CN112819955A - Improved reconstruction method based on digital image three-dimensional model - Google Patents

Improved reconstruction method based on digital image three-dimensional model Download PDF

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CN112819955A
CN112819955A CN202110281772.7A CN202110281772A CN112819955A CN 112819955 A CN112819955 A CN 112819955A CN 202110281772 A CN202110281772 A CN 202110281772A CN 112819955 A CN112819955 A CN 112819955A
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刘江峰
林远健
李晓昭
黄炳香
张凯
孟庆彬
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Abstract

The invention discloses an improved reconstruction method based on a digital image three-dimensional model, which is based on binary image information of a two-dimensional slice image of a porous medium, adopts a single-point probability function, a two-point probability function and a linear path function to represent the pore information of a real porous medium, and only performs incremental calculation in a specific direction with an exchange pixel as a center to establish a system statistical function and a system energy updating form of a simulated annealing algorithm when random position exchange of pore pixels occurs. The incremental calculation uses an incremental calculation method of a two-point probability function and a linear path function to replace the global calculation adopted by the traditional simulated annealing method. And stopping reconstruction until the annealing system is updated to meet the cooling criterion, outputting a reconstruction structure, and generating a three-dimensional model of the porous medium. The method avoids repeated calculation of a large amount of data, shortens the time for updating the system, improves the reconstruction efficiency of the porous medium image, and has higher accuracy and efficiency.

Description

Improved reconstruction method based on digital image three-dimensional model
Technical Field
The invention relates to the technical field of three-dimensional image reconstruction, in particular to an improved reconstruction method based on a digital image three-dimensional model.
Background
In the whole process of image reconstruction by using the simulated annealing algorithm, the most time-consuming part is the calculation of the statistical function value of the reconstruction system. For the conventional simulated annealing algorithm, after each pixel position exchange, the statistical function value must be updated by traversing the pixel points at all positions, and then the system update can be judged to be accepted. In fact, in the actual program implementation process, in order to reduce the complexity of the algorithm and to shorten the calculation time of the program, most scholars only choose to calculate the statistical function values in specific directions, and most commonly choose to calculate the statistical function values in mutually orthogonal directions [1,2,3 ]. In this case, the influence of pixel position switching on the overall statistical function value of the system is only caused by the change of the calculated value in a specific direction centering on the switching pixel point, and the pixel points at other positions have no influence on the calculation of the statistical function value.
[1]Yeong C L Y,Torquato S.Reconstructing random media.Ii.Three-dimensional media from two-dimensional cuts[J].Physical Review E,1998,58(1):224-233.
[2]Ju Y,Zheng J,Epstein M,et al.3d numerical reconstruction of well-connected porous structure of rock using fractal algorithms[J].Computer Methods in Applied Mechanics and Engineering,2014,279:212-226.
[3]Karsanina M V,Gerke K M,Skvortsova E B,et al.Universal spatial correlation functions for describing and reconstructing soil microstructure[J].Plos One,2015,10(5):0126515.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems, the invention provides an improved reconstruction method based on a digital image three-dimensional model, which shortens the reconstruction time and improves the reconstruction efficiency.
The technical scheme is as follows: in order to realize the purpose of the invention, the technical scheme adopted by the invention is as follows: an improved reconstruction method based on a digital image three-dimensional model comprises the following steps:
step 1, carrying out gray level conversion on an original image to obtain a gray level image; calculating gradient amplitude of pixels by using a Sobel operator, carrying out pixel replacement to obtain a replaced histogram based on gradient, dividing gray levels, carrying out threshold segmentation on an original gray level image, and obtaining a reference binary image of a simulated annealing algorithm;
step 2, counting the porosity of the reference image according to the single-point probability function, randomly generating an initial reconstruction image, and extracting and representing contribution information about the pore structure of the reference image obtained in the step 1 by using the two-point probability function and the linear path function;
and 3, taking the weighted sum of the square difference of the contribution values of the two-point probability function and the square difference of the contribution values of the linear path function of the reference image and the initial reconstruction image as an initial energy value C, and expressing as follows:
Figure BDA0002978819690000021
wherein R is the statistical distance of the distance between two pixels in the image, R is the maximum statistical distance between two pixels, α and β are weight coefficients, α + β is 1, S (R), l (R) are the two-point probability function value and the linear path function value of the system to be reconstructed, respectively, S (R)0(r),L0(r) two point probability function values and linear path function values of the reference image, respectively;
step 4, randomly selecting the position exchange of the pore and the matrix pixel point, updating energy by adopting a mode of performing incremental calculation in a specific direction of an exchange pixel center, searching pixels in the specific direction of the pore when pixel exchange occurs, and performing incremental delta C calculation according to a two-point probability function and a linear path function respectively;
step 5, based on Metropolis criterion, the acceptance criterion for rebuilding the system updating is that P is more than or equal to rand (0,1), P is the acceptance probability of the new system, if the criterion is met, the exchange of the positions of the pore and matrix pixel points is accepted, and the original system is updated; otherwise, rejecting the exchange of the positions of the pores and the matrix pixel points, keeping the original system unchanged, and returning to the step 4 to continue the exchange of the pores and the matrix pixel points at other positions; the acceptance probability is calculated as follows:
Figure BDA0002978819690000022
wherein T is the temperature used in the simulated annealing process;
step 6, continuously repeating the iteration process from the step 4 to the step 5 under the same temperature condition until the reconstruction system reaches a stable equilibrium state; then, cooling is carried out according to a certain cooling rule, so that the system can reach a balance under any temperature condition; when the temperature or the energy of the system is lower than a certain critical value, the system reconstruction is finished, and a reconstructed binary image matrix is output, so that a three-dimensional model of the porous medium is generated.
Further, the threshold value is selected in the step 1 in a gray scale division mode, and a reference image of a simulated annealing method is obtained through a mean value segmentation technology; dividing the gray level in the following form:
[0.255]＝[0,GP]+[GP,GV]+[GV,255]；
wherein G isP,GVThe gray values are respectively at the highest peak position and the middle lowest valley position on the left side of the gradient histogram; taking the optimal threshold value as T*＝(GP+GV) And/2, performing threshold segmentation on the original image to obtain a reference binary image simulating an annealing algorithm.
Has the advantages that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
although the traditional method only selects a specific direction to calculate the statistical function, the complexity of the algorithm is reduced, and the calculation time of the program is shortened, a large amount of data is repeatedly calculated, and the reconstruction efficiency is low. The improved simulated annealing algorithm provided by the invention only needs to perform incremental calculation in a specific direction taking the exchange pixel as a center, and does not need to perform global calculation adopted by the conventional simulated annealing algorithm. On the premise of ensuring the accuracy of the reconstructed model, the improved simulated annealing algorithm obviously improves the reconstruction efficiency of the model, and simultaneously makes up the defects of high economic cost, low pore resolution and the like of the physical scanning reconstruction technology.
The method is based on binary image information of a two-dimensional slice image of a real porous medium, and adopts a single-point probability function, a two-point probability function and a linear path function to represent pore information (porosity, pore correlation and pore connectivity) of the real porous medium, and when random position exchange of pore pixels is generated, an updating form of a system statistical function and system energy of a simulated annealing algorithm is established in a mode of performing incremental calculation only in a specific direction with the exchange pixels as centers. The incremental calculation uses an incremental calculation method of a two-point probability function and a linear path function to replace the global calculation adopted by the traditional simulated annealing method. And when the annealing system updating meets the Metropolis cooling criterion, stopping the system updating and the reconstruction, and outputting a reconstructed binary image matrix to generate the three-dimensional model of the porous medium. The improved algorithm avoids repeated calculation of a large amount of data in common simulated annealing algorithms, greatly shortens the updating time of the system, obviously improves the reconstruction efficiency of porous medium images, particularly the reconstruction of large-scale three-dimensional images, and has higher accuracy and efficiency than the conventional simulated annealing algorithms.
Drawings
FIG. 1 is a flow chart of a simulated annealing algorithm;
FIG. 2 is a row and column of selected pixels;
FIG. 3 is a one-dimensional example image;
FIG. 4 is a one-dimensional example image with three and four consecutive adjacent pore phases.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
In the three-dimensional image reconstruction, the simulated annealing algorithm comprises 5 steps: firstly, acquiring and preprocessing a reference image; generating a reference image and an initial reconstruction image; thirdly, selecting and calculating a statistical function; fourthly, calculating and updating system energy; and fifthly, finishing temperature cooling and rebuilding. The specific flow is shown in fig. 1. The invention relates to an improved reconstruction method based on a digital image three-dimensional model, which comprises the following steps:
step 1, performing Gray level conversion on an original RGB color image according to a formula Gray of 0.299 × R +0.587 × G +0.114 × B to obtain a Gray level image of a medium; dividing the gray value into a low part, a middle part and a high part based on the gray digital image, and adjusting the contrast according to the principle of enhancing the contrast of the pixel points in the middle gray value interval and weakening the contrast of the pixel points in the low gray value interval and the high gray value interval; combining the two preprocessing methods to obtain a preprocessed image; then, calculating the gradient amplitude of the pixel by using a Sobel operator, carrying out pixel replacement to obtain a replaced histogram based on the gradient, and dividing the gray level in the following form:
[0.255]＝[0,GP]+[GP,GV]+[GV,255]；
wherein G isP,GVThe gray values are respectively at the highest peak position and the middle lowest valley position on the left side of the gradient histogram; taking the optimal threshold value as T*＝(GP+GV) And/2, performing threshold segmentation on the original image to obtain a reference binary image simulating an annealing algorithm.
Step 2, counting the porosity of the reference image according to the single-point probability function, randomly generating an initial reconstruction image, and extracting and representing contribution information about the pore structure of the reference image obtained in the step 1 by using the two-point probability function and the linear path function; the single-point probability function, the two-point probability function and the linear path function expression are respectively as follows:
Figure BDA0002978819690000041
wherein I (x) is the attribute value of a pixel point at the x position in the image, the pore space is 1, and the matrix is 0; r is the statistical distance of the distance between two pixels in the image; and < > represents averaging the calculated values inside the image.
And 3, taking the weighted sum of the square difference of the contribution values of the two-point probability function and the square difference of the contribution values of the linear path function of the reference image and the initial reconstruction image as an initial energy value C, and expressing as follows:
Figure BDA0002978819690000042
wherein R is the statistical distance of the distance between two pixels in the image, R is the maximum statistical distance between two pixels, α and β are weight coefficients, α + β is 1, S (R), l (R) are the two-point probability function value and the linear path function value of the system to be reconstructed, respectively, S (R)0(r),L0(r) two point probability function values and linear path function values of the reference image, respectively;
and 4, because the reconstruction system of the simulated annealing method is carried out by using a random algorithm, the most time-consuming part is the calculation of a statistical function value of the reconstruction system, when a pore pixel or a matrix pixel is randomly selected in the reconstruction system and pixel exchange is carried out, the system enters a new state, the energy value of the system is changed, and the process is the energy updating of the annealing system. The invention provides an improved simulated annealing algorithm, namely, after pixel position exchange, incremental calculation is only needed to be carried out in a specific direction taking an exchange pixel as a center, and global calculation adopted by a conventional simulated annealing algorithm is not needed, which is the core of the improved simulated annealing algorithm. The method comprises the following specific steps:
randomly selecting the position exchange of pores and matrix pixel points, updating energy by adopting a mode of performing incremental calculation in a specific direction of an exchange pixel center, searching pixels in the specific direction of a delay pixel point (pore) when pixel exchange occurs, and performing incremental delta C calculation according to a two-point probability function and a linear path function respectively;
now, let CiniAnd CnewBefore and after pixel position exchange respectively corresponding to reconstructed imageSelecting the contribution value of the pixel point (pore phase or matrix phase) to the statistical function, the change of the system statistical function value caused by this pixel position exchange can be calculated by the following formula:
△C＝Cnew-Cini
the updated statistical function value of the system can be easily calculated according to the calculated statistical function increment; therefore, the incremental calculation of the statistical function is the key to improving the simulated annealing algorithm.
The two-point probability function and the increment calculation method of the linear path function will be described in detail below.
A first part: the contribution of the aperture pixel to the two-point probability function is calculated.
(1) As in the 2D image shown in fig. 2, the contribution value of the aperture pixel point to the entire system is twice as large as its own contribution value, and the correlation is expressed as follows:
Ctotal＝2Cind
in the above formula, CtotalA total contribution to the overall system for the presence of aperture pixels at the selected location; cindIs the individual contribution value of the aperture pixel to the system at the selected location.
(2) As shown in fig. 3, two points of probability function incremental calculations are performed. The upper row in the figure: a one-dimensional example image having an aperture phase and a matrix phase; descending: each pixel considers only its own contribution value; pixel contribution values as shown in fig. 3, the distance r between system pixels is 1, and the individual contribution of the selected aperture to the system is 2; because the calculation of the two-point probability function needs to traverse each pixel point in the row, the contribution of the existence of the pore phase at the selected position to the pore phases positioned at the two sides of the pore phase is 1 respectively; when the traversal of each pixel in the system is complete, the two-point probability function has a value of 4 (position in FIG. 3), which is twice the individual contribution of the pore phase at the selected position.
In the actual calculation process, the increment of the two-point statistical function before and after the pixel position exchange can be expressed as:
Figure BDA0002978819690000051
in the above formula, the first and second carbon atoms are,
Figure BDA0002978819690000052
and
Figure BDA0002978819690000053
and the individual contribution values of the pore phase pixel points to the two-point statistical function of the system at the selected positions before and after the pixel position exchange respectively correspond to the individual contribution values.
A second part: and (4) calculating the increment of the linear path function.
(1) And according to the fact that the linear path function contains connectivity information of the system internal pores, giving a calculation method of the linear path function of the continuous adjacent pore phases, as shown in figure 4. The upper row in the figure: successive adjacent apertures; left-most column: different distances r between two arbitrary pixels in the system; rightmost column: the sum of the contributions of each pixel to the linear path function at different distances r in the system.
FIG. 4 shows the relationship between the linear path function and the distance r, where for N consecutive adjacent pore phases existing in the selected calculation direction, the sum C of the contributions of all pores in the system to the linear path function is given at a certain statistical distance rsumCan be expressed as follows:
Figure BDA0002978819690000054
(2) incremental calculation of the linear path function: searching for a pore pixel along four directions (taking 2D image reconstruction as an example) respectively by taking a pixel point (a pore or a matrix) at a selected position as a center, and taking the matrix pixel as a searching boundary; and counting the number of the pore pixels in the searching process to finally obtain the number of the pore pixels which are continuously adjacent in four directions, wherein the matrix pixels are respectively marked as N0-u、N0-d、N0-lAnd N0-rThe aperture pixels are respectively marked as N1-u、N1-d、N1-lAnd N1-r(ii) a Finally, theThe total number of consecutive adjacent pores centered around the selected pore and the matrix pixel is calculated in the same row and column directions, respectively.
For the initial system before pixel position swapping, the total number of consecutive adjacent phases of apertures in the row and column directions can be calculated by the following equation:
Figure BDA0002978819690000055
in the formula
Figure BDA0002978819690000061
And
Figure BDA0002978819690000062
respectively the total number of continuous adjacent pore phases in the row and column directions of the initial system before pixel position exchange;
for the updated system after the pixel position exchange, the initial pore phase is updated to the matrix phase, the pore connectivity may be weakened, and the initial matrix phase is updated to the pore phase, the pore connectivity may be strengthened, so the above formula needs to be modified to calculate the total number of consecutive adjacent pore phases of the updated system in the row and column directions, which is as follows:
Figure BDA0002978819690000063
in the formula
Figure BDA0002978819690000064
And
Figure BDA0002978819690000065
respectively updating the system after pixel position exchange, and counting the total continuous adjacent pore phases in the row and column directions;
finally, the linear path function increment of the updating system is obtained:
Figure BDA0002978819690000066
step 5, based on Metropolis criterion, the acceptance criterion for rebuilding the system updating is that P is more than or equal to rand (0,1), P is the acceptance probability of the new system, if the criterion is met, the exchange of the positions of the pore and matrix pixel points is accepted, and the original system is updated; otherwise, rejecting the exchange of the positions of the pores and the matrix pixel points, keeping the original system unchanged, and returning to the step 4 to continue the exchange of the pores and the matrix pixel points at other positions; the acceptance probability is calculated as follows:
Figure BDA0002978819690000067
wherein T is the temperature used in the simulated annealing process;
step 6, under the same temperature condition, continuously repeating the iterative process of 'pixel exchange probability judgment acceptance/rejection' from the step 4 to the step 5 until the reconstruction system reaches a stable equilibrium state; then slowly cooling according to a certain cooling rule, so that the system can reach a balance under any temperature condition; and the energy of the system is gradually reduced along with the gradual reduction of the temperature of the system, and in general, when the temperature or the energy of the system is lower than a certain critical value, the system reconstruction is finished, and a reconstructed binary image matrix is output, so that a three-dimensional model of the porous medium is generated.

Claims (2)

1. An improved reconstruction method based on a digital image three-dimensional model is characterized in that: the method comprises the following steps:
step 1, carrying out gray level conversion on an original image to obtain a gray level image; calculating gradient amplitude of pixels by using a Sobel operator, carrying out pixel replacement to obtain a replaced histogram based on gradient, dividing gray levels, carrying out threshold segmentation on an original gray level image, and obtaining a reference binary image of a simulated annealing algorithm;
step 2, counting the porosity of the reference image according to the single-point probability function, randomly generating an initial reconstruction image, and extracting and representing contribution information about the pore structure of the reference image obtained in the step 1 by using the two-point probability function and the linear path function;
and 3, taking the weighted sum of the square difference of the contribution values of the two-point probability function and the square difference of the contribution values of the linear path function of the reference image and the initial reconstruction image as an initial energy value C, and expressing as follows:
Figure FDA0002978819680000011
wherein R is the statistical distance of the distance between two pixels in the image, R is the maximum statistical distance between two pixels, α and β are weight coefficients, α + β is 1, S (R), l (R) are the two-point probability function value and the linear path function value of the system to be reconstructed, respectively, S (R)0(r),L0(r) two point probability function values and linear path function values of the reference image, respectively;
step 4, randomly selecting the position exchange of the pore and the matrix pixel point, updating energy by adopting a mode of performing incremental calculation in a specific direction of an exchange pixel center, searching pixels in the specific direction of the pore when pixel exchange occurs, and performing incremental delta C calculation according to a two-point probability function and a linear path function respectively;
step 5, based on Metropolis criterion, the acceptance criterion for rebuilding the system updating is that P is more than or equal to rand (0,1), P is the acceptance probability of the new system, if the criterion is met, the exchange of the positions of the pore and matrix pixel points is accepted, and the original system is updated; otherwise, rejecting the exchange of the positions of the pores and the matrix pixel points, keeping the original system unchanged, and returning to the step 4 to continue the exchange of the pores and the matrix pixel points at other positions; the acceptance probability is calculated as follows:
Figure FDA0002978819680000012
wherein T is the temperature used in the simulated annealing process;
step 6, continuously repeating the iteration process from the step 4 to the step 5 under the same temperature condition until the reconstruction system reaches a stable equilibrium state; then, cooling is carried out according to a certain cooling rule, so that the system can reach a balance under any temperature condition; when the temperature or the energy of the system is lower than a certain critical value, the system reconstruction is finished, and a reconstructed binary image matrix is output, so that a three-dimensional model of the porous medium is generated.
2. The improved digital image-based three-dimensional model reconstruction method of claim 1, wherein: selecting a threshold in the step 1 by adopting a gray scale division form, and acquiring a reference image of a simulated annealing method by using a mean segmentation technology; dividing the gray level in the following form:
[0.255]＝[0,GP]+[GP,GV]+[GV,255]；
wherein G isP,GVThe gray values are respectively at the highest peak position and the middle lowest valley position on the left side of the gradient histogram; taking the optimal threshold value as T*＝(GP+GV) And/2, performing threshold segmentation on the original image to obtain a reference binary image simulating an annealing algorithm.
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