtains accurate similar collection, next this similar collection will be utilized to complete from former three-dimensional Space is to the conversion in translation transformation space.Operating process is for by matching similar concentration any two points, it is possible to try to achieve A series of translation transformation, each translation transformation is actually a translation vector, a point in corresponding three-dimensional space, Point T as identified in Fig. 4 is a required translation vector.After having matched a little, we are just available final Each translation transformation distribution situation in three dimensions, as shown in Figure 4.

In order to be physically easier to perform and observe, the present embodiment also needs the translation transformation in three dimensions by finding suitably Two-dimensional projection plane, maps accordingly.Initially with document 10Fischler M., Bolles R.Random Sample Consensus:A paradigm for model fitting with applications to image analysis And automated cartography.Commun.ACM, the consistent stochastical sampling (Random of 1981,24 (6): 381-395. Sample Consensus, RANSAC) method completes the determination of two dimensional surface, and the final purpose of this method is to allow a little as far as possible Many falls in the plane tried to achieve.Then we the more all translation vectors in three dimensions in Fig. 4 are projected to this two dimension put down On face.Projection result is as shown in Figure 5.Wherein Fig. 5 is designated (t₁,t₂) point be in Fig. 4 and be designated the point of T in this two dimension Projection situation in plane.

Step (2) model is estimated.

Having obtained a two dimensional surface about translation transformation distribution on last stage, the target in this stage is by this Point in two dimensional surface is analyzed, and finds out their grid regular pattern.Advise present in above-mentioned two dimensional surface to find out Rule pattern, it is thus necessary to determine that about its two class parameters: the generation vector g of regular pattern₁、g₂And dimension N in each direction₁、 N₂.In order to reach this purpose, next will build and minimize one about the energy function of point on this two dimensional surface.

Step (21) two-dimensional space midpoint clusters.

Owing to same translation transformation can be by 2 different in three dimensions to obtaining, and different points is to trying to achieve Translation transformation more or less can there are some errors, be thus likely to occur same translation transformation and project on two dimensional surface After be not on same point, and be distributed across certain point small neighbourhood in.For this problem, we are first on two dimensional surface Point cluster, thus can ask for follow-up regular pattern with cluster centre.Use document 11Comaniciu herein D.,Meer P.2002.Mean shift:a robust approach toward feature space analysis.IEEE Transactions on pattern analysis and machine intelligence,24 (5): average and variance (mean-shift) method of 603-619. completes to cluster accordingly work, in the cluster that Fig. 5 is tried to achieve Shown in the heart such as Fig. 6 (a).

Step (22) determines the main shaft in cluster back plane.

Seek the matching method of translation transformation time point pair according to step (13), be not difficult to know the translation transformation one that displacement is zero Surely there will be.Therefore these two main shafts that the present embodiment is to be asked for needed zero, and can not overlap.With step (13) three Looking for two dimensional surface to be similar in dimension space, the determination of main shaft still uses consistent stochastical sampling (Random Sample Consensus, RANSAC) method, only herein for determining that a straight line crossing initial point has only to select a non-initial point again ?.Find main shaft to be able to determine the initial value that regular pattern generates vector, and obtain the corresponding dimension in each direction. The method that specifically determines is: g₁And g₂Be set to that cluster centre nearest from initial point on two major axes orientations and initial point constitute to Amount, as shown in Fig. 6 (b)；Article two, main shaft generates on distance and the correspondence direction of the farthest cluster centre of initial point and initial point to The ratio of the length of amount rounds and is respectively defined as n₁And n₂, as shown in Fig. 6 (b).Because n₁And n₂Corresponding simply half side of main shaft To dimension, so the dimension actual value in each direction of the regular pattern of correspondence should be N₁=2*n₁+ 1, N₂=2*n₂+ 1, and N₁And N₂Value will not change again.

Step (23) seeks the grid regular pattern in two-dimensional space.

After said process, the present embodiment obtains a N₁×N₂The grid regular pattern of size, each grid Point x_ijIt is represented by following form

x_ij=ig₁+jg₂-n₁≤i≤n₁and-n₂≤i≤n₂ (2)

Now have been known in two dimensional surface regular pattern in the dimension of all directions, and it is raw to obtain this regular pattern Become the initial value of vector.In order to ask for this end value generating vector, next build combined energy function by starting.Below I Will introduce this combined energy function item by item.Section 1 is used for measuring connecing of its corresponding nearest cluster centre of all mesh points Short range degree, concrete form is

E_X→C=Σ_iΣ_jα_ij ²||x_ij-c (i, j) | |² (3)

Wherein (i is j) from x to c_ijNearest cluster centre.Similarly, all cluster centres of Section 2 tolerance are corresponding to it The degree of closeness of nearest mesh point

$E_{C\→X}={\mathrm{\Σ}}_{k=1}^{\left|C\right|}{\mathrm{\β}}_k^2{\left|\right|c_k-x\left(k\right)\left|\right|}^2---\left(4\right)$

Wherein | C | represents total number of cluster centre, and x (k) represents from c_kNearest mesh point.For in (3) and (4) formula C (i, j) and x (k), the two value will re-start calculating in the iterative process of each step, is the value being continually changing. α_ijAnd β_kBeing two the new unknown quantitys introduced during this optimizes, they are used to detect the abnormity point in regular pattern and lack Lose point.Wherein α_ijRepresent mesh point x_ijIt is mapped as the credibility of its nearest cluster centre, β_kRepresent cluster centre c_kMap Credibility for its nearest mesh point.α_ijAnd β_kValue be closer to 1, indicate that the coupling between cluster centre and mesh point can Reliability is the highest, and the size of the two value will determine that we select which point on two dimensional surface to ask for introductory die next stage The basic translation transformation of regular texture in type.Because we do not have any about shortage of data or the priori of exception, so During the optimization in this stage, α_ijAnd β_kInitial value be all set to 1.Correspondingly, have also been introduced two for the two parameter New energy, their effect is total number that tolerance mesh point cluster centre nearest with it is effectively matched:

E_α=∑_i∑_j(1-α_ij ²)² (5)

E_β=∑_k(1-β_k ²)² (6)

Combine our objective energy function of above-mentioned four energy:

E=γ (E_X→C+E_C→X)+(1-γ)(E_α+E_β) (7)

Wherein γ is coordination parameter (span is 0～1, and the present embodiment value is 0.01).Finally our target is just To minimize E, obtain regular pattern generate vector end value:

$g_1,g_2,\left\{{\mathrm{\α}}_{\mathrm{ij}}\right\},\left\{{\mathrm{\β}}_k\right\}=\underset{g_1,g_2,\left\{{\mathrm{\α}}_{\mathrm{ij}}\right\},\left\{{\mathrm{\β}}_k\right\}}{\arg \min }E---\left(8\right)$

The present embodiment uses Gaussian weighting marks method to minimize combinations thereof energy, the result obtained such as Fig. 6 a～Fig. 6 d Shown in, for the regular texture of the 6*2 in experimental data shown in Fig. 2, Fig. 7 gives one in two-dimension translational transformation space The grid regular pattern of 11*3.Wherein Fig. 6 a two main shafts of all cluster centres in being translation transformation space；Fig. 6 b is initial Grid regular pattern, the line of band arrow is this grid g₁And g₂Initial value；Fig. 6 c and 6d is respectively on final grid rule model α_ijAnd β_kThe situation of value.

Step (3), polymerization obtains the repetitive construct unit of regular texture on initial threedimensional model.

Model is estimated to have tried to achieve the regular texture on initial model and is transformed to after two-dimension translational transformation space on this plane Regular pattern.In order to find three class parameters of regular texture on initial threedimensional model: the representative structural unit of this regular texture, Basic translation transformation group T₁, T₂And the dimension in all directions, current embodiment require that and proceed as follows: first, utilize two dimension Counter second and the 3rd class parameter released on initial threedimensional model in regular texture three class parameter of the parameter of regular pattern in plane, Then go to ask first kind parameter according to Equations of The Second Kind parameter, thus the most just try to achieve the repetitive construct unit of regular texture.

The N that we will try to achieve for step (2) below₁×N₂Grid regular pattern illustrates how to be back-calculated to obtain introductory die The generation parameter of regular texture in type.Mode of asking for according to translation transformation is easy to infer on initial threedimensional model rule knot The dimension of the 3rd class parameter all directions of structure is respectively (n₁+ 1) and (n₂+ 1), i.e. N in two-dimension translational transformation space₁× N₂Regular pattern is by (a n on correspondence initial model₁+1)×(n₂+ 1) regular texture.And for basic translation transformation group T₁With T₂, can be according to the generation vector g of regular pattern₁And g₂Deduction obtains.Find T₁And T₂Specific practice as follows: for every master Axle, the α corresponding about each mesh point on main shaft and nearest cluster centre thereof tried to achieve according to step (2)_ijAnd β_kValue, Find the two value all close to 1 mesh point x_ij, then choose x_ijNearest cluster centre c_kArbitrary in the cluster at place Point is the most flat to can try to achieve in the direction according to the point on two repetitive construct unit on the initial model that this point is corresponding Move conversion.There is basic translation transformation group T₁And T₂, it is possible to try to achieve a translational movement relation between similar concentration any two points, This translational movement is T₁And T₂A linear combination, the determination method of combination coefficient is: according to the translation of similar concentration the two point The cluster centre at conversion place, it is possible to obtain the mesh point that this cluster centre is nearest, from formula (2), the i of this mesh point with J is the combination coefficient of correspondence.

So far, two yuan of parameters during regular texture generates parameter on initial model are had been obtained for, next by profit By basic translation transformation group T₁And T₂Go to be polymerized the representative structure list obtaining last yuan of still unknown parameter regular texture Unit, polymerization is actually a continuous process expanding point, comprises the following steps:

Step (31), defines a set S being initially empty, and puts p on the basis of a point of optional similar concentration₀, add Set S.

The most now the present embodiment also has the point represented in structural unit, and it is exactly the phase that step (1) is tried to achieve Like any point concentrated, this point is designated as p₀, add S.

Step (32), to any not point in set S, as long as one point of existence is setting with the distance of this point in set S In the range of Ding, set point value is 1000～3000, then this point is called the consecutive points p of S₁, to the consecutive points p gathering S₁, calculate Consecutive points are registrated to registration error ω brought during datum mark.

The computational methods of registration error are: first will a p₀、p₁By the above-mentioned p tried to achieve₀To putting down of similar concentration i-th point Shifting amount translates, and then finds the most nearest some p on initial threedimensional model respectively_i0、p_i1, i therein represents similar collection In i-th point, its span is 1 to arrive | Ω |, and | Ω | represents total number of similar centrostigma, and then ω is represented by:

$\mathrm{\ω}={\mathrm{\Σ}}_{i=1}^{\left|\mathrm{\Ω}\right|}(p_1-((p_{i1}-p_{i0})+p_0))---\left(9\right)$

Step (33), after trying to achieve registration error, we determine p as follows₁Going or staying: for given threshold value (institute State the general value of threshold value be one close to 0 real number, the present embodiment value 0.07), if ω is less than this threshold value, then p₁Add S； Otherwise, p is abandoned₁.Repeat step (32) until no point can not add again.

After some expansion terminates, we just obtain the representative structural unit parameter of regular texture on initial model, add The basic translation transformation tried to achieve and dimensional parameter, just constitute all parameter systems of create-rule structure, thus Complete the whole algorithm flow of the present embodiment.For the input model of Fig. 2 (a), and according to our selected datum mark, this Embodiment structural unit extracts result as it is shown in fig. 7, the regular texture that will obtain a 6*2.

The invention provides a kind of three-dimensional building model structure based on transformation space and find method, implement this technology The method of scheme and approach are a lot, and the above is only the preferred embodiment of the present invention, it is noted that for the art Those of ordinary skill for, under the premise without departing from the principles of the invention, it is also possible to make some improvements and modifications, these change Enter and retouch and also should be regarded as protection scope of the present invention.Each ingredient the clearest and the most definite in the present embodiment all can use prior art to add To realize.

Claims (1)

1. a three-dimensional building model structure based on transformation space finds method, it is characterised in that comprise the following steps:

Step (1), carries out transform analysis to the sample building of user's input, initial threedimensional model space is transformed into two-dimension translational Transformation space；Wherein the sample building of user's input is the triangle gridding mould of the triangle relation comprising three-dimensional coordinate and point a little Type；

Step (2), carries out model estimation in two-dimension translational transformation space, tries to achieve the grid rule in two-dimension translational transformation space Pattern；

Step (3), releases regular texture on initial threedimensional model according to the grid regular pattern in two-dimension translational transformation space is counter Generation parameter, recycle these parameter aggregations and obtain the repetitive construct unit of this regular texture；

In step (1), by estimating that similar point possible with in analysis input model concentrates the translation transformation between any two points to close System, is transformed into two-dimension translational transformation space by initial threedimensional model space, concretely comprises the following steps:

Step (11), tentatively asks for similar collection, is divided by the point in initial threedimensional model according to the curvature of point, forms one group Initial similar collection, determines that one of them initial similar collection carries out next step and operates:

Step (12), rejects the point of this similar concentration redundancy to the initial similar centralized procurement local registration method determined；

Step (13), carries out transformed mappings to the similar collection after local registration, it is achieved initial threedimensional model space is to two-dimension translational The conversion of transformation space；

In step (2), comprise the following steps:

Step (21), uses average and variance method to cluster all points in two-dimension translational transformation space；

Step (22), two main shafts in using consistent random algorithm to determine cluster back plane；

Step (23), uses Gaussian weighting marks method to minimize a combined energy, estimates the grid rule in two-dimensional space Rule pattern:

Each item of described combined energy is respectively as follows:

E_X→CMeasure connecing of all mesh points cluster centre nearest with it Short range degree；

E_C→XMeasure all cluster centres mesh point nearest with it close to journey Degree；

E_αMeasure total number that all mesh points cluster centre nearest with it is effectively matched；

E_βMeasure total number that all cluster centres mesh point nearest with it is effectively matched；

Final energy equation is:

E=γ (E_X→C+E_C→X)+(1-γ)(E_α+E_β),

Wherein, γ is a coordination parameter, and γ is used for weighing every pair of mesh point and the energy term of cluster centre degree of closeness and net Lattice point and cluster centre are effectively matched the energy term of total number, and γ span is 0～1, N₁And N₂For grid regular pattern often Dimension on individual direction, | C | represents total number of cluster centre, and (i j) is off-network lattice point x to c_ijNearest cluster centre, wherein i Span be 1 to N₁, the span of j is 1 to N₂, x (k) represents from kth cluster centre c_kNearest mesh point, its The span of middle k is 1 to arrive | C |, α_ijRepresent mesh point x_ijIt is mapped as the credibility of its nearest cluster centre, β_kRepresent cluster Center c_kIt is mapped as the credibility of its nearest mesh point；

In step (3), pushed back regular texture on initial threedimensional model by the grid regular pattern in two-dimension translational transformation space is counter Basic translation transformation group T₁And T₂, then utilize basic translation transformation group T₁And T₂Polymerization obtains the repetition structure of this regular texture Make unit, comprise the following steps:

Step (31), defines a set S being initially empty, and puts p on the basis of a point of optional similar concentration₀, add set S；

Step (32), to any not point in set S, as long as there is the some distance with this point in set S at setting model In enclosing, set point value is 1000～3000, then this point is called the consecutive points p of S₁, to the consecutive points p gathering S₁, calculate adjacent Point is registrated to registration error ω brought during datum mark；

Step (33), if ω is less than given threshold value, then by described consecutive points p₁Add set S, otherwise refuse；Return step (32) until no point does not adds again, repetitive construct unit is finally given；

In step (32), registration error computing formula is:

$\mathrm{\ω}={\mathrm{\Σ}}_{i=1}^{\left|\mathrm{\Ω}\right|}(p_1-(\left(p_{i1}-p_{i0}\right)+p_0\left)\right),$

Wherein, p₁Represent datum mark p₀Consecutive points, | Ω | represents total number of similar centrostigma, p_i0Represent datum mark p₀By p₀ After translating to the translational movement relation of similar concentration i-th point on initial threedimensional model with datum mark p₀Nearest point, p_i1Represent point p₁By p₀After translating to the translational movement of similar concentration i-th point on initial threedimensional model with a p₁Nearest point, translational movement therein It it is basic translation transformation group T₁And T₂A linear combination.