CN104063896A - 3D building model structure discovery method based on transformation space - Google Patents
3D building model structure discovery method based on transformation space Download PDFInfo
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Abstract
The invention relates to model structure analysis method. Firstly, an initial 3D model space is converted into a 2D translational transformation space through transformation analysis, thus a detection problem of inputting a rule structure is converted into a problem of firstly detecting a grid rule mode in a 2D space and secondly carrying out backstepping. For the grid rule mode detection problem in the 2D space, an energy minimization method is utilized to estimate the relevant parameters, a complete rule mode can be detected, and the method is also suitable for the condition with the existence of abnormal points or missing points. Finally the generation parameter of the corresponding rule structure on a 3D model is obtained through backstepping according to the grid rule mode, and the corresponding repeated construction unit is extracted. According to the method, the corresponding repeated construction unit of a translation repeat structure in a building model can be rapidly extracted.
Description
Technical field
The present invention relates to a kind of model structure analysis method, belong to Computer Image Processing and computer graphics techniques field, is a kind of three-dimensional building model structure discover method based on transformation space specifically.
Background technology
We are around found everywhere various buildingss, are not difficult to find all can have regular texture more or less in each buildings, and as having the window of same structure in certain region, or the tectonic element such as door.And by the tectonic element of these repetitions, identify relevant design style of building just in our a lot of situations.If therefore can detect the repetitive structure comprising in BUILDINGS MODELS with some ad hoc approach, will be familiar with and understand existing BUILDINGS MODELS us provides great help.Modal BUILDINGS MODELS structural unit detection method adopts manual interactive mode to carry out the extraction of tectonic element, 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 this class methods time and effort consuming, needing user to treat analytical model has deep understanding could obtain complete tectonic element.Along with the development of technology, Recent study personnel are by geometric transformation characteristics such as the symmetry comprising in model, translation, rotations, adopt half mutual or automatic mode to realize the detection of BUILDINGS MODELS tectonic element.
From geometric transformation angle, carry out the research process of model structure analysis, mainly be divided into three phases: start its application most and mainly appear in figure, 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, 2003, 25 (4): 418-432. etc. introduce.It is more difficult wanting directly above-mentioned picture structure analytical approach to be applied in the structure analysis of three-dimensional model.Therefore, then constantly in research process, by using for reference picture structure, analyzing thought, also many methods that can complete for the structure analysis of three-dimensional model have been there are, as document 5Mitra N.J., Guinbas L.J., Pauly is and approximate symmetry detection for3d geometry.ACM Transactions on Graphics M.2006.Partial, 25 (3): 560-568. and document 6Pauly M., Mitra N.J., Wallner J., Pottmann H., Guibas L.J.Discovering structural regularity in3d geometry.ACM Transactions on Graphics, 2008, 27 (3): 43:1-43:11. etc. introduce.The emphasis of said method is all that repeat pattern detects, and they are all to treat model structure relation with a kind of angle of plane.In recent years, people expect expressing abundanter model by more complicated tectonic element membership credentials, thereby there is Analysis of Hierarchy Structure method, 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. etc. introduce.By propose the concept of " level " in structure analysis process, no longer with the angle of plane, treat a model face, and regarded as, many levels, consist of, these class methods have realized the deciphering of the irregular structure that cannot understand ordinary construction detection method.
Summary of the invention
Goal of the invention: technical matters to be solved by this invention is for the deficiencies in the prior art, provides a kind of three-dimensional building model structure discover method based on transformation space.
Technical scheme: in order to solve the problems of the technologies described above, the invention discloses a kind of three-dimensional building model structure discover method based on transformation space, the method is for the building sample of user input, can its tectonic element comprising of rapid extraction, comprises the following steps:
Step (1), carries out transform analysis to the sample building of user's input, and initial three-dimensional model space is transformed into two-dimension translational transformation space; Wherein user inputs the triangle grid model that sample building is the triangle relation that comprises three-dimensional coordinate a little and point;
Step (2) is carried out model estimation in two-dimension translational transformation space, tries to achieve the grid regular pattern in two-dimension translational transformation space;
Step (3), according to the anti-generation parameter of releasing regular texture on initial three-dimensional model of grid regular pattern in two-dimension translational transformation space, recycles the repetitive construct unit that these parameter aggregations obtain this regular texture.
In step of the present invention (1), by estimating to concentrate the translation transformation relation between any two points with point that may be similar in analysis input model, initial three-dimensional model space is transformed into two-dimension translational transformation space, concrete steps are:
Step (11), tentatively asks for similar collection, will in initial three-dimensional model, may be divided in the set of a point by similar point, and determines that one of them prima facies carries out next step operation like collection:
Step (12), rejects the point of this similar concentrated redundancy to prima facies like centralized procurement with local method for registering;
Step (13), carries out transformed mappings to the similar collection after local registration, realizes initial three-dimensional model space to the conversion of two-dimension translational transformation space.
Step of the present invention comprises the following steps in (2):
Step (21), adopts average moving method to carry out cluster to the point in two-dimension translational transformation space;
Step (22), adopts two main shafts in consistent random algorithm hard clustering back plane;
Step (23), adopts Gauss's Newton iteration method to minimize a combined energy, estimates the grid regular pattern in two-dimensional space.
Each of described combined energy is respectively:
E
x → C=∑
i∑
jα
ij 2|| x
ij-c (i, j) ||
2, the degree of closeness of measuring all net points cluster centre nearest with it;
measure the degree of closeness of all cluster centres net point nearest with it;
E
α=∑
i∑
j(1-α
ij 2)
2, measure total number that all net points effectively mate with its nearest cluster centre;
E
β=∑
k(1-β
k 2)
2, measure total number that all cluster centres effectively mate with its nearest net point.
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 net point and effectively mates total number energy term with cluster centre degree of closeness energy term and net point with cluster centre, and γ span is 0～1, N
1and N
2for the dimension of grid regular pattern in each direction, | C| represents total number of cluster centre, and c (i, j) is from net point x
ijnearest cluster centre, wherein the span of i is 1 to N
1, the span of j is 1 to N
2, x (k) represents from k cluster centre c
knearest net point, wherein the span of k is 1 to arrive | C|, α
ijrepresent net point x
ijbe mapped as the confidence level of its nearest cluster centre, β
krepresent cluster centre c
kbe mapped as the confidence level of its nearest net point.
In step of the present invention (3), the anti-basic translation transformation group T that pushes back regular texture on initial three-dimensional model of grid regular pattern in two-dimension translational transformation space
1and T
2, then utilize basic translation transformation group T
1and T
2polymerization obtains the repetitive construct unit of this regular texture, comprises the following steps:
Step (31), defines one and is initially empty S set, and an optional similar concentrated point is reference point p
0, add S set;
Step (32), to any not point in S set, as long as exist the distance of a point and this point in setting range in S set, setting range value is 1000～3000, claims this point for the consecutive point p of S
1, the consecutive point p of pair set S
1, calculate the registration error ω bringing when consecutive point are registrated to reference point;
Step (33), if ω is less than given threshold value, adds S set by described consecutive point, otherwise refusal; Return to step (32) until do not have again point to add, finally obtain repetitive construct unit;
In step (32), registration error computing formula is:
Wherein, p
1represent reference point p
0consecutive point, | Ω | represent total number of similar centrostigma, p
i0represent reference point p
0press p
0after being related to translation to the similar translational movement of concentrating i point initially on three-dimensional model with reference point p
0nearest point, p
i1represent some p
1press p
0after being related to translation to the similar translational movement of concentrating i point initially on three-dimensional model with a p
1nearest point, translational movement is wherein basic translation transformation group T
1and T
2a linear combination.
Beneficial effect: model structure analysis method of the present invention is compared advantage with existing model structure analysis method and is: for the three-dimensional grid model of input, can, under the prerequisite of prior imformation the unknowns of the aspects such as repetitive construct cell configuration, size, position, complete fast the analysis of its model structure.In addition, method of the present invention not only can detect intact grid regular pattern, to existing situation abnormal or disappearance part applicable equally.
Accompanying drawing explanation
Below in conjunction with the drawings and specific embodiments, the present invention is done further and illustrated, above-mentioned and/or otherwise advantage of the present invention will become apparent.
Fig. 1 is the main process flow diagram of the present invention.
Fig. 2 a and Fig. 2 b are that the prima facies at the reference point manually demarcated on initial model and reference point place is like collection.
Fig. 3 a and Fig. 3 b are prima facies like collection and similar collection after local registration.
Fig. 4 is the three dimensions that translation vector forms.
Fig. 5 is that spot projection in three dimensions is to two dimensional surface.
Fig. 6 a, Fig. 6 b, Fig. 6 c and Fig. 6 d are respectively β in two main shafts crossing initial point after translation transformation space clustering, initial mesh 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 tectonic element extracts result.
Embodiment
As shown in Figure 1, the present invention includes following steps:
Step (1), carries out transform analysis to the sample building of user's input, and initial three-dimensional model space is transformed into two-dimension translational transformation space; Wherein user inputs the triangle grid model that sample building is the triangle relation that comprises three-dimensional coordinate a little and point;
Step (2) is carried out model estimation in two-dimension translational transformation space, tries to achieve the grid regular pattern in this space;
Step (3), according to the anti-generation parameter of releasing regular texture on initial three-dimensional model of grid regular pattern in two-dimension translational transformation space, recycles the repetitive construct unit that these parameter aggregations obtain this regular texture.
More particularly, the present invention is under the prerequisite of prior imformation the unknown of the aspects such as three-dimensional building model repetitive construct cell configuration, size, position, adopt the structure analysis method of estimating repeat pattern simultaneously and detecting constitutional repeating unit, completed fast the structure analysis of its model.First by transform analysis, initial three-dimensional model space is transformed into a two-dimension translational transformation space, thereby the problem of asking for regular texture repeat pattern on input model has been changed into the grid regular pattern first asked in the translation transformation space anti-problem pushing away again.For grid regular pattern test problems in translation transformation space, the present invention utilizes energy minimization method to do model estimation, find out existence grid regular pattern wherein, in this step, not only can detect intact grid regular pattern, for having some abnormity point or the situation of missing point, can find repeat pattern wherein equally.Last according to the counter correlation parameter of releasing regular texture on three-dimensional model of grid regular pattern in translation transformation space, extract corresponding repetitive construct unit.
Embodiment
According to embodiment, each step of the present invention is described below.
Due to singularity of the present invention, part accompanying drawing disclosed in this invention, has to use the accompanying drawing with gradation effect to represent.
Step (1), carries out transform analysis to the sample building of user's input, and initial three-dimensional model space is transformed into two-dimension translational transformation space.
Step (11) is tentatively asked for similar collection.
This step wishes to mark off point set that may be similar in input model, is referred to as similar collection.Similar collection is the tie that change in three-dimensional model space and translation transformation space, by similar concentrated any two points is matched and asks for corresponding translation transformation, just can be transformed into from input model space the translation transformation space that similar collection is asked for.Specific practice is as follows: for the institute on initial three-dimensional model a little, ask for two principal curvatures k of each sample point
1, k
2, first according to H
2/ K divides doing a little once, and the point that the absolute value of this value difference is less than to certain threshold value (the general span of described threshold value is 0-0.005, the present embodiment value 0.001) is divided in a set, wherein H=(k
1+ k
2)/2 are mean curvature, K=k
1k
2for Gaussian curvature, according to the size of H, K value, previous step division result further to be classified respectively more afterwards, the criteria for classifying is the absolute value of H, K value difference to be all less than to certain threshold value (the general span of described threshold value is 10
-7-10
-5, the present embodiment value 10
-6) point be divided in a set.So just all initial points are divided.
But because the similar collection quantity of asking for is too much, in order to simplify subsequent operation, the present embodiment is when asking for a class formation unit, first manually on input model, demarcate a reference point, as the point identifying in Fig. 2 a, then according to determining the final similar collection that participates in calculating to this reference point similar situation, as the point identifying in Fig. 2 b, subsequent algorithm operates like collection this prima facies.
The Main Function that carries out aforesaid operations has two, and the one,, relative initial data set, this step has reduced the number of point greatly, can effectively reduce the running time of next step local registration; The 2nd,, the some set of trying to achieve like this has a feature, and the point that belongs to same regular pattern can be in same set, can guarantee finally can find the similar collection that only comprises a regular pattern.
The local registration of step (12).
After dividing through previous step, just similar collection has been carried out tentatively solving, now, prima facies is like concentrating the point that still can contain some redundancies, therefore the object of local registration is rejected prima facies exactly like concentrating incorrect point, finally obtains reliable similar collection, meanwhile, can also proofread and correct the position of similar concentrated part point, thereby make the translation transformation of next step requirement more accurate.
First, the reference point (point of circles mark in Fig. 3 a) of demarcating like concentrated user for prima facies, ask for institute on its fettucelle representing a little in initial three-dimensional model, in order to allow certain error range, on the present embodiment agreement three-dimensional model if from the distance of reference point the point within the scope of h, all can be regarded as on this fettucelle, tried to achieve point is designated as to { x
1, x
2..., x
n.Wherein the setting of parameter h will be determined according to different model data features, and the present embodiment value is 3000.
Secondly, for rejecting similar concentrated redundant points, adopt document 9Pottmann H., Huang Q.-X, Yang Y.-L, Hu S.-M.Geometry and convergence analysis of algorithms for registration of3D shapes.Int.J.Computer Vision, 2006,67 (3): the closest approach iteration of 277-296. (Iterative Closest Point, ICP) algorithm concentrates each point except reference point to operate to similar.First this point and reference point coordinate are subtracted each other and try to achieve translation transformation, as the initial value of mobile mapping α in closest approach iteration (Iterative Closest Point, ICP) algorithm, then utilize α to the { x a little of the institute on reference point dough sheet
1, x
2..., x
nmove, after this, on corresponding point dough sheet, ask for the closest approach of mobile rear each point, be designated as { y
1, y
2..., y
n.Finally minimize objective function:
X wherein
i+=α
+x
i, α
+unknown in this objective function, be to α correction.Constantly repeat above-mentioned ICP operation until the poor absolute value of the result of trying to achieve for twice before and after (1) formula (the general value of described scope is and approaches 0 real number, the present embodiment value 1e-8) within the specific limits.If the final error F (the general value of described critical error is and approaches 0 real number, the present embodiment value 0.3) within the scope of critical error trying to achieve after certain some closest approach iteration, accepts this point, and by the α wherein trying to achieve
+as the similarity transformation between this point and reference point; Otherwise, by this point from then on similar concentrate weed out.Result after local registration as shown in Figure 3 b.
Step (13) transformed mappings.
After previous step, the present embodiment has obtained accurate similar collection, next will utilize this similar collection to complete the conversion from former three dimensions to translation transformation space.Operating process is by similar concentrated any two points is matched, just can be in the hope of a series of translation transformation, in fact each translation transformation is exactly a translation vector, and a point in corresponding three-dimensional space, as the some T being identified in Fig. 4 is a required translation vector.After having matched a little, we just can obtain the distribution situation of final each translation transformation in three dimensions, as shown in Figure 4.
In order to be easier to operation and to observe, the present embodiment also needs the translation transformation in three dimensions to pass through to find suitable two-dimensional projection's plane, shines upon accordingly.First adopt document 10Fischler M., Bolles R.Random Sample Consensus:A paradigm for model fitting with applications to image analysis and automated cartography.Commun.ACM, 1981,24 (6): the consistent stochastic sampling of 381-395. (Random Sample Consensus, RANSAC) method completes determining of two dimensional surface, and the final purpose of this method is to allow a little as much as possible dropping in the plane of trying to achieve.Then we project to all translation vectors in three dimensions in Fig. 4 on this two dimensional surface again.Projection result as shown in Figure 5.Wherein in Fig. 5, be designated (t
1, t
2) point be the projection situation of point on this two dimensional surface that is designated T in Fig. 4.
Step (2) model is estimated.
Obtained on last stage a two dimensional surface distributing about translation transformation, the target of this one-phase is by the point in this two dimensional surface is analyzed, and finds out their grid regular pattern.In order to find out the regular pattern existing in above-mentioned two dimensional surface, need to determine the two class parameters about it: the generation vector g of regular pattern
1, g
2and the dimension N of each direction
1, N
2.In order to reach this object, next will build and minimize an energy function about putting on this two dimensional surface.
Step (21) two-dimensional space mid point cluster.
Due to same translation transformation can by three dimensions different 2 to obtaining, and more or less can there are some errors to the translation transformation of trying to achieve in different points, so just may occur that after same translation transformation projects on two dimensional surface be not on same point, but be distributed in the small neighbourhood of certain point.For this problem, we first carry out cluster to the point on two dimensional surface, so just can ask for follow-up regular pattern with cluster centre.Adopt document 11Comaniciu D. herein, Meer is shift:a robust approach toward feature space analysis.IEEE Transactions on pattern analysis and machine intelligence P.2002.Mean, 24 (5): the average of 603-619. moves (mean-shift) method and completes corresponding cluster work, the cluster centre of trying to achieve for Fig. 5 is as shown in Fig. 6 (a).
Main shaft in step (22) hard clustering back plane.
According to step (13), ask the right matching method of translation transformation time point, be not difficult to know that displacement is that zero translation transformation is bound to occur.Therefore these two main shafts that the present embodiment will be asked for needed true origin, and can not overlap.And step (13) looks for two dimensional surface similar in three dimensions, determining of main shaft still adopts consistent stochastic sampling (Random Sample Consensus, RANSAC) method, only here in order to determine that a straight line of crossing initial point only need to select a non-initial point again.Finding main shaft is in order to determine that regular pattern generates vectorial initial value, and obtains the corresponding dimension of each direction.Concrete definite method is: g
1and g
2be made as respectively on two major axes orientations the vector forming from the nearest cluster centre of initial point and initial point, as shown in Fig. 6 (b); Article two, on main shaft, from the ratio that generates vectorial length on the distance of cluster centre farthest of initial point and initial point and correspondence direction, round and be defined as respectively n
1and n
2, as shown in Fig. 6 (b).Because n
1and n
2the corresponding just dimension of half direction of main shaft, so the dimension actual value of corresponding each direction of regular pattern should be N
1=2*n
1+ 1, N
2=2*n
2+ 1, and N
1and N
2value can not change again.
Step (23) is asked the grid regular pattern in two-dimensional space.
After said process, the present embodiment obtains a N
1* N
2the grid regular pattern of size, each net point x wherein
ijcan be expressed as form
x
ij＝ig
1+jg
2-n
1≤i≤n
1and-n
2≤i≤n
2(2)
Now known in two dimensional surface that regular pattern is in the dimension of all directions, and obtained this regular pattern and generate vectorial initial value.In order to ask for this, generate vectorial end value, next will start to build combined energy function.Below we will introduce this combined energy function item by item.First degree of closeness that is used for measuring its corresponding nearest cluster centre of all net points, concrete form is
E
X→C＝Σ
iΣ
jα
ij 2||x
ij-c(i，j)||
2(3)
Wherein c (i, j) is from x
ijnearest cluster centre.Similarly, the degree of closeness of second its corresponding nearest net point of all cluster centres of tolerance
Wherein | C| represents total number of cluster centre, and x (k) represents from c
knearest net point.For the c (i, j) in (3) and (4) formula and x (k), these two values all will re-start calculating in the iterative process of each step, are the values constantly changing.α
ijand β
kbe two new unknown quantitys introducing in this optimizing process, they are for detecting abnormity point in regular pattern and missing point.α wherein
ijrepresent net point x
ijbe mapped as the confidence level of its nearest cluster centre, β
krepresent cluster centre c
kbe mapped as the confidence level of its nearest net point.α
ijand β
kvalue more close to 1, just show that the matching confidence between cluster centre and net point is higher, and the large young pathbreaker of these two values determines which on two dimensional surface we select put to ask for the basic translation transformation of regular texture on initial model next stage.Because we are without any about shortage of data or abnormal priori, so in the optimizing process in this stage, α
ijand β
kinitial value be all made as 1.Correspondingly, for these two parameters, also introduced two new energy, their effect is total number that tolerance net point effectively mates with its nearest cluster centre:
E
α＝∑
i∑
j(1-α
ij 2)
2(5)
E
β＝∑
k(1-β
k 2)
2(6)
Our the target energy function that combines that above-mentioned four energy get final product:
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 minimizes E exactly, obtains regular pattern and generates vectorial end value:
The present embodiment adopts Gauss's Newton iteration method to minimize combinations thereof energy, the result obtaining is as shown in Fig. 6 a～Fig. 6 d, for the regular texture of the 6*2 in experimental data shown in Fig. 2, Fig. 7 has provided the grid regular pattern of a 11*3 in two-dimension translational transformation space.Wherein Fig. 6 a is two main shafts of all cluster centres in translation transformation space; Fig. 6 b is initial mesh regular pattern, with the line of arrow grid g for this reason
1and g
2initial value; Fig. 6 c and 6d are respectively α on final grid rule model
ijand β
kthe situation of value.
Step (3), polymerization obtains the repetitive construct unit of regular texture on initial three-dimensional model.
Model has been estimated to try to achieve the regular texture on initial model and has been transformed to the regular pattern in this plane after two-dimension translational transformation space.In order to find three class parameters of regular texture on initial three-dimensional model: this regular texture represent tectonic element, basic translation transformation group T
1, T
2and the dimension in all directions, the present embodiment need to proceed as follows: first, utilize the parameter of regular pattern in two dimensional surface instead to release the second and the 3rd class parameter in regular texture three class parameters on initial three-dimensional model, then according to Equations of The Second Kind parameter, go to ask first kind parameter, thereby also just tried to achieve the repetitive construct unit of regular texture.
Below our N that will try to achieve for step (2)
1* N
2grid regular pattern illustrates the generation parameter that how to be back-calculated to obtain regular texture on initial model.According to the mode of asking for of translation transformation be easy to infer regular texture on initial three-dimensional model the 3rd class parameter---the dimension of all directions is respectively (n
1+ 1) and (n
2+ 1), i.e. N in two-dimension translational transformation space
1* N
2regular pattern is by (a n on corresponding initial model
1+ 1) * (n
2+ 1) regular texture.And for basic translation transformation group T
1and T
2, can be according to the generation vector g of regular pattern
1and g
2deduction obtains.Find T
1and T
2specific practice as follows: for every main shaft, according to step (2), try to achieve about each net point on main shaft and the nearest corresponding α of cluster centre thereof
ijand β
kvalue, find these two values all to approach 1 net point x
ij, then choose x
ijnearest cluster centre c
kany point in the cluster at place, puts according to this basic translation transformation that point on two repetitive construct unit on corresponding initial model makes progress to trying to achieve the party.There is basic translation transformation group T
1and T
2, just can be in the hope of a translational movement relation between similar concentrated any two points, this translational movement is T
1and T
2a linear combination, definite method of combination coefficient is: according to the similar cluster centre of concentrating the translation transformation place of these two points, can obtain the nearest net point of this cluster centre, from formula (2), the i of this net point and j are corresponding combination coefficient.
So far, obtain regular texture on initial model and generated two yuan of parameters in parameter, next will utilize basic translation transformation group T
1and T
2go polymerization to obtain last yuan of still unknown parameter---regular texture represent tectonic element, in fact polymerization is exactly a process that constantly expands point, comprises the following steps:
Step (31), defines one and is initially empty S set, and an optional similar concentrated point is reference point p
0, add S set.
In fact now the present embodiment also has the point representing in tectonic element, and it is exactly the similar concentrated any point that step (1) is tried to achieve, and this point is designated as to p
0, add S.
Step (32), to any not point in S set, as long as exist the distance of a point and this point in setting range in S set, setting range value is 1000～3000, claims this point for the consecutive point p of S
1, the consecutive point p of pair set S
1, calculate the registration error ω bringing when consecutive point are registrated to reference point.
The computing method of registration error are: first will put p
0, p
1by the above-mentioned p trying to achieve
0carry out translation to the similar translational movement of i point of concentrating, then on initial three-dimensional model, find respectively with it nearest some p
i0, p
i1, i wherein represents similar i concentrated point, its span is 1 to arrive | and Ω |, | Ω | represent total number of similar centrostigma, then ω can be expressed as:
Step (33), tries to achieve after registration error, and we decide p as follows
1going or staying: for given threshold value (the general value of described threshold value is one and approaches 0 real number, the present embodiment value 0.07), if ω is less than this threshold value, p
1add S; Otherwise, abandon p
1.Repeating step (32) is not until have point to add again.
After some expansion finishes, what we had just obtained regular texture on initial model represents tectonic element parameter, basic translation transformation and the dimension parameter of before adding, having tried to achieve, just formed all parameter systems of create-rule structure, thereby completed the whole algorithm flow of the present embodiment.For the input model of Fig. 2 (a), and according to our selected reference point, the present embodiment tectonic element extracts result as shown in Figure 7, will obtain the regular texture of a 6*2.
The invention provides a kind of three-dimensional building model structure discover method based on transformation space; method and the approach of this technical scheme of specific implementation are a lot; the above is only the preferred embodiment of the present invention; should be understood that; for those skilled in the art; under the premise without departing from the principles of the invention, can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.In the present embodiment not clear and definite each ingredient all available prior art realized.
Claims (4)
1. the three-dimensional building model structure discover method based on transformation space, is characterized in that, comprises the following steps:
Step (1), carries out transform analysis to the sample building of user's input, and initial three-dimensional model space is transformed into two-dimension translational transformation space; Wherein user inputs the triangle grid model that sample building is the triangle relation that comprises three-dimensional coordinate a little and point;
Step (2) is carried out model estimation in two-dimension translational transformation space, tries to achieve the grid regular pattern in two-dimension translational transformation space;
Step (3), according to the anti-generation parameter of releasing regular texture on initial three-dimensional model of grid regular pattern in two-dimension translational transformation space, recycles the repetitive construct unit that these parameter aggregations obtain this regular texture.
2. a kind of three-dimensional building model structure discover method based on transformation space according to claim 1, it is characterized in that, in step (1), by estimating to concentrate the translation transformation relation between any two points with point that may be similar in analysis input model, initial three-dimensional model space is transformed into two-dimension translational transformation space, and concrete steps are:
Step (11), tentatively asks for similar collection, according to the curvature of point, the point in initial three-dimensional model is divided, and forms one group of prima facies like collection, determines that one of them prima facies carries out next step operation like collection:
Step (12), rejects the point of this similar concentrated redundancy to described prima facies like centralized procurement with local method for registering;
Step (13), carries out transformed mappings to the similar collection after local registration, realizes initial three-dimensional model space to the conversion of two-dimension translational transformation space.
3. a kind of three-dimensional building model structure discover method based on transformation space according to claim 2, is characterized in that, in step (2), comprises the following steps:
Step (21), adopts average moving method to carrying out a little cluster in two-dimension translational transformation space;
Step (22), adopts two main shafts in consistent random algorithm hard clustering back plane;
Step (23), adopts Gauss's Newton iteration method to minimize a combined energy, estimates the grid regular pattern in two-dimensional space:
Each of described combined energy is respectively:
e
c → Xmeasure the degree of closeness of all cluster centres net point nearest with it;
e
αmeasure total number that all net points effectively mate with its nearest cluster centre;
e
βmeasure total number that all cluster centres effectively mate with its nearest net point;
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 net point and effectively mates total number energy term with cluster centre degree of closeness energy term and net point with cluster centre, and γ span is 0～1, N
1and N
2for the dimension of grid regular pattern in each direction, | C| represents total number of cluster centre, and c (i, j) is from net point x
ijnearest cluster centre, wherein the span of i is 1 to N
1, the span of j is 1 to N
2, x (k) represents from k cluster centre c
knearest net point, wherein the span of k is 1 to arrive | C|, α
ijrepresent net point x
ijbe mapped as the confidence level of its nearest cluster centre, β
krepresent cluster centre c
kbe mapped as the confidence level of its nearest net point.
4. a kind of three-dimensional building model structure discover method based on transformation space according to claim 3, it is characterized in that, in step (3), the anti-basic translation transformation group T that pushes back regular texture on initial three-dimensional model of grid regular pattern in two-dimension translational transformation space
1and T
2, then utilize basic translation transformation group T
1and T
2polymerization obtains the repetitive construct unit of this regular texture, comprises the following steps:
Step (31), defines one and is initially empty S set, and an optional similar concentrated point is reference point p
0, add S set;
Step (32), to any not point in S set, as long as exist the distance of a point and this point in setting range in S set, setting range value is 1000～3000, claims this point for the consecutive point p of S
1, the consecutive point p of pair set S
1, calculate the registration error ω bringing when consecutive point are registrated to reference point;
Step (33), if ω is less than given threshold value, adds S set by described consecutive point, otherwise refusal; Return to step (32) until do not have again point to add, finally obtain repetitive construct unit;
In step (32), registration error computing formula is:
Wherein, p
1represent reference point p
0consecutive point, | Ω | represent total number of similar centrostigma, p
i0represent reference point p
0press p
0after being related to translation to the similar translational movement of concentrating i point initially on three-dimensional model with reference point p
0nearest point, p
i1represent some p
1press p
0to after similar translational movement translation of concentrating i point initially on three-dimensional model with a p
1nearest point, translational movement is wherein basic translation transformation group T
1and T
2a linear combination.
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