CN108122202A - A kind of map Linear element multi-scale information derived method based on Shape context - Google Patents
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Abstract
The invention discloses a kind of map Linear element multi-scale information derived methods based on Shape context, using the Shape context of point as the shape description of figure, for the point set corresponding to entity of the same name under size ruler, the matching of corresponding points can find best match by calculating the matching degree between the Shape context and each point each put.Matching can be obtained by the Map Expression of middle scale ruler by shape interpolating method after completing.It using the accuracy assessment method of quantification, is weighed using the position vector distance of weighting, contrast experiment finds out the factor for influencing precision, selects suitable space-division method.The characteristic point in conventional method, such as inflection point, radian maximum point etc. is not required in point matching process based on Shape context, therefore with preferable robustness and adaptability.The experimental results showed that the Linear element Morphing for taking whole contextual information into account can improve the precision of the continuous dimensional variation of map.
Description
Technical Field
The invention belongs to the technical field of geographic information, relates to a multi-scale information derivation method for linear elements, and particularly relates to a multi-scale information derivation method for completing linear elements by using a point set matching and shape interpolation method based on shape context.
Background
In recent years, rapid development of WEB2.0, network maps and LBS has brought new requirements for continuous scale expression of maps, and people hope to realize multi-view and multi-level visual expression of spatial information. In order to meet the requirements of people, a map continuous comprehensive technology is provided. The basic idea of Morphing, also called graph Morphing, is to use some interpolation method to make the initial graph a smoothly and continuously morph to the target graph B. In this smooth transition, the intermediate state has both the characteristics of a and B. The topology of a and B may be similar or different. This is in accordance with the idea of the map continuous integration technique.
The vector graphics Morphing transformation involves two basic processes, namely, graphics feature matching and shape interpolation. The aim of pattern feature matching is to extract feature points (lines) on the beginning and end patterns and establish a corresponding relationship between the two. The matching of the graphic features of the linear elements is mostly performed based on the features of the point sets. At present, common point pattern matching algorithms can be roughly divided into two categories, one is an algorithm based on transformation relation solution, and the problem of point pattern matching is solved by estimating space transformation parameters between point patterns and utilizing parameter recovery or simulating transformation between the point patterns, which is also called an algorithm based on transformation parameter estimation. The algorithms mainly comprise an iterative closest point algorithm, a soft assignment algorithm and the like. The other is an algorithm based on solving of matching relation, which solves the matching problem of point patterns by extracting the characteristics of point concentration points and then applying a matching identification method to obtain the matching relation between the point patterns.
The shape interpolation is to change each part of the initial graph to the position of the corresponding part of the target graph along a certain path on the basis of graph feature matching so as to obtain an intermediate state graph sequence. The selection of the interpolation path determines whether the intermediate state is smooth and natural, and common interpolation methods include a linear interpolation method, an interpolation method based on a target boundary, an interpolation method considering an internal region of a target, and the like.
In the GIS field, the Morphing concept is used to achieve continuous integration of map data. As the accuracy of the Morping transformation is mainly influenced by the matching accuracy, a plurality of experts and scholars do a series of work in the aspect of optimizing the matching, point encryption is mainly carried out on the small-scale graph until the point number is consistent with the point number of the large-scale graph, and then one-to-one correspondence is carried out according to the point number so as to establish the matching relation; regarding the vertex at the larger radian as a characteristic point, and then establishing a matching relation based on the relation of displacement; extracting characteristic points of linear elements on a small-scale map by a constrained Delaunay triangulation network, and then establishing global optimization matching between the characteristic points and the vertexes of the large-scale linear elements by adopting a simulated annealing technology; taking the bent structure as an entry point, and providing a matching method based on the bent structure; and converting the traditional vector coordinates into a steering angle function, and realizing edge feature matching based on the steering angle function. The methods need to find characteristic points to establish corresponding matching; or the matching is carried out after simple interpolation without the need of characteristic points, and the context information of elements is not considered. For map elements, small scale elements are usually obtained by performing comprehensive transformation on a large scale, such as simplifying, deleting, exaggerating and typical operations of bending. Therefore, the best matching of each point on the large scale can be searched to complete the matching of the corresponding point starting from the point on the small scale. Before and after synthesis, the size scale has similar context information. The shape context is a widely used object shape descriptor, the shape is described through the relation between point sets, namely the context information, the method does not need the points to have special points which are considered in the conventional methods such as maximum curvature, large radian and the like, and the adaptability and the robustness are strong.
Disclosure of Invention
In order to solve the problems of continuous scale transformation of the existing map current state elements, the invention provides a linear element multi-scale information derivation method based on shape context.
The technical scheme adopted by the invention is as follows: a map linear element multi-scale information derivation method based on shape context is characterized by comprising the following steps:
step 1: dividing the linear element space;
step 1.1: for a same-name linear entity, the linear entity is put at a larger scale R A Denoted A below, on a smaller scale R B Denoted by B below; denote a as a set of M contour points, i.e., a = (p) 0 ,p 1 ,...p i ,...,p M-1 ) (ii) a Denote B as a set of N contour points, i.e. B = (q) 0 ，q 1 ,...q j ,...,q N-1 )；
Step 1.2: respectively establishing a logarithmic polar coordinate system by taking each contour point of A as an origin, and for two dimensional angles theta and polar diameters lg rho of each coordinate system, carrying out S equal division on the angles theta, carrying out T equal division on the polar diameters lg rho, and respectively dividing S x T sub-region bins;
step 1.3: repeating the operation of the step 1.2 on the B to finish the region segmentation;
step 2: point set matching based on shape context;
step 2.1: after the space region is divided, p is removed from the statistical contour i The distribution number of other points outside the points in each divided region, each region obtains a statistical value, S x T sub-region bins obtain a sequence containing S x T data, a vector formed by the sequence represents the shape context of the point, namely a vector with S x T components, and the vector is visualized in a histogram form, so that a shape histogram is obtained; for the shape A, obtaining M vectors of S-T dimension, and storing the M vectors by using a matrix to realize the digital expression of the shape A;
step 2.2: repeating the operation of the step 2.1 on the shape B to realize the digital expression of the shape B;
step 2.3: measuring the matching degree between the two points by adopting chi-square distribution statistical test, calculating the matching cost between all the points A and B to obtain a matching cost matrix, converting the point set matching problem into a bipartite graph matching problem, taking the point with the minimum matching cost as the most similar corresponding point, and processing the maximum matching problem of the bipartite graph by utilizing a Hungary algorithm;
and step 3: performing shape interpolation based on the point set matching result;
step 3.1: the contour points on the line elements are utilized to divide the line into line segments, and a large scale R A The expression A below is split into { p } 0 p 1 ,p 1 p 2 ,p 2 p 3 ,…,p 203 p M-1 R, small scale B The expression B below is split into { q } 0 q 1 ,q 1 q 2 ,…,q 26 q N-1 Obtaining the corresponding relation between the sub-line segments according to the corresponding relation between the outline points; after the matching line segments are obtained, carrying out shape interpolation in a segmented mode, wherein a connecting line between matching points is an interpolation path;
find a subset A of B sub(u) And the corresponding subset B in A sub(j) Then:
step 3.2: let f1 and f2 denote the domains [0,1 ] respectively]To A sub(i) And B sub(j) F denotes the continuous function of the intermediate state after shape interpolation, the corresponding subset is C sub(k) (ii) a Therefore, there are:
f＝(1-g)*f 1 +g*f 2 (5)
wherein g is a normalized intermediate scale between a large scale and a small scale, and g is more than or equal to 0 and less than or equal to 1;
from this, when g =0, f = f1, i.e., C sub(k) ＝A sub(i) (ii) a When g =1, f = f2, i.e. C sub(k) ＝B sub(j) (ii) a When in use0<g&1, f is an intermediate expression between f1 and f2, and the magnitude of g controls the bias degree of the interpolation result;
step 3.3: calculating a normalized intermediate dimension g;
in the formula, R A Representing a large scale, R B Denotes a small proportion, R C Represents the middle scale;
step 3.4: and (3) carrying out the same treatment on each group of the rest corresponding point sets to obtain an intermediate state after continuous scale transformation:
and finally, multi-scale derivation of the map current situation elements is realized.
The invention provides a linear element Morphing (continuous scale transformation) method considering overall context information. To take into account the overall context information of an element, a shape context is mainly introduced as a shape descriptor. The point matching method based on the shape context does not need characteristic points in the conventional method, such as inflection points, maximum radian points and the like, so that the method has better robustness and adaptability. Experimental results show that the linear element Morphing considering the overall context information can improve the accuracy of continuous scale change of the map.
Drawings
FIG. 1 is a flow diagram of an embodiment of the invention;
FIG. 2 is a diagram illustrating context calculation of shapes in an embodiment of the present invention, wherein (a), (b) denote sets of edge points for two shapes, three points marked O,. Diamond,. DELTA.respectively; (c) A logarithmic polar coordinate system is represented, wherein lg rho is divided into 5 parts, theta is divided into 12 parts on average, and the total area is 60, namely 60 bins; (d) (e), (f) o,. Delta.three points correspond to shape contexts which are similar because o,. Delta.are relevant points and which are uncorrelated in position and vary widely in shape context;
FIG. 3 is a representation of a presence element on a scale of size in an embodiment of the present invention, wherein (a) represents a large scale representation A,205 vertices; (B) small scale representation B,28 vertices;
FIG. 4 is a graph of simulated data Morphing effects based on the method of the present invention;
fig. 5 shows the real contour data Morphing effect based on the method of the present invention.
Detailed Description
In order to facilitate understanding and implementation of the present invention for persons of ordinary skill in the art, the present invention is further described in detail with reference to the drawings and examples, it is to be understood that the implementation examples described herein are only for illustration and explanation of the present invention and are not to be construed as limiting the present invention.
This example was conducted in accordance with the flowchart of fig. 1, and experiments were conducted using the simulation data and the true contour data of the size scale, respectively. The verification experiment uses simulation data, in which fig. 3 (a) is an expression a of a linear element on a large scale, and fig. 3 (B) is an expression B of the same-name element on a small scale. The real contour data were on a scale of 1. The data structure of the selected contour line is complex and has more bending, and the synthesis from a large scale to a small scale comprises a plurality of synthesis operators such as simplification, exaggeration, representativeness and the like. The experimental process related algorithm is based on a VS2010 integrated development environment and is realized by adopting C # language programming.
Referring to fig. 1, the method for deriving multi-scale information of map linear elements based on shape context according to the present invention includes the following steps:
step 1: dividing the linear element space;
step 1.1: for a same-name linear entity, the linear entity is put at a larger scale R A For lower useA represents; at a smaller scale R B Denoted below by B, a is represented as a set of 205 contour points and B is represented as a set of 28 contour points (as shown in fig. 3).
Step 1.2: a logarithmic polar coordinate system is established with each contour point of a as an origin, and for two-dimensional angles θ and polar diameters lg ρ of each coordinate system, the angles θ are divided into 5 equal parts, the polar diameters lg ρ are divided into 12 equal parts, and 60 sub-regions (bins) are respectively divided (as shown in fig. 2 (c)).
Step 1.3: and (4) repeating the operation of the step 1.2 on the B to complete the region segmentation.
And 2, step: point set matching based on shape context;
step 2.1, after the space region is divided, for 205 contour points on the A contour, counting any points p on the contour i The distribution number of other points except the point in each divided region can obtain a statistical value in each region, 60 sub-regions (bins) can obtain a sequence containing 60 data, and a vector formed by the sequence represents the shape context of the point, namely a vector with 60 components, and is visualized in a histogram form, so that a shape histogram can be obtained. The shape histogram of each other point in the point set is calculated, for a,205 vectors of 60 dimensions can be obtained, so that the 205 vectors can be stored by a matrix of 205 × 60, and the digital expression of the shape a is realized.
Step 2.2: and repeating the operation of the step 2.1 on the shape B to realize the digital expression of the shape B.
Step 2.3: the obtained shape context descriptor has histogram distribution characteristics, so that the matching degree between two points is measured by adopting a chi-square distribution statistical test, and the matching degree can be described by using a mathematical formula matching cost. And (3) calculating the matching cost between all the points A and B to obtain a matching cost matrix, changing the point set matching problem into a typical bipartite graph matching problem on the basis, taking the point with the minimum matching cost as the most similar corresponding point, and solving the maximum matching problem of the bipartite graph by using a Hungarian algorithm.
The mathematical description in step 2.3 translates into the following specific steps,
step A1, defining the matching cost of two points as: c ij ＝C(p i ,q j ) And the concrete calculation formula is as follows,
in the formula, h i (k),h j (k) Respectively representing a point p on the A pattern i And point q on graph B j Is calculated for the value in the kth bin in the shape histogram of (1). C ij The larger the point is, the larger the matching cost of two points is, the smaller the similarity between two points is, and the smaller the possibility that the two points are corresponding points to each other is.
Step A2, after obtaining the matching cost between all points of the two shapes, the aim of point pattern matching is to find a matching relation pi, so that formula 2 obtains the minimum value.
Wherein π (i) is the corresponding point number of i.
The specific flow of the hungarian algorithm in step 2.3 is as follows,
step B1, assuming that the bipartite graph G = (V, E), which is an undirected graph, the vertex V can be divided into two disjoint sets a and B, while the two vertices associated with each edge in this graph belong to set a and B, respectively. A corresponds to a contour point set on a large scale, and B corresponds to a contour point set on a small scale.
Step B2, for G, if any two edges in the edge set { E } of a sub-graph M of G have no common vertex, then M is a match, and the subset with the most edges in the subset is the maximum match of the graph. Starting from each point on B, respectively, the maximum matching is obtained through the augmented track, and the maximum matching of all the points on the matching edge is found in A, and the maximum matching is called as perfect matching. Thus, perfect matching is established for each point on the B, and the corresponding point on the corresponding large scale is found to complete point set matching.
And 3, step 3: performing shape interpolation based on the point set matching result;
step 3.1: the contour points on the line elements divide the line into line segments, in this example, the expression A at a large scale is divided into { p } 0 p 1 ,p 1 p 2 ,p 2 p 3 ,…,p 203 p 204 204 sub-line segments in total; the expression B at small scale is subdivided into { q } 0 q 1 ,q 1 q 2 ,…,q 26 q 27 27 sub-line segments in total. The corresponding relation between the sub-line segments can be obtained according to the corresponding relation between the contour points, such as the line segment q 0 q 1 Corresponding line segment p 0 p 10 Line segment q 1 q 2 Corresponding line segment p 10 p 13 . After the matching line segments are obtained, shape interpolation can be performed in a segmented mode, and a connecting line between matching points is an interpolation path. Find a subset A of B sub(i) And the corresponding subset B in A sub(j) . Then:
step 3.2: let f1 and f2 denote the domains [0,1 respectively]To A sub(i) And B sub(j) F denotes the continuous function of the intermediate state after shape interpolation, the corresponding subset is C sub(k) . Therefore, there are:
f＝(1-g)*f 1 +g*f 2 ,(0≤g≤1) (5)
wherein g is a normalized intermediate scale parameter between the large and small scales. From this, when g =0, f = f1, i.e., C sub(k) ＝A sub(i) (ii) a When g =1, f = f2, i.e. C sub(k) ＝B sub(j) (ii) a When 0 is present<g&And when the value is 1, f is an intermediate expression between f1 and f2, and the size of g controls the bias degree of the interpolation result.
Step 3.3: the normalized intermediate scale parameter g is calculated by the following formula:
in the formula, R A Representing a large scale, R B Denotes a small proportion, R C Represents the middle scale;
and 3.4, finally, carrying out the same treatment on each group of the rest corresponding point sets, and finally obtaining an intermediate state after the Morphing:
the shape control parameters g in the results are 0,0.2,0.4,0.6,0.8,1, respectively, from left to right. Where g =0,1 corresponds to the original expression at the scale of the size, respectively. g =0.4 corresponds to the interpolation result at scale bar 1 26000, g =0.6 corresponds to the interpolation result at scale bar 1. This completes the multi-scale derivation of the map's presence elements (as shown in fig. 5).
The invention creatively takes the shape context of the point set as the shape descriptor, considers the context information of elements in the point pattern matching process and solves the problems in the technical background. The innovation points of the invention are as follows:
(1) Shape description is performed using shape context, and its core idea is to describe the geometry by the relationship between points in a point set and points, i.e. its contextual information. All points in the point set are treated together by the method, so that special points (such as inflection points, points with maximum curvature and the like) in the conventional method are not needed, and therefore the adaptability and the robustness are strong.
(2) The method has the advantages that the optimal matching points corresponding to the large scale are found out from the contour points on the small scale in the point set matching process, all the contour points on the small scale can be fully utilized, the overall structural characteristics of the same-name elements before and after integration, namely the overall context information, can be well considered, and the Morphising precision can be effectively improved.
(3) Contour points on the line elements divide the line into line segments, in this example, the expression A at a large scale is divided into { p } 0 p 1 ,p 1 p 2 ,p 2 p 3 ,…,p 203 p 204 204 sub-line segments in total; the expression B in the small scale is subdivided into { q } 0 q 1 ,q 1 q 2 ,…,q 26 q 27 27 sub-line segments in total. The corresponding relation between the sub-line segments can be obtained according to the corresponding relation between the contour points, such as the line segment q 0 q 1 Corresponding line segment p 0 p 10 Line segment q 1 q 2 Corresponding line segment p 10 p 13 . After the matching line segments are obtained, shape interpolation can be performed in a segmented manner, and a connecting line between matching points is an interpolation path.
(4) In order to quantify the accuracy of Morphing, a new evaluation method is introduced, and a weighted bit vector distance is adopted for measurement. The method solves the problems that a single measuring index can be changed greatly and the single measuring index lacks robustness in a multi-scale transformation environment.
Through experimental comparison, in the point set matching process, point one-to-one matching is carried out from the pure geometric angle based on a linear interpolation algorithm, and the context information of the points is ignored. The invention has great improvement, fully considers the shape context information of the points in the process of matching and improves the matching precision. The shape interpolation result shows that mutation and deformation occur in part of the results based on the linear interpolation algorithm, which does not meet the general requirements of drawing synthesis. The method has the advantages of better result, smooth and flat transition, higher integral position precision and capability of realizing continuous scale transformation.
It should be understood that parts of the specification not set forth in detail are well within the prior art.
It should be understood that the above description of the preferred embodiments is given for clarity and not for any purpose of limitation, and that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (3)
1. A map linear element multi-scale information derivation method based on shape context is characterized by comprising the following steps:
step 1: dividing the linear element space;
step 1.1: for a given linear entity, it is scaled to a larger scale R A Denoted A below, on a smaller scale R B Denoted by B below; denote a as a set of M contour points, i.e., a = (p) 0 ,p 1 ,...p i ,...,p M-1 ) (ii) a Denote B as a set of N contour points, i.e. B = (q) 0 ，q 1 ,...q j ,...,q N-1 )；
Step 1.2: respectively establishing a logarithmic polar coordinate system by taking each contour point of A as an origin, and for two dimensional angles theta and polar diameters lg rho of each coordinate system, carrying out S equal division on the angles theta, carrying out T equal division on the polar diameters lg rho, and respectively dividing S x T sub-region bins;
step 1.3: repeating the operation of the step 1.2 on the B to complete the region segmentation;
step 2: point set matching based on shape context;
step 2.1: after the space region is divided, p is removed from the statistical contour i The distribution number of other points outside the points in each divided region, each region obtains a statistical value, S x T sub-region bins obtain a sequence containing S x T data, a vector formed by the sequence represents the shape context of the point, namely a vector with S x T components, and the vector is visualized in a histogram form, so that a shape histogram is obtained; for the shape A, obtaining M vectors with S x T dimensions, and storing the M vectors by using a matrix to realize the digital expression of the shape A;
step 2.2: repeating the operation of the step 2.1 on the shape B to realize the digital expression of the shape B;
step 2.3: measuring the matching degree between two points by adopting chi-square distribution statistical test, calculating the matching cost between all the points A and B to obtain a matching cost matrix, converting the point set matching problem into a bipartite graph matching problem, taking the point with the minimum matching cost as the most similar corresponding point, and processing the maximum matching problem of the bipartite graph by utilizing a Hungary algorithm;
and 3, step 3: performing shape interpolation based on the point set matching result;
step 3.1: the contour points on the line elements are used for dividing the line into line segments with a large scale R A The expression A below is subdivided into { p } 0 p 1 ,p 1 p 2 ,p 2 p 3 ,…,p 203 p M-1 R, small scale B The expression B below is subdivided into { q } 0 q 1 ,q 1 q 2 ,…,q 26 q N-1 Obtaining the corresponding relation between the sub-line segments according to the corresponding relation between the outline points; after the matching line segments are obtained, carrying out shape interpolation in a segmented mode, wherein a connecting line between matching points is an interpolation path;
find a subset A of B sub(i) And corresponding subset B of A sub(j) And then:
step 3.2: let f1 and f2 denote the domains [0,1 ] respectively]To A sub(i) And B sub(j) F denotes the continuous function of the intermediate state after shape interpolation, the corresponding subset is C sub(k) (ii) a Therefore, there are:
f＝(1-g)*f 1 +g*f 2 (5)
wherein g is a normalized intermediate scale between a large scale and a small scale, and g is more than or equal to 0 and less than or equal to 1;
from this, when g =0, f = f1, i.e., C sub(k) ＝A sub(i) (ii) a When g =1, f = f2, i.e. C sub(k) ＝B sub(j) (ii) a When 0 is present<g&1, f is an intermediate expression between f1 and f2, and the magnitude of g controls the bias degree of the interpolation result;
step 3.3: calculating a normalized intermediate scale g;
in the formula, R A Representing a large scale, R B Denotes a small proportion, R C Represents the middle scale;
step 3.4: and (3) carrying out the same treatment on each group of the rest corresponding point sets to obtain an intermediate state after continuous scale transformation:
and multi-scale derivation of the map current situation elements is realized.
2. The shape context based map line element multi-scale information derivation method as claimed in claim 1, wherein: in step 2.3, chi-square distribution statistical test is adopted to measure the matching degree between two points, and the specific implementation process is as follows:
the matching cost of two points is defined as:
in the formula, h i (k),h j (k) Respectively represent a point p on the shape A i And point q on shape B j The value in the kth bin in the shape histogram of (1); c ij The larger the matching cost of two points is, the phase between the two points isThe smaller the similarity is, the smaller the possibility that the points are corresponding to each other is;
after the matching cost between all points of the two shapes is obtained, the aim of point pattern matching is to find a matching relation pi, so that the formula (2) obtains the minimum value;
in the formula, pi (i) is a point number corresponding to i.
3. The shape context based map line element multi-scale information derivation method as claimed in claim 1, wherein: the maximum matching problem of the bipartite graph is processed by using the Hungarian algorithm in the step 2.3, and the specific implementation process is as follows:
assuming that a bipartite graph G = (V, E), which is an undirected graph, the vertex V is divided into two disjoint sets a and B, and the two vertices associated with each edge in the graph G belong to the set a and B; a corresponds to a contour point set on a large scale, and B corresponds to a contour point set on a small scale;
if any two edges in the edge set { E } of a sub-graph M of graph G do not have a common vertex, then M is a match, and the subset with the most edges in such subset is the maximum match of the graph; respectively starting from each point on B, obtaining maximum matching through an augmentation track, finding the maximum matching of all the points on the matching edge on A, and the maximum matching is called as perfect matching; thus, perfect matching is established for each point on the B, and the corresponding point on the corresponding large scale is found to complete point set matching.
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| CN112766385A (en) * | 2021-01-22 | 2021-05-07 | 武汉大学 | Many-source vector line data geometric matching and attribute fusion method |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112766385A (en) * | 2021-01-22 | 2021-05-07 | 武汉大学 | Many-source vector line data geometric matching and attribute fusion method |
| CN114913263A (en) * | 2021-02-06 | 2022-08-16 | 兰州交通大学 | Automatic linear ground object simplification method based on multi-scale spatial similarity |
| CN114913263B (en) * | 2021-02-06 | 2023-11-14 | 兰州交通大学 | Linear ground object automatic simplification method based on multi-scale spatial similarity |
| CN114419136A (en) * | 2021-12-13 | 2022-04-29 | 国家基础地理信息中心 | Method and device for evaluating relative accuracy of topographic map and storage medium |
| CN116310417A (en) * | 2023-03-10 | 2023-06-23 | 济南大学 | Approximate graph matching method and system based on shape context information |
| CN116310417B (en) * | 2023-03-10 | 2024-04-26 | 济南大学 | Approximate graph matching method and system based on shape context information |
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