CN102254338A - Automatic obtaining method of three-dimensional scene optimal view angle based on maximized visual information - Google Patents

Abstract

The invention provides an automatic obtaining method of a three-dimensional scene optimal view angle based on maximized visual information. The surface geometrical characteristic of a scene is represented through utilizing the curvature of all vertices of the three-dimensional scene, and the characteristic area of the three-dimensional scene is solved through utilizing a self-adaptive clustering method. As for each sampling view point, the visual characteristic total amount and the visual display effect on all characteristic areas are estimated, and the optimal view angle for observing the three-dimensional scene is found out finally on the basis of a clustering algorithm and a statistical method. In the method, the surface geometrical characteristic information of the given three-dimensional scene is fully utilized, the visual quality of each characteristic area is taken into consideration when the maximized visual information amount is obtained, the optimal view angle is solved, and the visual demand for people to observe the three-dimensional scene is fully met.

Description

The automatic acquisition methods of three-dimensional scenic optimal viewing angle based on the maximization visual information

Technical field

The present invention relates to a kind of electronic 3-D model disposal route, be specifically related to a kind of automatic acquisition methods of three-dimensional scenic optimal viewing angle based on the maximization visual information.

Background technology

In recent years, along with computer technology and rapid development of network technology, increasing three-dimensional scene models is used for fields such as environment navigation, virtual reality, digital city.

A given three-dimensional model is when different angles is observed it, because the visual information that different visual angles has been carried the different directions of this three-dimensional model may show the diverse form of expression.The essence of seeking optimal viewing angle is to find out the viewpoint of a carrying maximum fault information, and this viewpoint helps people and more in depth removes to observe and understand given three-dimensional model.In recent years, the optimal viewing angle problem has obtained the broad research of academia, and is applied in a lot of practical problemss, as shape recognition and classification, three-dimensional model view editor, based on the playing up of image, three-dimensional model search etc.

For which type of visual angle is this problem of optimal viewing angle, goes back neither one authority's definition now.When research optimal viewing angle problem, people go to define according to the own practical application of being faced usually.By research computer graphical psychology, people such as Blanz have proposed four attributes of decision optimal viewing angle: be beneficial to identification, familiarity, can use function representation and aesthetical standard, and optimal viewing angle is subjected to the geometrical property of three-dimensional model to influence (Blanz to a great extent, V, etal., What object attributes determine canonical views? PERCEPTION-LONDON-, 1999.28:p.575-600.).In conjunction with these achievements in research, optimal viewing angle often is defined as providing for people the visual angle of the maximum visual informations of this model.Wherein, visual information can further show as descriptors such as curvature, topology or profile entropy, and optimal viewing angle be exactly make as much as possible these descriptors in given angular field of view as seen.

Traditional method of finding the solution the three-dimensional model optimal viewing angle mainly contains: based on (G.D.Birkhoff such as traditional aesthetical standard such as golden sections, Mathematics of aesthetics, The world of mathematics (1956), pp.2185--2195.), define an information descriptor, the viewpoint of this information descriptor of definition maximization is best viewpoint (Page then, D.L.and Koschan, A.F.and Sukumar, S.R.and Roui-Abidi, B.and Abidi, M.A, Shape analysis algorithm based on information theory, in Proc.of Proceedings of International Conference on Image Processing (2003), pp.229--232. etc.), optimal viewing angle acquisition methods (Denton based on semanteme, T.and Demirci, M.F.and Abrahamson, J.and Shokoufandeh, A.and Dickinson, S, Selecting Canonical Views for View-Based 3-D Object Recognition, in Proc.of International Conference on Pattern Recognition (2004), pp.273--276. etc.).

Yet, three-dimensional model only comprises single object usually, and three-dimensional scenic includes a large amount of objects usually, and presents different shapes and material, and this just makes the method for traditional optimal viewing angle at three-dimensional model can not be transplanted to the optimal viewing angle of three-dimensional scenic well.For three-dimensional scenic, its optimal viewing angle should satisfy following two conditions: can see the object in the scene as much as possible; Make visible object visual effect reach best as far as possible.

Summary of the invention

The object of the present invention is to provide a kind of automatic acquisition methods of three-dimensional scenic optimal viewing angle based on the maximization visual information.

For achieving the above object, the technical solution used in the present invention is:

1), determines that its direction that makes progress is a positive dirction, and this three-dimensional scenic is carried out normalization with regard to the positive dirction of determining to given three-dimensional scenic;

2), face viewpoint at the episphere of unit ball and carry out uniform sampling according to the three-dimensional scenic after the normalization;

3) obtain the curvature on each summit, three-dimensional scenic surface, in order to characterize the geometric properties on three-dimensional scenic surface;

4) ask for the characteristic area on three-dimensional scenic surface based on the method for three-dimensional scenic surface vertices curvature cluster, and the curvature value that adopts each characteristic area cluster centre is as this regional eigenwert, in order to characterize this regional significance level;

5) based on principal component analysis (PCA) (PCA) method each characteristic area interior location relation of the three-dimensional scenic obtained is analyzed, is obtained the principal direction of each characteristic area, in order to weigh step 2) viewpoint of respectively sampling is to the visual quality of this characteristic area;

6) be core to see maximum characteristic areas and to obtain optimum visual quality, propose energy function, and ask for the optimal viewing angle of optimizing energy function based on the method for statistics based on characteristic area eigenwert and the visual quality of characteristic area.

Its concrete execution in step is as follows:

Step 1: the three-dimensional scenic S for given, determine the direction that it makes progress, and this three-dimensional scenic is carried out normalization with regard to the positive dirction of determining, obtain the three-dimensional scenic M after the normalization;

Step 2: to the three-dimensional scenic M after the normalization, carry out uniform sampling on first sphere of unit ball, viewpoint collection V obtains sampling;

Step 3: mean curvature is asked on each summit to the three-dimensional scenic M after the normalization, obtains the curvature chart M of scene M _c

Step 4: to curvature chart M _cIn each summit p _i∈ M _c, define one 7 dimensional feature vector e (p _i) remove to describe its geometric properties:

[formula one]

$e\left(p_i\right)=(x_i,y_i,z_i,n_i^x,n_i^y,n_i^z,{\mathrm{\κ}}_i)$

Wherein, (x _i, y _i, z _i) expression summit p _iCoordinate,

Expression summit p _iNormal vector, k _iExpression summit p _iThe curvature value at place;

With the clustering algorithm of average drifting to proper vector e (p _i) do cluster, with curvature chart M _cBe divided into series of features zone M _c={ C ₁, C ₂..., C _N, to characteristic area set M _cIn each characteristic area C _iWith its cluster centre c _iRepresent the geometric properties that this is regional;

Step 5: to each characteristic area C _i, obtain all summit p of this intra-zone with principal component analysis (PCA) (PCA) _j∈ C _iCoordinate { x _j, y _j, z _jThree proper vector { t _j, s _j, r _j;

Step 6: for the sampling viewpoint v that obtains in the step 2 _i∈ V utilizes the characteristic area M that tries to achieve in the step 4 _c={ C ₁, C ₂..., C _NAnd corresponding cluster centre { c ₁, c ₂..., c _N∈ C, obtain visualization feature information energy function VN (v _i):

[formula two]

$\mathrm{VN}\left(v_i\right)=\left|\right|\underset{c_j\∈C}{\mathrm{\Σ}}({\mathrm{\κ}}_j\·{\mathrm{\δ}}_j)\left|\right|/N$

Wherein, k _jExpression cluster centre c _jCurvature value, N is total characteristic area number, target function δ _jBe defined as follows:

[formula three]

Step 7: for the sampling viewpoint v that obtains in the step 2 _i∈ V utilizes step 5 to each characteristic area C _iProper vector { the t that tries to achieve _j, s _j, r _j, obtain the visual mass-energy function VF (v of three-dimensional scenic M _i):

[formula four]

$\mathrm{VF}\left(v_i\right)=\underset{c_j\∈C}{\mathrm{\Σ}}\left|\right|t_j\·(v_i-c_j)\left|\right|/\left(\right|\left|t_j\right||\·||v_i-c_j|\left|\right)$

Wherein, { c ₁, c ₂..., c _N∈ C is the cluster centre of each characteristic area;

Step 8: utilize the result of step 6 and step 7, obtain each sampling viewpoint v _iThe energy function f of ∈ V _i:

[formula five]

f _i＝(VN(v _i)-ω·VF(v _i)

VN (v wherein _i) and VF (v _i) be respectively the visualization feature information energy function and the visual mass-energy function of trying to achieve in step 6 and the step 7, ω is the weights of visual mass-energy function;

Step 9: in conjunction with each sampling viewpoint v _iThe coordinate of ∈ V and its corresponding energy function define one 4 dimensional feature vector

In order to describe the visual information of this viewpoint:

[formula six]

Wherein, (x _i, y _i, z _i) be sampling viewpoint v _iCoordinate, f _iThe sampling viewpoint v that tries to achieve for step 8 _iCorresponding energy function;

With the clustering algorithm of average drifting to proper vector

Do cluster, obtain a series of cluster centre VC={VC ₁, VC ₂..., VC _K;

Step 10: the cluster centre VC={VC that traversal step nine is tried to achieve ₁, VC ₂..., VC _K, relatively their energy function item defines optimal viewing angle

For:

[formula seven]

$\tilde{v}=\underset{{\mathrm{VC}}_i\∈\mathrm{VC}}{\arg \min }{f}_i$

Wherein, f _iExpression cluster centre VC _iThe energy function item of ∈ VC;

Step 11: the optimal viewing angle of trying to achieve according to step 10

Utilize its coordinate information that three-dimensional scenic is done parallel projection, obtain the perspective view of optimal viewing angle.

The present invention at first, a given three-dimensional scene models, need to determine its direction (Fu that makes progress, Hongbo and Cohen-Or, Daniel and Dror, Gideon and Sheffer, Alla, Upright orientation of man-made objects, ACM Transactions on Graphics (2008), pp.42:1--42:7.).According to the positive dirction of determining, the input scene is carried out normalization.Then, at the unit ball episphere viewpoint is carried out uniform sampling (Polonsky, O.and Patan é, G and Biasotti, S.and Gotsman, C.and Spagnuolo, M, What ' s in an Image? The Visual Computer (2005), PP.840--847.).

The present invention judges that the core rule of best viewpoint is to obtain maximum visual information.In practical study, the researchist can artificially stipulate the visual information descriptor of three-dimensional model usually, as curvature, topology or profile entropy etc., in order to the geometrical property on characterization model surface.The three-dimensional model feature descriptor that the present invention takes is the mean curvature value on each summit of model.Be different from the single object of three-dimensional model, the simple structure of homogenous material, three-dimensional scenic contains usually and surpasses an object and a kind of material.Therefore, the complexity of three-dimensional scenic is much larger than simple three-dimensional model, and the conventional visual information method based on the maximization three-dimensional model is absorbed in the local optimum predicament when being applied on the three-dimensional scenic easily, can not finely satisfy three-dimensional scenic optimal viewing angle problem.Therefore, be applied to average drifting clustering method (Comaniciu among the present invention, D.and Meer, P, Mean shift:A robust approach toward feature space analysis, IEEE Transactions on Pattern Analysis and Machine Intelligence (2002), pp.603--619.).By cluster, whole three-dimensional scenic can be divided into a series of characteristic area.Maximization visual information method based on characteristic area is found the solution the optimal viewing angle that obtains, can fully take into account the interested position of each people in the whole three-dimensional scenic, weigh of the contribution of each zone of whole three-dimensional scenic to visual information, and emphasis need not be confined to certain outstanding especially position, thereby the predicament of jumping out local optimum smoothly.

Simultaneously, the present invention has not only considered maximum visual information, also on the basis that obtains maximum visual information, and the visual quality of each characteristic area of optimization.For each characteristic area that marks off, utilize principal component analytical method (PCA) that all summits in the zone are analyzed, and obtain its three principal directions.For each characteristic area, we are the best line-of-sight direction with the direction vertical with its principal direction.Therefore, only need to calculate the inner product of sight line and principal direction, just can assess out the visual effect quality of certain viewpoint this characteristic area.

Take all factors into consideration two factors of maximum visual information and the best visual effect, rationally arrange the weights of the two, construct respectively the sample energy function of viewpoint quality of evaluation.Then, utilize the average drifting clustering algorithm that each sampling viewpoint is carried out cluster once more, obtain the cluster centre of a series of viewpoints.At last, the method for utilizing statistics sorts to the energy function of each viewpoint cluster centre, and the cluster centre of choosing gained energy function maximum is as best viewpoint position, and utilizes parallel projection to obtain the perspective view of optimal viewing angle.

Description of drawings

Fig. 1 is the process flow diagram that the present invention is based on the automatic acquisition methods of three-dimensional scenic optimal viewing angle of maximization visual information;

Fig. 2 is a synoptic diagram of the present invention;

Fig. 3 shows that different visual angles embodies the different information of three-dimensional scenic, provides the traditional defective of optimal viewing angle method for solving on the three-dimensional scenic problem at three-dimensional model simultaneously;

Fig. 4 shows the cluster centre of each characteristic area and three principal directions that each characteristic area principal component analysis (PCA) (PCA) is tried to achieve;

Fig. 5 shows the sample cluster centre of viewpoint and choosing of optimal viewing angle, analyzes the convergent tendency that increase of optimal viewing angle with sampling viewpoint number simultaneously;

Fig. 6 shows the partial 3-D scene optimal viewing angle perspective view that the inventive method tries to achieve (the 1st row), is given in the traditional comparing result (the 3rd, 4 are listed as) at the optimal viewing angle method of three-dimensional model of the characteristic area cluster centre (the 2nd row) of this three-dimensional model under this visual angle and two kinds simultaneously.

Embodiment

Below with the present invention is described in detail with reference to the accompanying drawings.

Fig. 1 is a process flow diagram of the present invention.The present invention mainly is divided into 11 steps:

Referring to Fig. 1,2:

Step 1: the three-dimensional scenic S for given, determine the direction that it makes progress, be defined as positive dirction.And this three-dimensional scenic is carried out normalization with regard to the positive dirction of determining, obtain the three-dimensional scenic M after the normalization;

Step 2: to the three-dimensional scenic M after the normalization, carry out uniform sampling on the episphere of the unit ball that surrounds M, viewpoint collection V obtains sampling.For different sampling viewpoints, because it has carried the geometric properties information of the different directions of three-dimensional scenic M, its visual effect may present the distinct form of expression (Fig. 3).

Step 3: for a given three-dimensional model, its surperficial geometric properties information spinner will be presented as the curvature feature between each summit, surface.Therefore,, obtain the mean curvature on each summit, obtain the curvature chart M of scene M the three-dimensional scenic M after the normalization _c

Step 4: the curvature chart M that obtains scene M _cAfter, need provide mathematical description of a quantification to each summit in the curvature chart.For each summit p in the curvature chart _i∈ M _c, define one 7 dimensional vector e (p _i) remove to describe its geometric properties:

[formula one]

$e\left(p_i\right)=(x_i,y_i,z_i,n_i^x,n_i^y,n_i^z,{\mathrm{\κ}}_i)$

Wherein, (x _i, y _i, z _i) expression summit p _iCoordinate,

Expression summit p _iNormal vector, k _iExpression summit p _iThe curvature value at place.Vector e (p _i) comprised the geometric position information and the surface characteristics information on current summit simultaneously.

Traditional optimal viewing angle algorithm at three-dimensional model is as (V á zquez, P.P.and Feixas, M.and Sbert, M.and Llobet, A, Viewpoint entropy:a new tool for obtaining good views of molecules, in Proc.of Proceedings of the Symposium on Data Visualisation 2002 (2002), pp.183--188.) etc. be absorbed in local optimum predicament (as Fig. 3) easily, therefore be unsuitable for solving the best problem of three-dimensional scenic.The present invention uses the average drifting clustering algorithm to proper vector e (p _i) do cluster, cluster result is with curvature chart M _cBe divided into series of features zone M _c={ C ₁, C ₂..., C _N.To each characteristic area C _i, with its cluster centre c _iRepresent the geometric properties that this is regional, some c _iVector expression be:

[formula two]

$\mathrm{\β}\left(c_i\right)=(x_i,y_i,z_i,n_i^x,n_i^y,n_i^z,{\mathrm{\κ}}_i)$

Wherein, (x _i, y _i, z _i) the cluster centre c that calculates of expression _iCoordinate,

The cluster centre c that expression is calculated _iNormal vector, k _iThe cluster centre c that expression is calculated _iThe curvature value at place.

Step 5: to each characteristic area C _i, use principal component analysis (PCA) (PCA) to all summit p of this intra-zone _j∈ C _iCoordinate { x _j, y _j, z _jAnalyze, and obtain its three proper vector { t _j, s _j, r _j(Fig. 4).Wherein, this summit, zone is distributed that play a decisive role is vectorial t _j(three eigenwerts supposing it are arranged as λ ₁〉=λ ₂〉=λ ₃).

Step 6: for the sampling viewpoint v that obtains in the step 2 _i∈ V utilizes the characteristic area M that tries to achieve in the step 4 _c={ C ₁, C ₂..., C _NAnd corresponding cluster centre { c ₁, c ₂..., c _N∈ C, the some c that defines in the formula two utilized _iVector expression e (c _i), obtain visualization feature information energy function VN (v _i):

[formula three]

$\mathrm{VN}\left(v_i\right)=\left|\right|\underset{c_j\∈C}{\mathrm{\Σ}}({\mathrm{\κ}}_j\·{\mathrm{\δ}}_j)\left|\right|/N$

Wherein, k _jExpression cluster centre c _jCurvature value, N is total characteristic area number, target function δ _jBe defined as follows:

[formula four]

Wherein, current view point v _iCan see cluster centre c _jBy determine type D (v _i, c _j) decision:

[formula five]

Wherein, determine type D (v _i, c _j) be defined as:

[formula six]

D(v _i，c _j)＝(p(v _i)-p(c _j)).(n(c _j))

In the formula, the coordinate of p (.) expression point, n (.) represents the normal vector of this point.

Step 7: for the sampling viewpoint v that obtains in the step 2 _i∈ V utilizes step 5 to each characteristic area C _iProper vector { the t that tries to achieve _j, s _j, r _j, obtain the visual mass-energy function VF (v of three-dimensional scenic M _i):

[formula seven]

$\mathrm{VF}\left(v_i\right)=\underset{c_j\∈C}{\mathrm{\Σ}}\left|\right|t_j\·(v_i-c_j)\left|\right|/\left(\right|\left|t_j\right||\·||v_i-c_j|\left|\right)$

Wherein, { c ₁, c ₂..., c _N∈ C is the cluster centre of each characteristic area.By step 5 as can be known, because t _jBe vector that this summit, zone is distributed and plays a decisive role, during to this regional visual quality, only need satisfy sight line and vectorial t in the calculating sampling viewpoint _jVertically just can obtain good effect (referring to Fig. 5).

Step 8: utilize the result of step 6 and step 7, obtain each sampling viewpoint v _iThe energy function f of ∈ V _i:

[formula eight]

f _i＝(VN(v _i)-ω·VF(v _i)

VN (v wherein _i) and VF (v _i) be respectively the visualization feature information energy function and the visual mass-energy function of trying to achieve in step 6 and the step 7, ω is the weights of visual mass-energy function.Energy function f _iBig more, just represent this viewpoint to meet people's visual demand more.

Step 9: in conjunction with each sampling viewpoint v _iThe coordinate of ∈ V and its corresponding energy function define one 4 dimensional vector

In order to describe the visual information of this viewpoint:

[formula nine]

Wherein, (x _i, y _i, z _i) be sampling viewpoint v _iCoordinate, f _iThe sampling viewpoint v that tries to achieve for step 8 _iCorresponding energy function.

With reference to step 4, use the average drifting clustering algorithm to proper vector

Do cluster, obtain a series of cluster centre VC={VC ₁, VC ₂..., VC _K.For each cluster centre VC _i, can define one 4 dimensional vector α (VC _i):

[formula ten]

α(VC _i)＝(x _i，y _i，z _i，f _i)

In the formula, (x _i, y _i, z _i) be the coordinate of sampling viewpoint cluster centre, f _iEnergy function value for the sampling viewpoint cluster centre of trying to achieve.

Step 10: the cluster centre VC={VC that traversal step nine is tried to achieve ₁, VC ₂..., VC _K, utilize the vectorial α (VC that describes each cluster centre visual characteristic _i), compare their energy function item f _i, the definition optimal viewing angle

For:

[formula 11]

$\tilde{v}=\underset{{\mathrm{VC}}_i\∈\mathrm{VC}}{\arg \min }{f}_i$

Wherein, f _iExpression cluster centre proper vector α (VC _i) the energy function item.

Step 11: the optimal viewing angle of trying to achieve according to step 10

Utilize its coordinate information that three-dimensional scenic is done parallel projection, obtain the perspective view of optimal viewing angle.(Fig. 6)

As mentioned above, the present invention proposes a kind of automatic acquisition methods of three-dimensional scenic optimal viewing angle based on the maximization visual information.The curvature of utilizing each summit of three-dimensional scenic is in order to characterizing the surface geometry feature of this scene, and utilizes clustering method to obtain the characteristic area of this three-dimensional scenic.For each sampling viewpoint, assess its visual properties total amount with and to the visual effect of each characteristic area, finally find out the optimal viewing angle of this three-dimensional scenic based on clustering algorithm and statistical method.This method makes full use of the geometric properties information on given three-dimensional scenic surface, takes into account the visual quality of each characteristic area when obtaining the maximum visual quantity of information, and the optimal viewing angle of obtaining fully caters to people's visual demand.

Although with reference to the accompanying drawings the present invention is explained and describe, the professional and technical personnel should be appreciated that, without departing from the spirit and scope of the present invention, can carry out various other changes, additions and deletions therein or to it.

Claims (2)

1. One kind based on the maximization visual information the automatic acquisition methods of three-dimensional scenic optimal viewing angle, it is characterized in that comprising following steps:

   1), determines that its direction that makes progress is a positive dirction, and this three-dimensional scenic is carried out normalization with regard to the positive dirction of determining to given three-dimensional scenic;

   2), face viewpoint at the episphere of unit ball and carry out uniform sampling according to the three-dimensional scenic after the normalization;

   3) obtain the curvature on each summit, three-dimensional scenic surface, in order to characterize the geometric properties on three-dimensional scenic surface;

   4) ask for the characteristic area on three-dimensional scenic surface based on the method for three-dimensional scenic surface vertices curvature cluster, and the curvature value that adopts each characteristic area cluster centre is as this regional eigenwert, in order to characterize this regional significance level;

   5) based on principal component analysis (PCA) (PCA) method each characteristic area interior location relation of the three-dimensional scenic obtained is analyzed, is obtained the principal direction of each characteristic area, in order to weigh step 2) viewpoint of respectively sampling is to the visual quality of this characteristic area;

   6) be core to see maximum characteristic areas and to obtain optimum visual quality, propose energy function, and ask for the optimal viewing angle of optimizing energy function based on the method for statistics based on characteristic area eigenwert and the visual quality of characteristic area.
2. 2. the automatic acquisition methods of three-dimensional scenic optimal viewing angle based on the maximization visual information as claimed in claim 1, its concrete execution in step is as follows:

   Step 1: the three-dimensional scenic S for given, determine the direction that it makes progress, and this three-dimensional scenic is carried out normalization with regard to the positive dirction of determining, obtain the three-dimensional scenic M after the normalization;

   Step 2: to the three-dimensional scenic M after the normalization, carry out uniform sampling on first sphere of unit ball, viewpoint collection V obtains sampling;

   Step 3: mean curvature is asked on each summit to the three-dimensional scenic M after the normalization, obtains the curvature chart M of scene M _c

   Step 4: to curvature chart M _cIn each summit p _i∈ M _c, define one 7 dimensional feature vector e (p _i) remove to describe its geometric properties:

   [formula one]

   $e\left(p_i\right)=(x_i,y_i,z_i,n_i^x,n_i^y,n_i^z,{\mathrm{\κ}}_i)$

   Wherein, (x _i, y _i, z _i) expression summit p _iCoordinate,

   

   Expression summit p _iNormal vector, k _iExpression summit p _iThe curvature value at place;

   With the clustering algorithm of average drifting to proper vector e (p _i) do cluster, with curvature chart M _cBe divided into series of features zone M _c={ C ₁, C ₂..., C _N, to characteristic area set M _cIn each characteristic area C _iWith its cluster centre c _iRepresent the geometric properties that this is regional;

   Step 5: to each characteristic area C _i, obtain all summit p of this intra-zone with principal component analysis (PCA) (PCA) _i∈ C _iCoordinate { x _j, y _j, z _jThree proper vector { t _j, s _j, r _j;

   Step 6: for the sampling viewpoint v that obtains in the step 2 _i∈ V utilizes the characteristic area M that tries to achieve in the step 4 _c={ C ₁, C ₂..., C _NAnd corresponding cluster centre { c ₁, c ₂..., c _N∈ C, obtain visualization feature information energy function VN (v _i):

   [formula two]

   $\mathrm{VN}\left(v_i\right)=\left|\right|\underset{c_j\∈C}{\mathrm{\Σ}}({\mathrm{\κ}}_j\·{\mathrm{\δ}}_j)\left|\right|/N$

   Wherein, k _jExpression cluster centre c _jCurvature value, N is total characteristic area number, target function δ _jBe defined as follows:

   [formula three]

   

   Step 7: for the sampling viewpoint v that obtains in the step 2 _i∈ V utilizes step 5 to each characteristic area C _iProper vector { the t that tries to achieve _j, s _j, r _j, obtain the visual mass-energy function VF (v of three-dimensional scenic M _i):

   [formula four]

   $\mathrm{VF}\left(v_i\right)=\underset{c_j\∈C}{\mathrm{\Σ}}\left|\right|t_j\·(v_i-c_j)\left|\right|/\left(\right|\left|t_j\right||\·||v_i-c_j|\left|\right)$

   Wherein, { c ₁, c ₂..., c _N∈ C is the cluster centre of each characteristic area;

   Step 8: utilize the result of step 6 and step 7, obtain each sampling viewpoint v _iThe energy function f of ∈ V _i:

   [formula five]

   f _i＝(VN(v _i)-ω·VF(v _i)

   VN (v wherein _i) and VF (v _i) be respectively the visualization feature information energy function and the visual mass-energy function of trying to achieve in step 6 and the step 7, ω is the weights of visual mass-energy function;

   Step 9: in conjunction with each sampling viewpoint v _iThe coordinate of ∈ V and its corresponding energy function define one 4 dimensional feature vector

   

   In order to describe the visual information of this viewpoint:

   [formula six]

   Wherein, (x _i, y _i, z _i) be sampling viewpoint v _iCoordinate, f _iThe sampling viewpoint v that tries to achieve for step 8 _iCorresponding energy function;

   With the clustering algorithm of average drifting to proper vector

   

   Do cluster, obtain a series of cluster centre VC={VC ₁, VC ₂..., VC _K;

   Step 10: the cluster centre VC={VC that traversal step nine is tried to achieve ₁, VC ₂..., VC _K, relatively their energy function item defines optimal viewing angle

   

   For:

   [formula seven]

   $\tilde{v}=\underset{{\mathrm{VC}}_i\∈\mathrm{VC}}{\arg \min }{f}_i$

   Wherein, f _iExpression cluster centre VC _iThe energy function item of ∈ VC;

   Step 11: the optimal viewing angle of trying to achieve according to step 10

   

   Utilize its coordinate information that three-dimensional scenic is done parallel projection, obtain the perspective view of optimal viewing angle.

Images