CN110473459A - Point group based on network Voronoi diagram is chosen - Google Patents
Point group based on network Voronoi diagram is chosen Download PDFInfo
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- CN110473459A CN110473459A CN201810449283.6A CN201810449283A CN110473459A CN 110473459 A CN110473459 A CN 110473459A CN 201810449283 A CN201810449283 A CN 201810449283A CN 110473459 A CN110473459 A CN 110473459A
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Abstract
Point group synthesis is the important component of Automated Map Generalization, for tradition based on the defect being connected between point group in the algorithm of Voronoi diagram using Euclidean distance rather than real network distance, proposes a kind of point group integration algorithm based on network weights Voronoi diagram.Algorithm basic ideas are as follows: (1) utilize the network weights Voronoi diagram of network development method building point group；(2) the network weights Voronoi area of a polygon and extension segmental arc total length that each pair of point is answered are calculated, and on this basis, is that statistics, special topic included in point group, topology and metric select the quantificational description factor respectively；(3) it proposes " concentric circles " algorithm, solves the problems, such as that point group is accepted or rejected.Experiment shows that the point group after integrating preferably maintains the various information of original point group, and obtained result more rationally and meets actual geographic space characteristics.
Description
Technical field
Point group synthesis is the important component of Map Generalization, is referred to during map scale reduces from original point group
Middle subclass of the extraction containing certain amount point, the purpose is to correctly express the whole of point group as far as possible in the case where number is reduced
Body information.Its related algorithm comparative maturity, the representative are the point groups based on Voronoi diagram and weighted Voronoi diagrams figure
Integration algorithm.Algorithm calculates the selection probability of point group by ordinary Voronoi diagram or weighted Voronoi diagrams figure, and then put
It accepts or rejects.The Voronoi diagram wherein used is plane Voronoi diagram, i.e., plane is considered as homogeneous space, and between any two points
It is that straight line is reachable, using the distance between euclidean distance metric two o'clock.But in actual geographic space, various geographic elements it
Between connect each other and betide network path and unconventional Euclidean distance, the Voronoi diagram subdivision based on Euclidean distance is ignored
Connection between point group with it is sensible be the path distance along road network the fact；Moreover, have algorithm not care for
And influence of the related roads to point group radiation scope, and in actual life, the radiation scope of point group is often with its peripheral path
It is closely related, the sensible degree of associated road and category of roads etc. can all influence the radiation scope of point group.
Background technique
Network Voronoi diagram (N-VD, network weighted Voronoi diagram) is on the basis of Voronoi diagram
On plane is changed to cyberspace, Euclidean distance is replaced with real network path distance.Meanwhile building process has incorporated road
The factors such as road grade and communication direction.Compared with plane Voronoi diagram, network Voronoi diagram be divide point group radiation scope compared with
For accurate method.For this purpose, network Voronoi diagram is introduced point group synthesis by the present invention, it is desirably to obtain more reasonable and meets reality
The point group synthesis result of border geospatial feature.
Summary of the invention
Algorithm flow is as shown in Figure 1.Algorithm basic ideas are as follows: (1) utilize the network weights of network development method building point group
Voronoi diagram；(2) the network weights Voronoi area of a polygon and extension segmental arc total length that each pair of point is answered are calculated, and with this
It is that statistics, special topic included in point group, topology and metric select the quantificational description factor respectively for foundation；(3) it proposes
" concentric circles " algorithm solves the problems, such as that point group is accepted or rejected.
1. the building of N-VD figure
City space is sensible, connection is stretched along road network, carries out Voronoi diagram to cyberspace on this basis and draws
Point, that is, network weights Voronoi diagram is constructed, it is the important step for analyzing point group radiation scope.Below to its building process
It is described:
(1) network rasterizing
Plane operation lacks effective route searching strategy, in order to information such as the position shapes that effectively identifies road network, first adopts
Network rasterizing is carried out with path unit subdivision method.As Fig. 2 illustrates that path unit subdivision method and tradition delete the area of lattice model
, step is not described as follows: Step1: by network path by its node division be different segmental arcs, such as segmental arc L1 in Fig. 2 (a)
L2 etc.；Step2: using for reference plane and delete lattice thought, subdivision is encrypted to spatial network " segmental arc ", using the subdivision unit section of segmental arc as net
Lattice are deleted in network model tissue, so that establishing network deletes lattice data model (Fig. 2 (c)).
After network road rasterizing, point group is projected on cyberspace road according to nearby principle, is fallen into
It deletes lattice unit and is denoted as point entity, delete lattice unit as P2-P6 is corresponding in Fig. 3.For network edge after rasterizing, the lattice of deleting on side can be with
Be divided into 3 seed types: the free time deletes lattice: member occupancy is not occurred deletes lattice (deleting lattice S1 in Fig. 3)；Lattice are deleted in extension: currently having deleted lattice
Member is occurred to occupy, but its neighborhood is deleted in lattice and deletes lattice there are unappropriated.It is referred to as that lattice (deleting in Fig. 3 is deleted in extension that then this, which deletes lattice,
Lattice S2).；Occupy and delete lattice: currently deleting lattice and its neighborhood deletes lattice and member occupancy is occurred, then currently deleting lattice is referred to as to occupy to delete lattice (Fig. 3
In delete lattice S3).
(2) extended operation
On the basis of point group rasterizing, using the corresponding lattice unit collection of deleting of original point group as member occurs, moved towards along real road
It is extended, is included the atural object for meeting certain condition in its surrounding neighbors in the region.Its extended operation process can
With description are as follows:
Step1: as initial member is occurred into for the lattice unit collection of deleting after the projection of original point group, as the P2-P6 in Fig. 3 is corresponding black thick
Line segment mark deletes lattice unit.
Step2: member occurs initially as source, outside sprawling is synchronized along the road network after rasterizing, encounters road friendship
Prong is separated into different tributaries and continues to extend, until road roadhead or while meeting with other tributaries terminate, as shown in Figure 4.
As can be seen that Fig. 4 be point group and road segment segment weight are accordingly to be regarded as it is identical, and when all road segment segments are two way
Spreading result.But in practically space, extension will be by the restriction of point group weight, road segment segment weight and road direction.This
A little restrict can be described as:
1) weight put is bigger, is that the tributary expansion rate of generation member is faster with it, is expressed as formula: LB=k*W (p) (1)
Wherein, LB is the extension step-length on the tributary direction, and k is the first extension step-length in segmental arc of generation that weight is 1, W
(p) weighting function of the point is indicated.
2) corresponding segmental arc weight is higher in expansion process, and the tributary expansion rate passed through thereon is faster, indicates are as follows: and LB=
k*W(x) (2)
Wherein, LB is the extension step-length on the tributary direction, and k is the extension step-length in tributary in road segment segment that weight is 1, W (x)
The weighting function of road segment segment where indicating the segmental arc.
3) expansion process can be restricted by segmental arc direction, and showing as tributary can only be expressed as along the Directional Extension of segmental arc
Formula: LB=k*F (P1, P2) (3)
Wherein LB indicates the extension step-length on the tributary direction, and lattice element length is deleted in k expression, and F (P1, P2) is to judge tributary side
To P1 and the whether consistent function of the sensible direction P2 of road segment segment, (if consistent, this functional value is 1；Otherwise for 0).
(3) network weights Voronoi diagram is generated
In conclusion the generation step of network weights Voronoi diagram is as follows:
Step1: network rasterizing.Road network is divided into different network segmental arcs according to road junction, then to segmental arc
Carry out the processing of network rasterizing.
Step2: member occurs for initialization.The delete lattice unit nearest apart from point group distance is defined as the first of extended operation and originates
Raw member.
Step3: member occurs initially as starting segmental arc, correspondence network extension: is extended to the outside along corresponding propagation direction
A step-length, and update and delete lattice identity property.
Step4: judgement is current to occur member, if it deletes lattice for extension, continues on corresponding direction and extends to the outside, until hair
Neighbouring to delete lattice be to occupy to delete lattice by raw member all.
Based on above step, weighted network Voronoi diagram is as shown in Figure 5.
2. point deletion
(1) point group importance measurement index
On the basis of above-mentioned network weights Voronoi diagram, by analysis, following two factor is set as the measurement of point group importance and is referred to
Mark, and using it as foundation, it may be assumed that
1) the network Voronoi area of a polygon of point group.By extended operation, with several segmental arcs that each point is starting by shape
At a polygonal region, the peripheral polygon of these segmental arcs is acquired, is referred to as network Voronoi polygon (such as Fig. 6 (b)
The corresponding polygon S1 of middle P1), its size can be used as the measurement foundation of point group associated weight and point group local distribution density,
A therefore important evidence for choosing its area as point group.Specifically as shown in formula (5):
(4)
Wherein, Pi1 indicates network Voronoi area of a polygon institute accounting of the point in point group, the network that Ai is at i-th point
Voronoi area of a polygon.
2) the extension segmental arc total length of point group.Not only network Voronoi diagram area corresponding with it is related for the weight of point, also
It is related to the extension segmental arc total length of point.As shown in fig. 6, the network Voronoi diagram area of point P1 is big compared with P2；And the arc of P1 extension
Section total length is less than P2.Therefore as another standard that point group is chosen.Specifically as shown in formula (6):
(5)
Wherein, Pi2 indicates extension segmental arc total length institute accounting of the point in point group, the extension segmental arc total length that li is at i-th point.
(2) definition and expression of constraint condition
According to the above two classes factor, point is divided into three types: it is high-grade must retain (I type), inferior grade directly gives up (II
Type), fall between participation choose competition (III type) [15].Define two kinds of selection constraint conditions:
1) grade constraint condition.In order to guarantee effective transmission of original point group thematic information, algorithm follows that " network Voronoi is polygon
Shape area it is bigger or its extend segmental arc total length it is longer, corresponding to the easier reservation of point " rule carry out point group selection.Choosing
Retain 1 type point during taking, deletes 1 type point.Wherein:
Type I=Pi | its extension segmental arc total length of the corresponding big OR of network Voronoi area of a polygon of Pi point is big }
Type II=Pi | its extension segmental arc total length of the corresponding small AND of network Voronoi area of a polygon of Pi point is small }
2) proximity relations constraint condition.In point group combined process, in order to change the topology information of point group as small as possible, calculate
The principle that method follows " not deleting N-VD neighbours' point simultaneously as far as possible " carries out point group choice [9,10].Specific manifestation are as follows: point group may
For one of following three kinds of states: " freedom ", " fixation " and " deletion ", setting each initial point is " freedom "；It is being intended to delete
When certain point, judge whether its polygon neighbours point is " freedom ", if so, by this point be labeled as " deletion ", while by its
Coverage neighbours' point carries out " fixation "；Otherwise " fixation " point is changed to " freedom " point, starts next round delete operation.
(3) deletion put
Step1: the number n deleted in advance in combined process a little is acquired according to root law: where N0 is original image scale bar, N '
For target drawing scale；
Step2: the Pi1 and Pi2 of all the points in point group are acquired using formula (4), (5).It is corresponded to and is indicated in Pi1 as cross
Coordinate, Pi2 is (Fig. 7 (a)) in the plane right-angle coordinate of ordinate, and is referred to as weighted value point.Weighted value is smaller at this time
Point (1 type point) closer to coordinate origin, therefore use the method that 1/4 concentric circles is done as the center of circle using origin, successively weight selection value
It is lesser, proximity relations judgement and delete operation are carried out to it, behind be called " concentric circles " method.
Step3: it using coordinate origin as origin, is being sat using weighted value point and the minimum value of coordinate origin distance as initial radium
1/4 circle is drawn in mark system, will be located at the corresponding point of weighted value point on circular arc and is labeled as " deletion ", and " fixation " its polygon neighbours
Point.
Step4: using the minimum planes distance in plane coordinate system between weighted value point as increment, radius value is updated, with original
Point is that 1/4 concentric circles (such as Fig. 7 (b) shown in) is done in the center of circle in coordinate system, on its circular arc and itself and previous concentric circles
" freedom " point in the annulus of composition is marked as " deleting " if its all neighbours' point is not flagged as " deleting "
And " fixation " its all neighbours' point.Compare n and the number for being marked as the point " deleted ", if n value is larger, repeatedly Step4；If
Two values are identical, then turn Step6；Otherwise turn Step5.
Step5:, the last round of point for being added to " deletion " label is changed to " freedom ", (6) acquire these points as the following formula
Unit area influences number np ', and by its descending sort, is successively carried out to the point for being located at sequence end using proximity constraint condition
Differentiate and add " deletion " label, and " fixation " label is added to neighbours, until being equal to n labeled as the total number of the point of " deletion "
When turn Step6；
(6)
It is that the corresponding unit area of p point influences crowd's numerical value in formula；Np is the corresponding influence crowd quantity of p point；Sp is p point pair
The coverage area of a polygon answered.
Step6: deleting the point for being marked as " deleting " in original point group, and residual point-group then constitutes synthesis result, algorithm
Terminate.
Detailed description of the invention:
Fig. 1 is algorithm flow chart
Fig. 2 is that tradition deletes lattice model and network deletes lattice model.Wherein (a) original road；(b) tradition deletes lattice model；(c) network
Delete lattice model
Fig. 3 be occur first point P delete result of formatting
Fig. 4 is extended operation process.Wherein (a) one extension result；(b) result is completed in extension
Fig. 5 is the generation of network weights Voronoi diagram.Wherein the network of restrictive condition is added in (a)；(b) network weights
Voronoi diagram
Fig. 6 is that the weight of point extends segmental arc total length with it.The wherein corresponding network Voronoi polygon of (a) P1 point and extension
Segmental arc；(b) the corresponding network Voronoi polygon of P2 point and extension segmental arc
Fig. 7 is the deletion process of point.The wherein corresponding weighted value point of (a) original point group；(b) " concentric circles " algorithm of point is deleted
Fig. 8 is the point group Comprehensive Experiment based on network Voronoi diagram.Wherein 96 points (1:50K) in (a) original map；
(b) weighted network Voronoi diagram；(c) point group (1:100K) after synthesis.
Claims (1)
1. calculating the selection probability of point group by ordinary Voronoi diagram or weighted Voronoi diagrams figure in existing algorithm, and then carry out a little
Choice；The Voronoi diagram wherein used is plane Voronoi diagram, i.e., plane is considered as homogeneous space, and any two points it
Between be that straight line is reachable, using the distance between euclidean distance metric two o'clock；But in actual geographic space, various geographic elements
Between connect each other and betide network path and unconventional Euclidean distance, the Voronoi diagram subdivision based on Euclidean distance is neglected
Omited between point group connection with it is sensible be the path distance along road network the fact；Moreover, having algorithm does not have
Take influence of the related roads to point group radiation scope into account, and in actual life, the radiation scope of point group often with its peripheral path
It is closely related, the sensible degree of associated road and category of roads etc. can all influence the radiation scope of point group；Network Voronoi
Scheme (N-VD, network weighted Voronoi diagram) and plane is changed to network sky on the basis of Voronoi diagram
Between, Euclidean distance is replaced with real network path distance, meanwhile, building process has incorporated category of roads and communication direction etc.
Factor, compared with plane Voronoi diagram, network Voronoi diagram is the division more accurate method of point group radiation scope, for this purpose,
Network Voronoi diagram is introduced point group synthesis by the present invention, polygon by calculating the corresponding network Voronoi of point group on this basis
Shape area and extension segmental arc total length, and be indicated in after it is normalized respectively using Voronoi area of a polygon as abscissa, with
Segmental arc total length is to realize the selection of point group in utilization " concentric circles " method in the two-dimensional coordinate system of ordinate.
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Application publication date: 20191119 |