CN112750178A - River system multi-scale geometric similarity hierarchical measurement method - Google Patents
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Abstract
The invention discloses a hierarchical measurement method for river multi-scale geometric similarity, which comprises the following steps: the geometric characteristics of the river system are divided into three levels of information characteristics: the shape characteristic of a single river, the structural characteristic of a local area and the distribution characteristic of a global scope. Firstly, calculating the shape similarity of a single river by combining an angle chain code method and a Hausdorff distance, then determining a local characteristic region according to Koch's ' two-eight law ', and popularizing the method to M: and N, computing the similarity of the river local structure, finally synthesizing the integral descriptor to obtain the global distribution similarity, and constructing a difference index P on the basis, so that the similarity computation and the comprehensive quality evaluation can be carried out. The method considers the special space distribution characteristics and the highly structured fractal characteristics of the river system, the calculation result accords with the cognition of people, and the method can be effectively applied to the geometric similarity calculation of the multi-scale river system.
Description
Technical Field
The invention relates to the field of drawing synthesis, in particular to a multi-scale geometric similarity measurement method for a river system under hierarchical analysis.
Background
When the drawing synthesis is carried out, although the space precision and the shape characteristics of the target are damaged, the expressed geometric information still keeps certain similarity, so the quality of the drawing synthesis quality can be judged through the geometric similarity of the space target.
The current methods for measuring the geometric similarity of spatial data mainly fall into two categories: the first type measures similarity based on Euclidean distance, Hausdorff distance, Frechet distance, Fourier shape descriptor and the like, but the method is designed for a single target and cannot be directly applied to geometric similarity calculation of group targets. The second category adopts the concept of statistical mean values such as tortuosity, average length, line group density and the like, measures similarity through the overall change information of statistical group targets, and ignores the change of local characteristics before and after drawing synthesis.
The river system is used as a basic group element of the map, and has specific space distribution characteristics and highly structured characteristics, such as space distribution characteristics of a tree shape, a feather shape and a chessboard shape, and self-similarity characteristics brought by a fractal structure. Therefore, it is necessary to expand the existing geometric similarity calculation method according to the geometric features of the river system to realize the correct calculation and reasonable expression of the geometric similarity of the multi-scale river system.
Disclosure of Invention
In view of this, the invention provides a multi-scale geometric similarity measurement method for river systems under hierarchical analysis, which divides the geometric similarity of the river systems into three levels of information characteristic similarity: the similarity of the shape characteristics of a single river, the similarity of the structural characteristics of a local area and the similarity of the distribution characteristics of a global range; the method combines an included angle chain code method and a Hausdorff distance, and can calculate M through coordinate system conversion on the basis of Koch 'two eight law': the geometric similarity of the river system of N and the difference index P constructed by the three similarities can synchronously express the change of global distribution characteristics and local structure characteristics before and after the integration of the multi-scale river system mapping. FIG. 1 is a general flow chart of the present invention, which includes three parts, namely single river shape feature similarity calculation, local region structure feature similarity calculation and global range distribution feature similarity calculation.
The invention discloses a hierarchical measurement method for multi-scale geometric similarity of a river system, which considers the special fractal characteristics of the river system, improves the traditional mean value index method, accords with the human cognition of a calculation result, and can be effectively applied to the calculation of the multi-scale geometric similarity of the river system.
Drawings
In order to more clearly express the embodiments of the present invention and the core solutions in the technology, the drawings used in the description of the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are only schematic diagrams of the present invention, and for those skilled in the art of drawing, other drawings can be obtained according to the provided drawings without creative efforts.
Fig. 1 is a flow chart of multi-scale geometric similarity calculation of river systems according to the present invention.
Fig. 2 is a schematic diagram of an included angle chain code method provided by the present invention.
Fig. 3 is a schematic diagram of coordinate system conversion provided by the present invention.
Fig. 4 is a schematic diagram of the regular grid partitioning provided by the present invention.
FIG. 5 is experimental data provided by the present invention.
Table 1 shows the similarity calculation results.
TABLE 1
Detailed Description
The technical solutions of the present invention will be described in detail below with reference to the accompanying drawings in the embodiments of the present invention, and of course, the described embodiments are only some embodiments of the present invention, but include the main ideas and innovation points of the present invention. All other embodiments, which can be obtained by a person skilled in the art of graphics synthesis without any inventive step, based on the embodiments described herein, are within the scope of the present invention.
The following steps are part of the similarity measure of the shape features of a single river:
step 1: calculating the angle sequence of corresponding dimension by using an included angle chain code method, and simultaneously calculating the arc segment length corresponding to each angle on the basis, such as alpha in (a) of FIG. 21Corresponding line segment
Beta in FIG. 2(b)1Corresponding line segment
Respectively obtaining the length sequences (p)1，p2…p7)、(q1，q2…q7)。
Step 2: the angle sequence and the length sequence are collected to obtain: m { (p)1，α1)，(p2，α2)…(p7，α7)}、N＝{(q1，β1)，(q2，β2)…(q7，β7) And constructing a polar coordinate system (p) by taking the origin of coordinates O as a pole, the anticlockwise direction as a positive direction, the length as a polar diameter and the angle as a polar anglei，αi)、(qi，βi) As shown in fig. 3(a) and 3(b), the polar coordinate system is converted into a rectangular coordinate system as shown in fig. 3(c) and 3 (d).
Step 3: calculating the Hausdorff distance between the two point groups, and obtaining the similarity between the two curves according to a formula (1):
wherein H (P, Q) is the Hausdorff distance between two point groups, SmaxIs the maximum value of the distance between any two points in the large-scale point group.
The following steps are part of the similarity measurement of the local structure features:
step 4: regular grid division is carried out on the small-scale river system, sorting is carried out by utilizing distribution density of confluent points in the grid, and the first 20% of the non-empty grid after sorting is taken as a local characteristic region (the region with the same density and large bending degree is taken) according to the 'two-eight law' of Koch. Taking the integrated river system 1:50000 in fig. 4(b) as an example, dividing the river system into 9 areas, respectively calculating and sequencing the number of junctions in each area, wherein the number of junctions corresponding to the area (i-ninu) is respectively: (3,0,0,0,9,3,0,1,2), then zone (r) and zone (r) are river networks characterizing structural features within the region.
Step 5: and (3) carrying out grid attribution judgment on the river, when the merging point falls on the boundary of the grid, counting the point into the grid with high density of the merging point, and counting into the grid with high bending degree when the densities are the same.
Step 6: the grid attribution judgment is carried out on the merging point, and the following three conditions are adopted: firstly, a river connecting convergence points in the grid is classified as the grid whether the river is in the grid or not; secondly, in the nodes between the confluence point sequences, whether the river of the node is in the grid or not, the river section from the node to the next node is counted into the grid; and thirdly, only counting the river falling into the grid for the node at the tail end of the junction sequence.
Step 7: and (4) carrying out homonymous region search and matching on the original river system to obtain a river network of the original river system representing local structure characteristics.
Step 8: the similarity measurement method of the shape features of the single river is popularized to the following steps: in the multiple rivers of N, the feature point clusters obtained by each line segment in the same line cluster are collected under the same coordinate, and the Hausdorff distance of two total point clusters is calculated to obtain the geometric feature similarity, as shown in formula (2):
in the formula, H (P)m，Qn) Is the Hausdorff distance between the total point groups, m, n are the total number of point groups, i.e. the number of line segments in each line group, SmaxIs the maximum value of the distance between any two points in the large-scale point group.
Step 9: calculating the total similarity of all structural feature regions, as shown in formula (3):
in the formula, Mi＝ti/T,tiRepresenting the number of confluent points contained in the ith area, k being the total number of the structural feature areas, T being the total number of confluent points in all the areas representing the structural features of the river system,
the similarity of geometric features in a single structural feature area is shown, and SIM _ local is the similarity of local structural features.
The following steps are the similarity measure part of the global distribution features:
step 10: calculating fractal dimension by using covering method, setting side length of grid as alpha and number of grids containing river as N (alpha), and obtaining a group (alpha) when length of alpha is changed1，α2，α3，…，αn) Corresponding to a group (N (alpha)1)，N(α2)，N(α3)，…，N(αn)). Logarithm of grid length and total number of non-empty grids, and then (ln alpha)1，lnα2，…，lnαn) On the abscissa, corresponds to (lnN (. alpha.))1)，lnN(α2)，…，lnN(αn) ) is plotted against the ordinate, and then the curve is fitted using the least squares method, resulting in the formula:
lnN(α)＝A-Dlnα (4)
in the formula (4), D is the fractal dimension of the water system, A is the intercept of the fitted curve and the ordinate, and the numerical range of the river fractal dimension is between [1 and 2 ].
Step 11: and (3) calculating the fractal dimension similarity, as shown in formula (5):
in the formula, G1、G2In order to integrate the fractal dimension of the front and rear river systems, the denominator delta is assigned as 1 to amplify the difference of the fractal dimension similarity between the multi-scale river systems.
Step 12: calculating the development coefficient and similarity of the river network, classifying the river by a Strahler classification method, and further calculating the development coefficients of the river network of all levels of tributaries, wherein the development coefficient similarity of all levels of the river network is shown as a formula (6), and the development coefficient similarity of the global river network is shown as a formula (8):
Kw＝Lw/L0 (6)
in the formula, LwLength of class w tributaries, L0Length of the main river, KwIs the network growth coefficient, Kw1、Kw2The development coefficients of the w-grade tributaries of the original river system and the integrated river system are KmaxFor larger values between the two, SimdcIs the similarity of the development coefficient of the river system w-level tributary, Sim1、Sim2,…,SimwFor the similarity of the development coefficients of the river networks at all levels,
the global river network development coefficient similarity is obtained.
Step 13: and (3) calculating the river frequency and the similarity, wherein the calculation formula is shown as a formula (9), and the river frequency similarity can be obtained through a formula (10):
Rf＝N/F (9)
wherein N is the total number of rivers in the study area, F is the total area of the study area, Rf1、Rf2To integrate the river frequency, R, before and aftermaxFor larger values between the two, SimrfRiver frequency similarity.
Step 14: calculating the density and similarity of the river network, wherein the calculation formula of the density of the river network is shown as a formula (11), and the similarity of the density of the river network is shown as a formula (12):
in the formula, LijIs the length of the jth strip in the ith river, NiIs the total number of i-th river, w is the highest level of the river, F is the total area of the study area, RdIs the density of the river network, Rd1、Rd2For integration of the density of the river network, RmaxFor larger values between the two, SimndAnd the density similarity of the river network.
Step 15: calculating global distribution feature similarity, when overall measurement is carried out on the global distribution feature similarity of a river system target, highlighting the key role of fractal in distribution feature description, giving the fractal dimension describing self-similarity a weight of 0.4, and respectively giving a weight of 0.2 to a river network development coefficient, a river network density and a river frequency, so as to obtain a global distribution feature similarity calculation formula as follows:
the method comprises the following steps of:
step 16: unifying the local structure feature similarity and the global distribution feature similarity into a total similarity SIM (subscriber identity module), as shown in a formula (14), and meanwhile, constructing a difference index P of the local structure and the global distribution to assist in evaluating the rationality of the total similarity calculation, as shown in a formula (15), when the value P is positive, expressing that the expression of the local structure feature is emphasized in the river system comprehensive process, discarding more global distribution features, and otherwise, reversing; the larger the value of | P | is, the more obvious the comprehensive degree is, and the larger the scale span is.
SIM＝μ1SIM_local+μ2SIM_global (14)
Wherein SIM _ local is similar to local structureDegree, SIM _ global is the global distribution feature similarity, SmaxFor the larger of the two, mu is determined according to the "two-eight law" in fractal1Take 0.2, mu20.8 is taken.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. The formulas and methods, concepts and principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown above but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (4)
1. A hierarchical measurement method for river system multi-scale geometric similarity comprises three parts, namely single river shape feature similarity calculation, local region structure feature similarity calculation and global range distribution feature similarity calculation:
the single river shape feature similarity calculation steps are as follows:
s1: calculating the angle sequence of the two curves by using an included angle chain code method, and calculating the length of an arc segment corresponding to each angle on the basis;
s2: the angle sequence and the length sequence are collected, a polar coordinate system (p) is constructed by taking the origin of coordinates O as a pole, the anticlockwise direction as a positive direction, the length as a polar diameter and the angle as a polar anglei，αi)、(qi，βi) Then converting the polar coordinate system into a rectangular coordinate system;
s3: calculating the Hausdorff distance between the two point groups;
the local region structure feature similarity calculation steps are as follows:
s4: regular grid division is carried out on the integrated river system, sorting is carried out by utilizing distribution density of merging points in the grid, and the first 20% of the sorted non-empty grid is taken as a local characteristic region according to the 'two-eight law' of Koch;
s5: carrying out grid attribution judgment on the river and the merging point;
s6: carrying out homonymous region search and matching on the original river system to obtain a river network of the original river system representing local structure characteristics;
s7: collecting the feature point groups obtained by each line segment in the same line group under the same coordinate, and calculating the Hausdorff distance of the two total point groups to obtain the similarity of a single feature area;
s8: calculating the total similarity of all structural feature areas;
the global scope distribution feature similarity calculation steps are as follows:
s9: calculating the similarity of the fractal dimensions by using a coverage method;
s10: classifying the river by a Strahler classification method, and calculating the river network development coefficient and similarity of branches at all levels;
s11: calculating river frequency and similarity;
s12: calculating the density and similarity of the river network;
s13: calculating global distribution characteristic similarity and difference index P;
s14: and (6) ending.
2. The method for hierarchical measurement of geometric similarity according to the river system of claim 1, wherein in step S3, the similarity of the shape features of the single river is calculated by using the steps S1 to S2.
3. The method for measuring geometric similarity of a multi-scale river system under hierarchical subdivision according to claim 1 or claim 2, wherein in step S8, M: similarity of local structural features of the N river systems.
4. The method for measuring geometrical similarity of multi-scale river systems under hierarchical subdivision according to claim 1, claim 2 or claim 3, wherein in step S13, global distribution feature similarity is calculated.
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| CN117251740B (en) * | 2023-09-22 | 2024-04-19 | 兰州交通大学 | Multi-feature-considered point group similarity evaluation method |
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