CN107204042B - Heterogeneous core three-dimensional structure reconstruction algorithm based on form completeness - Google Patents

Heterogeneous core three-dimensional structure reconstruction algorithm based on form completeness Download PDF

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CN107204042B
CN107204042B CN201710406622.8A CN201710406622A CN107204042B CN 107204042 B CN107204042 B CN 107204042B CN 201710406622 A CN201710406622 A CN 201710406622A CN 107204042 B CN107204042 B CN 107204042B
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CN107204042A (en
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滕奇志
高明亮
何小海
卿粼波
王正勇
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Sichuan University
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
    • G06T17/10—Constructive solid geometry [CSG] using solid primitives, e.g. cylinders, cubes
    • G—PHYSICS
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    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
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Abstract

The three-dimensional reconstruction of the rock core based on a single image aims to ensure that three orthogonal sections of a reconstructed structure have the statistical characteristics or morphological characteristics of a training image. For a two-dimensional training image with obvious heterogeneous characteristics, a three-dimensional structure with three orthogonal sections having a similar form to the training image does not exist, and a reconstruction mode of simultaneously controlling the three orthogonal sections by using the training image cannot be adopted. Therefore, the invention aims at realizing the three-dimensional reconstruction target of the rock core by using a single image with heterogeneous characteristics. The invention firstly provides a two-dimensional training image form completeness judgment method, and can accurately predict the specific form which can appear on each orthogonal section of a three-dimensional structure according to the analysis method, thereby indicating a proper reconstruction mode for a given training image and providing corresponding measures for links such as characteristic region extraction, characteristic region restoration and the like.

Description

Heterogeneous core three-dimensional structure reconstruction algorithm based on form completeness
Technical Field
The invention relates to a technology for randomly simulating a heterogeneous three-dimensional (3D) core structure from a two-dimensional (2D) training image by using a computer mathematical modeling method, belonging to the technical field of image processing.
Background
The heterogeneous structure of the core exists due to the comprehensive factors of the formation effect, the sedimentation effect, the diagenesis effect and the like in the formation process of the core. The heterogeneity determines the quality of the reservoir, and influences the effect of oil field development. This heterogeneity appears to a different degree in different reservoir cores. Such heterogeneity is small as in conventional oil and gas production sandstone cores; in unconventional oil and gas extraction shale cores, this heterogeneous nature can be quite significant. Different scholars propose different partitioning schemes for reservoir heterogeneity, generally dividing reservoir heterogeneity into macroscopic heterogeneity (interlayer heterogeneity, planar heterogeneity, and intralevel heterogeneity) and microscopic heterogeneity (pore heterogeneity, particle heterogeneity, and filler heterogeneity). In the digital core three-dimensional reconstruction, the heterogeneity refers to the heterogeneity of microscopic pores of the core.
The three-dimensional structure of the rock core can be obtained through two modes of physical imaging and mathematical modeling. The invention aims to reconstruct a three-dimensional structure of a heterogeneous rock core from a single two-dimensional training image by means of a computer mathematical modeling method.
At present, in the computer mathematical modeling process, a training image is generally used for simultaneously controlling three orthogonal sections of a three-dimensional structure, so that the three orthogonal sections of a reconstructed structure have a shape similar to that of the training image. Generally, when the training image has better homogeneity, a more ideal three-dimensional reconstruction structure can be obtained by adopting the reconstruction mode. On the other hand, heterogeneous core images often have the characteristics of multiple sizes of pores, uneven distribution and the like, so that the shape difference of each orthogonal section of a three-dimensional structure of the core is large. Namely, the ideal three-dimensional reconstruction result cannot be obtained by using the conventional reconstruction mode for the heterogeneous core image.
For the three-dimensional reconstruction research of heterogeneous cores, the academic community is in the exploration stage at present. Although the related literature describes that the core structure with non-stationary characteristics can be reconstructed, the CCSIM algorithm proposed by Tahmasebi in 2012 fails to give a concrete theory for convincing the reconstruction of the three-dimensional structure with non-stationary characteristics, so that the algorithm cannot actually reconstruct the non-stationary three-dimensional structure stably and effectively. Tahmasebi in 2016 then proposed to reconstruct a shale three-dimensional structure with multiple size features from a single image using the modified CCSIM algorithm. In consideration of the shale resolution under the condition of satisfying the gas seepage characteristic, the image which can be reconstructed is only a visual field with a small size of the core. The view at this size is not actually effective in representing the core's seepage characteristics. Meanwhile, the two-dimensional view field image at the size cannot effectively represent the overall characteristics of the three-dimensional structure, that is, the view field image is not suitable for three-dimensional reconstruction. In short, the three-dimensional reconstruction of the heterogeneous core is still in the initial development stage, and a lot of contents which need to be further studied exist.
The invention is subsidized by the national science foundation project 'three-dimensional image reconstruction of rock microscopic heterogeneous structure and resolution improvement technical research (61372174)', so as to solve the problems in the prior art and provide a new algorithm for three-dimensional reconstruction of heterogeneous cores.
Disclosure of Invention
The invention starts from a mode of reconstructing a three-dimensional structure based on a single training image, firstly defines an orthogonal chord, then respectively provides a training image form completeness evaluation method by analyzing the training image form, the form of each orthogonal section of the three-dimensional structure and the relation between the orthogonal chord and simultaneously considering three orthogonal sections and two orthogonal sections, and finally provides a heterogeneous core three-dimensional reconstruction algorithm according to the evaluation analysis method and specific measures of characteristic region extraction and characteristic region restoration in algorithm design. The specific principle content of the invention comprises the following four aspects:
1. training image form completeness analysis method considering three orthogonal sections simultaneously
In order to make each orthogonal section of the reconstructed three-dimensional structure have the statistical characteristics and morphological characteristics of the training image, in the three-dimensional reconstruction process based on a single training image, the same training image is used to simultaneously constrain the three orthogonal sections of the target three-dimensional structure, as shown in fig. 1.
To illustrate the satisfying relationship between the orthogonal slices in the reconstruction process shown in fig. 1, fig. 2-6 give definitions of lines, chords, and orthogonal chords. Fig. 2 is a two-dimensional core image and fig. 3 is a partial morphology extracted from fig. 2. The directional line segment starting from and ending in the same phase in the direction d in FIG. 4 and having all pixel points belonging to the phase is called chord, and is denoted by CdAnd (4) showing. Any part of the chord is called a line, denoted LdNamely, satisfies the formula (1). C in FIG. 4yIs a chord in the y direction, and LxIs a line in the x-direction. C is to bedThe number of the pixel points is called CdChord length of (1) (C)d) Denotes that L is correspondingly reduceddThe number of the pixel points is called LdLength of (1) isd) And (4) showing.
Figure BDA0001311077390000021
To the point of the drawing 5
Figure BDA0001311077390000022
Chord C ofxAnd CyMake upTo structure Cx⊥CyCalled the orthogonal chord, is labeled as equation (2). The phase in FIG. 6 is correspondingly taken to be orthogonal to the point
Figure BDA0001311077390000023
Line L ofxAnd LyFormed structure Lx⊥LyCalled the orthogonal line, and is denoted by the formula (3).
Figure BDA0001311077390000024
Figure BDA0001311077390000025
In order to show the relationship between the orthogonal chord lengths of different orthogonal sections in the three-dimensional core, a real core structure with the dimension size of 128 multiplied by 128Micro-CT shown in figure 7(a) is used for illustration. Fig. 7(b) shows the partial region shown in fig. 7(a), and the size is 31 × 31 × 31. FIG. 7(c) is a schematic view showing a midpoint of the three-dimensional structure shown in FIG. 7(b)
Figure BDA0001311077390000031
Cross-sectional view orthogonal to (a). FIG. 7(d) shows S corresponding to FIG. 7(c)xy、SzxAnd SyzThree orthogonal sections.
The key role that the orthogonal chords have in the three-dimensional reconstruction is found by analyzing fig. 7: first, the orthogonal strings can effectively represent the specific shape of the training image in the three-dimensional reconstruction. The reconstruction structure has the similar shape with the training image in each orthogonal section, and the shape is formed by the orthogonal chord corresponding to the training image. Secondly, each pixel point corresponds to an orthogonal chord, so when a local form is regarded as being formed by a series of pixel points, the local form can also be regarded as being formed by combining a series of orthogonal chords. The specific morphology of the training image can be measured by each point.
Continuing the intensive study of FIG. 7, it was found that
Figure BDA0001311077390000032
In the orthogonal tangent plane Sxy、SzxAnd SyzRespectively correspond to the projection points
Figure BDA0001311077390000033
And
Figure BDA0001311077390000034
the determined orthogonal chord satisfies equation (4):
Figure BDA0001311077390000035
to be provided with
Figure BDA0001311077390000036
For example, it is represented by SzxPoint in tangent plane
Figure BDA0001311077390000037
Determined orthogonal line
Figure BDA0001311077390000038
The line length of the ith line in the x direction is equal to SxyPoint in tangent plane
Figure BDA0001311077390000039
Determined orthogonal line
Figure BDA00013110773900000310
The length of the line of the ith line in the x direction of the drawing table is required to be long, and the two lines in the x direction of each tangent plane can be combined into a chord.
According to the reconstruction method shown in figure 1 and the physical meaning represented by the orthogonal chords, with SxyMidpoint of tangent plane
Figure BDA00013110773900000311
For example, if at SzxAnd SyzThere are points satisfying the formula (4) respectively
Figure BDA00013110773900000312
And
Figure BDA00013110773900000313
description of the invention
Figure BDA00013110773900000314
And
Figure BDA00013110773900000315
can form a point in three-dimensional space
Figure BDA00013110773900000316
And point
Figure BDA00013110773900000317
The corresponding morphology in the three orthogonal sections belongs to the training image, as shown in fig. 8. Briefly, the training image is provided for reconstructing a waypoint
Figure BDA00013110773900000318
The determined morphology is complete. On the contrary, if the point is right
Figure BDA00013110773900000319
Can not be at SzxAnd SyzFind a point satisfying the formula (4)
Figure BDA00013110773900000320
And
Figure BDA00013110773900000321
when it is, the point is described
Figure BDA00013110773900000322
Can not form a point
Figure BDA00013110773900000323
When in use
Figure BDA00013110773900000324
At SxyThe shape of the tangent plane is a point
Figure BDA00013110773900000325
At the determined form (orthogonal chord), at SzxAnd SyzThe shape (orthogonal chord) corresponding to the tangent plane still belongs to the training image. Briefly, the training image is provided for reconstructing a waypoint
Figure BDA00013110773900000326
The determined morphology is incomplete.
2. Training image form completeness analysis method in simultaneous consideration of two orthogonal sections
In practice for some two-dimensional images, although there is no three-dimensional structure with three orthogonal slices all having similar morphology, there is a three-dimensional structure with two orthogonal slices both having similar morphology. That is, the two-dimensional image is complete when two orthogonal sections are reconstructed to have a three-dimensional structure with a similar shape. In a three-dimensional structure SzxAnd SxyThe orthonormal slice is taken as an example, and the completeness shown in the formula (5) needs to be satisfied in the three-dimensional reconstruction. The specific meanings are shown in the attached figure 8.
Figure BDA0001311077390000041
The invention introduces a completeness parameter RcIs used for expressing the number of points N meeting the completeness requirement of a certain phasesAnd the total number of points NallThe ratio therebetween, i.e.
Figure BDA0001311077390000042
3. Feature region extraction
The characteristic region is that most of the shapes in the region can only appear on one section of the three-dimensional structure. The feature region is mainly determined from the following aspects.
(1) And judging the form completeness in a mode of controlling the reconstruction of two orthogonal sections. Here, the section with the lowest completeness is selected from the three determination results as a reference image, and taking the heterogeneous two-dimensional core image shown in fig. 9 as an example, the reference image selected at this time is shown in fig. 10.
(2) And judging the form completeness in a mode of controlling the reconstruction of three orthogonal sections. The slice with the highest completeness is selected as the reference image, as shown in fig. 11.
(3) Size I of the decision areax×Iy. The decision region size refers to the size of the range of points for which the search does not satisfy the completeness requirement. It is clear that the size of this region is directly determined by the mean particle size of the two phases of the training image. Taking the core two-dimensional image as an example, the decision area is directly dependent on the average size of the rock facies and pores, i.e., the average chord length size of the two facies. And the average chord lengths of the rock facies and the pore facies can be represented by (7) and (8). And the size of the final decision region Ix×IyIs the sum of the average sizes of the two phases, and can be represented by the formula (9).
Figure BDA0001311077390000043
Figure BDA0001311077390000044
Figure BDA0001311077390000051
(4) Ratio R of the number of points not meeting the completeness requirement in the two orthogonal tangent plane control modes to the size of the region2The parameter represents the probability that the judgment area can only appear in one section of the three-dimensional structure, and the threshold value of the parameter is set as
Figure BDA0001311077390000052
Indicating that a certain decision region is deemed to be likely to appear only on one slice of the three-dimensional structure when the rate at which the region does not meet the completeness requirement is greater than the threshold.
(5) Ratio R of the number of points satisfying the completeness requirement in the three orthogonal tangent plane control modes to the size of the region3The parameter represents the probability of the decision region possibly occurring in three orthogonal sections of the three-dimensional structure at the same time. In the invention, the threshold value of the parameter is set as
Figure BDA0001311077390000053
Indicating that when the rate at which a certain decision region satisfies the completeness requirement is greater than the threshold value, the region is considered to be excluded from a range that may only occur on one slice of the three-dimensional structure. The final extracted feature region is shown in fig. 12.
4. Feature region repair
The characteristic region restoration refers to restoring a characteristic region using a region other than the characteristic region in the original two-dimensional image, as shown in fig. 13. The specific repairing method of the invention adopts a block matching algorithm which mainly comprises a plurality of key links.
(1) And repairing the size of the template. The repair template determines the mode of each repair and the morphology of the overall repair area. In order to effectively balance the continuity and variability between adjacent repair modules, the invention adopts the sum of the average chord length of the pore phase and the average chord length of the rock phase of the known area as the size of the repair template. Namely SxAnd SyCalculated by equation (10). Wherein
Figure BDA0001311077390000054
And (i ═ x, y ═ j ═ p, g) represents the average chord length of the j phase in the i direction.
Figure BDA0001311077390000055
(2) Size of the matching region
Figure BDA0001311077390000056
And
Figure BDA0001311077390000057
1/4 size of the repair template size is used in the present invention, i.e., the size of the repair template is used
Figure BDA0001311077390000058
Figure BDA0001311077390000059
Satisfies the formula (11). It should be noted that the matching area is not formed by
Figure BDA00013110773900000510
Forming a rectangular area. The matching area has no fixed form because the area to be filled has no fixed form. In actual operation, the area refers to that a first point at the upper left corner of a certain area to be filled is taken as a reference, and the repairing template is moved back upwards
Figure BDA00013110773900000511
Size and left backspace
Figure BDA00013110773900000512
The known area size is included after the size.
Figure BDA00013110773900000513
(3) The best matching area. The optimal matching area refers to a known area which is scanned point by point in the original training image by using a repairing template, and when the similarity between the matching area in a certain scanning area and the corresponding matching area in the area to be repaired is highest, the scanning area is called as the optimal matching area. After the best matching block is obtained, the best matching area can be filled in the corresponding area in the area to be repaired. When filling, only the area to be repaired needs to be filled, that is, the known matching area remains unchanged. The final restored image is fig. 14.
Drawings
FIG. 1 is a three-dimensional reconstruction method based on two-dimensional images;
FIG. 2 is a two-dimensional core image;
FIG. 3 shows a partial view taken from FIG. 2;
FIG. 4 illustrates chords and lines in a two-dimensional image;
FIG. 5 orthogonal chords in a two-dimensional image;
orthogonal lines in the two-dimensional image of FIG. 6;
FIG. 7 illustrates the relationship of points to orthogonal chords in a three-dimensional structure;
FIG. 8 is a graph of the cross chord relationship of each cross section in the three-dimensional reconstruction process;
FIG. 9 illustrates a two-dimensional training image according to an embodiment of the present invention;
FIG. 10 is a graph illustrating the completeness of control over two slice profiles in an embodiment of the present invention;
FIG. 11 is a diagram illustrating the completeness of control over the morphology of three slices according to an embodiment of the present invention;
FIG. 12 is a feature region extracted in an embodiment of the present invention;
FIG. 13 is an image inpainting principle in an embodiment of the invention;
FIG. 14 is an image after restoration in an embodiment of the invention;
FIG. 15 is a three-dimensional structure reconstructed in an embodiment of the invention;
FIG. 16 is a three-dimensional structure referenced in an embodiment of the present invention;
FIG. 17 is a comparison result of two-point correlation functions in x-direction of the reconstructed structure and the reference structure according to an embodiment of the present invention;
FIG. 18 is a comparison of two-point correlation functions in the y-direction of the reconstructed structure and the reference structure according to an embodiment of the present invention;
FIG. 19 is a comparison of x-direction linear path functions of a reconstructed structure and a reference structure according to an embodiment of the present invention;
FIG. 20 is a comparison of the y-direction linear path functions of the reconstructed structure and the reference structure according to an embodiment of the present invention;
Detailed Description
The following describes the specific implementation process of the present invention in further detail with reference to a specific case, but the implementation case only describes the implementation method of the present invention in detail, and should not be construed as any limitation to the protection content of the present invention. The specific implementation process of the invention comprises the following steps:
and step one, calculating completeness data of the training image under the condition of controlling three orthogonal sections according to the formula (4).
And secondly, calculating completeness data of the training image under the condition of controlling two orthogonal sections according to the formula (5).
And thirdly, determining the morphological reappearance condition of each orthogonal section of the corresponding given training image in the target three-dimensional structure by combining the analysis results of the previous two steps, thereby determining the corresponding reconstruction mode. Taking fig. 9 as an example, the form completeness of the pore phase in the three orthogonal sections is relatively high, and a mode of simultaneously controlling the three orthogonal sections can be adopted. The presence of a feature region is very low in controlling both reconstruction modes, i.e. it is stated that the feature region can only appear in one orthogonal slice of the three-dimensional structure. Therefore, the characteristic region is determined firstly, then the characteristic region is repaired by adopting an image repairing technology, then a reconstruction mode of simultaneously controlling three orthogonal sections is adopted, the repaired image is taken as a training image, a three-dimensional structure is reconstructed, and finally the characteristic region is formed on one orthogonal section of the reconstructed three-dimensional structure. In this case SxyCutting into a section.
Fourthly, extracting the feature region of the image, namely selecting the result with the lowest completeness from the results considering the completeness of the two orthogonal sections, as shown in figure 10, and selecting the result with the highest completeness from the results considering the completeness of the three orthogonal sections, as shown in figure 11, and determining a result map with the feature region, as shown in figure 12.
Fifthly, repairing the characteristic region, namely filling the marked characteristic region by using the known region pair in the figure 13, and adopting the block matching mode stated above in the specific filling process. The results after repair are shown in FIG. 14.
And sixthly, reconstructing a three-dimensional structure by taking the repaired image, shown in figure 14, as a training image in three-dimensional reconstruction and adopting a reconstruction mode of simultaneously controlling three orthogonal sections.
Seventh, it can be seen from the above description that the feature region shape in the training image can only appear on one orthogonal slice of the three-dimensional structure, and thus the feature region shape is further formed on one slice of the reconstructed three-dimensional structure, and the final reconstructed structure is shown in fig. 15, and fig. 16 is the three-dimensional structure referred to.
In order to show the effect of the present invention, the two-point correlation function and the linear path function commonly used in random image reconstruction are used to perform quantitative comparison on the reconstructed result in this embodiment. The results of the comparison are shown in FIGS. 17-20. As can be seen from the figure, the statistical function curve of the reconstructed image and the original image has better coincidence. Therefore, the three-dimensional reconstruction work of the heterogeneous core can be effectively realized by adopting the method.
The above embodiments are merely preferred embodiments of the present invention, and are not intended to limit the technical solutions of the present invention, and any technical solutions that can be implemented on the basis of the above embodiments without creative efforts should be considered to fall within the protection scope of the present invention.

Claims (1)

1. The heterogeneous core three-dimensional structure reconstruction algorithm based on the form completeness is realized by the following steps:
step 1: determining a specified two-dimensional training image, and analyzing a form completeness result when three orthogonal sections are considered;
step 2: determining a specified two-dimensional training image, and analyzing a form completeness result when two orthogonal sections are considered;
and step 3: extracting a characteristic region corresponding to the specified two-dimensional training image;
and 4, step 4: performing image restoration on the characteristic region of the specified two-dimensional training image;
and 5: reconstructing a three-dimensional structure with only one section conforming to the characteristic region;
wherein, determining a specified two-dimensional training image, and taking three orthogonal sections into consideration, the analysis method is represented by formula (1):
Figure FDA0002761171110000011
to be provided with
Figure FDA0002761171110000012
For example, it is represented bySzxPoint in tangent plane
Figure FDA0002761171110000013
Determined orthogonal line
Figure FDA0002761171110000014
The line length of the ith line in the x direction is equal to SxyPoint in tangent plane
Figure FDA0002761171110000015
Determined orthogonal line
Figure FDA0002761171110000016
The length of the line of the ith line in the x direction requires that two lines in the x direction of each tangent plane can be combined into a chord; with SxyMidpoint of tangent plane
Figure FDA0002761171110000017
For example, if at SzxAnd SyzThere are points satisfying the formula (1) respectively
Figure FDA0002761171110000018
And
Figure FDA0002761171110000019
description of the invention
Figure FDA00027611711100000110
And
Figure FDA00027611711100000111
can form a point in three-dimensional space
Figure FDA00027611711100000112
And point
Figure FDA00027611711100000113
The forms corresponding to the three orthogonal sections all belong to training images; wherein, in the d directionThe directed line segment starting at the same phase and ending at the same phase and all the pixel points belonging to the phase is called chord, CdIs represented by CyIs a chord in the y-direction; any part of the chord is called a line, denoted LdIs represented by LxIs a line in the x-direction; c is to bedThe number of the pixel points is called CdChord length of (1) (C)d) Denotes that L is correspondingly reduceddThe number of the pixel points is called LdLength of (1) isd) It is shown that,
Figure FDA00027611711100000114
is orthogonal to the point
Figure FDA00027611711100000115
Line L ofxAnd LyFormed structure Lx⊥LyReferred to as the orthogonal lines;
wherein, determining a specified two-dimensional training image, and taking two orthogonal sections into consideration, the analysis method is represented by the formula (2):
Figure FDA0002761171110000021
since the line is part of a chord, equation (2) relaxes the effect of building a three-dimensional point
Figure FDA0002761171110000022
A constraint of time; but at the same time only the target three-dimensional structure S is taken into accountzxAnd SxyThe section is in morphological relation with the training image, and the pair S is abandonedyzLimiting the shape of the section;
wherein, the characteristic region that the appointed two-dimensional training image corresponds is drawed, and the characteristic region is that the overwhelming majority of shapes in this region can only appear on a tangent plane of three-dimensional structure, and the step is:
(1) judging the form completeness in a mode of controlling the reconstruction of two orthogonal sections; selecting a section with the lowest completeness from the three judgment results as a reference image;
(2) judging the form completeness in a mode of controlling the reconstruction of three orthogonal sections; the section with the highest completeness is selected as a reference image;
(3) size I of the decision areax×Iy(ii) a The size of the judgment area refers to the size of the range of the points which do not meet the requirement of completeness; it is clear that the size of this region is directly determined by the mean particle size of the two phases of the training image; taking a core two-dimensional image as an example, the judgment area directly depends on the average size of rock facies and pores, namely the average chord length of the two facies; and the average chord lengths of the rock phase and the pore phase can be represented by (3) and (4); and the size of the final decision region Ix×IyIs the sum of the average sizes of the two phases, namely can be represented by the formula (5);
Figure FDA0002761171110000023
Figure FDA0002761171110000024
Figure FDA0002761171110000025
(4) ratio R of the number of points not meeting the completeness requirement in the two orthogonal tangent plane control modes to the size of the region2The parameter represents the probability that the judgment area can only appear in one section of the three-dimensional structure, and the threshold value of the parameter is set to be
Figure FDA0002761171110000026
Indicating that when the rate of a certain judgment region not meeting the completeness requirement is larger than the threshold value, the region is determined as possibly appearing on one section of the three-dimensional structure;
(5) the number of points satisfying the completeness requirement in the mode of controlling three orthogonal tangent planes and the methodRatio R of area sizes3The parameter represents the probability that the judgment area may appear in three orthogonal tangent planes of the three-dimensional structure at the same time, and the threshold value of the parameter is set as
Figure FDA0002761171110000031
Indicating that when the ratio of satisfying the completeness requirement of a certain judgment region is larger than the threshold value, the region is determined to be excluded from the range which can only appear on one section of the three-dimensional structure;
the image restoration of the feature area of the designated two-dimensional training image means that the feature area is restored by using the area except the feature area in the original two-dimensional image, and the specific restoration method adopts a block matching algorithm and comprises the following steps:
(1) repairing the size of the template; the repair template determines the form of each repair mode and the overall repair area; in order to effectively balance the continuity and variability between adjacent repair modules, the sum of the average chord length of the pore phase and the average chord length of the rock phase of a known area is used as the size of the repair template; namely SxAnd SyCalculating by the formula (6); wherein
Figure FDA0002761171110000032
Figure FDA0002761171110000033
Representing the average chord length of the j phase in the i direction;
Figure FDA0002761171110000034
(2) size of the matching region
Figure FDA0002761171110000035
And
Figure FDA0002761171110000036
1/4 size using the dimensions of the repair template, i.e.
Figure FDA0002761171110000037
Satisfies the formula (7); the matching region is not composed of
Figure FDA0002761171110000038
A rectangular area is formed; the matching area has no fixed form because the area to be filled has no fixed form; in actual operation, the area refers to that a first point at the upper left corner of a certain area to be filled is taken as a reference, and the repairing template is moved back upwards
Figure FDA0002761171110000039
Size and left backspace
Figure FDA00027611711100000310
The known region size included after the size;
Figure FDA00027611711100000311
(3) a best matching region; the optimal matching area refers to a known area which is scanned point by point in the original training image by using a repairing template, and when the similarity between the matching area in a certain scanning area and the corresponding matching area in the area to be repaired is highest, the scanning area is called as the optimal matching area; after the best matching block is obtained, filling the best matching area into a corresponding area in the area to be repaired; when filling, only the area to be repaired needs to be filled, that is, the known matching area remains unchanged.
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