CN106055694B - Geographic curve tortuosity measuring method based on information entropy - Google Patents
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Abstract
The invention discloses a geographic curve tortuosity measuring method based on information entropy, relating to the technical field of geographic information science, which sequentially finishes the work of identifying bending units, overlapping and determining bending nesting relations under different scales, establishing a bending hierarchical tree, deleting invalid bending and measuring the tortuosity of a geographic curve based on the information entropy theory, adopts the comprehensive complexity combining the size complexity and the hierarchical complexity to describe the tortuosity, completely displays the partial and the whole tortuosity of the curve, simultaneously comprehensively considers the nesting relation among different levels of bending, overcomes the defects of the prior art, can better describe the tortuosity of the curve, comprehensively reflects the form and the structural characteristics of the curve, is less influenced by the length of the curve, fully utilizes the bending hierarchical tree to completely reflect the adjacent relation and the hierarchical characteristics among the bending, and the information entropy theory is adopted to measure the complexity, the operation is easy to realize, and the method has important significance for the research of the geographic characteristics.
Description
Technical field
The present invention relates to Geographical Information Sciences technical fields, and in particular to a kind of geographical line tortuosity based on comentropy
Measure.
Background technique
The tortuosity of geographical line is that a kind of description method of geographical feature curve and geography that curve itself is contained are special
Sign has important relationship, is of great significance to the research of geographical feature, and common geographical feature describes method description very not
Clearly, such as the tortuosity in coastline description multi-purpose " extremely tortuous ", " more tortuous ", " opposing straight " fuzzy concept are sentenced
It is disconnected, lack specific judge index, is highly detrimental to the determination of baselines of territorial sea type；Therefore, quantitative expression curve tortuosity has
There is important application value.
Current main use is based on tortuosity index, is based on the methods of angular amount calculation and FRACTAL DIMENSION to geographical line complications
It is measured.Tortuosity index is the quantizating index that can reflect line feature configuration, and tortuosity exponential number is got over
Greatly, then curve is more complicated, but tortuosity index cannot reflect the tortuosity of the funiclar curve of complicated nesting, can not comprehensively reflect song
The form of line；The angle value on curve between straightway is added based on the tortuosity measure that angular amount is calculated, with addition
As a result the complexity of curve is indicated, but this representation method is influenced by length of curve；Fractal dimension method is mainly studied not
The self-similarity of regular things, but fractal dimension is a statistic, it is only capable of the overall condition of reflection curve, and can not be with
The specific bending unit of curve is corresponding, and FRACTAL DIMENSION is a characteristic of curve, cannot obtain other of curve by FRACTAL DIMENSION
Structure feature for various length comprehensively can not react its tracing pattern and structure feature by curve.
Summary of the invention
(1) the technical issues of solving
Technical problem to be solved by the invention is to provide a kind of geographical line tortuosity measurement side based on comentropy
Method, to solve the above problems.
(2) technical solution
In order to achieve the above object, the present invention is achieved by the following technical programs: a kind of geography based on comentropy is bent
Line tortuosity measure, comprising the following steps:
1) identify bending unit: the adhesion for carrying out different in width to curve converts, by the result of adhesion transformation and original song
Line superposition obtains the bending polygon of different scale, and connection bending division points are bent identification figure, by bent with original geography
Line carries out intersection operation and obtains the bending under each scale, and calculates the quantizating index of each bending unit, is stored in related category
In property domain；
2) it is superimposed the bending nest relation determined under different scale, establishes bending hierarchical tree: more to the bending of different levels
Side shape is laid out analysis, judges the ownership of each bending polygon, establishes each curved bending hierarchical tree；
3) it deletes invalid bending: deleting each layer of invalid bending, finally obtain the bending unit of each level；
4) tortuosity based on information entropy theory measurement geographical line: bending hierarchical tree is calculated using information entropy theory and is represented
Geographical line tortuosity.
Further, the bending division points are primitive curve and the intersection point for being bent transformation line.
Further, the bending nest relation under determining different scale is superimposed by judging that each bending is more in different levels
The ownership of side shape is realized, the bending polygon under each scale is superimposed with the bending polygon under upper level large scale,
It determines the ownership of small scale polygon, to obtain corresponding nest relation, determines the level of each bending unit, finally build
The vertical bending hierarchical tree using primitive curve as root node.
Further, the method for establishing bending hierarchical tree is to loop to determine from bottom to up every to each curved hierarchical tree
One layer has whether the leaf node of parents' node has sibling, if there is sibling, which retains, if without sibling,
Then delete the node；One layer of search is continued up, judges whether this layer of leaf node has parents' node, if nothing, end loop, if
Have, then continue to judge whether it has sibling, until having traversed each layer of all leaf nodes.
Further, it is described be bent into that the bending division of non-upper layer obtains in vain it is direct by upper layer bending inherit from it is curved
It is bent.
Further, information entropy theory is used to calculate the method for the geographical line tortuosity that bending hierarchical tree represents to use
The compositive complexity of size complexity and level complexity measures the tortuosity of geographical line, the calculation formula of compositive complexity
Are as follows:
ZC=P1SCA+P2SCL+P3SCW+P4LC,
Wherein, weight shared by different types of complexity is respectively indicated, the sum of weight is 1.
Further, the SC is size complexity, using bending unit as basic unit in the calculating of the SC, is calculated public
Formula are as follows:
It wherein, is the sum of effective bending unit of bending hierarchical tree, for effective curved quantity in every one kind.
Further, the LC is level complexity, with one layer of hierarchical tree for basic unit in the calculating of the LC, meter
Calculate formula are as follows:
Wherein, it is the sum of effective bending unit of bending hierarchical tree, is effective curved quantity in every layer.
(3) beneficial effect
It is single to be sequentially completed identification bending for the present invention provides a kind of geographical line tortuosity measure based on comentropy
Member, the bending nest relation being superimposed under determining different scale simultaneously establish bending hierarchical tree, delete invalid bending and are based on comentropy
The work of the tortuosity of theory measurement geographical line, using the compositive complexity for combining size complexity and level complexity
Carry out tortuosity description, completely present curve part and whole tortuosity, while more comprehensively considering curved
Nest relation between bent different levels overcomes the defect of the prior art, can preferably describe curve tortuosity, comprehensively instead
The form and structure feature for reflecting curve, influenced by length of curve it is small, make full use of bending hierarchical tree completely reflect be bent between
Proximity relations and level characteristic, and complexity is measured using information entropy theory, easily operated realization has the research of geographical feature
It is significant.
Detailed description of the invention
Fig. 1 is that present invention circle adhesion converts exploded view；
Fig. 2 is that adhesion of the present invention converts front and back areal shape variation schematic diagram；
The bending figure that the different conversion curves of Fig. 3 present invention obtain；
Fig. 4 is that the bending figure that the different conversion curves of the present invention obtain corresponds to level tree graph；
Fig. 5 is present invention bending area, bending length and bending width diagram；
Fig. 6 is flow chart of the invention；
Fig. 7 is the bending division points connection figure of primitive curve C of the present invention and different scale；
Fig. 8 is the adhesion Transformation Graphs of the invention converted when width is 6 nautical miles；
Fig. 9 is the adhesion Transformation Graphs of the invention converted when width is 3.8 nautical miles；
Figure 10 is that the present invention converts bending level tree graph corresponding to adhesion Transformation Graphs when width is 6 nautical miles and 3.8 nautical miles；
Figure 11 is that the present invention deletes leaf node front curve 18 corresponding bending level tree graph of each layer without brother；
Figure 12 is to be bent 18 corresponding bending level tree graphs after present invention circulation deletes leaf node of each layer without brother；
Figure 13 is the adhesion Transformation Graphs of the invention converted when width is 1 nautical mile；
Figure 14 is the adhesion Transformation Graphs of the invention converted when width is 0.4 nautical mile；
Figure 15 is that the present invention converts adhesion Transformation Graphs corresponding level tree graph when width is 1 nautical mile；
Figure 16 is that the present invention converts adhesion Transformation Graphs corresponding level tree graph when width is 0.4 nautical mile；
Figure 17 is the level that the present invention converts adhesion Transformation Graphs corresponding level tree graph interior joint 8 when width is 0.4 nautical mile
Tree graph.
Figure 18 is primitive curve C schematic diagram of the present invention；
Figure 19 is the curved-ray tracing figure of curve C of the present invention；
Figure 20 is that bending of the invention is superimposed schematic diagram；
Figure 21 is the bending level tree graph that the present invention deletes invalid bending front curve 2；
Figure 22 is the bending level tree graph that the present invention deletes bending 2 after invalid bending；
Figure 23 is the bending level tree graph that the present invention deletes primitive curve C after invalid bending.
In figure:
1-a, original image；1-b, shell adding transformation；1-c, shell adding Transformation Graphs；1-d, husking transformation；1-e, coloured picture blackening；1-f, it sloughs off
Skin Transformation Graphs；1-g, stacking chart；
2-a, the unconverted circular arc of adhesion transformation front and back figure (circular arc that central angle is not more than 180 degree)；2-b, adhesion become
Change the circular arc (circular arc that central angle is greater than 180 degree) that front and back figure changes；2-c, straight line and circular arc composite figure；
3-A, primitive curve；3-B, primitive curve are bent level tree graph；3-C, primitive curve press one adhesion Transformation Graphs of scale；
3-D, primitive curve and by one adhesion of scale transformation after stacking chart；3-E, primitive curve and by one adhesion of scale transformation after stacking chart
Corresponding bending level tree graph；3-F, primitive curve press two adhesion Transformation Graphs of scale；3-G, primitive curve and by two adhesion of scale become
Change rear stacking chart；
The corresponding bending hierarchical tree of primitive curve 3-A without adhesion transformation in 4-A, Fig. 3；Primitive curve in 4-B, Fig. 3
The bending hierarchical tree that 3-A is obtained after adhesion transformation line 3-B transformation；Primitive curve 3-A is through adhesion transformation line 3-C in 4-C, Fig. 3
The bending hierarchical tree obtained after transformation；The flex layers that primitive curve 3-A is obtained after adhesion transformation line 3-D transformation in 4-D, Fig. 3
Secondary tree.
7-a, primitive curve C；Bending division points connection figure when 7-b, L are 6 nautical miles；Bending when 7-c, L are 3.8 nautical miles
Division points connection figure；Bending division points connection figure when 7-d, L are 2 nautical miles；Bending division points connection when 7-e, L are 1 nautical mile
Figure；Bending division points connection figure when 7-f, L are 0.4 nautical mile；
Bending level tree graph corresponding to adhesion Transformation Graphs when 9-a, L are 6 nautical miles；Adhesion converts when 9-b, L are 3.8 nautical miles
The corresponding bending level tree graph of figure；
11-a, it deletes in the 4th layer without bending hierarchical tree corresponding to bending 18 after fraternal leaf node；11-b, the 3rd is deleted
After leaf node without brother in layer, bending hierarchical tree corresponding to bending 18；11-c, it deletes in the 2nd layer without fraternal leaf node
Afterwards, bending hierarchical tree corresponding to bending 18；It is curved corresponding to bending 18 in 11-d, the 1st layer of deletion after the leaf node without brother
Bent hierarchical tree；
The curved-ray tracing figure that 19-a, Figure 18 primitive curve C adhesion width obtain when being 200km；19-b, Figure 18 primitive curve
The curved-ray tracing figure that C adhesion width obtains when being 50km；19-c, Figure 18 primitive curve C adhesion width obtain curved when being 30km
Song identification figure；The curved-ray tracing figure that 19-d, Figure 18 primitive curve C adhesion width obtain when being 15km；
The corresponding bending superposition signal of the curved-ray tracing figure that 20-a, Figure 18 primitive curve C adhesion width obtain when being 200km
Figure；The corresponding bending of the curved-ray tracing figure that 20-b, Figure 18 primitive curve C adhesion width obtain when being 50km is superimposed schematic diagram.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention,
Technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is the present invention one
Divide embodiment, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art are not making
Every other embodiment obtained, shall fall within the protection scope of the present invention under the premise of creative work.
In conjunction with shown in Fig. 1~23, comprising the following steps:
1) identify bending unit: the adhesion for carrying out different in width to curve converts, by the result of adhesion transformation and original song
Line superposition obtains the bending polygon of different scale, and connection bending division points are bent identification figure, by bent with original geography
Line carries out intersection operation and obtains the bending under each scale, and calculates the quantizating index of each bending unit, is stored in related category
In property domain；
2) it is superimposed the bending nest relation determined under different scale, establishes bending hierarchical tree: more to the bending of different levels
Side shape is laid out analysis, judges the ownership of each bending polygon, establishes each curved bending hierarchical tree；
3) it deletes invalid bending: deleting each layer of invalid bending, finally obtain the bending unit of each level；
4) tortuosity based on information entropy theory measurement geographical line: bending hierarchical tree is calculated using information entropy theory and is represented
Geographical line tortuosity.
Preferably, the bending division points are primitive curve and the intersection point for being bent transformation line.
Preferably, the bending nest relation being superimposed under determining different scale is by judging that each bending is polygon in different levels
The ownership of shape is realized, the bending polygon under each scale is superimposed with the bending polygon under upper level large scale, really
The ownership of fixed small scale polygon determines the level of each bending unit to obtain corresponding nest relation, final to establish
Bending hierarchical tree using primitive curve as root node.
Preferably, the method for establishing bending hierarchical tree is to loop to determine from bottom to up each to each curved hierarchical tree
Layer has whether the leaf node of parents' node has sibling, if there is sibling, which retains, if without sibling,
Delete the node；One layer of search is continued up, judges whether this layer of leaf node has parents' node, if nothing, end loop, if
Have, then continue to judge whether it has sibling, until having traversed each layer of all leaf nodes.
Preferably, it is described be bent into that the bending division of non-upper layer obtains in vain it is direct by upper layer bending inherit from it is curved
It is bent.
Preferably, information entropy theory is used to calculate the method for the geographical line tortuosity that bending hierarchical tree represents as using ruler
The compositive complexity of very little complexity and level complexity measures the tortuosity of geographical line, the calculation formula of compositive complexity
Are as follows:
ZC=P1SCA+P2SCL+P3SCW+P4LC,
Wherein, weight shared by different types of complexity is respectively indicated, the sum of weight is 1.
Preferably, the SC is size complexity, using bending unit as basic unit in the calculating of the SC, calculation formula
Are as follows:
It wherein, is the sum of effective bending unit of bending hierarchical tree, for effective curved quantity in every one kind.
Preferably, the LC is level complexity, with one layer of hierarchical tree for basic unit in the calculating of the LC, is calculated
Formula are as follows:
Wherein, it is the sum of effective bending unit of bending hierarchical tree, is effective curved quantity in every layer.
For the sake of ease of implementation, adhesion of the present invention is introduced first to convert, be bent hierarchical tree, bending unit amount
Change index and comentropy (complexity):
(1) adhesion converts
Buffer area transformation based on map algebra can be convenient and be quickly obtained point, line, surface and answer that buffer width is L
The buffer area of miscellaneous entity, and according to the difference of range conversion, divided into internal buffer transformation and the transformation of outer buffer area.
Specific algorithm are as follows: range conversion (inside and outside) directly is implemented to entity using respective distance scale first, obtains full sky
Between each point distance；Then taking distance value is all pixels of 1~L (L is to buffer sector width), is extracted buffer area (inside and outside).This
When outer buffer area is known as shell, internal buffer is known as skin.Entity adds the process of outer buffer area for " shell adding " transformation, and entity goes interior slow
The process in area is rushed as " husking " transformation.
Shell adding transform definition to figure X is formula one:
XK0(L)=X ∪ XB0(l, L)=X+XB0(L),
In formula, X is entity sets, K0(L) indicate that the shell adding for implementing L converts, B0(1, L) show to take distance value from 1 to
The picture dot of L, i.e. width are the buffer area of L；XB0(L) it is shell, refers to the neighbouring shell with a thickness of L of entity appearance.
Husking transform definition to figure X is formula two:
XKI(L)=X XBI(l, L)=X-XBI(L),
In formula, KI(L) indicate that the peeling for implementing L converts, XBI(L) it is skin, refers to that solid object surface thickness is the level of L.
It is converted using shell adding and husking, can further obtain adhesion transformation, adhesion transformation can define such as formula three:
X·L(l1, l2)=XKO(l1)·KI(l2),
In formula, l1, l2To be suitable for positive integer or 0, it is l that adhesion transformation, which carries out width to figure first,1Shell adding transformation,
Then, then to it carrying out width is l2Husking transformation；Under normal circumstances, take shell adding width equal with husking width, even l1=
l2, and it is referred to as adhesion width 1.
Adhesion converts the conformal effect to areal shape, has characteristics that
A, to the basic standards figure such as circle, straight line, there is the characteristic for keeping grown form constant, i.e. " keeping tie ", " protecting convex "
Characteristic.
By taking the test pattern of curve circle as an example, such as Fig. 1, pair radius is the circle of r, and the shell adding that progress width is L first converts,
Transformed figure is still round, radius R=r+L, then carries out the husking that width is L to transformed figure and convert, then
The transformed figure 1-f and original image 1-a that will cast off a skin is overlapped, and obtains stacking chart 1-g, is obtained 1-a and 1-f and is completely coincident, this
Illustrate that circle figure before and after adhesion transformation remains unchanged.
B, for concave, convex, Straight Combination figure, there is " protecting convex ", " keeping tie ", " filling out recessed " characteristic.
In adhesion transformation, the variation degree of circular arc figure before and after transformation depends on the central angle of circular arc, when circular arc
When central angle is not more than 180 ° (being presented as convex), adhesion transformation front and back figure is remained unchanged, and is embodied and is protected convex morphological character, such as
Shown in Fig. 2-a, when central angle is greater than 180 °, adhesion transformation performance subtracts recessed morphological character, as shown in Fig. 2-b；Circular arc and straight
Line composite figure graphic change degree in adhesion transformation is related with the two angle, when angle is greater than 180 °, straight line and circular arc
Protrusion is formed, adhesion transformation front and back figure is constant, and when angle is less than 180 °, straight line and circular arc form recess portion, as adhesion becomes
Change width increase, recess portion gradually filled and led up, as shown in fig. 2-c, further demonstrate adhesion transformation protect it is convex, keep tie, fill out recessed guarantor
Shape characteristic.
C, it is controllable " to fill out recessed " degree.
The metamorphosis characteristic converted according to adhesion: if adhesion transformation width is L, width (is bent width definition herein
For the curved recessed width of maximum, it being denoted as D) concave curve less than 2L will be gradually smooth, and bending width is smaller, and transformation width is got over
Greatly, smooth effect is more obvious, meanwhile, wide bending will be filled and led up below, and the relationship of CRITICAL CHANGES width L' and maximum recessed width D are full
Sufficient formula four:
This also means that going out CRITICAL CHANGES width L' with the maximum recessed width D inverse of circular arc, then width L' is carried out to figure and is glued
It even converts, the result of transformation will fill and lead up all recess portions in figure.Such as table 1, the circular arc of pair radius R=20 pixel, different central angles
Width is carried out as L adhesion transformation, takes the transformation results in the case of tri- kinds of L' of L < L', L=L' and L > respectively, it is known that, adhesion becomes
It changes rear figure smoothness to increase, guarantor is convex, keep tie, fills out recessed trend increases with L and aggravated；When adhesion transformation width L increases to L=
L' is converted if continuing the adhesion that width is D (D > L), and figure no longer changes.
1 radius R=20 pixel of table, the circular arc adhesion change situation of different central angles
Characteristic of the adhesion transformation in the holding of areal shape with " protecting convex ", " keeping tie ", " filling out recessed ", and " filling out recessed "
The value for the width L that degree can be converted by adhesion control, can be never real in ipsilateral and different levels using these characteristics
The automatic identification of existing curved unit.
(2) it is bent hierarchical tree
It is bent hierarchical tree, refers to the adhesion transformation identification bending based on different scale, it is curved in the case where obtaining different scale
On the basis of, the nest relation of bending unit is described with a hierarchical tree.In bending hierarchical tree, under a certain adhesion change of scale
The bending identified represents one layer of hierarchical tree, and each bending represents a node of this layer.
Below will be by curved standard type --- for circular arc, illustrate the basic conception for being bent hierarchical tree.Such as 3- in Fig. 3
A, curve L are formed by four layers of different size of bending nesting, and 1 (representing curve L) of maximum bending is from left to right successively nested
1a, 1b, 1c tri- bendings, and these three bendings successively nesting 1a.1,1a.2,1a.3,1b.1,1b.2,1c.1,1c.2 seven
A bending, again nested 1c.2a, 1c.2b two bendings of bending 1c.2.The adhesion under three different scales is carried out to curve L to become
It changes, obtained transformation line is followed successively by 3-B, 3-C and 3-D in Fig. 3, and the stacking chart of transformation line and primitive curve is followed successively by Fig. 3
3-E, 3-F and 3-G, one layer in the corresponding bending hierarchical tree of each adhesion change of scale, to establish corresponding under each scale
Bending hierarchical tree.Such as 4-B, 4-C and 4-D of Fig. 4, root node 1 represents curve L；There are three child nodes for node 1, are followed successively by knot
Point 1a, 1b, 1c indicate successively nested 1a, 1b, 1c tri- bendings of curve L；Node 1a, 1b, 1c have 3 child nodes, 2 respectively
A child node and 2 child nodes illustrate to be bent 1a, 1b, 1c successively nested 3 bendings, 2 bendings and 2 bendings；Class according to this
It pushes away ....Finally, the leaf node of tree represents lower minimum bend unit that can be identified of a certain adhesion change of scale.
In bending hierarchical tree, each bending unit in curve corresponds to a node, and the structure of hierarchical tree reflects curved
Topological property between song, and the quantizating index of bending unit can store in the correspondence node of bending hierarchical tree.In this way,
Hierarchical tree can be bent with one to express and be bent nested topological property in one section of curve, meanwhile, it can also describe each curved
The size and form of Qu Danyuan.That is, hierarchical tree can be bent with one to describe the complications of one section of curve.The bending level
The ability of tree one section of curve tortuosity of description is shown in Table 2:
Table 2 is bent the ability that level tree table reaches curve tortuosity
(3) bending unit quantizating index
Bending unit is the smallest unit of constituent curve, should be a bit of segmental arc, for convenience of right
The measurement of its various index is bent in hierarchical tree and substitutes line with face, is represented with the bending polygon that adhesion transformation identifies each
A bending unit.Existing bending unit quantizating index mainly includes bending unit area, length, width etc..It introduces in detail below
The quantizating index of bending unit.
A. it is bent area S
Bending area S refers generally to be bent the connect straight line of Origin And Destination and the enclosed area of a polygon of bending section, as in Fig. 5 directly
The enclosed area of a polygon of segmental arc between line segment AB and A point, B point.
B. bending length L
Bending length L is defined as the total length of bending unit, such as the total length of the half interval contour of AB (or BC) in Fig. 5.Herein
Middle bending length can be obtained directly in ArcGIS by attribute evaluator computational length.
C. it is bent width W
As in the case of, bending width W be defined as the linear distance between the bending Origin And Destination, such as AB or BC in Fig. 5
Between linear distance.Bending width based on adhesion transformation still uses this definition, but the determination for being bent endpoint is to be based on
Adhesion converts comprehensive line.Concrete operations are as follows: in the step of identifying bending, polygon is bent, to bending polygon perimeter
Ask difference that bending width can be obtained with bending length.
(4) complexity and comentropy
Comentropy is the measurement to the useful degree of information.In earth science research, comentropy is that research characteristic has with what is be distributed
Effect means, and complexity is the description to composition, two seem different concepts and but have very close connection.Herein with multiple
It is miscellaneous to spend to measure the tortuosity of curve, in the form of this carrys out quantitative description curve.
Entropy can measure a certain phenomenon or event in spatial concentration or the degree of dispersion, be probabilistic scientific appellation.
Entropy is the tissue degree of system and the measurement of order degree, can be used to characterize the uncertainty degree of system, removes the flat of redundancy
Equal information is comentropy.Comentropy can be used to the size of metric amount, the useful degree of description information.Pass through comentropy
It can effectively realize the quantization of information, specific calculation formula such as formula five:
Wherein, P in formulaiIt is event xiProbability of occurrence, n indicates that event one shares n, and logarithmic function takes different bottoms,
Calculated entropy result is different.
Comentropy is widely used, but entropy theory be abstracted in scientific scope it is hard to understand.Zhang Xuewen is in Generalized Sets
In theory mysterious entropy concept and Entropy principle are transformed very popular, while expanding its application field again.
He substitutes entropy with complexity from the angle of composition opinion, proposes the concept and complexity law of Generalized Sets.Through
Transformation is crossed, information entropy theory is more easy-to-understand, more easily applies.
Composition opinion asks all problematic generalization of group with the composition of unified model and law study different field
Topic.Wherein, Generalized Sets are the mathematical models for studying unified component law.Set language can be used for qualitative analysis,
And Generalized Sets language then can be used for quantitative analysis.Set is that have the totality of the things of special properties, is mainly closed in set
Infuse which members different two-by-two is known as.And Generalized Sets will not only specify this difference, while also pay close attention to common point: by altogether
Property by element classification, specify element in every class it is each how many.If a totality can be divided into the identical individual in multiple status,
And each individual has determining attribute value, then this totality is known as Generalized Sets.Can not only have one in Generalized Sets
Attribute, while multidimensional Generalized Sets can also be known as there are many attribute.One-dimensional Generalized Sets are mainly studied herein.For
Accurate description Generalized Sets, need to introduce two new concepts, i.e. mark and individual.Mark refers to different two-by-two in set
Element, and individual refers to type belonging to element, and individual is the fundamental that composition is gathered.Mark is used to describe difference, a
Body then stresses to illustrate that status is identical between each element.
Generalized Sets are a kind of mathematical models, are corresponding to it so having a distribution function.Function herein and universal
Function in the mathematics of meaning is different, it can be an empirical equation, and what is mainly illustrated is exactly the problem of composition.Clear one kind
Composition, exactly finds an objective law, and every kind of composition can be described with Generalized Sets, so each Generalized Sets
Distribution function is exactly a rule.Clear each specific Generalized Sets are exactly clearly a kind of composition, find an objective law,
It is in fact exactly to obtain a distribution function.Table 3 show the example of some Generalized Sets:
3 Generalized Sets example explanation of table
| Generalized Sets | Individual title | Mark name | The problem of distribution function will illustrate |
| Population | Everyone | The age of people | The people of all ages and classes it is each how many |
| Mountain | Every mountain | The height above sea level on mountain | The mountain of Different Altitude it is each how many |
| Lake | Each lake | The area in lake | The lake of different area it is each how many |
| Soil | Every square kilometre of soil | Land type | Different types of territory it is each how many |
| River | Every section of branch | The length of branch | The branch of different length how many |
Complexity can describe the composition situation of Generalized Sets, react its internal state, the calculation formula of complexity such as formula
6:
N indicates the number of value of statistical indicant in formula, that is, shares how many class；niIndicate quantity individual in every kind of value of statistical indicant, i.e.,
Element number in every class；N indicates individual total amount.Each Generalized Sets have distinctive complexity itself, complexity
Minimum value is 0, and the value of all elements is all identical at this time, only a classification.The complexity it can be seen from complicated dynamic behaviour formula
Value it is related with the bottom of logarithmic function used when calculating, the bottom of logarithm is different, and the complexity value acquired is also different.
Individual difference in Generalized Sets is bigger, and complexity is also bigger.When the feature of each individual is identical i.e. not
Have differences thing, complexity zero.The difference that value of statistical indicant is expressed as with the language of Generalized Sets is bigger, and complexity value is bigger；
Value of statistical indicant is identical, then complexity is zero.Popular understanding, composition is more complicated, and complexity is bigger.
Comentropy indicates uncertain, and complexity indicates that abundant degree, the two have certain relationship.Comentropy is from random
The angle analysis things of test, finally obtains the uncertainty of result；Complexity is the angle analysis things from inherent difference,
Performance of this species diversity in Generalized Sets is that there are different values of statistical indicant, and finally obtained is the abundant degree of things, i.e., should
What kind of Generalized Sets be made of.The calculation formula one of comentropy and the calculation formula two of complexity are analyzed, wherein Pi=ni/ N,
This relationship is brought into the calculation formula two of complexity, and combines formula one, pair of available comentropy and complexity
It should be related to: C=NH.By this relational expression it is found that positive correlation trend is presented in complexity and comentropy, complexity is bigger, comentropy
Also bigger, that is, form more complicated, final result is more uncertain.Just because of proportional relationship between the two, very about comentropy
More knowledge are also included into the concept of complexity naturally[63].According to this relationship also it can be concluded why having not
The degree of determination is that the complexity because one Generalized Sets of objective reality have complexity, just because of composition just results in result not
Certainty.
Embodiment 1:
It is bent below in conjunction with curve is carried out using bending hierarchical tree in attached drawing 6 and embodiment the present invention will be described in detail technical solution
Folding degree describes method, and for curve C shown in 7-a in Fig. 7, the detailed establishment process for being bent hierarchical tree is as follows:
1) curve generalization is carried out based on adhesion transformation, is bent polygon；
To primitive curve C implement adhesion transformation, obtain curve adhesion transformation line (be divided into interior transformation line and outside thread-changing,
Only outer transformation line is selected to be illustrated, interior transformation line is similar here), and bending polygon is constructed with primitive curve C.
Specifically, implementing width respectively to primitive curve C is 6 nautical miles, 3.8 nautical miles, 2 nautical miles, 1 nautical mile and 0.4 nautical mile
Adhesion transformation, obtains the transformation line under different scale, the intersection point of primitive curve and bending transformation line is known as to be bent division points, even
It connects bending division points and obtains curved-ray tracing figure shown in Fig. 7.
Bending division points line is constructed into bending polygon with curve C respectively, it, can be with for converting width and be 6 nautical miles
Obtain 18 bending polygons as shown in Figure 8, corresponding 18 bending units (number 1-18).
2) Overlap Analysis judges the ownership for being bent polygon；
Analysis is laid out to the bending polygon of different levels, the ownership of each bending polygon is judged, establishes each
Curved bending hierarchical tree.The bending polygon of adhesion transformation width L=3.8 in the sea is taken, each bending is adjacent with upper one
The bending of large scale adhesion transformation (L=6 in the sea) is compared, such as Fig. 9, through observation shows that: bending 18 be split into three it is curved
Song is respectively bent 18.1,18.2,18.3, while being bent 8 and being split into two bendings, is respectively bent 8.1 and 8.2, other are curved
Qu Ze is not divided.
Being bent the process of relationship on above-mentioned determining curve between different levels is identified by eye-observation, is being had
In body implementation process, it can be realized by judging the ownership of each bending polygon in different levels.
Detailed process is as follows, takes the bending polygon that adhesion transformation width is L1, is the bending of L2 (L2 < L1) with width
Polygon is laid out analysis, loops to determine the ownership of each bending polygon when width is L2.Assuming that polygon P2 is adhesion
Convert width be L2 when a certain bending polygon, polygon P1 be adhesion transformation width be L1 when a certain bending polygon,
If polygon P2 belongs to polygon P1, illustrate in bending hierarchical tree, it is curved for being bent node C2 corresponding to polygon P2
The child node of node C1 corresponding to bent polygon P1.The process of above-mentioned judgement bending polygon ownership, which recycles, to be executed, until all
Bending traversal finishes.
3) the corresponding hierarchical tree of each bending under out to out is established；
In order to clearly indicate the relationship between a certain node and its child node, it is assumed that one node of label is 1, if it only has one
A child node, is generally referenced as 1.1；If it has multiple child nodes (being set as n), successively labeled as 1.1,1.2,1.3 ...,
1.n；If 1.n also has multiple child nodes (being set as m), successively labeled as 1.n.1,1.n.2,1.n.3 ... 1.n.m.
According to the method for judge polygon ownership in 2), to width L=6 nautical miles, 3.8 nautical miles, 2 nautical miles, 1 nautical mile of transformation and
Identical treatment process is implemented in bending under 0.4 nautical mile, the corresponding hierarchical tree of available each bending, such as table 3:
The bending hierarchical tree of the different transformation width of table 3
In bending hierarchical tree, the determination of each node parents node depends on the node and corresponds to curved ownership.If knot
Bending 18.1 is overlapped be bent corresponding to upper one layer of node, it is clear that be bent 18.1 and belong to by the corresponding bending 18.1 of point 18.1
In bending 18, then parents' node of node 18.1 is node 18, such as the 9-a and 9-b in Figure 10.In addition, in bending hierarchical tree
The attribute of each node all corresponds to the quantizating index of bending unit.
4) leaf node without brother in each layer is deleted, the bending hierarchical tree of entire curve is established；
To each curved hierarchical tree, looping to determine each layer from bottom to up has whether the leaf node of parents' node has brother
Younger brother's node, if there is sibling, which retains；If deleting the node without sibling.One layer of search is continued up,
Judge whether this layer of leaf node has parents' node, if nothing, end loop；If so, then continuing to judge whether it has fraternal knot
Point ... is until traversed each layer of all leaf nodes.
Now illustrate the process for deleting leaf node of each layer without brother in bending hierarchical tree for being bent 18.Figure 11 is to delete
Before leaf node of each layer without brother, bending hierarchical tree corresponding to bending 18, since the 4th layer of hierarchical tree of bending, under
The leaf node of supreme each layer of traversal, judges whether it has sibling.Observe the leaf knot of the 4th layer of hierarchical tree of bending in Figure 11
Point, the number of node with Arabic numerals " 1 " ending, show that all leaf nodes of this layer without sibling, need to be deleted
It removes, the obtained 11-a in result such as Figure 12；Continue up the leaf node in the 3rd layer of cyclic search, it is known that there are two nodes
Number is not with Arabic numerals " 1 " ending, the two nodes are respectively 18.2.1.2 and 18.2.3.2, delete the two nodes
The last one digit number of number, obtains the 2nd layer of node (i.e. parents' node) 18.2.1 and 18.2.3, can determine the two nodes
Under child node (node 18.2.1.1,18.2.1.2 and 18.2.3.1,18.2.3.2 on i.e. the 3rd layer) have sibling, no
It needs to delete；Other leaf nodes on 3rd layer are implemented to delete node operation, the obtained 11- in result such as Figure 12 without sibling
b；All leaf nodes for continuing up the 2nd layer of search spread delete the leaf node without brother using identical judgment method
18.1.1 and 18.3.1, the 11-c in obtained result such as Figure 12；Continue up the 1st layer of search spread of all leaf nodes, leaf
Node 18.1 and 18.3 has sibling, is not required to delete；Without leaf node in 0th layer, it is not required to judge.So far, it is bent hierarchical tree
In each layer of leaf node traverse completion, the operation for illustrating to delete the leaf node without brother in each layer is finished, and traverses
Hierarchical tree corresponding to bending 18 after the completion is as shown in the 11-d in Figure 12.Table 4 is to loop through each bending hierarchical tree, is deleted
Except the result after leaf node of each layer without brother.
Finally, 18 bendings for being 1-18 to number increase parents' node C (as root node C), obtain primitive curve C's
It is bent hierarchical tree, such as Figure 16~17.Certainly, each node being bent in hierarchical tree has common attribute --- bending unit
Quantizating index, to describe the size and form characteristic of bending unit itself.
In fact, the adhesion transformation under any scale could set up the bending hierarchical tree that height is 1.Such as Fig. 8, to original
Curve C carries out adhesion transformation, and width L=6 in the sea, then generates 18 bendings, and these bendings are in the same of bending hierarchical tree
Layer, obtain as shown in Fig. 9-a be highly 1 bending hierarchical tree.If continue to implement curve C primary less than 6 nautical miles of width or
Multiple adhesion transformation, then can establish the bending hierarchical tree that height is not less than 1, such as Fig. 9-b and Figure 15, Figure 16 and Figure 17.Adhesion
The selection of number of transitions and transformation width determines the height of bending hierarchical tree and the degree of each node.It is bent the height of hierarchical tree
Degree determines the nested number of bending；The degree of each node then illustrates curved degree of crushing corresponding to the node.The two
Numerical value can be used as one of the performance that bending hierarchical tree describes curve tortuosity ability.
Table 4 deletes the hierarchical tree in each bending hierarchical tree after leaf node of each layer without brother
Bending hierarchical tree is the expression based on bending hierarchical structure, can be complete based on the identification bending of adhesion transform method
Reflection bending between proximity relations and level characteristic.In structure tree, there is proximity relations between same layer neighborhood of nodes；
The a certain node and N-1 layers of parents' node of n-th layer have hierarchical relationship, describe curved nested structure.Such as Fig. 9-a,
Node 1 is adjacent with 2, and corresponding to bending has proximity relations；Such as Fig. 9-b, node 8.1,8.2 and node 8, node 18.1,18.2,
There is hierarchical relationship, corresponding bending embodies the nested structure between bending between 18.3 and node 18.
(1) bending of same level；
By taking node 8, node 12 and node 18 as an example, illustrate to be bent the ability that hierarchical tree describes curve tortuosity:
Firstly, from Figure 16~17 as can be seen that being bent the height of hierarchical tree corresponding to node 8, node 12 and node 18
It is equal, it is 4, is maximum three trees of height in node 1-18, shows to be bent in curved section corresponding to these three nodes embedding
The number of set is most, is relative complex bending.The conclusion is consistent with the result of eye recognition in Fig. 8.
Secondly, the degree of node 8, node 12 and node 18 is respectively 2,1 and 3, show that its subtree tree is respectively 2,1 and 3,
That is bending 8, bending 12 and bending 18 are split into 2 bendings, 1 bending and 3 bendings respectively.Certainly, this is one
Value relative to comprehensive scale.
Again, the difference of the tortuosity of curved section 8, curved section 12 and curved section 18 can the son as corresponding to these three nodes
The difference of tree is measured.For example, the tree (i.e. the degree of node) of subtree, the depth (the nested number of bending) of subtree, tree node
Harmony, difference of the quantizating index of node of division etc..We can tentatively judge, the node 12 compared with node 18 of node 8
On the one hand complexity is because the number (7) of the total node of node 12 on the other hand may be used much smaller than node 8 (16) and node 18 (13)
Judged from a number for its subtree, the difference etc. of its subtree can also be compared.
It is then possible to according to the harmony of the harmonious judgment curves tortuosity of tree node division.To node 8 and node
18, it is clear that the division of node 18 is more balanced, and degree (or being averaged) Lai Hengliang of subtree corresponding to its each layer of node can be used in this.
In addition, there is proximity relations, such as node 8.1 and node 8.2 between the neighborhood of nodes of same layer.
(2) bending of different levels；
Firstly, the difference of level where bending node shows that bending unit is different in the nested number of whole curve.For example,
In Figure 16~17, node 8.1 and the place node 8.1.2.1 level are respectively 1 and 3, and the height of hierarchical tree corresponding to node 8 is
4, illustrate that being bent 8.1 in the nested number of whole curve is 3 (height of tree and the differences of place level)；It is bent the embedding of 8.1.2.1
Covering number is 1.This is consistent with the result in Figure 16~17.
Secondly, the nest relation before different layers bending can be determined by judging whether it is father-child node.For example,
There are three the child nodes of node 18, respectively 18.1,18.2,18.3, illustrates 18 nesting of bending, three bendings, respectively
18.1,18.2 and 18.3.
In short, the tortuosity of a corresponding one section of curve of bending hierarchical tree, it can both describe the big of bending unit itself
Small morphological feature can also describe the topological property between bending unit.
Embodiment 2:
Below in conjunction with attached drawing 6 and embodiment the present invention will be described in detail technical solution, for curve C shown in Figure 18, bending
The detailed establishment process of hierarchical tree is as follows:
1) bending unit is identified.
Implement the adhesion that width is 200km, 50km, 30km and 15km respectively to the primitive curve C of Figure 18 to convert, obtain not
With the transformation line under scale, the intersection point of primitive curve and bending transformation line is known as to be bent division points, connection bending division points obtain
The curved-ray tracing figure as shown in 19-a~19-d into Figure 19.
2) it is superimposed the bending nest relation determined under different scale, establishes bending hierarchical tree.
Analysis is laid out to the bending polygon of different levels, the ownership of each bending polygon is judged, establishes each
Curved bending hierarchical tree.Such as to above-mentioned curve C, take the bending polygon of adhesion transformation width L=50km, by each bending with
The bending of adhesion transformation L=200km is compared, such as Figure 20, through observation shows that: 3 division bending 3.1 and 3.2 of bending, bending
8 are split into bending 8.1 and 8.2, and bending 9 is split into bending 9.1 and 9.2, other bendings are not divided then.On above-mentioned determining curve not
The process of relationship is bent between same level to be identified by eye-observation, in the specific implementation process, can be by sentencing
The ownership of each bending polygon is realized in disconnected different levels.Detailed process is as follows:
The bending polygon that adhesion transformation width is L1 is taken, is laid out with width for the bending polygon of L2 (L2 < L1)
Analysis loops to determine the ownership of each bending polygon when width is L2.Assuming that polygon P2 be adhesion transformation width be L2 when
A certain bending polygon, polygon P1 be adhesion transformation width be L1 when a certain bending polygon, if polygon P2 belong to
In polygon P1, then for explanation in bending hierarchical tree, being bent node C2 corresponding to polygon P2 is that bending polygon P1 institute is right
Answer the child node of node C1.
3) invalid bending is deleted
Invalid bending is the leaf for being presented without the brotgher of node without bending obtained from division, in bending hierarchical tree
Node.To each curved hierarchical tree, looping to determine each layer from bottom to up has whether the leaf node of parents' node has fraternal knot
Point, if there is sibling, which retains；If deleting the node without sibling.One layer of search is continued up, is judged
Whether this layer of leaf node has parents' node, if nothing, terminates circulation；If so, then continuing to judge whether it has sibling ...
Until having traversed each layer of all leaf nodes.
Now illustrate the process for deleting leaf node of each layer without brother in bending hierarchical tree for being bent 2.Figure 21 is to delete
Except bending hierarchical tree corresponding to leaf node front curve 2 of each layer without brother, Figure 22 is after deleting each layer without the brotgher of node
The result figure of bending 2.
Primitive curve C is as shown in figure 23 to deserved flex layers time tree after deleting invalid bending.
The height of bending hierarchical tree determines that the nested number of bending, the degree of each node then illustrate corresponding to the node
Curved degree of crushing, the two numerical value can be used to measure bending level tree curve tortuosity.
4) tortuosity based on complexity (comentropy) theoretical measurement geographical line
The tortuosity of curve, also known as curve complexity, refer to come in every shape on curve, bending of different sizes is in different layers
It is mutually nested on secondary.Bending hierarchical tree can effectively describe the morphological feature of description curve, and a bending hierarchical tree is exactly one
Curve.Regard curve as a Generalized Sets, calculates the complexity of bending hierarchical tree, the complications of curve are indicated with this
Degree realizes the morphological feature of quantitative description curve.The basis of complicated dynamic behaviour is by all bending units for participating in calculating point
Class.In the calculating of this paper, two kinds of mode classifications are mainly used, first is that according to the size (quantizating index expression) of bending unit point
Class；Second is that the hierarchical classification based on bending hierarchical tree itself.So to the bending hierarchical tree complexity for describing curve tortuosity
Two kinds can be divided into, be size complexity and level complexity respectively.The song of geographical line is finally measured with compositive complexity
Folding degree.
(1) size complexity
Size complexity is the calculating based on bending unit, and each bending unit is regarded as to the basic element of constituent curve
It is i.e. individual, use curved quantizating index as the feature of individual.
Calculation based on bending unit is the composition for considering line for bending unit is unit, mainly utilizes each spy
The number of the bending unit possessed under value indicative is calculated.The problem of this calculation mainly illustrates is various sizes of
How many is bent.It is the Generalized Sets language representation of the calculation shown in table 4.Since the size of bending unit is basic
It is different from, so stringent, to calculate number according to specific numerical value nonsensical.Here it is counted using the method for classification
Number: it according to a certain attribute value (area, length, width) of all bending units, is divided according to a certain rule of specialty different
Attribute value section, each section are a classification.
4 Generalized Sets of table indicate curve
| Generalized Sets | Individual title | Mark name | The problem of distribution function will illustrate |
| Curve | Each bending | Each curved area | The bending of different area how many |
| Curve | Each bending | Each curved length | The bending of different length how many |
| Curve | Each bending | Each curved height | The bending of different height how many |
| Curve | Each bending | Each curved width | The bending of different in width how many |
By taking this Measure Indexes of area as an example, the calculation formula of complexity are as follows:
Wherein, n indicates the number of institute's facet product classification, niIndicate bending unit in each section how many, N is composition
The total number of the bending unit of curve.
According to the property of logarithmic function, the calculation formula of size complexity SC is formula seven:
Wherein, N is bent the sum of effective bending unit of hierarchical tree, niFor effective curved quantity in every one kind.Together
Sample, logarithmic function take different bottoms, and calculated complexity result is different.By taking the curve C in Fig. 7 as an example, it is complicated to calculate size
Degree, size complexity result are calculated with 10 the bottom of for.The specific size information of the bending unit of curve is as shown in table 5:
The bending unit attribute of 5 curve C of table
| Id | TreeName | Area | Perimeter | Baseline | Length | Radius | OlayR |
| 1 | 1 | 6135.29 | 471.31 | 75.34 | 395.98 | 200 | 0 |
| 2 | 2 | 7304.83 | 477.05 | 132.67 | 344.38 | 200 | 0 |
| 3 | 3 | 2323.95 | 302.15 | 88.83 | 213.33 | 200 | 0 |
| 4 | 4 | 30.41 | 50.43 | 24.90 | 25.53 | 200 | 0 |
| 5 | 5 | 1867.01 | 236.28 | 101.10 | 135.17 | 200 | 0 |
| 6 | 6 | 6500.34 | 579.97 | 74.82 | 505.15 | 200 | 0 |
| 7 | 7 | 988.07 | 147.90 | 43.77 | 104.14 | 200 | 0 |
| 8 | 8 | 2787.62 | 347.55 | 86.38 | 261.16 | 200 | 0 |
| 9 | 9 | 5219.08 | 431.02 | 126.85 | 304.17 | 200 | 0 |
| 10 | 10 | 2324.24 | 242.83 | 82.58 | 160.25 | 200 | 0 |
| 11 | 3.2 | 961.70 | 150.87 | 40.90 | 109.97 | 50 | 200 |
| 12 | 3.1 | 601.65 | 121.22 | 37.45 | 83.77 | 50 | 200 |
| 13 | 9.2 | 1745.74 | 182.80 | 55.43 | 127.37 | 50 | 200 |
| 14 | 9.1 | 1838.18 | 211.00 | 61.16 | 149.84 | 50 | 200 |
| 15 | 8.1 | 1548.95 | 192.77 | 39.97 | 152.80 | 50 | 200 |
| 16 | 8.2 | 788.26 | 148.59 | 45.56 | 103.03 | 50 | 200 |
| 17 | 2.2.2 | 1308.36 | 184.13 | 59.00 | 125.13 | 30 | 50 |
| 18 | 2.2.1 | 1092.67 | 156.96 | 46.79 | 110.17 | 30 | 50 |
| 19 | 1.1.1.1 | 459.41 | 112.48 | 37.27 | 75.21 | 15 | 30 |
| 20 | 1.1.1.2 | 103.30 | 76.01 | 34.01 | 42.00 | 15 | 30 |
| 21 | 1.1.1.3 | 672.62 | 116.45 | 31.50 | 84.95 | 15 | 30 |
| 22 | 6.1.1.1 | 157.76 | 71.41 | 25.66 | 45.74 | 15 | 30 |
| 23 | 6.1.1.2 | 209.58 | 72.33 | 22.83 | 49.50 | 15 | 30 |
| 24 | 6.1.1.3 | 820.77 | 113.11 | 17.68 | 95.43 | 15 | 30 |
| 25 | 6.1.1.4 | 429.63 | 89.26 | 19.82 | 69.45 | 15 | 30 |
| 26 | 6.1.1.5 | 693.95 | 119.70 | 25.06 | 94.64 | 15 | 30 |
| 27 | 6.1.1.6 | 178.77 | 78.24 | 29.65 | 48.58 | 15 | 30 |
In the experiment with computing of size complexity, mainly participates in calculating using three kinds of Measure Indexes herein, respectively be bent
Area, length and the base length of unit.These three types of indexs are divided into 10 classes in the way of equidistantly classifying, class interval is maximum
Value and 1/10th of the difference of minimum value.Classification results are as shown in table 6:
The classification of 6 quantizating index of table
| Classification | Areal extent | Number | Length range | Number | Width range | Number |
| 1 | 30.14—757.85 | 10 | 25.53—73.49 | 6 | 17.68——29.18 | 6 |
| 2 | 757.85—1485.29 | 6 | 73.49—121.25 | 9 | 29.18——40.68 | 6 |
| 3 | 1485.29—2212.73 | 4 | 121.25—169.14 | 6 | 40.68——52.18 | 4 |
| 4 | 2212.73—2940.17 | 3 | 169.14—217.00 | 1 | 52.18——63.68 | 3 |
| 5 | 2940.17—3667.61 | 0 | 217.00—264.86 | 1 | 63.68——75.18 | 1 |
| 6 | 3667.61—4395.05 | 0 | 264.86—312.72 | 1 | 75.18——86.68 | 3 |
| 7 | 4395.05—5122.49 | 0 | 312.72—360.58 | 1 | 86.68——98.18 | 1 |
| 8 | 5122.49—5849.93 | 1 | 360.58—408.44 | 1 | 98.18——109.68 | 1 |
| 9 | 5849.93—6577.37 | 2 | 408.44—456.30 | 0 | 109.68——121.18 | 0 |
| 10 | 6577.37—7304.83 | 1 | 456.30—505.15 | 1 | 121.18——132.67 | 2 |
According to formula seven, using the size complexity for the curve C that area is calculated as Measure Indexes are as follows:
Using the size complexity for the curve C that length is calculated as Measure Indexes are as follows:
SCL=27*log (27) -9*log (9) -6*log (1)=20.721,
Using the size complexity for the curve C that width is calculated as Measure Indexes are as follows:
SCW=27*log (27) -12*log (6) -9*log (9) -6*log (1)=23.436.
(2) level complexity
It is i.e. individual to regard each layer of hierarchical tree as a basic component units, and bending contained in each level
Number is value of statistical indicant.
This mode is the composition that curve is considered as unit of level, mainly utilizes bending included in each level
Number is to be calculated.Substantial this calculation is exactly to be classified using level, pays close attention to the composition of every class.The mistake of calculating
The problem of mainly illustrating in journey is exactly to be bent how many level of hierarchical tree, how many bending in each level is come anti-with this
Answer curve whether complicated.For theoretically, level is more, and curve is more complicated, and the more irregular curved quantity the more multiple in level
It is miscellaneous.It is as shown in table 7 that this mode is described with Generalized Sets language:
7 Generalized Sets of table indicate curve
| Generalized Sets | Individual title | Mark name | The problem of distribution function will illustrate |
| Curve | Each level | Curved quantity in each level | How many bending unit of different levels |
Its complicated dynamic behaviour formula are as follows:
Wherein, n indicates that the bending hierarchical tree shares how many a levels, niIndicate bending unit in each level how many
The number of bending unit in i.e. each result figure layer, N are the total numbers of the bending unit of constituent curve.Logarithmic function takes difference
Bottom, calculated result is different.
According to the property of logarithmic function, the calculation formula of level complexity LC is formula eight:
Wherein, N is the sum for being bent effective bending unit of hierarchical tree, and ni is effective curved number in every layer.
By formula it is found that logarithmic function takes different bottoms, calculated level complexity result is different.With the song in Figure 18
For line C, size complexity is calculated, size complexity result is calculated with 10 the bottom of for.For primitive curve C, the bending hierarchical tree
Five layers are shared, there is an effectively bending in first layer, there are 10 effectively bendings in the second layer, there are 6 effectively bendings in third layer,
There are 2 effectively bendings in 4th layer, there are 9 effectively bendings in layer 5, shares 28 effectively bendings.
According to formula eight, the level complexity of curve C are as follows:
LC=28*log (28) -10*log (10) -6*log (6) -2*log (2) -9*log (9)=16.661.
(3) compositive complexity
The tortuosity of geographical line, compositive complexity ZC are measured in terms of level with size two using compositive complexity
It can be defined as formula nine:
ZC=P1SCA+P2SCL+P3SCW+P4LC,
Wherein, Pi(i=1 ..., 4) respectively indicates weight shared by different types of complexity, and the sum of weight is 1.It is real
Border test when can design multiple groups weighted value, respectively obtain the compositive complexity of different curves, then empirically method determine compared with
For reasonable one group of weight, therefore the complexity representation method of available measurement geographical line.
To sum up, the embodiment of the present invention, which has the following beneficial effects:, is sequentially completed identification bending unit, the determining different rulers of superposition
The lower bending nest relation of degree simultaneously establishes bending hierarchical tree, deletes and be bent in vain and measure geographical line based on information entropy theory
The work of tortuosity is retouched using the carry out tortuosity of the compositive complexity that combines size complexity and level complexity
State, completely present curve part and whole tortuosity, while more comprehensively consider bending different levels between it is embedding
Set relationship overcomes the defect of the prior art, can preferably describe curve tortuosity, comprehensively reflects the form and knot of curve
Structure feature, influenced by length of curve it is small, make full use of bending hierarchical tree completely reflect bending between proximity relations and level spy
Property, and complexity is measured using information entropy theory, easily operated realization is of great significance to the research of geographical feature.
It should be noted that, in this document, relational terms such as first and second and the like are used merely to a reality
Body or operation are distinguished with another entity or operation, are deposited without necessarily requiring or implying between these entities or operation
In any actual relationship or order or sequence.Moreover, the terms "include", "comprise" or its any other variant are intended to
Non-exclusive inclusion, so that the process, method, article or equipment including a series of elements is not only wanted including those
Element, but also including other elements that are not explicitly listed, or further include for this process, method, article or equipment
Intrinsic element.In the absence of more restrictions, the element limited by sentence "including a ...", it is not excluded that
There is also other identical elements in process, method, article or equipment including the element.
The above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although with reference to the foregoing embodiments
Invention is explained in detail, those skilled in the art should understand that: it still can be to aforementioned each implementation
Technical solution documented by example is modified or equivalent replacement of some of the technical features；And these modification or
Replacement, the spirit and scope for technical solution of various embodiments of the present invention that it does not separate the essence of the corresponding technical solution.
Claims (7)
1. a kind of geographical line tortuosity measure based on comentropy, which comprises the following steps:
1) identify bending unit: the adhesion for carrying out different in width to curve converts, and the result that adhesion converts is folded with primitive curve
Add, obtain the bending polygon of different scale, connection bending division points are bent identification figure, by with original geographical line into
Row intersection operation obtains the bending under each scale, and calculates the quantizating index of each bending unit, is stored in association attributes domain
In；
2) it is superimposed the bending nest relation determined under different scale, establishes bending hierarchical tree: to the bending polygon of different levels
It is laid out analysis, the ownership of each bending polygon is judged, establishes each curved bending hierarchical tree；
3) it deletes invalid bending: deleting each layer of invalid bending, finally obtain the bending unit of each level；
4) ground that bending hierarchical tree represents the tortuosity based on information entropy theory measurement geographical line: is calculated using information entropy theory
Manage the tortuosity of curve；
Wherein, information entropy theory is used to calculate the method for the geographical line tortuosity that bending hierarchical tree represents as using size complexity
It spends with the compositive complexity of level complexity and measures the tortuosity of geographical line, the calculation formula of compositive complexity are as follows:
ZC=P1SCA+P2SCL+P3SCW+P4LC,
Wherein, Pi(i=1,2 ..., 4) weight shared by different types of complexity is respectively indicated, the sum of weight is 1；SCA
Size complexity for the curve being calculated using area as Measure Indexes；SCL is calculated by Measure Indexes of length
The size complexity of curve；SCW is the size complexity for the curve being calculated using width as Measure Indexes；LC is that level is complicated
Degree.
2. a kind of geographical line tortuosity measure based on comentropy according to claim 1, it is characterised in that: institute
Stating bending division points is primitive curve and the intersection point for being bent transformation line.
3. a kind of geographical line tortuosity measure based on comentropy according to claim 1, it is characterised in that: folded
The bending nest relation under determining different scale is added to realize by judging the ownership of each bending polygon in different levels, it will
Bending polygon under each scale is superimposed with the bending polygon under upper level large scale, determines returning for small scale polygon
Belong to, to obtain corresponding nest relation, determines the level of each bending unit, it is final to establish using primitive curve as root section
The bending hierarchical tree of point.
4. a kind of geographical line tortuosity measure based on comentropy according to claim 1, it is characterised in that: build
The method of vertical bending hierarchical tree is to loop to determine the leaf knot that each layer has parents' node from bottom to up to each curved hierarchical tree
Whether point has sibling, if there is sibling, which retains, if deleting the node without sibling；It continues up
One layer of search, judges whether this layer of leaf node has parents' node, if nothing, end loop, if so, then continuing to judge whether it has
Sibling, until having traversed each layer of all leaf nodes.
5. a kind of geographical line tortuosity measure based on comentropy according to claim 1, it is characterised in that: institute
It states and is bent into the direct bending from the bending succession of upper layer that non-upper layer bending division obtains in vain.
6. a kind of geographical line tortuosity measure based on comentropy according to claim 5, which is characterized in that institute
Stating SC is size complexity, using bending unit as basic unit in the calculating of the SC, calculation formula are as follows:
Wherein, N is the sum for being bent effective bending unit of hierarchical tree, niFor effective curved quantity in every one kind.
7. a kind of geographical line tortuosity measure based on comentropy according to claim 5, which is characterized in that institute
Stating LC is level complexity, with one layer of hierarchical tree for basic unit in the calculating of the LC, calculation formula are as follows:
Wherein, N is the sum for being bent effective bending unit of hierarchical tree, niFor effective curved quantity in every layer.
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