CN106055694A - Geographic curve tortuosity measuring method based on information entropy - Google Patents
Geographic curve tortuosity measuring method based on information entropy Download PDFInfo
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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 field, be specifically related to a kind of geographical line tortuosity based on comentropy
Measure.
Background technology
The tortuosity of geographical line is a kind of description method of geographical feature curve, and the geographical spy that curve itself is contained
Having levied important relationship, the research to geographical feature is significant, and conventional geographical feature describes method and describes the most not
Clearly, sentence as the tortuosity in coastline describes the misty idea such as multiplex " extremely tortuous ", " more tortuous ", " opposing straight "
Disconnected, lack clear and definite judge index, be highly detrimental to the determination of baselines of territorial sea type；Therefore, quantitative expression curve tortuosity tool
There is important using value.
Currently mainly use based on tortuosity index, calculate based on angular metric and the method such as FRACTAL DIMENSION is tortuous to geographical line
Measure.Tortuosity index is a quantizating index that can reflect line feature configuration, and tortuosity exponential number is more
Greatly, then curve is the most complicated, but tortuosity index can not reflect the tortuosity of complicated nested funiclar curve, it is impossible to comprehensively reflect song
The form of line；Angle value between straightway on curve is added by the tortuosity measure calculated based on angular metric, be added
Result represents the complexity of curve, but this method for expressing is affected by length of curve；Fractal dimension method is mainly studied not
The self-similarity of rule things, but fractal dimension is a statistic, and it is only capable of reflecting the overall condition of curve, and cannot be with
The bending unit correspondence that curve is concrete, FRACTAL DIMENSION is a characteristic of curve, can not obtain other of curve by FRACTAL DIMENSION
Architectural feature, all cannot react its tracing pattern and architectural feature for various length ground curve all sidedly.
Summary of the invention
(1) solve the technical problem that
The technical problem to be solved there is provided a kind of geographical line tortuosity tolerance side based on comentropy
Method, to solve the problems referred to above.
(2) technical scheme
For realizing object above, the present invention is achieved by the following technical programs: a kind of based on comentropy geographical bent
Line tortuosity measure, comprises the following steps:
1) bending unit is identified: curve is carried out the adhesion conversion of different in width, result adhesion converted and original song
Line superposition, obtains the bending polygon of different scale, connects bending division points and is bent identification figure, by geographical bent with original
Line carries out intersecting computing and obtains the bending under each yardstick, and calculates the quantizating index of each bending unit, being stored in relevant genus
In property territory；
2) the bending nest relation under superposition determines different scale, sets up bending hierarchical tree: the bending to different levels is many
Limit shape is laid out analyzing, it is judged that the polygonal ownership of each bending, sets up the bending hierarchical tree of each bending；
3) invalid bending is deleted: delete the invalid bending of each layer, finally give the bending unit of each level；
4) tortuosity based on information entropy theory tolerance geographical line: use information entropy theory to calculate bending hierarchical tree and represent
The tortuosity of geographical line.
Further, described bending division points is the intersection point of primitive curve and bending transformation line.
Further, the bending nest relation under superposition determines different scale is by judging that in different levels, each bending is many
The ownership of limit shape realizes, and is superposed with the bending polygon under upper level large scale by the bending polygon under each yardstick,
Determine the polygonal ownership of little yardstick, thus obtain corresponding nest relation, determine the level of each bending unit, finally build
The vertical bending hierarchical tree using primitive curve as root node.
Further, the method setting up bending hierarchical tree is the hierarchical tree to each bending, and cycle criterion is every from bottom to up
Whether one layer of leaf node having parents' node has sibling, if there being sibling, then this node retains, if without sibling,
Then delete this node；Continue up one layer of search, it is judged that whether this layer of leaf node has parents' node, if nothing, then end loop, if
Have, then continue to judge whether it has sibling, until having traveled through all leaf nodes of each layer.
Further, described invalid be bent into non-upper strata bending division obtain direct by upper strata bending inherit and come curved
Bent.
Further, information entropy theory is used to calculate the method for the geographical line tortuosity that bending hierarchical tree represents for using
The compositive complexity of size complexity and level complexity measures the tortuosity of geographical line, the computing formula of compositive complexity
For:
ZC=P1SCA+P2SCL+P3SCW+P4LC,
Wherein, represent that the weight shared by different types of complexity, weight sum are 1 respectively.
Further, described SC is size complexity, with bending unit as elementary cell in the calculating of described SC, calculates public affairs
Formula is:
Wherein, for bending the sum of effective bending unit of hierarchical tree, for the quantity of the effectively bending of each apoplexy due to endogenous wind.
Further, described LC is level complexity, with one layer of hierarchical tree as elementary cell in the calculating of described LC, and meter
Calculation formula is:
Wherein, for bending the sum of effective bending unit of hierarchical tree, for the quantity of the effectively bending in every layer.
(3) beneficial effect
The invention provides a kind of geographical line tortuosity measure based on comentropy, be sequentially completed identification bending single
Unit, superposition determine the bending nest relation under different scale and set up bending hierarchical tree, delete invalid bending and based on comentropy
The work of the tortuosity of theoretical tolerance geographical line, uses compositive complexity size complexity and level complexity combined
The description carrying out tortuosity, intactly present the part of curve and overall tortuosity, consider curved simultaneously the most all sidedly
Nest relation between bent different levels, overcomes the defect of prior art, can preferably describe curve tortuosity, the most instead
Reflect form and the architectural feature of curve, affected by length of curve little, make full use of bending hierarchical tree and completely reflect between bending
Proximity relations and level characteristic, and use information entropy theory to measure complexity, it is easy to operation realizes, and the research to geographical feature has
Significant.
Accompanying drawing explanation
Fig. 1 is present invention circle adhesion conversion exploded view；
Fig. 2 is areal shape change schematic diagram before and after adhesion of the present invention conversion；
The bending figure that Fig. 3 difference of the present invention conversion curve obtains；
Fig. 4 is the bending figure correspondence level tree graph that difference conversion curve of the present invention obtains；
Fig. 5 is that the present invention bends area, bending length and bending width indication figure；
Fig. 6 is the flow chart of the present invention；
Fig. 7 is the bending division points connection figure of primitive curve C of the present invention and different scale；
Fig. 8 is that to convert width be adhesion Transformation Graphs when 6 nautical miles to the present invention；
Fig. 9 is that to convert width be adhesion Transformation Graphs when 3.8 nautical miles to the present invention；
Figure 10 is the bending level tree graph that the present invention converts when width is 6 nautical miles and 3.8 nautical miles corresponding to adhesion Transformation Graphs；
Figure 11 is that the present invention deletes each layer of bending level tree graph without leaf node front curve 18 correspondence of brother；
Figure 12 is the bending level tree graph bending 18 correspondences after the present invention circulates the leaf node deleting each layer of nothing brother；
Figure 13 is that to convert width be adhesion Transformation Graphs when 1 nautical mile to the present invention；
Figure 14 is that to convert width be adhesion Transformation Graphs when 0.4 nautical mile to the present invention；
Figure 15 is the level tree graph that the present invention converts that when width is 1 nautical mile, adhesion Transformation Graphs is corresponding；
Figure 16 is the level tree graph that the present invention converts that when width is 0.4 nautical mile, adhesion Transformation Graphs is corresponding；
Figure 17 is the level that the present invention converts level tree graph interior joint 8 corresponding to adhesion Transformation Graphs 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 the bending superposition schematic diagram of the present invention；
Figure 21 is the bending level tree graph that the present invention deletes invalid bending front curve 2；
Figure 22 is that the present invention deletes the bending level tree graph bending 2 after invalid bending；
Figure 23 is that the present invention deletes the bending level tree graph of primitive curve C after invalid bending.
In figure:
1-a, artwork；1-b, shell adding convert；1-c, shell adding Transformation Graphs；1-d, conversion of casting off a skin；1-e, coloured picture blackening；1-f, slough off
Skin Transformation Graphs；1-g, stacking chart；
The figure unconverted circular arc circular arc of 180 degree (central angle be not more than) before and after 2-a, adhesion conversion；2-b, adhesion become
Change the circular arc (central angle circular arc more than 180 degree) that before and after's figure changes；2-c, straight line and circular arc composite figure；
3-A, primitive curve；3-B, primitive curve bending level tree graph；3-C, primitive curve press yardstick one adhesion Transformation Graphs；
3-D, primitive curve and press yardstick one adhesion conversion after stacking chart；3-E, primitive curve and press yardstick one adhesion conversion after stacking chart
Corresponding bending level tree graph；3-F, primitive curve press yardstick two adhesion Transformation Graphs；3-G, primitive curve and press yardstick two adhesion become
Change rear stacking chart；3-H, primitive curve with press yardstick two adhesion conversion after stacking chart corresponding bending level tree graph；3-I, original song
Yardstick three adhesion Transformation Graphs pressed by line；3-J, primitive curve and press yardstick three adhesion conversion after stacking chart；3-K, primitive curve and press
Stacking chart's correspondence bending level tree graph after yardstick three adhesion conversion；
Without the bending hierarchical tree corresponding for primitive curve 3-A of adhesion conversion in 4-A, Fig. 3；Primitive curve in 4-B, Fig. 3
The bending hierarchical tree that 3-A obtains after adhesion transformation line 3-B converts；In 4-C, Fig. 3, primitive curve 3-A is through adhesion transformation line 3-C
The bending hierarchical tree obtained after conversion；The flex layers that in 4-D, Fig. 3, primitive curve 3-A obtains after adhesion transformation line 3-D converts
Secondary tree.
7-a, primitive curve C；7-b, L are bending division points connection figure when 6 nautical miles；7-c, L are bending when 3.8 nautical miles
Division points connects figure；7-d, L are bending division points connection figure when 2 nautical miles；7-e, L are that bending division points when 1 nautical mile connects
Figure；7-f, L are bending division points connection figure when 0.4 nautical mile；
Bending level tree graph corresponding to adhesion Transformation Graphs when 9-a, L are 6 nautical miles；Adhesion conversion when 9-b, L are 3.8 nautical miles
Bending level tree graph corresponding to figure；
Without bending bending hierarchical tree corresponding to 18 after the leaf node of brother in 11-a, deletion the 4th layer；11-b, deletion the 3rd
In Ceng after the leaf node of nothing brother, bending bending hierarchical tree corresponding to 18；Without the leaf node of brother in 11-c, deletion the 2nd layer
After, bending bending hierarchical tree corresponding to 18；11-d, delete in the 1st layer the leaf node without brother after, curved corresponding to bending 18
Bent hierarchical tree；
19-a, Figure 18 primitive curve C adhesion width is the curved-ray tracing figure obtained during 200km；19-b, Figure 18 primitive curve
C adhesion width is the curved-ray tracing figure obtained during 50km；19-c, Figure 18 primitive curve C adhesion width is obtain during 30km curved
Bent identification is schemed；19-d, Figure 18 primitive curve C adhesion width is the curved-ray tracing figure obtained during 15km；
20-a, Figure 18 primitive curve C adhesion width is the bending superposition signal that the curved-ray tracing figure obtained during 200km is corresponding
Figure；20-b, Figure 18 primitive curve C adhesion width is the bending superposition schematic diagram that the curved-ray tracing figure obtained during 50km is corresponding.
Detailed description of the invention
For making the purpose of the embodiment of the present invention, technical scheme and advantage clearer, below in conjunction with the embodiment of the present invention,
Technical scheme in the embodiment of the present invention is clearly and completely described, it is clear that described embodiment is the present invention one
Divide embodiment rather than whole embodiments.Based on the embodiment in the present invention, those of ordinary skill in the art are not making
The every other embodiment obtained under creative work premise, broadly falls into the scope of protection of the invention.
Shown in Fig. 1～23, comprise the following steps:
1) bending unit is identified: curve is carried out the adhesion conversion of different in width, result adhesion converted and original song
Line superposition, obtains the bending polygon of different scale, connects bending division points and is bent identification figure, by geographical bent with original
Line carries out intersecting computing and obtains the bending under each yardstick, and calculates the quantizating index of each bending unit, being stored in relevant genus
In property territory；
2) the bending nest relation under superposition determines different scale, sets up bending hierarchical tree: the bending to different levels is many
Limit shape is laid out analyzing, it is judged that the polygonal ownership of each bending, sets up the bending hierarchical tree of each bending；
3) invalid bending is deleted: delete the invalid bending of each layer, finally give the bending unit of each level；
4) tortuosity based on information entropy theory tolerance geographical line: use information entropy theory to calculate bending hierarchical tree and represent
The tortuosity of geographical line.
Preferably, described bending division points is the intersection point of primitive curve and bending transformation line.
Preferably, the bending nest relation under superposition determines different scale is by judging that in different levels, each bending is polygon
The ownership of shape realizes, and is superposed, really with the bending polygon under upper level large scale by the bending polygon under each yardstick
The fixed polygonal ownership of little yardstick, thus obtain corresponding nest relation, determine the level of each bending unit, finally set up
Using primitive curve as the bending hierarchical tree of root node.
Preferably, the method setting up bending hierarchical tree is the hierarchical tree to each bending, and cycle criterion is each from bottom to up
Layer has whether the leaf node of parents' node has sibling, if there being sibling, then this node retains, if without sibling, then
Delete this node；Continue up one layer of search, it is judged that whether this layer of leaf node has parents' node, if nothing, then end loop, if
Have, then continue to judge whether it has sibling, until having traveled through all leaf nodes of each layer.
Preferably, described invalid be bent into non-upper strata bending division obtain direct by upper strata bending inherit and come curved
Bent.
Preferably, information entropy theory is used to calculate the method for the geographical line tortuosity that bending hierarchical tree represents for using chi
The compositive complexity of very little complexity and level complexity measures the tortuosity of geographical line, the computing formula of compositive complexity
For:
ZC=P1SCA+P2SCL+P3SCW+P4LC,
Wherein, represent that the weight shared by different types of complexity, weight sum are 1 respectively.
Preferably, described SC is size complexity, with bending unit as elementary cell in the calculating of described SC, and computing formula
For:
Wherein, for bending the sum of effective bending unit of hierarchical tree, for the quantity of the effectively bending of each apoplexy due to endogenous wind.
Preferably, described LC is level complexity, with one layer of hierarchical tree as elementary cell in the calculating of described LC, calculates
Formula is:
Wherein, for bending the sum of effective bending unit of hierarchical tree, for the quantity of the effectively bending in every layer.
For the sake of ease of implementation, adhesion conversion, bending hierarchical tree, the bending unit amount that the present invention relates to first is introduced
Change index and comentropy (complexity):
(1) adhesion conversion
Relief area based on map algebra conversion can obtain point, line, surface that buffer width is L and multiple easily and quickly
The relief area of miscellaneous entity, and according to the difference of range conversion, divided into internal buffer conversion and outer relief area converts.
Specific algorithm is: directly entity is implemented range conversion (inside and outside) first by respective distance yardstick, obtains full sky
Between the distance of each point；Then take all pixels that distance value is 1～L (L is relief area width), extract relief area (inside and outside).This
Time outer relief area is referred to as shell, internal buffer is referred to as skin.Entity adds the process of outer relief area and converts for " shell adding ", and entity goes interior slow
The process rushing district converts for " casting off a skin ".
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) represent that the shell adding implementing L converts, B0(1, L) show to take distance value from 1 to
The picture dot of L, i.e. width are the relief area of L；XB0(L) it is shell, refers to that entity appearance is the shell of L adjacent to thickness.
Transform definition of casting off a skin figure X is formula two:
XKI(L)=X XBI(l, L)=X-XBI(L),
In formula, KI(L) represent that the peeling implementing L converts, XBI(L) it is skin, refers to that solid object surface thickness is the aspect of L.
Utilize shell adding and conversion of casting off a skin, adhesion conversion can be obtained further, adhesion conversion definable such as formula three:
X·L(l1, l2)=XKO(l1)·KI(l2),
In formula, l1, l2For suitable positive integer or 0, first adhesion conversion carries out width to figure is l1Shell adding conversion,
Then, then it being carried out width is l2Conversion of casting off a skin；Generally, it is equal with width of casting off a skin to take shell adding width, even l1=
l2, and it is referred to as adhesion width 1.
The adhesion conversion conformal effect to areal shape, has characteristics that
A, to the basic standard figure such as circle, straight line, there is the characteristic keeping grown form constant, i.e. " keep tie ", " protecting convex "
Characteristic.
As a example by the test pattern circle of curve, such as Fig. 1, pair radius is the circle of r, first carries out the shell adding conversion that width is L,
Figure after conversion is still for round, and its radius is R=r+L, then the figure after conversion is carried out the conversion of casting off a skin that width is L, then
Figure 1-f after conversion of casting off a skin is overlapped with artwork 1-a, obtains stacking chart 1-g, obtain 1-a with 1-f and be completely superposed, this
Illustrate that circle figure before and after adhesion converts keeps constant.
B, for concave, convex, Straight Combination figure, there is " protecting convex ", " keeping tie ", " filling out recessed " characteristic.
In adhesion converts, circular arc intensity of variation of figure before and after conversion depends on the central angle of circular arc, when circular arc
When central angle is not more than 180 ° (being presented as convex), before and after adhesion conversion, figure keeps constant, embodies and protects convex morphological character, as
Shown in Fig. 2-a, when central angle is more than 180 °, adhesion conversion performance subtracts recessed morphological character, as shown in Fig. 2-b；Circular arc is with straight
Line composite figure graphic change degree in adhesion converts is relevant with both angles, when angle is more than 180 °, and straight line and circular arc
Forming protuberance, before and after adhesion conversion, figure is constant, and when angle is less than 180 °, straight line forms recess with circular arc, along with adhesion becomes
Changing width to increase, recess gradually filled and led up, as shown in fig. 2-c, demonstrate further adhesion conversion protect convex, keep tie, fill out recessed guarantor
Shape characteristic.
C, " filling out recessed " degree are controlled.
Metamorphosis characteristic according to adhesion conversion: if adhesion conversion width is L, then width (bending width definition herein
For the recessed width of maximum of this bending, it is designated as D) will gradually smooth less than the bow of 2L, and bending width is the least, conversion width is more
Greatly, smooth effect is the most obvious, and meanwhile, the widest bending will be filled and led up, and the relation of CRITICAL CHANGES width L' wide D recessed with maximum is full
Foot formula four:
This also means that, go out CRITICAL CHANGES width L' with the maximum recessed wide D inverse of circular arc, then figure is carried out width L' glue
Even conversion, the result of conversion will fill and lead up all recesses in figure.Such as table 1, pair radius R=20 pixel, the circular arc of different central angle
Carrying out width is L adhesion conversion, takes the transformation results in the case of L ＜ L', L=L' and L ＞ L' tri-kinds respectively, it is known that, adhesion becomes
Changing rear figure smoothness to increase, guarantor is convex for it, keep tie, fill out recessed trend increases with L and aggravates；When adhesion conversion width L increases to L=
L', if proceeding the adhesion conversion that width is D (D ＞ L), figure no longer changes.
Table 1 radius R=20 pixel, the circular arc adhesion change situation of different central angles
Adhesion converts has " protecting convex ", " keeping tie ", the characteristic of " filling out recessed " in the holding of areal shape, and " filling out recessed "
The value of the width L that degree can be converted by adhesion controls, and utilizes these characteristics, can be never real in ipsilateral and different levels
The automatic identification of existing curved unit.
(2) bending hierarchical tree
Bending hierarchical tree, refers to that adhesion based on different scale conversion identifies bending, bending under 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 a layer of hierarchical tree, and each bending represents a node of this layer.
Below by as a example by the standard type circular arc of bending, illustrate to bend the basic conception of hierarchical tree.Such as 3-in Fig. 3
A, curve L are formed by four layers of different size of bending nesting, and maximum bending 1 (representing curve L) is the most nested
1a, 1b, 1c tri-bending, and nested successively 1a.1,1a.2,1a.3,1b.1,1b.2,1c.1, the 1c.2 seven of these three bending
Individual bending, 1c.2a, 1c.2b two bending that bending 1c.2 is nested again.Curve L carries out the adhesion under three different scales become
Changing, the transformation line obtained is followed successively by 3-B, 3-C and 3-D in Fig. 3, and transformation line is followed successively by Fig. 3 with the stacking chart of primitive curve
3-E, 3-F and 3-G, a layer in each adhesion change of scale correspondence bending hierarchical tree, thus set up under each yardstick corresponding
Bending hierarchical tree.Such as 4-B, 4-C and 4-D of Fig. 4, root node 1 represents curve L；Node 1 has three child nodes, is followed successively by knot
Point 1a, 1b, 1c, represent 1a, 1b, 1c tri-bending of curve L nesting successively；Node 1a, 1b, 1c have respectively 3 child nodes, 2
Individual child node and 2 child nodes, illustrate to bend 3 bendings of 1a, 1b, 1c nesting successively, 2 bendings and 2 bendings；Class according to this
Push away ....Finally, the leaf node of tree represents lower minimum bend unit that can identify of a certain adhesion change of scale.
In bending hierarchical tree, the corresponding node of each bending unit in curve, the structure of hierarchical tree reflects curved
Topological property between song, and the quantizating index of bending unit can be stored in the corresponding node of bending hierarchical tree.So,
Just can express the topological property bending nesting in one section of curve with a bending hierarchical tree, meanwhile, also can describe each curved
The size and form of Qu Danyuan.It is to say, the complications of one section of curve can be described with a bending hierarchical tree.This bending level
Tree describes the ability of one section of curve tortuosity and is shown in Table 2:
Table 2 bends level tree table and reaches the ability of curve tortuosity
(3) bending unit quantizating index
Bending unit is the minimum unit of constituent curve, should be a bit of segmental arc, for convenience of right
The tolerance of its various indexs, substitutes line with face in bending hierarchical tree, and the bending polygon identified with adhesion conversion represents respectively
Individual bending unit.Existing bending unit quantizating index mainly includes bending unit area, length, width etc..Introduce in detail below
The quantizating index of bending unit.
A. bending area S
Bending area S refers generally to bend the connected straight line of Origin And Destination and the enclosed area of a polygon of bending section, as straight in Fig. 5
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 directly be obtained by attribute evaluator computational length in ArcGIS.
C. bending width W
In the case of as, bending width W is defined as the air line distance between this bending Origin And Destination, such as AB or BC in Fig. 5
Between air line distance.Bending width based on adhesion conversion still uses this definition, but the determination of bending end points be based on
Adhesion converts comprehensive line.Concrete operations are: in the step identifying bending, be bent polygon, to bending polygon girth
Ask difference can be bent width with bending length.
(4) complexity and comentropy
Comentropy is the tolerance of degree useful to information.In earth science research, comentropy is research characteristic and the having of distribution
Effect means, and complexity is the description to composition, two seem different concepts and but have the closest contact.Herein with multiple
Miscellaneous degree measures the tortuosity of curve, carrys out the form of quantitative description curve with this.
Entropy can measure a certain phenomenon or event in spatial concentration or scattered degree, is probabilistic science appellation.
Entropy is tissue degree and the tolerance of order degree of system, can be used to characterize the uncertainty degree of system, removes the flat of redundancy
All information is comentropy.Comentropy can be used to the size of metric amount, describes the useful degree of information.Pass through comentropy
Can effectively realize the quantization of information, its concrete computing formula such as formula five:
Wherein, P in formulaiIt it is event xiProbability of occurrence, n represents that event one has n, and logarithmic function takes the different ends,
The entropy result calculated is different.
Comentropy is widely used, but the theory of entropy is abstract hard to understand in science category.Zhang Xuewen is at Generalized Sets
Theory is transformed the most popular mysterious entropy concept and Entropy principle, expands again its application simultaneously.
He substitutes entropy from the angle complexity of composition opinion, it is proposed that the concept of Generalized Sets and complexity law.Warp
Crossing transformation, information entropy theory is more easy-to-understand, more easily applies.
Composition opinion, by all of composition problem vague generalization, is asked with the composition of unified model and law study different field
Topic.Wherein, Generalized Sets is used to study the mathematical model of unified component law.Set language may be used for qualitative analysis,
Generalized Sets language then may be used for quantitative analysis.Set is things overall with special properties, mainly closes in set
Note which the most different units have.And Generalized Sets not only to specify this difference, common point to be paid close attention to: by altogether
Property by element classification, the element of the most every apoplexy due to endogenous wind is respectively arranged with how many.If one totally can be divided into the individuality that multiple status is identical,
And each individuality has the property value determined, then this is totally known as Generalized Sets.Generalized Sets has been possible not only to one
Attribute, can also have many attribute simultaneously, be known as multidimensional Generalized Sets.The Generalized Sets that main research is one-dimensional.For
Describe Generalized Sets accurately, need to introduce two new concepts, be i.e. mark and individual.Mark refers in set the most different
Element, and individuality refer to the kind belonging to element, individuality be composition set fundamental.Mark is used for describing difference, individual
Body then stresses to illustrate that between each key element, status is identical.
Generalized Sets is a kind of mathematical model, so it is the most corresponding to have a distribution function.Function herein is with universal
Function in the mathematics of meaning is different, and it can be an empirical equation, and main explanation is exactly the problem formed.A kind of
Composition, it is simply that find that an objective law, every kind of composition can use the incompatible description of Generalized Set, so each Generalized Sets
Distribution function is exactly a rule.Specifying each concrete Generalized Sets is exactly a kind of composition, finds an objective law,
Obtain a distribution function the most exactly.Table 3 show the example of some Generalized Sets:
Table 3 Generalized Sets example explanation
| Generalized Sets | Individual title | Mark name | The problem that distribution function is to be illustrated |
| Population | Everyone | The age of people | The people of all ages and classes is respectively arranged with how many |
| Mountain | Every mountain | The height above sea level on mountain | The mountain of Different Altitude is respectively arranged with how many |
| Lake | Each lake | The area in lake | The lake of different area is respectively arranged with how many |
| Soil | Every square kilometre of soil | Land type | Different types of territory is respectively arranged with how many |
| River | Mei Duan branch | The length of branch | The branch of different length has how many |
Complexity can describe the composition situation of Generalized Sets, reacts its internal state, the computing formula of complexity such as formula
6:
In formula, n represents the number of value of statistical indicant, i.e. has how many classes；niRepresent quantity individual in every kind of value of statistical indicant, i.e.
The element number of every apoplexy due to endogenous wind；N represents individual total amount.Each Generalized Sets has distinctive complexity itself, complexity
Minima is 0, and now the value of all elements is the most identical, only a classification.By complicated dynamic behaviour formula it can be seen that complexity
Value relevant with the end of logarithmic function used when calculating, the end of logarithm, is different, and the complexity value tried to achieve is the most different.
Individual variation in Generalized Sets is the biggest, and its complexity is the biggest.When the feature of each individuality is identical the most not
There are differences thing, complexity is zero.The difference being expressed as value of statistical indicant with the language of Generalized Sets is the biggest, and complexity value is the biggest；
Value of statistical indicant is identical, then complexity is zero.Popular understanding, forms the most complicated, and complexity is the biggest.
Comentropy represents uncertain, and complexity represents abundant degree, and the two has certain relation.Comentropy is from random
The angle analysis things of test, finally gives the uncertainty of result；Complexity is the angle analysis things from inherent difference,
The performance in Generalized Sets of this species diversity is to there is different values of statistical indicant, and finally give is the abundant degree of things, i.e. should
What kind of Generalized Sets be made up of.Analyze computing formula one and the computing formula two of complexity, the wherein P of comentropyi=ni/ N,
This relation is brought in the computing formula two of complexity, and combines formula one, the right of comentropy and complexity can be obtained
Should be related to: C=NH.From this relational expression, complexity and comentropy present positive correlation trend, and complexity is the biggest, comentropy
The biggest, i.e. form the most complicated, final result is the most uncertain.Just because of proportional relationship therebetween, about comentropy very
Many knowledge are included into the concept of complexity the most naturally[63].Can also conclude that why have not according to this relation
Determining that degree is because one Generalized Sets of objective reality and has complexity, complicated just because of composition just result in result not
Definitiveness.
Embodiment 1:
Describing in detail below in conjunction with accompanying drawing 6 and embodiment uses bending hierarchical tree to carry out curve song in technical solution of the present invention
Folding degree describes method, and for the curve C shown in 7-a in Fig. 7, the process of setting up in detail of bending hierarchical tree is as follows:
1) convert march line generalization based on adhesion, be bent polygon；
To primitive curve C implement adhesion conversion, obtain curve adhesion transformation line (be divided into internal conversion line and outside thread-changing,
The most only selecting outer transformation line to illustrate, internal conversion line is similar), and build bending polygon with primitive curve C.
Specifically, primitive curve C implementing width respectively is 6 nautical miles, 3.8 nautical miles, 2 nautical miles, 1 nautical mile and 0.4 nautical mile
Adhesion converts, and obtains the transformation line under different scale, is referred to as bending division points by the intersection point of primitive curve with bending transformation line, even
Connect bending division points and obtain the curved-ray tracing figure shown in Fig. 7.
Bending division points line is built bending polygon respectively with curve C, to convert as a example by width is 6 nautical miles, permissible
Obtain 18 bending polygons as shown in Figure 8, corresponding 18 bending units (numbered 1-18).
2) Overlap Analysis, it is judged that bend polygonal ownership；
It is laid out analyzing to the bending polygon of different levels, it is judged that the polygonal ownership of each bending, sets up each
The bending hierarchical tree of bending.Take adhesion conversion width L=3.8 bending polygon in the sea, each bending is one adjacent with upper
The bending of large scale adhesion conversion (L=6 in the sea) compares, and such as Fig. 9, through observation shows that: bending 18 be split into three curved
Song, respectively bending 18.1,18.2,18.3, bending 8 simultaneously is split into two bendings, is respectively bending 8.1 and 8.2, and other are curved
Qu Ze does not divides.
Above-mentioned determine that the process bending relation on curve between different levels is identified by eye-observation, at tool
In body implementation process, can be by judging that in different levels, each polygonal ownership of bending realizes.
Detailed process is as follows, takes the bending polygon that adhesion conversion width is L1, with the bending that width is L2 (L2 ＜ L1)
Polygon is laid out analyzing, and when cycle criterion width is L2, each bends polygonal ownership.Assume that polygon P2 is adhesion
A certain bending polygon when conversion width is L2, polygon P1 is a certain bending polygon that adhesion converts when width is L1,
If polygon P2 belongs to polygon P1, then illustrate that, in bending hierarchical tree, bending node C2 corresponding to polygon P2 is curved
The child node of node C1 corresponding to bent polygon P1.The process circulation of above-mentioned judgement bending polygon ownership performs, until all
Bending all travels through complete.
3) hierarchical tree that under out to out, each bending is corresponding is set up；
In order to clearly indicate the relation between a certain node and its child node, it is assumed that labelling one node is 1, if it only has one
Individual child node, is generally referenced as 1.1；If it has multiple child node (being set to n), be labeled as 1.1 the most successively, 1.2,1.3 ...,
1.n；If 1.n also has multiple child node (being set to m), it is labeled as 1.n.1,1.n.2,1.n.3 ... 1.n.m the most successively.
According to 2) in judge the method that polygon belong to, to convert width L=6 nautical mile, 3.8 nautical miles, 2 nautical miles, 1 nautical mile and
Identical processing procedure is implemented in bending under 0.4 nautical mile, can obtain the hierarchical tree that each bending is corresponding, such as table 3:
The bending hierarchical tree of table 3 different conversion width
In bending hierarchical tree, the determination of each node parents' node, depend on the ownership that this node correspondence bends.If knot
The corresponding bending 18.1 of point 18.1, is overlapped bending corresponding to bending 18.1 and last layer node, it is clear that bend 18.1 and belong to
In bending 18, then parents' node of node 18.1 is node 18, such as 9-a and 9-b in Figure 10.Additionally, in bending hierarchical tree
The quantizating index of all corresponding bending unit of the attribute of each node.
4) delete the leaf node without brother in each layer, set up the bending hierarchical tree of whole curve；
Hierarchical tree to each bending, each layer of cycle criterion from bottom to up have parents' node leaf node whether have brother
Younger brother's node, if there being sibling, then this node retains；If without sibling, then delete this node.Continue up one layer of search,
Judge whether this layer of leaf node has parents' node, if nothing, then end loop；If having, then continue to judge whether it has brother's knot
Point ... until having traveled through all leaf nodes of each layer.
The each layer of process without the leaf node of brother during now bending hierarchical tree is deleted in explanation as a example by bending 18.Figure 11 is for deleting
Before each layer of leaf node without brother, bending bending hierarchical tree corresponding to 18, from the beginning of bending hierarchical tree the 4th layer, under
The leaf node that supreme traversal is each layer, it is judged that whether it has sibling.Observe the leaf knot bending hierarchical tree the 4th layer in Figure 11
Point, the numbering of its node all ends up with Arabic numerals " 1 ", shows that all leaf nodes of this layer, all without sibling, need to be deleted
Remove, the result obtained such as the 11-a in Figure 12；Continue up the leaf node in cyclic search the 3rd layer, it is known that have two nodes
Numbering is not to end up with Arabic numerals " 1 ", and the two node is respectively 18.2.1.2 and 18.2.3.2, deletes the two node
Last figure place of numbering, obtains node (i.e. parents' node) 18.2.1 and 18.2.3 of the 2nd layer, it may be determined that the two node
Under child node (node 18.2.1.1,18.2.1.2 and 18.2.3.1 on i.e. the 3rd layer, 18.2.3.2) have sibling, no
Need to delete；Other leaf nodes on 3rd layer, without sibling, are implemented to delete node operation, the result obtained such as the 11-in Figure 12
b；Continue up all leaf nodes of search spread the 2nd layer, use identical determination methods to delete the leaf node without brother
And 18.3.1, the result obtained such as the 11-c in Figure 12 18.1.1；Continue up all leaf nodes of search spread the 1st layer, leaf
Node 18.1 and 18.3 all has sibling, is not required to delete；Without leaf node in 0th layer, it is not required to judge.So far, bending hierarchical tree
In the leaf node of each layer all traveled through, the operation that the leaf node without brother is described to delete in each layer is finished, traversal
The hierarchical tree corresponding to bending 18 after completing is as shown in the 11-d in Figure 12.Table 4 is searching loop each bending hierarchical tree, deletes
Except each layer without the result after the leaf node of brother.
Finally, 18 bendings to numbered 1-18 increase parents node C (being root node C), obtain primitive curve C's
Bending hierarchical tree, such as Figure 16～17.Certainly, each node in bending hierarchical tree has common attribute bending unit
Quantizating index, to describe the size and form characteristic of bending unit itself.
It is true that the adhesion conversion under arbitrary yardstick could set up the bending hierarchical tree that height is 1.Such as Fig. 8, to original
Curve C carries out adhesion conversion, and its width L=6 in the sea, then produces 18 bendings, and these bendings are bending the same of hierarchical tree
Layer, obtaining height as shown in Fig. 9-a is the bending hierarchical tree of 1.If continue to curve C implement width less than 6 nautical miles once or
Repeatedly adhesion conversion, then can set up the height bending hierarchical tree not less than 1, such as Fig. 9-b and Figure 15, Figure 16 and Figure 17.Adhesion
Number of transitions and the selection of conversion width, determine height and the degree of each node of bending hierarchical tree.The height of bending hierarchical tree
Degree determines the number of times that bending is nested；The degree of each node then illustrates the degree of crushing of the corresponding bending of this node.The two
Numerical value can be as one of bending hierarchical tree performance describing curve tortuosity ability.
The hierarchical tree in each bending hierarchical tree after the leaf node of each layer of nothing brother deleted by table 4
Bending hierarchical tree is expression based on flex layers aggregated(particle) structure, bends based on adhesion alternative approach identification, can be complete
Reflection bending between proximity relations and level characteristic.In structure tree, between same layer neighborhood of nodes, there is proximity relations；
The a certain node of n-th layer and parents' node of N-1 layer have hierarchical relationship, describe the nested structure of bending.Such as Fig. 9-a,
Node 1 is adjacent with 2, and its corresponding bending has proximity relations；Such as Fig. 9-b, node 8.1,8.2 and node 8, node 18.1,18.2,
Having hierarchical relationship between 18.3 and node 18, the bending of its correspondence embodies the nested structure between bending.
(1) bending of same level；
As a example by node 8, node 12 and node 18, illustrate to bend hierarchical tree and describe the ability of curve tortuosity:
First, from Figure 16～17 it can be seen that the height of node 8, node 12 and the bending hierarchical tree corresponding to node 18
Equal, it is 4, for three trees that node 1-18 camber is maximum, shows the curved section corresponding to these three node bends embedding
The number of times of set is most, for relative complex bending.This 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, shows 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 yardstick.
Again, the difference of the tortuosity of curved section 8, curved section 12 and curved section 18 can be by the son corresponding to these three node
The difference of tree is weighed.Such as, a tree (i.e. the degree of node) of subtree, the degree of depth (number of times that bending is nested) of subtree, tree node
The harmony of division, the difference etc. of quantizating index of node.We can tentatively judge, node 8 is node 12 compared with node 18
Complexity, the number (7) being on the one hand because the total node of node 12 is much smaller than node 8 (16) and node 18 (13), on the other hand can
Judge from a number for its subtree, it is also possible to compare the difference etc. of its subtree.
It is then possible to the harmony of the harmonious judgment curves tortuosity according to tree node division.To node 8 and node
18, it is clear that node 18 divides and more equalizes, and this can use the degree (or averaging) of its subtree corresponding to each layer of node to weigh.
It addition, there is proximity relations between the neighborhood of nodes of same layer, such as node 8.1 and node 8.2.
(2) bending of different levels；
First, the difference of bending node place level shows that bending unit is different at the nested number of times of whole piece curve.Such as,
In Figure 16～17, node 8.1 and node 8.1.2.1 place level are respectively 1 and 3, and corresponding to node 8, the height of hierarchical tree is
4, illustrate that bending 8.1 is 3 (height of tree and the differences of place level) at the nested number of times of whole piece curve；Bending 8.1.2.1's is embedding
Set number of times is 1.This is consistent with the result in Figure 16～17.
Secondly, the nest relation before different layers bending can be by judging whether it is that father-child node determines.Such as,
The child node of node 18 has three, and respectively 18.1,18.2,18.3, illustrate to bend three bendings of 18 nestings, be respectively
18.1,18.2 and 18.3.
In a word, the tortuosity of a corresponding one section of curve of bending hierarchical tree, it both can describe the big of bending unit itself
Little morphological characteristic, it is also possible to describe the topological property between bending unit.
Embodiment 2:
Technical solution of the present invention is described in detail, for the curve C shown in Figure 18, bending below in conjunction with accompanying drawing 6 and embodiment
The process of setting up in detail of hierarchical tree is as follows:
1) bending unit is identified.
The primitive curve C of Figure 18 is implemented the adhesion conversion that width is 200km, 50km, 30km and 15km respectively, obtains not
With the transformation line under yardstick, the intersection point of primitive curve with bending transformation line is referred to as bending division points, connects bending division points and obtain
Curved-ray tracing figure as shown in 19-a～19-d in Figure 19.
2) the bending nest relation under superposition determines different scale, sets up bending hierarchical tree.
It is laid out analyzing to the bending polygon of different levels, it is judged that the polygonal ownership of each bending, sets up each
The bending hierarchical tree of bending.As to above-mentioned curve C, take the bending polygon of adhesion conversion width L=50km, by each bending with
The bending of adhesion conversion L=200km compares, and such as Figure 20, through observation shows that: bending 3 division bending 3.1 and 3.2, bending
8 are split into bending 8.1 and 8.2, and bending 9 is split into bending 9.1 and 9.2, and other bendings are not divided.Above-mentioned determine on curve not
The process bending relation between same level is identified by eye-observation, in specific implementation process, and can be by sentencing
In disconnected different levels, each polygonal ownership of bending realizes.Detailed process is as follows:
Take the bending polygon that adhesion conversion width is L1, be laid out with the bending polygon that width is L2 (L2 < L1)
Analyzing, when cycle criterion width is L2, each bends polygonal ownership.Assume that polygon P2 is that adhesion conversion width is when being L2
A certain bending polygon, polygon P1 is the adhesion conversion width a certain bending polygon when being L1, if polygon P2 ownership
In polygon P1, then illustrating in bending hierarchical tree, bending 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 bending obtained without division, the leaf being presented without the brotgher of node in bending hierarchical tree
Node.Hierarchical tree to each bending, each layer of cycle criterion from bottom to up has whether the leaf node of parents' node has brother's knot
Point, if there being sibling, then this node retains；If without sibling, then delete this node.Continue up one layer of search, it is judged that
Whether this layer of leaf node has parents' node, if nothing, then terminates circulation；If having, then continue to judge whether it has sibling ...
Until having traveled through all leaf nodes of each layer.
The each layer of process without the leaf node of brother during now bending hierarchical tree is deleted in explanation as a example by bending 2.Figure 21 is for deleting
Except each layer without brother leaf node front curve 2 corresponding to bending hierarchical tree, Figure 22 for delete each layer without the brotgher of node after
The result figure of bending 2.
After deleting invalid bending, primitive curve C is to deserved flex layers time tree as shown in figure 23.
The height of bending hierarchical tree determines the number of times that bending is nested, and the degree of each node then illustrates corresponding to this node
The degree of crushing of bending, the two numerical value can be used to tolerance bending level tree curve tortuosity.
4) tortuosity based on complexity (comentropy) theoretical tolerance geographical line
The tortuosity of curve, the bending also known as curve complexity, refer to come in every shape on curve, varying in size is at different layers
Mutually nested on secondary.Bending hierarchical tree can effectively describe the morphological characteristic of curve, and a bending hierarchical tree is exactly one
Bar curve.Curve is regarded as a Generalized Sets, calculates the complexity of bending hierarchical tree, represent the complications of curve with this
Degree, it is achieved the quantitative morphological characteristic describing curve.The basis of complicated dynamic behaviour is to be divided by all bending units participating in calculating
Class.In calculating herein, two kinds of mode classifications of main employing, one is the size (quantizating index represents) point according to bending unit
Class；Two is hierarchical classification based on bending hierarchical tree itself.So, in order to describe the bending hierarchical tree complexity of curve tortuosity
Two kinds can be divided into, be size complexity and level complexity respectively.Final compositive complexity measures the song of geographical line
Folding degree.
(1) size complexity
Size complexity is calculating based on bending unit, and each bending unit is regarded as the basic element of constituent curve
I.e. individual, with the quantizating index of bending as individual feature.
Calculation based on bending unit is to be the composition that unit considers line by bending unit, mainly utilizes each spy
The number of the bending unit being had under value indicative calculates.The problem that this calculation mainly illustrates is various sizes of
Bending has how many.The Generalized Sets language representation of this calculation it is shown in table 4.Owing to the size of bending unit is basic
Being different from, so strict, to calculate number according to concrete numerical value nonsensical.Here the method using classification is added up
Number: according to a certain property value (area, length, width) of all bending units, divide different according to a certain rule of specialty
Property value is interval, and each interval is a classification.
Table 4 Generalized Sets represents curve
| Generalized Sets | Individual title | Mark name | The problem that distribution function is to be illustrated |
| Curve | Each bending | The area of each bending | The bending of different area has how many |
| Curve | Each bending | The length of each bending | The bending of different length has how many |
| Curve | Each bending | The height of each bending | The bending of differing heights has how many |
| Curve | Each bending | The width of each bending | The bending of different in width has how many |
As a example by this metric of area, the computing formula of complexity is:
Wherein, n represents that institute's facet amasss the number of classification, niRepresenting the bending unit in each interval has how many, N is composition
Total number of the bending unit of curve.
According to the character of logarithmic function, the computing formula of size complexity SC is formula seven:
Wherein, the sum of effective bending unit of N bending hierarchical tree, niQuantity for the effectively bending of each apoplexy due to endogenous wind.With
Sample, logarithmic function takes the different ends, and the complexity result calculated is different.As a example by curve C in Fig. 7, calculate size complicated
Degree, size complexity result calculates with 10 the end of for.The concrete dimension information of the bending unit of curve is as shown in table 5:
The bending unit attribute of table 5 curve C
| 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, main three kinds of metric of use participate in calculating, and are respectively bending
The area of unit, length and base length.By the mode of equidistantly classification, this three classes index is divided into 10 classes, and class interval is maximum
/ 10th of the difference of value and minima.Classification results is as shown in table 6:
Table 6 quantizating index is classified
| 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, with the size complexity that area is metric calculated curve C it is:
SCA=27*log (27)-10*log (10)-6*log (6)-4*log (4)-3*log (3)-2*log (2)
=19.536,
With the size complexity of a length of metric calculated curve C it is:
SCL=27*log (27)-9*log (9)-6*log (1)=20.721,
With the size complexity that width is metric calculated curve C it is:
SCW=27*log (27)-12*log (6)-9*log (9)-6*log (1)=23.436.
(2) level complexity
Each layer of hierarchical tree is regarded as a basic component units i.e. individuality, and bending contained in each level is individual
Number is value of statistical indicant.
This mode is to consider the composition of curve in units of level, mainly utilizes the bending included in each level
Number calculates.The most this calculation utilizes level to classify exactly, pays close attention to the composition of every class.The mistake calculated
In journey, the problem of main explanation bends hierarchical tree exactly how many levels, has how many bendings in each level, comes anti-with this
Answer curve the most complicated.For in theory, level is the most, and curve is the most complicated, and in level, the quantity of bending is the most uneven more multiple
Miscellaneous.With Generalized Sets language, this mode is described as shown in table 7:
Table 7 Generalized Sets represents curve
| Generalized Sets | Individual title | Mark name | The problem that distribution function is to be illustrated |
| Curve | Each level | The quantity of bending in each level | Different levels have how many bending units |
Its complicated dynamic behaviour formula is:
Wherein, n represents that this bending hierarchical tree has how many levels, niRepresent the bending unit in each level has how many
The number of the bending unit in the most each result figure layer, N is total number of the bending unit of constituent curve.Logarithmic function takes difference
The end, result of calculation is different.
According to the character of logarithmic function, the computing formula of level complexity LC is formula eight:
Wherein, N is the sum of effective bending unit of bending hierarchical tree, niNumber for the effectively bending in every layer.
From formula, logarithmic function takes the different ends, and the level complexity result calculated is different.With the song in Figure 18
As a example by line C, calculating size complexity, size complexity result calculates with 10 the end of for.For primitive curve C, this bending hierarchical tree
Have five layers, ground floor have an effective bending, the second layer has 10 effective bendings, third layer has 6 effective bendings,
4th layer has 2 effective bendings, layer 5 has 9 effective bendings, have 28 effective bendings.
According to formula eight, the level complexity of curve C is:
LC=28*log (28)-10*log (10)-6*log (6)-2*log (2)-9*log (9)=16.661.
(3) compositive complexity
Compositive complexity is used to measure the tortuosity of geographical line, compositive complexity ZC in terms of level with size two
Can be defined as formula nine:
ZC=P1SCA+P2SCL+P3SCW+P4LC,
Wherein, Pi(i=1 ..., 4) represent that the weight shared by different types of complexity, weight sum are 1 respectively.Real
Can design during the experiment of border and organize weighted value more, respectively obtain the compositive complexity of different curve, then according to empirical method determines relatively
For rational one group of weights, therefore can obtain measuring the complexity method for expressing of geographical line.
To sum up, the embodiment of the present invention has the advantages that to be sequentially completed and identifies that bending unit, superposition determine different chi
Bending nest relation and setting up bending hierarchical tree, delete invalid bending and measure geographical line based on information entropy theory under Du
The work of tortuosity, use compositive complexity size complexity and level complexity combined carries out retouching of tortuosity
Stating, intactly present the part of curve and overall tortuosity, consider between bending different levels the most all sidedly is embedding
Set relation, overcomes the defect of prior art, can preferably describe curve tortuosity, reflects form and the knot of curve all sidedly
Structure feature, is affected little by length of curve, makes full use of proximity relations and level spy that bending hierarchical tree completely reflects between bending
Property, and using information entropy theory to measure complexity, it is easy to operation realizes, and the research to geographical feature is significant.
It should be noted that in this article, the relational terms of such as first and second or the like is used merely to a reality
Body or operation separate with another entity or operating space, and deposit between not necessarily requiring or imply these entities or operating
Relation or order in any this reality.And, term " includes ", " comprising " or its any other variant are intended to
Comprising of nonexcludability, so that include that the process of a series of key element, method, article or equipment not only include that those are wanted
Element, but also include other key elements being not expressly set out, or also include for this process, method, article or equipment
Intrinsic key element.In the case of there is no more restriction, statement " including ... " key element limited, it is not excluded that
Including process, method, article or the equipment of described key element there is also other identical element.
Above example only in order to technical scheme to be described, is not intended to limit；Although with reference to previous embodiment
The present invention is described in detail, it will be understood by those within the art that: it still can be to aforementioned each enforcement
Technical scheme described in example is modified, or wherein portion of techniques feature is carried out equivalent；And these amendment or
Replace, do not make the essence of appropriate technical solution depart from the spirit and scope of various embodiments of the present invention technical scheme.
Claims (8)
1. a geographical line tortuosity measure based on comentropy, it is characterised in that comprise the following steps:
1) bending unit is identified: curve is carried out the adhesion conversion of different in width, the result that adhesion converts is folded with primitive curve
Add, obtain the bending polygon of different scale, connect bending division points and be bent identification figure, by entering with original geographical line
Row intersects computing and obtains the bending under each yardstick, and calculates the quantizating index of each bending unit, is stored in association attributes territory
In；
2) the bending nest relation under superposition determines different scale, sets up and bends hierarchical tree: the bending polygon to different levels
It is laid out analyzing, it is judged that the polygonal ownership of each bending, sets up the bending hierarchical tree of each bending；
3) invalid bending is deleted: delete the invalid bending of each layer, finally give the bending unit of each level；
4) tortuosity based on information entropy theory tolerance geographical line: use information entropy theory to calculate the ground that bending hierarchical tree represents
The tortuosity of reason curve.
A kind of geographical line tortuosity measure based on comentropy the most according to claim 1, it is characterised in that: institute
State the intersection point that bending division points is primitive curve and bending transformation line.
A kind of geographical line tortuosity measure based on comentropy the most according to claim 1, it is characterised in that: folded
Add the bending nest relation determined under different scale by judging that in different levels, each polygonal ownership of bending realizes, and incites somebody to action
Bending polygon under each yardstick superposes with the bending polygon under upper level large scale, determines that little yardstick is polygonal and returns
Belonging to, thus obtain corresponding nest relation, determine the level of each bending unit, final foundation is saved using primitive curve as root
The bending hierarchical tree of point.
A kind of geographical line tortuosity measure based on comentropy the most according to claim 1, it is characterised in that: build
The method of vertical bending hierarchical tree is the hierarchical tree to each bending, and each layer of cycle criterion from bottom to up has the leaf of parents' node to tie
Whether point has sibling, if there being sibling, then this node retains, if without sibling, then deletes this node；Continue up
One layer of search, it is judged that whether this layer of leaf node has parents' node, if nothing, then end loop, if having, then continues to judge whether it has
Sibling, until having traveled through all leaf nodes of each layer.
A kind of geographical line tortuosity measure based on comentropy the most according to claim 1, it is characterised in that: institute
State invalid be bent into non-upper strata bending division obtain direct by upper strata bending inherit and come bending.
A kind of geographical line tortuosity measure based on comentropy the most according to claim 1, it is characterised in that adopt
The method calculating the geographical line tortuosity that bending hierarchical tree represents with information entropy theory is to use size complexity and level multiple
The compositive complexity of miscellaneous degree measures the tortuosity of geographical line, and the computing formula of compositive complexity is:
ZC=P1SCA+P2SCL+P3SCW+P4LC,
Wherein, Pi(i=1,2 ..., 4) represent that the weight shared by different types of complexity, weight sum are 1 respectively.
A kind of geographical line tortuosity measure based on comentropy the most according to claim 5, it is characterised in that institute
Stating SC is size complexity, and with bending unit as elementary cell in the calculating of described SC, computing formula is:
Wherein, N is the sum of effective bending unit of bending hierarchical tree, niQuantity for the effectively bending of each apoplexy due to endogenous wind.
A kind of geographical line tortuosity measure based on comentropy the most according to claim 5, it is characterised in that institute
Stating LC is level complexity, and with one layer of hierarchical tree as elementary cell in the calculating of described LC, computing formula is:
Wherein, N is the sum of effective bending unit of bending hierarchical tree, niQuantity for the effectively bending in every layer.
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