CN103927771A - Linear feature shifting method for self-adaptation setting of shape parameters of Snakes model - Google Patents

Abstract

The invention discloses a linear feature shifting method for self-adaptation setting of shape parameters of a Snakes model. The linear feature shifting method comprises the steps that shape parameters of a linear target are obtained according to the relation between the positioning priority and the shape parameters of the linear target; bends on the linear target are identified, and shape parameters of the bents are obtained on the basis of the relation between the curvatures and the shape parameters of the bends; the shape parameters of the bend where a finite element unit is located are used for establishing a finite element rigidity matrix, and the linear target in a map is shifted through a linear feature shifting method based on the Snakes model. The global optimization characteristic of the shifting method based on the Snakes model is reserved, the semantic relation between different map features and internal graphic characteristics of a map target are taken into consideration to a certain extent, and the map feature spatial relation and positional accuracy can be kept conveniently.

Description

Self-adaptation arranges the wire key element displacement method of Snakes mould shapes parameter

Technical field

The invention belongs to Automated Map Generalization technical field, particularly a kind of self-adaptation arranges the wire key element displacement method of Snakes mould shapes parameter.

Background technology

In Map Generalization process, because engineer's scale dwindles, map space is dwindled thereupon, and the symbol that simultaneously partial element has to be greater than physical size is exaggerated expressions, thereby may cause on map that contiguous between adjacent target conflicted, vision conflict and spatial relation conflicts.In order to keep the clarity of map, must use choose, merge, exaggerate, the operation such as displacement processed these conflicts, wherein displacement is to solve one operation that this type of conflicts the most frequently used.

Wire key element (as road, river etc.) on map, can regard the skeleton of map as, and it has a very wide distribution, complex structure.The emphasis that associated Automated Map Generalization problem is normally studied is also difficult point, the especially displacement problem of wire key element, and the spatial relationship relating between maintenance and the linear goal of each linear target geometric shape is safeguarded, more seems intricate.Nickerson ^[2]adopt basic method of geometry to be shifted to wire key element, more comprehensively solved the conflict between two linear targets, but be difficult to solve multiobject sophisticated collision problem.Burghardt and Meier ^[5]the shifting algorithm based on Snakes model proposing is a kind of Global Optimization Algorithm For Analysis of applicable wire map elements displacement, and multiobject challenge is had to more excellent effect.This algorithm adopts minimum energy principle, the description of energy is represented by the most basic shift amount, change and describe internal energy by the geometric configuration of wire key element before and after displacement, external energy is described with the space conflict of contiguous wire key element, by optimum shape and position after the displacement of finite element method calculated curve.

Form parameter (elastic parameter α and rigidity parameter beta) in Snakes model has determined elasticity and the rigidity of wire key element, has reflected model attributes, and displacement effect is had to certain control action.Burghardt and Meier ^[5], Bader ^[10]and Wu little Fang ^[11]all launch discussion around the problem that arranges of form parameter Deng scholar, proposed the cardinal rule that parameter arranges, but still lacked at present effective parameter setting method.

In literary composition, relate to following list of references:

[1]Lichtner W.Computer-Assisted Processes of Cartographic Generalization in Topographic Maps[J].Geo-Processing,1979Vol.1No.1.

[2]Nickerson B G.Automated Cartographic Generalization for Linear Features[J].Cartographica,1988Vol.25No.3.

[3]Mackaness W A.An Algorithm for Conflict Identification and Feature Displacement in Automated Map Generalization[J].Cartography and Geographic Information Systems,1994Vol.21No.4.

[4]Ruas A.A Method for Building Displacement in Automated Map Generalisation[J].International Journal of Geographic Information Science,1998Vol.12No.7.

[5]Burghardt D,Meier S.Cartographic Displacement Using the Snakes Concept[A].Semantic Modeling for the Acquisition of Topographic Information from Images and Maps[C],ed.By W and L Plümer,1997.

[6]Harrie L E.The Constraint Method for Solving Spatial Conflicts in Cartographic Generalization[J].Cartography and Geographic Information Science,1999Vol.26No.1.

[7] P.Solving Local and Global Space Conflicts in Map Generalization:Using a Finite Element Method[J].Cartography and Geographic Information Science,2000Vol.27No.1.

[8]Ware J M,Jones C B.Conflict Reduction in Map Generalization Using Iterative Improvement[J].GeoInformatica,1998Vol.2No.4.

[9]Wilson I D,Ware J M,Ware J A.A Genetic Algorithm approach to cartographicmap generalization.Computers in Industry,2003Vol.52No.3.

[10]Bader M.Energy Minimization Methods for Feature Displacement in Map Generalization[D].Zurich:University of Zürich,2001.

[11] Wu little Fang, Du Qingyun, Hu Yueming etc. based on the road net space conflict processing [J] that improves Snake model. mapping journal, 2008Vol.37No.2.

[12] Ai Tinghua. the displacement [J] of the groups of building based on Field Analysis. mapping journal, 2004Vol.35No.1.

Summary of the invention

The deficiency of existence is set in order to overcome form parameter in the wire key element displacement method based on Snakes model, and the present invention proposes a kind of self-adaptation and arranges the wire key element displacement method of Snakes mould shapes parameter.

For solving the problems of the technologies described above, the present invention adopts following technical scheme:

Self-adaptation arranges the wire key element displacement method of Snakes mould shapes parameter, comprising:

(1) adopt the Priority level for location of linear target and the relation of form parameter $\left\{\begin{array}{c}{\mathrm{\α}}_R={h_{\mathrm{\α}}}^{(g-1)}\mathrm{\α}\\ {\mathrm{\β}}_R={h_{\mathrm{\β}}}^{(g-1)}\mathrm{\β}\end{array}\right.$ Obtain the form parameter α of linear target _rand β _r, wherein, α and β are form parameter initial value, rule of thumb set in advance; G represents the Priority level for location of linear target, sets in advance as the case may be, and Priority level for location is larger, and the requirement that the positional precision to linear target when displacement and shape keep requires higher; h _αand h _βbe respectively the form parameter α of linear target _rand β _rcommon ratio, drawing experience according to the map sets in advance;

(2) bending in identification linear target, the curvature based on bending and the relation of form parameter with obtain bending form parameter α _cand β _c, wherein, k is bending curvature, k ₀for narrow curved threshold value, k ₀> 1; α _rand β _rfor the form parameter of bending place linear target; c > 1, k ₀all need to set in advance as the case may be with c;

(3) adopt the form parameter of finite element unit place bending to build finite element matrix K _l, and adopting the wire key element displacement method based on Snakes model to be shifted to map center line shape target, described finite element unit refers to the straight-line segment of adjacent point-to-point transmission in linear target.

The wire key element displacement method of employing described in step (3) based on Snakes model is shifted and further comprises sub-step map center line shape target:

2.1 set finite element matrix K _lobtain the overall stiffness matrix K of linear goal, suffered each conflict point in linear target in original map external force is formed to the initial stressed vector f of linear goal ⁽⁰⁾, by initial shift vector d ⁽⁰⁾in each element be set to 0;

2.2 by the shift vector d of overall stiffness matrix K, last iteration ^(t-1)stressed vector f with last iteration ^(t-1)substitution (I+ γ K) d ^(t)=d ^(t-1)+ γ f ^(t-1)equation, obtains the shift vector d of this iteration ^(t), then, execution step 2.3, wherein, d ^(t-1)initial value be the initial shift vector d that step 2.1 obtains ⁽⁰⁾; f ^(t-1)initial value is the initial stressed vector f described in step 2.1 ⁽⁰⁾; K is overall stiffness matrix, and in iteration optimization process, K remains unchanged; I is unit matrix; γ is iteration step length, arranges as the case may be;

2.3 motion-vector d based on this iteration ^(t)map center line shape target is shifted, then, execution step 2.4;

2.4 according to the stressed vector f of the stressed renewal last iteration that conflicts in the map after displacement ^(t-1)obtain the stressed vector f of this iteration ^(t), by the motion-vector d of this iteration ^(t)with stressed vector f ^(t)as the motion-vector of last iteration be subject to force vector, re-execute step 2.2, until meet the default condition of convergence.

The condition of convergence described in sub-step 2.4 comprises that the maximal value in force vector that is subject to that the map after displacement does not exist conflict, iterations to reach default maximum iteration time or this iteration is less than preset value.

In identification linear target described in step (2), a kind of embodiment of bending method is:

Be bent into the set of one group of finite element unit that on linear target line, moving direction is consistent, by using the point that in linear target, finite element unit moving direction changes as bending terminal, the judgement of the point that finite element unit moving direction changes can be by detecting in linear target often adjacent 4 P successively ₁, P ₂, P ₃, and P ₄realize, finite element unit moving direction is at P ₂the necessary and sufficient condition that point changes is $(\stackrel{\&RightArrow;}{P_1{P}_2}\&times;\stackrel{\&RightArrow;}{P_2{P}_3})\&CenterDot;(\stackrel{\&RightArrow;}{P_2{P}_3}\&times;\stackrel{\&RightArrow;}{P_3{P}_4})<0.$

Compared to the prior art, the present invention has following features:

Using bending as fundamental figure unit in linear target in map, set up respectively the quantitative relationship between curved shape feature, linear target Priority level for location and Snakes mould shapes parameter, strengthen the controllability of form parameter in Snakes model, taken better semanteme and the graphic constraint condition in map into account.The inventive method has not only been inherited global optimization's feature of the displacement method based on Snakes model, and taken to a certain extent semantic relation between different map elementses and the graphic feature of map objects inside into account, be more conducive to the maintenance of map elements spatial relationship and positional precision.

Brief description of the drawings

Fig. 1 is the para-curve schematic diagram that reflects quantitative relationship between bending curvature and Snakes mould shapes parameter in the present invention;

Fig. 2 is modeling language (UML) the class figure of road net model and Snakes shifting algorithm in the present invention;

Fig. 3 is that the global parameter of Snakes model arranges interface;

Fig. 4 is that the category of roads parameter of Snakes model arranges interface;

Fig. 5 is that the bending curvature parameter of Snakes model arranges interface;

Fig. 6 is the calculating schematic diagram of the suffered external force of conflict point in linear target;

Fig. 7 is bending recognition methods principle schematic;

Fig. 8 is the corresponding relation of each element position and line segment end points numbering in overall stiffness matrix in finite element matrix;

Fig. 9 is the particular flow sheet of the inventive method;

Figure 10 is the result that adopts the inventive method to carry out collision detection to certain mountain area segment path net;

Figure 11 is the traditional shift result based on Snakes model displacement method and the comparison diagram of original road net;

Figure 12 is the shift result of the inventive method and the comparison diagram of original road net;

Figure 13 is the partial enlarged drawing of the shift result of the inventive method and classic method, wherein, (a) is original map, is (b) shift result of classic method, is (c) shift result of the inventive method.

Embodiment

To existing theory, inventive concept and the embodiment that the present invention relates to be elaborated below.

1, the wire key element displacement theory based on Snakes model

Wire key element displacement method of the present invention adopts the wire key element displacement method based on Snakes model, the description of energy adopts the most basic shift amount to represent, change and describe internal energy by the geometric configuration of wire key element before and after displacement, describe external energy with the space conflict of vicinity wire key element.

Based on minimum energy principle, calculate optimum shape and position after linear target displacement.The mathematic(al) representation of shift amount is: s → d (s)=(x (s)-x ⁰(s), y (s)-y ⁰(s)) ^t, 0≤s≤l, wherein, l represents the length of linear target; S is the parametric variable that represents the position of any point in linear target, and for arbitrfary point in linear target, its corresponding s is the distance of linear target starting point along linear target to this point; x ⁰, y ⁰represent original line coordinate, i.e. line coordinates before displacement; X, y represent the line coordinates after displacement; D (s) is the parameter expression of shift amount.

Based on shift amount, gross energy E (d)=∫ is described _l(E _int+ E _ext) ds, wherein, E _intinternal energy, E _extit is external energy.Internal energy d'(s) and d " (s) be respectively first order derivative and the second derivative of shift amount d (s) about s, reflected the size of the change of shape that linear target produces due to displacement; α (s) and β (s) determine elasticity and the rigidity of Snakes model, and the attribute of reflection Snakes model, is used for controlling displacement effect, conventionally α (s) and β (s) are referred to as to the form parameter of Snakes model.External energy E _extthe overlapping generation of map symbol during by generation conflict, its value is directly proportional to overlapping region size, by external energy E _extimpel linear target movement and deformation, thereby manage conflict.

The principle of displacement of Snakes model is to keep gross energy minimum, therefore, and the shift amount of linear target each point need to ask E (d) to get minimum value time.Utilize Eulerian equation, Finite Element Method, through a series of mathematic(al) manipulations, obtain the overall matrix equation of Kd=f form, Xie Zhi, can obtain linear target shift amount everywhere.Wherein, K is stiffness matrix; D, by the shift vector that in linear target, each point shift amount and first order derivative thereof form, is the unknown number of matrix equation Kd=f; F is the force vector that is subject to being made up of the suffered external force of the each point in conflict range in linear target.

According to Finite Element Method, local matrix K corresponding to each line segment in linear target _l, d _l, f _las follows, " line segment " here refers to the straight-line segment of adjacent point-to-point transmission in linear target:

$K_L=\left[\begin{array}{cccc}\frac{6}{5}\frac{\mathrm{\&alpha;}{h}^2+10\mathrm{\&beta;}}{h^3}& \frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& -\frac{6}{5}\frac{\mathrm{\&alpha;}{h}^2+10\mathrm{\&beta;}}{h^3}& \frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}\\ \frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& \frac{2}{15}\frac{\mathrm{\&alpha;}{h}^2+30\mathrm{\&beta;}}{h}& -\frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& -\frac{1}{30}\frac{\mathrm{\&alpha;}{h}^2-60\mathrm{\&beta;}}{h}\\ -\frac{6}{5}\frac{\mathrm{\&alpha;}{h}^2+10\mathrm{\&beta;}}{h^3}& -\frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& \frac{6}{5}\frac{\mathrm{\&alpha;}{h}^2+10\mathrm{\&beta;}}{h^3}& -\frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}\\ \frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& -\frac{1}{30}\frac{\mathrm{\&alpha;}{h}^2-60\mathrm{\&beta;}}{h}& -\frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& \frac{2}{15}\frac{\mathrm{\&alpha;}{h}^2+30\mathrm{\&beta;}}{h}\end{array}\right]$

$d_L=\left[\begin{array}{c}d\left(x_0\right)\\ d^{\text{'}}\left(x_0\right)\\ d\left(x_1\right)\\ d^{\&prime;}\left(x_1\right)\end{array}\right];$

$f_L=\left[\begin{array}{c}\frac{1}{2}\mathrm{hf}\left(x_0\right)\\ \frac{1}{12}\mathrm{hf}\left(x_0\right)\\ \frac{1}{2}\mathrm{hf}\left(x_1\right)\\ -\frac{1}{12}\mathrm{hf}\left(x_1\right)\end{array}\right];$

Wherein, α and β are the constant form of α (s), β (s), i.e. the form parameter of line segment place bending; H is line segment length; x ₀, x ₁be respectively line segment starting point coordinate and terminal point coordinate; D (x ₀) and d (x ₁) represent that respectively line segment starting point and terminal are at x direction shift amount, d'(x ₀) and d'(x ₁) represent respectively line segment starting point and the terminal first order derivative at x direction shift amount, f (x ₀) and f (x ₁) expression line segment starting point and the component of the suffered external force of terminal in x direction.

When all linear targets are carried out shifting processing on view picture map, need to build respectively its local matrix to the each line segment that forms linear target, and successively local matrix be gathered in overall matrix K, f; Then, respectively the overall matrix equation in x and y direction is solved, obtain the shift amount of each point in linear target.

During overall situation matrix equation solves, because K is singular matrix, cannot try to achieve its inverse matrix, so cannot directly solve overall matrix equation.Therefore, need in matrix equation, increase boundary condition, singular matrix K is converted to conventional matrix, make it to separate.

In addition, if conflict area target is not very intensive, conflict may just be resolved in single job, but in fact most conflict area situation complexity, the target that participates in conflict is more, is not that single job can solve all conflicts completely.Now, will repeatedly carry out shifting function, progressively manage conflict.Specifically can adopt iteration optimization procedure progressively to solve all conflicts, iterative formula is shown in formula (1):

(I+γK)d ^(t)＝d ^(t-1)+γf ^(t-1) （1）

In formula (1), I is unit matrix, and t is iterations, d ^(t)with d ^(t-1)shift vector when shift vector while being the t time iteration respectively and (t-1) inferior iteration, f ^(t-1)while being (t-1) inferior iteration in linear target the stressed formation of each point be subject to force vector, γ is iteration step length, iteration step length rule of thumb arranges.

2, Snakes mould shapes parameter arranges cardinal rule and binding target

While adopting Snakes model to carry out the displacement of wire key element, need to further consider semantic constraint and the graphic constraint of wire key element, by the distortion that the size and shape of controlling displacement is set of wire key element weight and Snakes mould shapes parameter.For example, when road net is shifted, need to corresponding form parameter be set according to category of roads, road local bending feature.But about the setting of form parameter, have no at present comparison effective method, only can rule of thumb arrange with reference to following cardinal rule:

1. while increasing simultaneously or reduce parameter alpha and β, the most obvious to shift result impact effect, α and β are larger, are out of shape less; α and β are less, are out of shape larger;

2. β is constant, and when α value changes, α value is larger, and shift amount is fewer, is out of shape less; α value is less, and shift amount is larger, with former linear target position from away from more;

3. α is constant, and when β value changes, β value is larger, is out of shape less; β value is less, is out of shape larger;

4. the impact that the variation of α value produces displacement is larger than parameter beta.

In order to set up the quantitative relationship between Snakes mould shapes parameter and map objects feature, taking the Priority level for location of map Linear Objects and each section of bending curvature as binding target, design respectively the methods to set up of Snakes mould shapes parameters from semantic and two aspects of figure.

(1) relation of the Priority level for location of linear target and Snakes mould shapes parameter

On map, each wire key element has its intrinsic importance information separately, and this importance information can be used as the Priority level for location of different map objects in shifting process.For example, China is divided into all highways according to the volume of traffic of highway function and adaptation: highway, Class I highway, Class II highway, Class III highway, Class IV highway.In Snakes model, associated between the Priority level for location that can set up linear target and corresponding linear target form parameter.The Priority level for location of linear target is higher, and the requirement that the positional precision to linear target in the time of displacement and shape keep is also just higher, and the form parameter value of corresponding linear target just should arrange highlyer.Otherwise linear target Priority level for location is lower, corresponding form parameter just should arrange lowlyer.

The present invention adopt Geometric Sequence function (2) represent linear target Priority level for location and form parameter between relation:

$\left\{\begin{array}{c}{\mathrm{\&alpha;}}_R={h_{\mathrm{\&alpha;}}}^{(g-1)}\mathrm{\&alpha;}\\ {\mathrm{\&beta;}}_R={h_{\mathrm{\&beta;}}}^{(g-1)}\mathrm{\&beta;}\end{array}\right.---\left(2\right)$

In formula (2), α and β are original shape parameter, and original shape parameter is empirical value, and user rule of thumb provides; α _rand β _rfor the form parameter of linear target R, g ∈ { 1,2 ..., n} represents the Priority level for location of linear target, Priority level for location is higher, corresponding g value is larger, since 1, g is carried out to assignment respectively from low to high, according to the Priority level for location of linear target, the linear target that Priority level for location is minimum, its corresponding g is 1; h _αand h _βbe respectively form parameter α _rand β _rcommon ratio, drawing experience according to the map set.

(2) bending curvature and the relation of Snakes mould shapes parameter

In numerical map, linear target is to be made up of the bending of differently curved degree, and bending can be regarded the subsegment of linear target as, has showed respectively the local figure feature of each section in linear target.Shifting function will inevitably be carried out displacement and distortion to linear target, and in Snakes model, this displacement and distortion, under the effect of interior external enwergy, propagate into linear target everywhere.And from map making angle, in linear target, be shifted everywhere and the degree of being out of shape different, this is relevant with bending tortuous degree.The distortion of straight line or near linear part is more easily discovered than sweep, and it is inappropriate in actual mechanical process, line shifting being become to sweep, so larger form parameter should be set to straight-line segment, straight limit distortion; General bending, in shifting process, distortion is difficult for discovering, and can allow bending " absorption " larger shift amount and distortion in shifting process, so less form parameter should be set to bending.

But be not that curvature is larger, deformable degree is just larger.Narrow curved on curve, is considered to a kind of significantly graphic feature, in shifting process, will keep narrow curved shape invariance as far as possible.Therefore,, when bending curvature k is too little or when too large, all should not produce moderate finite deformation, now need to arrange larger form parameter.For straight-line segment, its curvature k=1; And narrow curved is a relative concept, not value of clearly defining of its curvature, need to come to determine as the case may be.In practical operation, can set as required a curvature threshold k ₀, by curvature k>=k ₀bending be classified as narrow curved.

For straight line and narrow curved, can their form parameter be set to maximum value; And for curvature between 1 and k ₀bending, its Snakes mould shapes parameter increases and is generally the trend of first falling rear liter with curvature, when curvature k rises to k from 1 ₀time, form parameter is first along with curvature increases and reduces, when arriving after critical value again along with curvature increases and increases.Might as well carry out the form parameter of matching bending with the change procedure of curvature with the symmetrical para-curve of opening upwards, see Fig. 1.

The above analysis, designs the piecewise function of bending form parameter according to bending curvature:

In formula (3) and (4), k ₀for narrow curved threshold value, k ₀> 1; α _rand β _rfor the form parameter of bending place linear target, can calculate and obtain according to formula (2); f ₁and f (k) ₂(k) all represent that opening upwards, axis of symmetry are (1+k ₀)/2 and 1 and k ₀peaked para-curve is got at place, sees Fig. 1, c be in the time being bent into straight line or narrow curved condition, its form parameter relatively under the multiple of linear target form parameter, c > 1; Parameter c and k ₀all need to choose as the case may be.

Describe the specific embodiment of the present invention in detail below in conjunction with above-mentioned theory and thinking, idiographic flow is referring to Fig. 9.

Step 1, builds the topological relation between map linear target according to digital map data.

This step belongs to the known technology in this area, for ease of understand, below taking road net as example over the ground between figure linear target the foundation of topological relation describe.

According to Snakes rigidity of model matrix and stressed vector calculation needs, design road net topology data model, this model definition road net the road object, link vertex object, road endpoint object and the triangular topological incidence relation that comprise, see Fig. 2, road net class in figure, road class, apex coordinate class and close tie-point class and be respectively used to describe summit in road network, road, road net and attribute and the method for several class objects of end points.The road net model that between these classes, one of interrelated formation comprises basic topology information and coordinate information.In road net model, a road net is made up of road list, vertex list and end points list; Article one, road comprises a starting point, a terminal and two and above summit, and starting point and terminal are referred to as end points, summit be form road axis to digital curve on each point; End points is also summit simultaneously, and the beginning or end that can be used as road is associated with one or more road.In addition, category of roads class is used for describing category of roads attributive character, is one of basic foundation arranging single road form parameter.

Step 2, arranges the basic parameter of Snakes model, according to the quantitative relationship of the Priority level for location of the basic gain of parameter linear target of Snakes model and form parameter and bending curvature and the quantitative relationship of form parameter.

In Fig. 2, the Snakes class of algorithms is the shifting algorithm realization based on Snakes model, and the Snakes class of algorithms has defined the basic parameter list of Snakes model, and parameter arranges interface and sees Fig. 3～5.

The global parameter of Snakes model is set, sees Fig. 3, comprise minimum interval threshold value, original shape parameter, maximum iteration time and iteration step length between map objects engineer's scale, map objects.The original shape parameter of Snakes model rule of thumb obtains, specifically can be: obtain at random original shape parameter, adopt original shape parameter to carry out shifting function, adjust current original shape parameter according to displacement effect, to obtain the more excellent original shape parameter of displacement effect.Maximum iteration time and iteration step length rule of thumb arrange, the minimum interval threshold value drawing norm setting according to the map between map objects engineer's scale, map symbol.In this concrete enforcement, map objects engineer's scale is set to 1:500000, and the minimum interval threshold value setting between map symbol is 0.2mm, and original shape parameter alpha is set to 10,000,000, β is set to 1,000,000, maximum iteration time is set to 2, and iteration step length is set to 0.1.

The category of roads parameter of Snakes model is set, sees Fig. 4, comprise the form parameter α of linear target and the common ratio h of β _αand h _β, the Priority level for location g of linear target and the symbol intervals of linear target.Symbol intervals drawing norm setting according to the map.Common ratio h _αand h _βdrawing experience is according to the map set; Priority level for location g arranges the requirement of positioning precision and shape maintenance according to linear target.In this concrete enforcement, common ratio h _αand h _βbe set to respectively 3 and 5, it is 3,2,1 that the Priority level for location of the linear targets such as highway, national highway, provincial highway sets gradually.According to the Priority level for location of original shape parameter, form parameter common ratio and linear target, adopt formula (2) to obtain the form parameter of each linear target.

The bending curvature parameter of Snakes model is set, sees Fig. 5, comprise narrow curved threshold value k ₀with maximal value parameter c, in this concrete enforcement, narrow curved threshold value k is set ₀=1.8, maximal value parameter c=10.According to the narrow curved threshold value k arranging ₀obtain para-curve with maximal value parameter c $f_1\left(k\right)=f_2\left(k\right)=4(c-1)\frac{{(k-\frac{1+k_0}{2})}^2}{{(k_0-1)}^2}+1.$

Step 3, detects the initial space conflict between map Linear Objects, and collision table is shown to the force vector that is subject in Snakes model.

Adopt buffer zone analysis and overlay analysis to detect the initial space conflict between map Linear Objects, if there is conflict, collision table is shown to the form that is subject to force vector in Snakes model, then perform step 4; Otherwise, directly finish, do not carry out shifting function.

Collision detection can be called space topological computing interface (ITopologicalIOperator), spatial relationship computing interface (IRelationalOperator), spatial neighbor analysis interface (IProximityOperator) and the overlay analysis interface (IBasicGeoProcessor) in ArcGIS Engine secondary development components, because collision detection belongs to the known technology in this area, do not repeat since then.

In this step, conflict is expressed as visually and has direction and big or small power, have the suffered external force f of the each conflict point P of linear target of conflict _pcan be expressed as:

$f_P=\underset{i\&NotEqual;j}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}}\left\{\begin{array}{c}\frac{v_i}{\left|v_i\right|}(r_{\mathrm{ij}}-\min \left(\right|v_i|,r_{\mathrm{ij}})),\mathrm{if}(P\&RightArrow;P+v_i>2r_{\mathrm{ij}})\\ 0,\mathrm{otherwise}\end{array}\right.$

In formula (5):

N is linear target number, and i, j are linear target numbering;

R _ijrepresent linear target L _iand L _jbetween the required minimum interval reaching, intersymbol minimum interval threshold value obtains according to the map, after the summation of the half of the symbol intervals to linear target i and linear target j, add the minimum interval threshold value between map symbol, is r _ij;

V _ifor conflict point P is to linear target L _ithe vector of upper closest approach, the special circumstances at tie-point place are closed in consideration, make P → P+v _iroute representing from a P along network arrives L _ithe path length of upper closest approach, as P → P+v _i> 2r _ijjust think linear target L _iand L _jthere is conflict, otherwise think to close the normal condition at tie-point place.

The calculating of the suffered external force of conflict point P can be referring to Fig. 6, the n relating in this computation process linear target refers to the linear target that all participation conflicts are surveyed, for example, when road is shifted, participate in the linear target that conflict surveys and comprise all road targets in road net and other linear target that may clash with road target, such as river.

By the suffered external force f of each conflict point P in linear target in initial space conflict _passemble the force vector that is subject in Snakes model.

Step 4, all bendings in identification map in linear target, and obtain each bending corresponding form parameter.

Adopt Wang and M ü ller(1998) (the list of references: Wang Zeshen of the curved recognition methods based on straight-line segment moving direction that proposes, M ü ller J.Line Generalization Based on Analysis of Shape Characteristics[J] .Cartography and Geographic Information Systems, 1998Vol.25No.1.) obtain all bendings in linear target in map, and calculate the curvature of each bending.This bending recognition methods is defined as bending the set of one group of adjacent straight line segment that on line, straight-line segment moving direction is consistent, by using the point that on curve, straight-line segment moving direction changes as bending terminal, blocks curve and forms bending.The judgement of the some position that digital curve upper curve section moving direction changes can be passed through every adjacent 4 P ₁, P ₂, P ₃, and P ₄(wherein every 3 not conllinear) detects to realize, sees Fig. 7, by four some P in order ₁, P ₂, P ₃, P ₄form three in order vector, moving is at P ₂the necessary and sufficient condition that point changes is: bending curvature k=l/d, l is bending length, d is bending base length, i.e. the line of terminal.

Identify after all bendings, adopt formula (3)～(4) to calculate the corresponding form parameter of each bending.

Step 5, builds Snakes model overall situation stiffness matrix.

Obtain the finite element matrix K of Snakes model according to the corresponding form parameter of bending _l, set finite element matrix K _lobtain the overall stiffness matrix K of linear goal.

The embodiment of this step is as follows:

To the Snakes model that comprises n summit, there is n-1 bar limit, i.e. line segment, each limit is as a finite element unit, and overall stiffness matrix K is by the stiffness matrix K of each finite element unit _lset forms, and overall stiffness matrix K is the banded symmetric matrix that a size is 2n*2n.

Owing to Unified number being carried out in the summit in all linear targets (comprising the pass tie-point between start-stop end points, intermediate node and adjacent linear target) in step 1, can carry out the set of matrix by summit numbering.First, initialization overall situation stiffness matrix, creates overall stiffness matrix by summit quantity in linear target, and matrix element is initialized as to 0; Then, by the form parameter of line segment place bending and line segment length substitution finite element matrix K _lcomputing formula, obtain finite element matrix K _l; Finally, " sit in the right seat " by the numbering of line segment two-end-point, by finite element matrix K _lin each element value be added to respectively overall stiffness matrix K.Finite element matrix K _lin the computing formula of each element as follows:

$K_L=\left[\begin{array}{cccc}\frac{6}{5}\frac{\mathrm{\&alpha;}{h}^2+10\mathrm{\&beta;}}{h^3}& \frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& -\frac{6}{5}\frac{\mathrm{\&alpha;}{h}^2+10\mathrm{\&beta;}}{h^3}& \frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}\\ \frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& \frac{2}{15}\frac{\mathrm{\&alpha;}{h}^2+30\mathrm{\&beta;}}{h}& -\frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& -\frac{1}{30}\frac{\mathrm{\&alpha;}{h}^2-60\mathrm{\&beta;}}{h}\\ -\frac{6}{5}\frac{\mathrm{\&alpha;}{h}^2+10\mathrm{\&beta;}}{h^3}& -\frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& \frac{6}{5}\frac{\mathrm{\&alpha;}{h}^2+10\mathrm{\&beta;}}{h^3}& -\frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}\\ \frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& -\frac{1}{30}\frac{\mathrm{\&alpha;}{h}^2-60\mathrm{\&beta;}}{h}& -\frac{1}{10}\frac{\mathrm{\&alpha;}{h}^2+60\mathrm{\&beta;}}{h^2}& \frac{2}{15}\frac{\mathrm{\&alpha;}{h}^2+30\mathrm{\&beta;}}{h}\end{array}\right]---\left(6\right)$

Fig. 8 has provided each element position and line segment point numbering i in overall stiffness matrix in finite element matrix, the corresponding relation of j, for example, the 1st element of the 1st row in finite element matrix be arranged in the capable 2i row of overall stiffness matrix 2i, the 2nd element of the 1st row in finite element matrix be arranged in the capable 2i+1 row of overall stiffness matrix 2i.

Step 6, is realized linear target is carried out to shifting function by iterative optimization method.

By initial shift vector d ⁽⁰⁾be made as [0,0 ..., 0] ^t, initial stressed vector f is made as the stressed vector f that in original map, conflict detects ⁽⁰⁾, overall stiffness matrix K, according to trying to achieve in step 5, carries out iterative to shift vector d:

(1) by the shift vector d of overall stiffness matrix K, last iteration ^(t-1)stressed vector f with last iteration ^(t-1)substitution (I+ γ K) d ^(t)=d ^(t-1)+ γ f ^(t-1)equation, obtains the shift vector d of this iteration ^(t), execution step (2); d ^(t-1)initial value be d ⁽⁰⁾, f ^(t-1)initial value is the stressed vector f of stressed formation of conflicting in original map ⁽⁰⁾; K is overall stiffness matrix, and in iteration optimization process, K remains unchanged; I is unit matrix; γ is iteration step length, and in this concrete enforcement, γ is 0.1.

(2) the motion-vector d based on this iteration ^(t)map center line shape target is shifted, then, execution step (3);

(3) judge whether iterations t reaches the maximum iteration time of setting, if reach, finishing iteration optimization; Otherwise execution step (4).

(4) whether the map detecting after displacement there is conflict, if there is conflict, execution step (5); Otherwise finishing iteration optimization.

(5) according to the stressed vector f of the stressed renewal last iteration that conflicts in the map after displacement ^(t-1)obtain the stressed vector f of this iteration ^(t), make iterations add 1, by the motion-vector d of this iteration ^(t)with stressed vector f ^(t)as the motion-vector of last iteration be subject to force vector, re-execute step (1).

The condition of convergence of iteration optimization process is not limited to carry in this embodiment, also can adopt other conditions of convergence, and for example can currently be subject to maximal value in force vector to be less than preset value is the condition of convergence.

Below in conjunction with application note of the present invention beneficial effect of the present invention.

Figure 10 is the result that adopts the inventive method to carry out collision detection to certain mountain area segment path net, comprises highway, national highway, provincial highway, river four class wire key elements in figure.Press the width on the relative ground of symbol under 1:50 ten thousand engineer's scales and draw buffer zone along the center line in each road and river, the lap between different buffer zones is the Overlapping Symbol conflict producing under target proportion chi.For ease of discussing, divide tri-battlegrounds of A, B and C, A battleground is highway and the conflicting of river; B battleground is highway and the conflicting of provincial highway; C battleground is national highway and the conflicting of provincial highway.River has higher positioning accuracy request in map, therefore, in this application example, river is made as irremovable.All road key elements form a network structure, carry out overall situation displacement by Snakes model.

Adopt respectively classic method and the inventive method to carry out overall situation displacement to Figure 10, Figure 11 is the traditional shift result based on Snakes model displacement method and the comparison diagram of original road net, and Figure 12 is the shift result of the inventive method and the comparison diagram of original road net.As can be seen from the figure, displacement distortion is initiated from collision position, propagates across the network to everywhere, and Figure 11～12 all can better keep one-piece construction and the topological relation of road net.

Contrast respectively A, B, tri-battlegrounds of C, find that displacement successful of the present invention is better than classic method, sees Figure 12～13.In Figure 11, the shift size of each conflict point is only strong and weak relevant to conflict, do not consider any other semanteme and graphic constraint condition, A battleground high speed highway displacement is too large, and the conflict in C battleground is still unresolved, and the translocation distance of narrow curved and the anglec of rotation all larger.In Figure 12, owing to having adopted Geometric Sequence that form parameter is set, the displacement of the highway of A battleground and distortion have been subject to certain inhibition, in B battleground the provincial highway of " weak tendency " with the antagonism of the highway of " advantage " in be forced to mobile larger distance.Because the form parameter to bending has been carried out personal settings, narrow curved has obtained higher form parameter, and the narrow curved in C battleground on national highway has been subject to protection, and the general bending on provincial highway is forced to mobile larger distance.

Figure 13 is that target proportion chi is ten thousand times shift result display effects of 1:50, and wherein, in Figure 13, (a) is original map; In Figure 13, (b) is traditional shift result based on Snakes model displacement method; The shift result that in Figure 13, (c) is the inventive method.The whole structure of (c) in (b) and Figure 13 in further contrast Figure 13, in Figure 13, (b) is although moved generally larger distance, but do not manage conflict better, in subrange, exist displacement excessive (as A battleground) and conflict effectively not to solve yet the problem of (as C battleground).Comparatively speaking, integral shift better effects if in (c) in Figure 13, and positional precision is also higher.

Claims (4)

1. self-adaptation arranges the wire key element displacement method of Snakes mould shapes parameter, it is characterized in that, comprising:

(1) adopt the Priority level for location of linear target and the relation of form parameter $\left\{\begin{array}{c}{\mathrm{\&alpha;}}_R={h_{\mathrm{\&alpha;}}}^{(g-1)}\mathrm{\&alpha;}\\ {\mathrm{\&beta;}}_R={h_{\mathrm{\&beta;}}}^{(g-1)}\mathrm{\&beta;}\end{array}\right.$ Obtain the form parameter α of linear target _rand β _r, wherein, α and β are form parameter initial value, rule of thumb set in advance; G represents the Priority level for location of linear target, sets in advance as the case may be, and Priority level for location is larger, and the requirement that the positional precision to linear target when displacement and shape keep requires higher; h _αand h _βbe respectively the form parameter α of linear target _rand β _rcommon ratio, drawing experience according to the map sets in advance;

(2) bending in identification linear target, the curvature based on bending and the relation of form parameter with obtain bending form parameter α _cand β _c, wherein, k is bending curvature, k ₀for narrow curved threshold value, k ₀> 1; α _rand β _rfor the form parameter of bending place linear target; c > 1, k ₀all need to set in advance as the case may be with c;

(3) adopt the form parameter of finite element unit place bending to build finite element matrix K _l, and adopting the wire key element displacement method based on Snakes model to be shifted to map center line shape target, described finite element unit refers to the straight-line segment of adjacent point-to-point transmission in linear target.

2. self-adaptation as claimed in claim 1 arranges the wire key element displacement method of Snakes mould shapes parameter, it is characterized in that:

The wire key element displacement method of described employing based on Snakes model is shifted and further comprises sub-step map center line shape target:

2.1 set finite element matrix K _lobtain the overall stiffness matrix K of linear goal, suffered each conflict point in linear target in original map external force is formed to the initial stressed vector f of linear goal ⁽⁰⁾, by initial shift vector d ⁽⁰⁾in each element be set to 0;

2.2 by the shift vector d of overall stiffness matrix K, last iteration ^(t-1)stressed vector f with last iteration ^(t-1)substitution (I+ γ K) d ^(t)=d ^(t-1)+ γ f ^(t-1)equation, obtains the shift vector d of this iteration ^(t), then, execution step 2.3, wherein, d ^(t-1)initial value be the initial shift vector d that step 2.1 obtains ⁽⁰⁾; f ^(t-1)initial value is the initial stressed vector f described in step 2.1 ⁽⁰⁾; K is overall stiffness matrix, and in iteration optimization process, K remains unchanged; I is unit matrix; γ is iteration step length, arranges as the case may be;

2.3 motion-vector d based on this iteration ^(t)map center line shape target is shifted, then, execution step 2.4;

2.4 according to the stressed vector f of the stressed renewal last iteration that conflicts in the map after displacement ^(t-1)obtain the stressed vector f of this iteration ^(t), by the motion-vector d of this iteration ^(t)with stressed vector f ^(t)as the motion-vector of last iteration be subject to force vector, re-execute step 2.2, until meet the default condition of convergence.

3. self-adaptation as claimed in claim 2 arranges the wire key element displacement method of Snakes mould shapes parameter, it is characterized in that:

The described condition of convergence comprises that the maximal value in force vector that is subject to that the map after displacement does not exist conflict, iterations to reach default maximum iteration time or this iteration is less than preset value.

4. self-adaptation as claimed in claim 1 arranges the wire key element displacement method of Snakes mould shapes parameter, it is characterized in that:

Method bending in described identification linear target is specially:

Be bent into the set of one group of finite element unit that on linear target line, moving direction is consistent, by using the point that in linear target, finite element unit moving direction changes as bending terminal, the judgement of the point that finite element unit moving direction changes can be by detecting in linear target often adjacent 4 P successively ₁, P ₂, P ₃, and P ₄realize, finite element unit moving direction is at P ₂the necessary and sufficient condition that point changes is $(\stackrel{\&RightArrow;}{P_1{P}_2}\&times;\stackrel{\&RightArrow;}{P_2{P}_3})\&CenterDot;(\stackrel{\&RightArrow;}{P_2{P}_3}\&times;\stackrel{\&RightArrow;}{P_3{P}_4})<0.$