CN109801332A - Determine the method and apparatus of Minkowski dimension - Google Patents
Determine the method and apparatus of Minkowski dimension Download PDFInfo
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Abstract
The embodiment of the invention provides a kind of method and apparatus of determining Minkowski dimension.The described method includes: determining the number of box side length and the number of non-empty packet according to attenuation coefficient, based on the box side length and the number of non-empty packet, obtain the scale of targeted graphical, using the scale of the targeted graphical as the longitudinal axis, the number of the box side length is as horizontal axis, it constitutes scatter plot and obtains the set of dimensions of Fractal Dimension in conjunction with the set of dimensions threshold value of Fractal Dimension；According to the set of dimensions of the Fractal Dimension, Minkowski dimension is obtained.The method and apparatus of determining Minkowski dimension provided in an embodiment of the present invention, by the scale for determining targeted graphical, and scatter plot is constituted according to scale, in conjunction with the set of dimensions threshold value of Fractal Dimension, obtain the set of dimensions of Fractal Dimension, Minkowski dimension is obtained according to the set of dimensions of Fractal Dimension, accurate Minkowski dimension can be obtained, avoids the error of unnecessary Minkowski dimension.
Description
Technical field
The present embodiments relate to technical field of image processing more particularly to a kind of methods of determining Minkowski dimension
And equipment.
Background technique
The method of the existing common Minkowski dimension (i.e. fractal dimension) for calculating fractal graph is r to take side length
Etui, fractal curve is covered, counting all non-empty packet numbers is N (r).Then box size is reduced, gained N (r) is certainly
So to increase, as r → 0, obtain Minkowski dimensionLimited r can only be taken in practical calculating,
A series of r and N (r) are found out, least square method fitting a straight line is then used in log-log coordinate system, the slope of gained straight line is
For required Minkowski dimension.This method can be by some complex targets for being unable to quantitative description or being difficult to quantitative description
A kind of conveniently method quantitative description of figure.But there is also some disadvantages, i.e., due to the complexity meeting of targeted graphical
So that the choosing method of size r, and the group number of selection r calculating N (r) will cause calculating error.Therefore, finding one kind can retouch
Complex target figure is stated, and is accurately obtained the Minkowski dimension of targeted graphical, when avoiding obtaining Minkowski dimension
Generate large error method, just become industry extensive concern the problem of.
Summary of the invention
In view of the above-mentioned problems existing in the prior art, the embodiment of the invention provides a kind of determining Minkowski dimensions
Method and apparatus.
In a first aspect, the embodiment provides a kind of methods of determining Minkowski dimension, comprising: according to declining
Subtract coefficient and determine the number of box side length and the number of non-empty packet, using the box side length and the number of non-empty packet as base
Plinth obtains the scale of targeted graphical, and using the scale of the targeted graphical as the longitudinal axis, the number of the box side length is as horizontal
Axis constitutes scatter plot in conjunction with the set of dimensions threshold value of Fractal Dimension and obtains the set of dimensions of Fractal Dimension；According to the Fractal Dimension
Set of dimensions, obtain Minkowski dimension.
Further, the attenuation coefficient, comprising: 0.5n、0.75nOr 0.8n；Wherein, n is attenuation steps, and be greater than etc.
In 9.
It is further, described to obtain the scale of targeted graphical based on the box side length and the number of non-empty packet,
If including: targeted graphical is line style, the box side length is multiplied with the number of non-empty packet, obtains the ruler of targeted graphical
Degree.
It is further, described to obtain the scale of targeted graphical based on the box side length and the number of non-empty packet,
If including: targeted graphical is that square being multiplied with the number of non-empty packet for the box side length is obtained targeted graphical by face type
Scale.
Further, described using the scale of the targeted graphical as the longitudinal axis, the number of the box side length as horizontal axis,
It constitutes scatter plot and obtains the set of dimensions of Fractal Dimension in conjunction with the set of dimensions threshold value of Fractal Dimension, comprising: if targeted graphical is line
Type then prolongs X direction, and the straight line that every adjacent two o'clock is constituted takes first point of the slope of the straight line greater than zero as most
Large scale takes the last one minus point of the slope of the straight line as minimum dimension, obtains the set of dimensions of Fractal Dimension.
Further, described using the scale of the targeted graphical as the longitudinal axis, the number of the size is constituted as horizontal axis
Scatter plot obtains the set of dimensions of Fractal Dimension in conjunction with the set of dimensions threshold value of Fractal Dimension, comprising: if targeted graphical is face type,
Prolong X direction, the straight line that every adjacent two o'clock is constituted takes minus first point of the slope of the straight line as maximum ruler
It is very little, it takes the last one point of the slope of the straight line greater than zero as minimum dimension, obtains the set of dimensions of Fractal Dimension.
Further, the set of dimensions according to the Fractal Dimension obtains Minkowski dimension, comprising: described
In the range of the set of dimensions of Fractal Dimension, useObtain Minkowski dimension；Wherein, D Min Kefu
This base dimension, r are box side length, and N (r) is the number of non-empty packet.
Second aspect, the embodiment provides a kind of devices of determining Minkowski dimension, comprising:
The set of dimensions of Fractal Dimension obtains module, for determined according to attenuation coefficient box side length number and non-empty packet
Number obtain the scale of targeted graphical based on the box side length and the number of non-empty packet, by the targeted graphical
Scale as the longitudinal axis, the number of the box side length constitutes scatter plot, in conjunction with the set of dimensions threshold of Fractal Dimension as horizontal axis
Value, obtains the set of dimensions of Fractal Dimension；
Minkowski dimension obtains module, for the set of dimensions according to the Fractal Dimension, obtains Minkowski dimension
Number.
The third aspect, the embodiment provides a kind of electronic equipment, comprising:
At least one processor；And
At least one processor being connect with processor communication, in which:
Memory is stored with the program instruction that can be executed by processor, and the instruction of processor caller is able to carry out first party
The method of Minkowski dimension is determined in the various possible implementations in face provided by any possible implementation.
Fourth aspect, the embodiment provides a kind of non-transient computer readable storage medium, non-transient calculating
Machine readable storage medium storing program for executing stores computer instruction, and computer instruction makes the various possible realization sides of computer execution first aspect
The method of Minkowski dimension is determined in formula provided by any possible implementation.
The method and apparatus of determining Minkowski dimension provided in an embodiment of the present invention, by the ruler for determining targeted graphical
Degree, and scatter plot is constituted according to the scale and obtains the set of dimensions of Fractal Dimension, most in conjunction with the set of dimensions threshold value of Fractal Dimension
Minkowski dimension is obtained according to the set of dimensions of the Fractal Dimension eventually, accurate Minkowski dimension can be obtained, kept away
Exempt from the error of Minkowski dimension caused by the complexity because of targeted graphical.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to do a simple introduction, it should be apparent that, the accompanying drawings in the following description is this hair
Bright some embodiments for those of ordinary skill in the art without creative efforts, can be with root
Other attached drawings are obtained according to these attached drawings.
Fig. 1 is the method flow diagram of determining Minkowski dimension provided in an embodiment of the present invention；
Fig. 2 is that targeted graphical provided in an embodiment of the present invention is line style and targeted graphical is the scatter plot of face type；
Fig. 3 is the apparatus structure schematic diagram of determining Minkowski dimension provided in an embodiment of the present invention；
Fig. 4 is the entity structure schematic diagram of electronic equipment provided in an embodiment of the present invention.
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
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described, it is clear that described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, those of ordinary skill in the art
Every other embodiment obtained without making creative work, shall fall within the protection scope of the present invention.In addition,
Technical characteristic in each embodiment or single embodiment provided by the invention can mutual any combination, to form feasible skill
Art scheme, but must be based on can be realized by those of ordinary skill in the art, when the combination of technical solution occur it is mutual
Contradiction or when cannot achieve, it will be understood that the combination of this technical solution is not present, also not the present invention claims protection scope
Within.
The embodiment of the invention provides a kind of methods of determining Minkowski dimension, referring to Fig. 1, this method comprises:
101, the number of box side length and the number of non-empty packet are determined, according to attenuation coefficient with the box side length and non-
Based on the number of empty packet, the scale of targeted graphical is obtained, using the scale of the targeted graphical as the longitudinal axis, the box side
Long number constitutes scatter plot in conjunction with the set of dimensions threshold value of Fractal Dimension and obtains the set of dimensions of Fractal Dimension as horizontal axis；
102, according to the set of dimensions of the Fractal Dimension, Minkowski dimension is obtained.
Wherein, attenuation coefficient can be 0.5n、0.75nOr 0.8n。
On the basis of the above embodiments, the method for the determination Minkowski dimension provided in the embodiment of the present invention, institute
State attenuation coefficient, comprising: 0.5n、0.75nOr 0.8n；Wherein, n is attenuation steps, and is more than or equal to 9.
On the basis of the above embodiments, the method for the determination Minkowski dimension provided in the embodiment of the present invention, institute
It states based on the box side length and the number of non-empty packet, obtains the scale of targeted graphical, comprising: if targeted graphical is line
The box side length is then multiplied with the number of non-empty packet, obtains the scale of targeted graphical by type.
On the basis of the above embodiments, the method for the determination Minkowski dimension provided in the embodiment of the present invention, institute
It states based on the box side length and the number of non-empty packet, obtains the scale of targeted graphical, comprising: if targeted graphical is face
Type, then square being multiplied the box side length with the number of non-empty packet, obtains the scale of targeted graphical.
On the basis of the above embodiments, the method for the determination Minkowski dimension provided in the embodiment of the present invention, institute
It states using the scale of the targeted graphical as the longitudinal axis, the number of the box side length constitutes scatter plot as horizontal axis, in conjunction with dividing shape
The set of dimensions threshold value of dimension, obtains the set of dimensions of Fractal Dimension, comprising: if targeted graphical is line style, prolong X direction, it will be every
The straight line that adjacent two o'clock is constituted takes first point of the slope of the straight line greater than zero as full-size, takes the straight line
The last one minus point of slope is used as minimum dimension, obtains the set of dimensions of Fractal Dimension.
On the basis of the above embodiments, the method for the determination Minkowski dimension provided in the embodiment of the present invention, institute
It states using the scale of the targeted graphical as the longitudinal axis, the number of the size constitutes scatter plot, in conjunction with Fractal Dimension as horizontal axis
Set of dimensions threshold value, obtain the set of dimensions of Fractal Dimension, comprising: if targeted graphical is face type, prolong X direction, will be per adjacent
The straight line that two o'clock is constituted, takes minus first point of the slope of the straight line as full-size, takes the slope of the straight line
The last one point greater than zero is used as minimum dimension, obtains the set of dimensions of Fractal Dimension.
On the basis of the above embodiments, the method for the determination Minkowski dimension provided in the embodiment of the present invention, institute
The set of dimensions according to the Fractal Dimension is stated, obtains Minkowski dimension, comprising: in the model of the set of dimensions of the Fractal Dimension
In enclosing, useObtain Minkowski dimension；Wherein, D is Minkowski dimension, and r is box side
Long, N (r) is the number of non-empty packet.
The method of determining Minkowski dimension provided in an embodiment of the present invention, by determining the scale of targeted graphical, and
Scatter plot, which is constituted, according to the scale obtains the set of dimensions of Fractal Dimension, final basis in conjunction with the set of dimensions threshold value of Fractal Dimension
The set of dimensions of the Fractal Dimension obtains Minkowski dimension, can obtain accurate Minkowski dimension, avoid because of mesh
It marks on a map the error of Minkowski dimension caused by the complexity of shape.
Specifically, the effect of embodiment provided by the invention may refer to Fig. 2, include: in Fig. 2 targeted graphical be line style
Scatter plot 201 and targeted graphical are the scatter plot 202 of face type.It should be noted that the scatter plot in Fig. 2 is with Koch curve
(being the scatter plot 201 of line style corresponding to targeted graphical) and Sierpinski triangle (are dissipating for face type corresponding to targeted graphical
Point diagram 202) for, using 0.8n as attenuation coefficient, obtained targeted graphical is the scatter plot 201 of line style and targeted graphical is face type
Scatter plot 202.In the scatter plot 201 that targeted graphical is line style and scatter plot 202 that targeted graphical is face type, selection has bright
Aobvious changing rule region (targeted graphical be line style scatter plot 201 in be abscissa 0 to 30 region, targeted graphical is face
It is the region of abscissa 0 to 20 in the scatter plot 202 of type) the number N (r) of corresponding box side length r and non-empty packet, it calculates
To Minkowski dimension (that is, fractal dimension).The Koch curve and Sierpinski triangle Min calculated in a conventional method can
Paderewski dimension is respectively 1.2466 and 1.6632, the Koch curve for selecting crucial point set to calculate with embodiment provided by the invention
And the Minkowski dimension of Sierpinski triangle is respectively 1.2614 and 1.6431, and theoretical Minkowski Fractal Dimension
It Wei 1.2618 and 1.585.It can be seen that no matter targeted graphical is line style or targeted graphical is face type, with prior art phase
Than the Minkowski dimension obtained using the method for determining Minkowski dimension provided in an embodiment of the present invention, accurate
There is very big promotion on degree.
The optimized integration of each embodiment of the present invention is the processing that sequencing is carried out by the equipment with processor function
It realizes.Therefore engineering in practice, can be by the technical solution of each embodiment of the present invention and its function package at various moulds
Block.Based on this reality, on the basis of the various embodiments described above, the embodiment provides a kind of determining Min Kefu
The device of this base dimension, the method which is used to execute the determination Minkowski dimension in above method embodiment.Referring to
Fig. 3, the device include:
The set of dimensions of Fractal Dimension obtains module 301, for determining the number and non-empty of box side length according to attenuation coefficient
The number of box obtains the scale of targeted graphical based on the box side length and the number of non-empty packet, by the target
The scale of figure constitutes scatter plot, in conjunction with the set of dimensions of Fractal Dimension as horizontal axis as the longitudinal axis, the number of the box side length
Threshold value obtains the set of dimensions of Fractal Dimension；
Minkowski dimension obtains module 302, for the set of dimensions according to the Fractal Dimension, obtains Minkowski
Dimension.
The device of determining Minkowski dimension provided in an embodiment of the present invention obtains mould using the set of dimensions of Fractal Dimension
Block and Minkowski dimension obtain module, constitute scatter plot, knot by determining the scale of targeted graphical, and according to the scale
The set of dimensions threshold value for closing Fractal Dimension, obtains the set of dimensions of Fractal Dimension, is finally obtained according to the set of dimensions of the Fractal Dimension
Minkowski dimension can obtain accurate Minkowski dimension, avoid Min caused by the complexity because of targeted graphical can
The error of Paderewski dimension.
The method of the embodiment of the present invention is to rely on electronic equipment to realize, therefore it is necessary to do one to relevant electronic equipment
Lower introduction.Based on this purpose, the embodiment provides a kind of electronic equipment, as shown in figure 4, the electronic equipment includes:
At least one processor (processor) 401, communication interface (Communications Interface) 404, at least one deposits
Reservoir (memory) 402 and communication bus 403, wherein at least one processor 401, communication interface 404, at least one storage
Device 402 completes mutual communication by communication bus 403.At least one processor 401 can call at least one processor
Logical order in 402, to execute following method: determining the number of box side length and of non-empty packet according to attenuation coefficient
Number, based on the box side length and the number of non-empty packet, obtains the scale of targeted graphical, by the ruler of the targeted graphical
Degree is used as the longitudinal axis, and the number of the box side length constitutes scatter plot and obtain in conjunction with the set of dimensions threshold value of Fractal Dimension as horizontal axis
To the set of dimensions of Fractal Dimension；According to the set of dimensions of the Fractal Dimension, Minkowski dimension is obtained.
In addition, the logical order in above-mentioned at least one processor 402 can be real by way of SFU software functional unit
Now and when sold or used as an independent product, it can store in a computer readable storage medium.Based in this way
Understanding, the technical solution of the present invention substantially portion of the part that contributes to existing technology or the technical solution in other words
Dividing can be embodied in the form of software products, which is stored in a storage medium, including several
Instruction is used so that a computer equipment (can be personal computer, server or the network equipment etc.) executes the present invention
The all or part of the steps of each embodiment the method.For example, according to attenuation coefficient determine box side length number and
The number of non-empty packet obtains the scale of targeted graphical based on the box side length and the number of non-empty packet, will be described
The scale of targeted graphical constitutes scatter plot, in conjunction with the ruler of Fractal Dimension as horizontal axis as the longitudinal axis, the number of the box side length
Very little group of threshold value, obtains the set of dimensions of Fractal Dimension；According to the set of dimensions of the Fractal Dimension, Minkowski dimension is obtained.And
Storage medium above-mentioned includes: USB flash disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory
The various media that can store program code such as device (RAM, Random Access Memory), magnetic or disk.
The apparatus embodiments described above are merely exemplary, wherein described, unit can as illustrated by the separation member
It is physically separated with being or may not be, component shown as a unit may or may not be physics list
Member, it can it is in one place, or may be distributed over multiple network units.It can be selected according to the actual needs
In some or all of the modules achieve the purpose of the solution of this embodiment.Those of ordinary skill in the art are not paying creativeness
Labour in the case where, it can understand and implement.
Through the above description of the embodiments, those skilled in the art can be understood that each embodiment can
It realizes by means of software and necessary general hardware platform, naturally it is also possible to pass through hardware.Based on this understanding, on
Stating technical solution, substantially the part that contributes to existing technology can be embodied in the form of software products in other words, should
Computer software product may be stored in a computer readable storage medium, such as ROM/RAM, magnetic disk, CD, including several fingers
It enables and using so that a computer equipment (can be personal computer, server or the network equipment etc.) executes each implementation
Method described in certain parts of example or embodiment.
Finally, it should be noted that the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations；Although
Present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that: it still may be used
To modify the technical solutions described in the foregoing embodiments or equivalent replacement of some of the technical features；
And these are modified or replaceed, technical solution of various embodiments of the present invention that it does not separate the essence of the corresponding technical solution spirit and
Range.
Claims (10)
1. a kind of method of determining Minkowski dimension characterized by comprising
Determine the number of box side length and the number of non-empty packet, according to attenuation coefficient with the box side length and non-empty packet
Based on number, the scale of targeted graphical is obtained, using the scale of the targeted graphical as the longitudinal axis, the number of the box side length
As horizontal axis, scatter plot is constituted in conjunction with the set of dimensions threshold value of Fractal Dimension and obtains the set of dimensions of Fractal Dimension；
According to the set of dimensions of the Fractal Dimension, Minkowski dimension is obtained.
2. the method for determining Minkowski dimension according to claim 1, which is characterized in that the attenuation coefficient, packet
It includes:
0.5n、0.75nOr 0.8n；
Wherein, n is attenuation steps, and is more than or equal to 9.
3. the method for determining Minkowski dimension according to claim 1, which is characterized in that described with the box side
Based on long and non-empty packet number, the scale of targeted graphical is obtained, comprising:
If targeted graphical is line style, the box side length is multiplied with the number of non-empty packet, obtains the scale of targeted graphical.
4. the method for determining Minkowski dimension according to claim 1, which is characterized in that described with the box side
Based on long and non-empty packet number, the scale of targeted graphical is obtained, comprising:
If targeted graphical is that square being multiplied with the number of non-empty packet for the box side length is obtained targeted graphical by face type
Scale.
5. the method for determining Minkowski dimension according to claim 3, which is characterized in that described by the target figure
The scale of shape constitutes scatter plot, in conjunction with the set of dimensions threshold of Fractal Dimension as horizontal axis as the longitudinal axis, the number of the box side length
Value, obtains the set of dimensions of Fractal Dimension, comprising:
If targeted graphical is line style, prolong X direction, the straight line that every adjacent two o'clock is constituted takes the slope of the straight line to be greater than
Zero first point takes the last one minus point of the slope of the straight line as minimum dimension, obtains as full-size
The set of dimensions of Fractal Dimension.
6. the method for determining Minkowski dimension according to claim 4, which is characterized in that described by the target figure
For the scale of shape as the longitudinal axis, the number of the size constitutes scatter plot as horizontal axis, in conjunction with the set of dimensions threshold value of Fractal Dimension,
Obtain the set of dimensions of Fractal Dimension, comprising:
If targeted graphical is face type, prolong X direction, the straight line that every adjacent two o'clock is constituted takes the slope of the straight line to be less than
Zero first point takes the last one point of the slope of the straight line greater than zero as minimum dimension, obtains as full-size
The set of dimensions of Fractal Dimension.
7. the method for determining Minkowski dimension according to claim 5 or 6, which is characterized in that described according to
The set of dimensions of Fractal Dimension obtains Minkowski dimension, comprising:
In the range of the set of dimensions of the Fractal Dimension, useObtain Minkowski dimension；Wherein,
D is Minkowski dimension, and r is box side length, and N (r) is the number of non-empty packet.
8. a kind of device of determining Minkowski dimension characterized by comprising
The set of dimensions of Fractal Dimension obtains module, for determining the number of box side length and of non-empty packet according to attenuation coefficient
Number, based on the box side length and the number of non-empty packet, obtains the scale of targeted graphical, by the ruler of the targeted graphical
Degree is used as the longitudinal axis, and the number of the box side length constitutes scatter plot and obtain in conjunction with the set of dimensions threshold value of Fractal Dimension as horizontal axis
To the set of dimensions of Fractal Dimension；
Minkowski dimension obtains module, for the set of dimensions according to the Fractal Dimension, obtains Minkowski dimension.
9. a kind of electronic equipment characterized by comprising
At least one processor, at least one processor, communication interface and bus；Wherein,
The processor, memory, communication interface complete mutual communication by the bus；
The memory is stored with the program instruction that can be executed by the processor, and the processor calls described program instruction,
To execute method as described in any one of claim 1 to 7.
10. a kind of non-transient computer readable storage medium, which is characterized in that the non-transient computer readable storage medium is deposited
Computer instruction is stored up, the computer instruction makes the computer execute the method as described in any one of claims 1 to 7.
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| CN110765962A (en) * | 2019-10-29 | 2020-02-07 | 刘秀萍 | Plant identification and classification method based on three-dimensional point cloud contour dimension values |
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| CN110765962A (en) * | 2019-10-29 | 2020-02-07 | 刘秀萍 | Plant identification and classification method based on three-dimensional point cloud contour dimension values |
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