CN108074223A - Fracture Networks extraction method in coal petrography sequence C T figures - Google Patents
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Abstract
The invention discloses Fracture Networks extraction method in a kind of coal petrography sequence C T figures, including：Non- coal petrography cavity area in original coal petrography sequence C T figures is removed, obtains satisfactory coal petrography sequence C T figures；Using the artifact filter algorithm based on three dimensions and the enhancing algorithms of the Laplace based on three-dimensional gradient, artifact filtering is done to satisfactory coal petrography sequence C T figures successively and is handled with the enhancing of crack border, obtain the enhanced coal petrography sequence C T figures in crack border；The Fracture Networks extraction model based on fracture water flow constraint is established, enhanced coal petrography sequence C T figures extract to obtain coal petrography sequence C T figure Fracture Networks from crack border；Using the coal petrography sequence C T figures Fracture Networks of acquisition as prior shape, optimize Fracture Networks with the Level Set Models constrained based on prior shape, obtain complete coal petrography sequence C T figure Fracture Networks.This method can be handled coal petrography sequence C T figures automatic lot, obtain the coal petrography Fracture Networks of complete and accurate.
Description
Technical field
The present invention relates to Fracture Networks in the fields such as coal or coal and gas power phenomenon more particularly to a kind of coal petrography sequence C T figures
Extraction method.
Background technology
At present, with the increase of China's coal-mine underground mining depth, coal occurrence condition even more complex, coal seam gas-bearing capacity
Increase therewith, the disasters such as coal and gas prominent, gas explosion occur frequently, have brought tremendous economic losses and hinder with a large amount of personnel
It dies.Fracture Networks in the coal petrography of deep are the storage and migration pathway of gassy seam gas, and exploitation and tunneling process cause coal
Stress field changes in rock mass, and then affects the extension, extension and the redistribution of Fracture Networks in crack in coal and rock.Coal
Charcoal production needs to build fluid migration model, and the Evolution grasped under Fracture Networks and mining induced stress act in coal petrography has weight
The meaning wanted.
Coal petrography belongs to the features such as discontinuous, heterogeneous natural geologic body, size, aperture, the roughness in crack in space
On have a larger anisotropy, Industrial CT Machine carries out same coal rock specimen tomoscan under the conditions of different confining pressures, and sweeping
It retouches section to show in the form of 2-D gray image, there is imaging directly perceived, high resolution, from the excellent of test specimen structure limitation
Point.
The accurate extraction of Fracture Networks, is directly related to the further investigation of follow-up coal petrography in coal petrography sequence C T.It is main at present
Manually the mode of delineating extracts the Fracture Networks in coal petrography sequence C T figures, and accuracy is big by people's subjective impact, and extraction efficiency is low；
And Digital image technology extracts Fracture Networks from CT figures, mainly has based on the side such as Threshold segmentation, edge detection, region growing
Method, these methods are not suitable with the coal petrography CT images for the characteristics such as contrast is low, details is more, border is weak, and with cannot inhibit noise,
Blurred picture details is easily disturbed, the shortcomings such as accuracy is low, and it is more to affect the computing permeability of follow-up coal, coal petrography damage, crack
The development of the research work such as field coupling.
The content of the invention
The object of the present invention is to provide Fracture Networks extraction methods in a kind of coal petrography sequence C T figures, can be to coal petrography sequence
The processing of CT figures automatic lot, obtains the coal petrography Fracture Networks of complete and accurate.
The purpose of the present invention is what is be achieved through the following technical solutions：
Fracture Networks extraction method in a kind of coal petrography sequence C T figures, including：
Non- coal petrography cavity area in original coal petrography sequence C T image datas is removed, obtains satisfactory coal petrography sequence C T figures
As data；
It is right successively using the artifact filter algorithm based on three dimensions and the enhancing algorithms of the Laplace based on three-dimensional gradient
Satisfactory coal petrography sequence C T image datas are done artifact filtering and are handled with the enhancing of crack border, and it is enhanced to obtain crack border
Coal petrography sequence C T image datas；
The Fracture Networks extraction model based on fracture water flow constraint is established, from the enhanced coal petrography sequence C T figures in crack border
As data extract to obtain coal petrography sequence C T figure Fracture Networks；
Using the coal petrography sequence C T figures Fracture Networks of acquisition as prior shape, with the level set mould constrained based on prior shape
Type optimizes Fracture Networks, obtains complete coal petrography sequence C T figure Fracture Networks.
As seen from the above technical solution provided by the invention, on the one hand, it avoids and delineates Fracture Networks by hand at present,
Effectively improve the accuracy of work efficiency and Fracture Networks；It on the other hand, can with crack circuit for edge enhancing arithmetic by artifact filtering
Effectively to inhibit artifact noise and improve crack border, and combination distinctive fracture water flow constraints extraction Fracture Networks can
Fast and accurately to extract Fracture Networks；On this basis, being further optimized makes Fracture Networks more complete and accurate.
Description of the drawings
In order to illustrate the technical solution of the embodiments of the present invention more clearly, required use in being described below to embodiment
Attached drawing be briefly described, it should be apparent that, the accompanying drawings in the following description is only some embodiments of the present invention, for this
For the those of ordinary skill in field, without creative efforts, other are can also be obtained according to these attached drawings
Attached drawing.
Fig. 1 is the flow of Fracture Networks extraction method in a kind of coal petrography sequence C T figures provided in an embodiment of the present invention
Figure；
Fig. 2 is original coal petrography sequence C T illustrated examples provided in an embodiment of the present invention；
Fig. 3 is original coal petrography sequence logarithmic transformation result figure provided in an embodiment of the present invention；
Fig. 4 is the handling result of step 1 provided in an embodiment of the present invention；
Fig. 5 extracts result for coal petrography sequence C T figures artifact provided in an embodiment of the present invention；
Fig. 6 goes division result for coal petrography sequence C T figure artifacts provided in an embodiment of the present invention；
Fig. 7 is the handling result of step 2 provided in an embodiment of the present invention；
Fig. 8 is the result provided in an embodiment of the present invention for implying complete Fracture Networks；
Fig. 9 is the handling result of step 3 provided in an embodiment of the present invention；
Figure 10 is the handling result of step 4 provided in an embodiment of the present invention.
Specific embodiment
With reference to the attached drawing in the embodiment of the present invention, the technical solution in the embodiment of the present invention is carried out clear, complete
Ground describes, it is clear that described embodiment is only part of the embodiment of the present invention, instead of all the embodiments.Based on this
The embodiment of invention, the every other implementation that those of ordinary skill in the art are obtained without making creative work
Example, belongs to protection scope of the present invention.
The embodiment of the present invention provides Fracture Networks extraction method in a kind of coal petrography sequence C T figures, as shown in Figure 1, it is led
Including：
Non- coal petrography cavity area in step 1, the original coal petrography sequence C T image datas of removal, obtains satisfactory coal petrography sequence
Arrange CT image datas.
This step the specific implementation process is as follows：
Carrier container of the loading chambers as coal rock specimen, cavity inside and outside wall shadow in original coal petrography sequence C T image datas
As showing as white annulus, original coal petrography sequence C T image datas are divided into matrix of coal and cricoid cavity area；Use logarithm
Becoming scaling method makes cricoid cavity area and matrix of coal area grayscale uniformity, can remove non-coal petrography cavity area in coal petrography CT
The interference in domain improves the computational efficiency and precision of Fracture Networks extraction algorithm.
Logarithmic transformation algorithmic formula is：
Wherein, flog(x, y, z) is the coal petrography sequence C T image datas after logarithmic transformation, and function f (x, y, z) is original coal
Rock sequence C T image datas represent the gray value at z width tomograph coordinates (x, y) in coal petrography sequence C T image datas；A is controlled
The downward shift amount of logarithmic curve, b control the bending degree of logarithmic curve, and c is the bottom of logarithm；
Afterwards, binary conversion treatment is done to above-mentioned handling result, obtaining contour area with profile lookup algorithm meets coal petrography examination
The region of part removes non-coal petrography cavity area therein, obtains satisfactory coal petrography sequence C T image datas
Step 2 enhances algorithm using the artifact filter algorithm based on three dimensions and the Laplace based on three-dimensional gradient,
Artifact filtering is done to satisfactory coal petrography sequence C T image datas successively to handle with the enhancing of crack border, crack border is obtained and increases
Coal petrography sequence C T image datas after strong.
Electromagnetic interference is inevitably had during CT tomoscans, makes occur wire, banding or cricoid in indivedual CT figures
Artifact, artifact may block crack, influence Fracture Networks and accurately extract.
Artifact has stochastic behaviour, i.e., artifact shape, position etc. are different in adjacent C T figures, using based on three dimensions
Artifact filter algorithm is handled sequence coal petrography three-dimensional data, it is necessary to obtain satisfactory coal petrography sequence first with gamma transformation
Artifact region in CT image datas is arranged, gamma transformation formula is：
Wherein,For satisfactory coal petrography sequence C T image datas, fgamma(x, y, z) is defeated for gamma transformation
The image data gone out, A are constant, and γ is regulated variable, to control image enhancement degree；When γ is less than 1, it can stretch in image
The relatively low region of gray level, γ values be more than 1 when, the region that gray level is higher in image can be stretched, at the same can compress gray level compared with
Low part can compress the higher part of gray level simultaneously.
Using the artifact filter algorithm filters artifact based on three dimensions, formula is：
Wherein,For satisfactory coal petrography sequence C T image datas, f3D-Artifact(x, y, z) is pseudo- for filtering
Shadow treated coal petrography sequence C T image datas, p (x, y, z) are fgamma(x, y, z) binaryzation as a result, for judging that the point is
No is artifact, if it is changes the gray value, is not, does not change the gray value.
The petrographic property of heterogeneous natural geologic body, making coal petrography sequence C T figures, there are noise is more, lower than degree, crack border is weak
The problems such as, coal petrography sequence C T figures as 3 d data field, each point in three-dimensional there are gradient, profit in the embodiment of the present invention
Enhance algorithm with the Laplace based on three-dimensional gradient, enhance crack border, formula is：
Wherein, f3D-Artifact(x, y, z) is filtering artifact treated coal petrography sequence C T image datas, f3D-Laplace(x,
Y, z) for the image data of coal petrography sequence C T after enhancing crack BORDER PROCESSING, t is field center coefficient of comparisons, as t≤0, neck
The gray value of domain center pixel is further reduced；On the contrary, as t ＞ 0, the gray scale of field center pixel is further improved；
Three-dimensional data second dervativeCalculation formula is：
Wherein, λ1、λ2、λ3It is the weighing factor coefficient of each dimension of three dimensions.
Step 3 establishes the Fracture Networks extraction model based on fracture water flow constraint, from the enhanced coal petrography sequence in crack border
Row CT image data extractions go out to obtain coal petrography sequence C T figure Fracture Networks.
Coal petrography sequence C T diagram data f enhanced to crack border3D-Laplace(x, y, z) does binary conversion treatment, obtains hidden
Result f containing complete Fracture NetworksEnhance(x, y, z), and all profiles are obtained using profile lookup algorithm, with eight chain code principles
It is one group of code for being referred to as chain code by each profile boundary coding, represents 8 directions with 0~7, boundary chain code combination is for shape
The calculating of shape area and perimeter；
Afterwards, using the Fracture Networks extraction model constrained based on fracture water flow, judge whether each profile belongs to crack
Network：
Fracture water flow constraints one：Coal petrography crack gray value calculates each profile and corresponds to original coal petrography in { 20,55 } scope
In the range whether the area grayscale average in sequence C T figures；
Fracture water flow constraints two：According to the progressive similitude in crack in neighbouring two width coal petrography sequence C T figures, meter
Calculate neighbouring two width coal petrography sequence C T figures all existing profile C at same coordinatezAnd Cz+1Similarity, sentence with reference to threshold value
Whether the two other profiles belong to crack, and contour line similarity is defined as：
Wherein, s1For profile CzAnd Cz+1The area of lap and s2For profile CzAnd Cz+1The not area of lap
With；
Contour area formula is：
Wherein, Δ y=yi-yi-1, Δ x=xi-xi-1, xiAnd yiThe transverse and longitudinal coordinate of respectively i-th boundary chain code-point, x0With
y0Respectively beginning boundary chain code-point transverse and longitudinal coordinate, n are the sum of code in boundary chain code；
Profile CzAnd Cz+1Under the scale of same position and standard, lap area is bigger, and different areas is got over
Small, then two profiles are more similar.Known by similarity measurement formula, 1) when the non-overlapping part of two profiles, ρ (Cz,Cz+1)=0；2)
ρ (the C when two profiles are completely superposedz,Cz+1)=1；3) generally there are 0≤ρ (Cz,Cz+1)≤1, and ρ (Cz,Cz+1) bigger, then CzWith
Cz+1It is more close.Illustratively, threshold value can be set to 0.8, if two crack similarities are more than 0.8, then it is assumed that meet condition.
Fracture water flow constraints three：The elongated features in crack are characterized with the relation of profile skeleton line and profile perimeter,
It is required that the skeleton line length of crack profile is less than the half of contour line perimeter, more than 1/3rd of contour line perimeter；Bone
Frame point decision criteria is：
Wherein, r1And r2Represent that adjacent skeletal point corresponds to the radius of greatest circle, (x1,y1) and (x2,y2) represent the two bones
The coordinate of frame point；After determining all skeletal points, adjacent skeletal point is connected from being shaped as profile skeleton line；
Skeleton line length and contour line length formula are：
Wherein, neFor verso number in line boundary chain code sequence, n is the sum of code in boundary chain code；
The profile for meeting above three fracture water flow constraints simultaneously belongs to Fracture Networks, and final take out obtains coal petrography sequence
Arrange CT figure Fracture Networks fCrackNet(x,y,z)。
Step 4, using the coal petrography sequence C T figures Fracture Networks of acquisition as prior shape, with the water constrained based on prior shape
Flat collection model obtains the coal petrography sequence C T figure Fracture Networks of complete and accurate.
Above-mentioned Processing Algorithm can cause crack border some influences, especially to weak boundary.What the embodiment of the present invention proposed
A kind of Level Set Models based on prior shape constraint, by the above-mentioned coal petrography sequence C T figure Fracture Networks f acquiredCrackNet(x,
Y, z) prior shape information as the model and initial evolution curve, using the model from f3D-LaplaceExtraction in (x, y, z)
The Fracture Networks of complete and accurate.
The energy function of Level Set Models based on prior shape constraint is：
Wherein, φ (x, y, z) is initial evolution curve fCrackNetThe level set function of (x, y, z), c1And c2It is just respectively
Beginning evolution curvilinear inner and external gradation of image average, by f3D-Laplace(x, y, z) is used as pending image, and Ω is its pixel
Point set, fCrackNet(x, y, z) obtains prior shape information according to the square of φ after affine transformationμ1、μ2、u3To be each
The weight coefficient of energy term, H () are Hai Shi functions, δε() is the regularization form of Dirac function；E is solved by the calculus of variations
(φ,c1,c2) corresponding Eulerian equation, it realizes and minimizes energy function E.
In order to illustrate the effect of said program, illustrated with reference to an example.
In this example, material therefor is tested using China Mining Univ.'s coal resources and safe working state key
Three axis of room autonomous Design research and development load real-time CT scan experimental system, and it is real to carry out the loading of three axis to the coal rock specimen for being rich in crack
It tests, carries out real-time CT scan for the structure under the conditions of three kinds of confining pressures inside different load phase coal petrographys, CT scan scale is 50
Micron, obtains original 970 width of coal petrography sequence C T Fig. 3 *.As shown in Fig. 2, for original coal petrography sequence C T illustrated examples, Fig. 2 a therein
To contain artifact coal petrography CT figures, Fig. 2 b scheme for normal coal petrography CT.
First, transformation of variables algorithm process is done to Fig. 2 a using abovementioned steps 1, handling result is as shown in Figure 3；And then
Binary conversion treatment is done, the region that contour area meets coal rock specimen is obtained with profile lookup algorithm, removes non-coal petrography chamber therein
Body region, step 1 final process result are as shown in Figure 4.
Secondly, the artifact in Fig. 4 is extracted using abovementioned steps 2, the results are shown in Figure 5；It recycles based on three dimensions
Artifact filter algorithm removes artifact, obtains image as shown in Figure 6；Afterwards, enhanced using the Laplace based on three-dimensional gradient and calculated
Method, enhances crack border, and step 2 final process result is as shown in Figure 7.
Again, binary conversion treatment is done to Fig. 7 using abovementioned steps 3, is implied the knot of complete Fracture Networks as shown in Figure 8
Fruit；Afterwards, the Fracture Networks extraction model based on fracture water flow constraint extracts coal petrography sequence C T figure Fracture Networks from Fig. 8, walks
Rapid 3 final process result is as shown in Figure 9.
Finally, further optimization is done to Fig. 9 using abovementioned steps 4, step 4 final process result is as shown in Figure 10.
Through the above description of the embodiments, those skilled in the art can be understood that above-described embodiment can
To be realized by software, the mode of necessary general hardware platform can also be added to realize by software.Based on such understanding,
The technical solution of above-described embodiment can be embodied in the form of software product, the software product can be stored in one it is non-easily
The property lost storage medium (can be CD-ROM, USB flash disk, mobile hard disk etc.) in, including some instructions with so that a computer is set
Standby (can be personal computer, server or the network equipment etc.) performs the method described in each embodiment of the present invention.
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention be not limited thereto,
Any one skilled in the art is in the technical scope of present disclosure, the change or replacement that can readily occur in,
It should be covered by the protection scope of the present invention.Therefore, protection scope of the present invention should be with the protection model of claims
Subject to enclosing.
Claims (5)
1. a kind of Fracture Networks extraction method in coal petrography sequence C T figures, which is characterized in that including：
Non- coal petrography cavity area in original coal petrography sequence C T image datas is removed, obtains satisfactory coal petrography sequence C T picture numbers
According to；
Using the artifact filter algorithm based on three dimensions and the enhancing algorithms of the Laplace based on three-dimensional gradient, successively to meeting
It is required that coal petrography sequence C T image datas do artifact filtering and handled with crack border enhancing, obtain the enhanced coal petrography in crack border
Sequence C T image datas；
The Fracture Networks extraction model based on fracture water flow constraint is established, from the enhanced coal petrography sequence C T picture numbers in crack border
According to extracting to obtain coal petrography sequence C T figure Fracture Networks；
It is excellent with the Level Set Models constrained based on prior shape using the coal petrography sequence C T figures Fracture Networks of acquisition as prior shape
Change Fracture Networks, obtain complete coal petrography sequence C T figure Fracture Networks.
2. Fracture Networks extraction method in a kind of coal petrography sequence C T figures according to claim 1, which is characterized in that institute
Non- coal petrography cavity area in the original coal petrography sequence C T image datas of removal is stated, and carries out related pretreatment, is obtained satisfactory
Coal petrography sequence C T image datas include：
Carrier container of the loading chambers as coal rock specimen, cavity inside and outside wall shadow table in original coal petrography sequence C T image datas
It is now white annulus, original coal petrography sequence C T image datas is divided into matrix of coal and cricoid cavity area；Use logarithmic transformation
Algorithm makes cricoid cavity area and matrix of coal area grayscale uniformity, and logarithmic transformation algorithmic formula is：
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Wherein, flog(x, y, z) is the coal petrography sequence C T image datas after logarithmic transformation, and function f (x, y, z) is original coal petrography sequence
CT image datas are arranged, represent the gray value at z width tomograph coordinates (x, y) in original coal petrography sequence C T image datas；A is controlled
The downward shift amount of logarithmic curve, b control the bending degree of logarithmic curve, and c is the bottom of logarithm；
Afterwards, binary conversion treatment is done to above-mentioned handling result, obtaining contour area with profile lookup algorithm meets coal rock specimen
Region removes non-coal petrography cavity area therein, obtains satisfactory coal petrography sequence C T image datas f 'log(x,y,z)。
3. Fracture Networks extraction method in a kind of coal petrography sequence C T figures according to claim 1, which is characterized in that institute
It states using the artifact filter algorithm based on three dimensions and the enhancing algorithms of the Laplace based on three-dimensional gradient, successively to conforming to
The coal petrography sequence C T image datas asked, which do artifact filtering and crack border enhancing processing, to be included：
Artifact region in satisfactory coal petrography sequence C T image datas is obtained using gamma transformation, gamma transformation formula is：
fgamma(x, y, z)=Af 'log(x,y,z)γ；
Wherein, f 'log(x, y, z) be satisfactory coal petrography sequence C T image datas, fgamma(x, y, z) exports for gamma transformation
Image data, A is constant, and γ is regulated variable, to control image enhancement degree；
Using the artifact filter algorithm filters artifact based on three dimensions, formula is：
Wherein, f 'log(x, y, z) be satisfactory coal petrography sequence C T image datas, f3D-Artifact(x, y, z) is filtering artifact
Coal petrography sequence C T image datas that treated, p (x, y, z) are fgammaThe result of (x, y, z) binaryzation；
Enhance algorithm using the Laplace based on three-dimensional gradient, enhance crack border, formula is：
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<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<msup>
<mo>&dtri;</mo>
<mn>2</mn>
</msup>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>t</mi>
<mo>&le;</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>n</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msup>
<mo>&dtri;</mo>
<mn>2</mn>
</msup>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>t</mi>
<mo>></mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
Wherein, f3D-Laplace(x, y, z) is coal petrography sequence C T image datas after enhancing crack BORDER PROCESSING, and t compares for field center
Coefficient, as t≤0, the gray value of field center pixel is further reduced；On the contrary, as t ＞ 0, the ash of field center pixel
Degree is further improved；
Three-dimensional data second dervativeCalculation formula is：
<mfenced open = "" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<msup>
<mo>&dtri;</mo>
<mn>2</mn>
</msup>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<msup>
<mo>&dtri;</mo>
<mn>2</mn>
</msup>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<msup>
<mo>&dtri;</mo>
<mn>2</mn>
</msup>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>u</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>3</mn>
</msub>
<msup>
<mo>&dtri;</mo>
<mn>2</mn>
</msup>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>=</mo>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<mo>&lsqb;</mo>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>-</mo>
<mn>1</mn>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>+</mo>
<mn>1</mn>
<mo>,</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>-</mo>
<mn>1</mn>
<mo>,</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>4</mn>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mn>0</mn>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<mo>&lsqb;</mo>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>+</mo>
<mn>1</mn>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>-</mo>
<mn>1</mn>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<mi>z</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<mi>z</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>4</mn>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mn>0</mn>
<mo>,</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>3</mn>
</msub>
<mo>&lsqb;</mo>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>e</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>,</mo>
<mi>y</mi>
<mo>+</mo>
<mn>1</mn>
<mo>,</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>,</mo>
<mi>y</mi>
<mo>-</mo>
<mn>1</mn>
<mo>,</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>4</mn>
<msub>
<mi>f</mi>
<mrow>
<mn>3</mn>
<mi>D</mi>
<mo>-</mo>
<mi>A</mi>
<mi>r</mi>
<mi>t</mi>
<mi>i</mi>
<mi>f</mi>
<mi>a</mi>
<mi>c</mi>
<mi>t</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mn>0</mn>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
Wherein, λ1、λ2、λ3It is the weighing factor coefficient of each dimension of three dimensions.
4. Fracture Networks extraction method in a kind of coal petrography sequence C T figures according to claim 1, which is characterized in that institute
It states and establishes the Fracture Networks extraction model based on fracture water flow constraint, from the enhanced coal petrography sequence C T image datas in crack border
Extracting to obtain coal petrography sequence C T figure Fracture Networks includes：
Coal petrography sequence C T diagram data f enhanced to crack border3D-Laplace(x, y, z) does binary conversion treatment, obtains implicit complete
The result f of Fracture NetworksEnhance(x, y, z), and all profiles are obtained using profile lookup algorithm, it will be each with eight chain code principles
Profile boundary coding is one group of code for being referred to as chain code, represents 8 directions with 0~7, boundary chain code combination is for shape area
With the calculating of perimeter；
Afterwards, using the Fracture Networks extraction model constrained based on fracture water flow, judge whether each profile belongs to Fracture Networks：
Fracture water flow constraints one：Coal petrography crack gray value calculates each profile and corresponds to original coal petrography sequence in { 20,55 } scope
In the range whether the area grayscale average in CT figures；
Fracture water flow constraints two：According to the progressive similitude in crack in neighbouring two width coal petrography sequence C T figures, in calculating
Under adjacent two width coal petrography sequence C T figures all existing profile C at same coordinatezAnd Cz+1Similarity, differentiate this with reference to threshold value
Whether two profiles belong to crack, and contour line similarity is defined as：
<mrow>
<mi>&rho;</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>C</mi>
<mi>z</mi>
</msub>
<mo>,</mo>
<msub>
<mi>C</mi>
<mrow>
<mi>z</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<mrow>
<msub>
<mi>s</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>s</mi>
<mn>2</mn>
</msub>
</mrow>
</mfrac>
</mrow>
Wherein, s1For profile CzAnd Cz+1The area of lap and s2For profile CzAnd Cz+1Not the area of lap and；
Contour area formula is：
<mrow>
<mi>S</mi>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<mo>|</mo>
<mi>&Delta;</mi>
<mi>x</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>y</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>&Delta;</mi>
<mi>y</mi>
<mo>)</mo>
</mrow>
<mo>|</mo>
</mrow>
Wherein, Δ y=yi-yi-1, Δ x=xi-xi-1, xiAnd yiThe transverse and longitudinal coordinate of respectively i-th boundary chain code-point, x0And y0Point
Not Wei beginning boundary chain code-point transverse and longitudinal coordinate, n be boundary chain code in code sum；
Fracture water flow constraints three：The elongated features in crack are characterized with the relation of profile skeleton line and profile perimeter, it is desirable that
The skeleton line length of crack profile is less than the half of contour line perimeter, more than 1/3rd of contour line perimeter；Skeletal point
Decision criteria is：
<mrow>
<mfrac>
<mrow>
<msup>
<msub>
<mi>r</mi>
<mn>1</mn>
</msub>
<mn>2</mn>
</msup>
<mo>-</mo>
<msup>
<msub>
<mi>r</mi>
<mn>2</mn>
</msub>
<mn>2</mn>
</msup>
</mrow>
<mrow>
<mi>m</mi>
<mi>a</mi>
<mi>x</mi>
<mrow>
<mo>(</mo>
<mi>a</mi>
<mi>b</mi>
<mi>s</mi>
<mo>(</mo>
<msub>
<mi>x</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>,</mo>
<mi>a</mi>
<mi>b</mi>
<mi>s</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>y</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>)</mo>
</mrow>
</mfrac>
<mo>&le;</mo>
<mn>1</mn>
<mo>;</mo>
</mrow>
Wherein, r1And r2Represent that adjacent skeletal point corresponds to the radius of greatest circle, (x1,y1) and (x2,y2) represent the two skeletal points
Coordinate；After determining all skeletal points, adjacent skeletal point is connected from being shaped as profile skeleton line；
Skeleton line length and contour line length formula are：
<mrow>
<mi>L</mi>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>n</mi>
</munderover>
<msub>
<mi>n</mi>
<mi>e</mi>
</msub>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mi>n</mi>
<mo>-</mo>
<msub>
<mi>n</mi>
<mi>e</mi>
</msub>
<mo>)</mo>
</mrow>
<msqrt>
<mn>2</mn>
</msqrt>
<mo>;</mo>
</mrow>
Wherein, neFor verso number in line boundary chain code sequence, n is the sum of code in boundary chain code；
The profile for meeting above three fracture water flow constraints simultaneously belongs to Fracture Networks, and final take out obtains coal petrography sequence C T
Figure Fracture Networks fCrackNet(x,y,z)。
5. Fracture Networks extraction method in a kind of coal petrography sequence C T figures according to claim 1, which is characterized in that institute
Stating the energy function of Level Set Models based on prior shape constraint is：
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<mi>E</mi>
<mrow>
<mo>(</mo>
<mi>&phi;</mi>
<mo>,</mo>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
<msub>
<mi>c</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>&mu;</mi>
<mn>1</mn>
</msub>
<mo>&CenterDot;</mo>
<munder>
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Wherein, φ (x, y, z) is initial evolution curve fCrackNetThe level set function of (x, y, z), c1And c2It is initially to develop respectively
Curvilinear inner and external gradation of image average, by f3D-Laplace(x, y, z) is used as pending image, and Ω is its pixel point set
It closes, fCrackNet(x, y, z) obtains prior shape information according to the square of φ after affine transformationμ1、μ2、u3For each energy
Weight coefficient, H () is Hai Shi functions, δε() is the regularization form of Dirac function；By the calculus of variations solve E (φ,
c1,c2) corresponding Eulerian equation, it realizes and minimizes energy function E.
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