CN112819955B - Improved three-dimensional model reconstruction method based on digital image - Google Patents
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Abstract
The invention discloses an improved reconstruction method based on a three-dimensional model of a digital image, 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 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 statistic function of a simulated annealing algorithm system and an updating form of system energy when random position exchange of pore pixels is generated. Wherein the incremental computation uses an incremental computation method of a two-point probability function and a linear path function instead of the global computation adopted by the traditional simulated annealing method. Stopping reconstruction until the updating of the annealing system reaches the condition that the cooling criterion is met, 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 high efficiency.
Description
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 conventional simulated annealing algorithms, after each pixel position exchange, the statistical function values must be updated by traversing all pixel points at all positions to determine that the system update can be accepted. In fact, in the actual program implementation process, in order to reduce the complexity of the algorithm and speed up the calculation time of the program, most students choose to perform the calculation of the statistical function value only in a specific direction, and most commonly choose to perform the calculation in mutually orthogonal directions [1,2,3]. In this case, the pixel position exchange has an influence on the statistical function value of the system as a whole, only due to a change in the calculated value in a specific direction centering on the exchanged 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 invention aims to: 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 achieve 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 the gradient amplitude of a pixel by using a Sobel operator, replacing the pixel to obtain a replaced histogram based on the gradient, dividing the gray level, and performing threshold segmentation on an original gray level image to obtain 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 reconstructed image, and extracting and characterizing the contribution information about the pore structure of the reference image obtained in the step 1 by using a two-point probability function and a linear path function;
and 3, taking a 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 reconstructed image as an initial energy value C, wherein the weighted sum is expressed as follows:
wherein R is the statistical distance between two pixels in the image, R is the maximum statistical distance between two pixels, alpha and beta are weight coefficients, alpha+beta=1, S (R), L (R) is the two-point probability function value and the linear path function value of the system to be reconstructed, S 0 (r),L 0 (r) two-point probability function values and linear path function values of the reference image, respectively;
step 4, randomly selecting the positions of the pores and the matrix pixel points for exchanging, updating energy in a mode of performing incremental calculation in a specific direction of exchanging pixel centers, searching the pixels in the specific direction of the pores when pixel exchanging 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 of the updating of the reconstruction system is P more than or equal to rand (0, 1), P is the acceptance probability of the new system, if the criterion is met, the replacement of the positions of the pores and the matrix pixel points is accepted, and the original system is updated; otherwise, refusing the exchange of the positions of the pores and the matrix pixels, keeping the original system unchanged, and returning to the step 4 to continue the exchange of the pores and the matrix pixels at other positions; the probability of acceptance is calculated as follows:
wherein T is the temperature used in the simulated annealing process;
step 6, continuously repeating the iterative processes of the steps 4 to 5 under the same temperature condition until the reconstruction system reaches a stable equilibrium state; then cooling according to a certain cooling rule, so that the system can reach a balance under any temperature condition; when the temperature or energy of the system is lower than a certain critical value, the system is rebuilt, and a rebuilt binary image matrix is output, so that a three-dimensional model of the porous medium is generated.
Further, in the step 1, the selection of the threshold value adopts a gray scale division form, and a reference image simulating an annealing method is obtained through a mean value taking segmentation technology; dividing gray level into the following modes:
[0.255]＝[0,G P ]+[G P ,G V ]+[G V ,255]；
wherein G is P ,G V Gray values at the highest crest at the left side and the lowest trough at the middle part of the gradient histogram are respectively obtained; taking the optimal threshold value as T * ＝(G P +G V ) And (2) carrying out threshold segmentation on the original image to obtain a reference binary image of the simulated annealing algorithm.
The beneficial effects are that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
in the traditional method, although only a specific direction is selected for calculating the statistical function, the complexity of the algorithm is reduced, the calculation time of a 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 centering on the exchange pixels, and does not need to perform global calculation adopted by the conventional simulated annealing algorithm. On the premise of ensuring the accuracy of the reconstruction model, the model reconstruction efficiency is obviously improved by improving the simulated annealing algorithm, and the defects of high economic cost, low pore resolution and the like of the physical scanning reconstruction technology are overcome.
The method is based on binary image information of a two-dimensional slice image of a real porous medium, 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 establishes a statistic function of a simulated annealing algorithm system and an updating form of system energy only by performing incremental calculation in a specific direction with an exchange pixel as a center when random position exchange of pore pixels is generated. Wherein the incremental computation uses an incremental computation method of a two-point probability function and a linear path function instead of the global computation adopted by the traditional simulated annealing method. And stopping system updating and stopping reconstruction until the annealing system updating reaches the condition that the cooling criterion of the metropolis is met, and outputting a reconstructed binary image matrix, so that a three-dimensional model of the porous medium is generated. The improved algorithm avoids repeated calculation of a large amount of data in the common simulated annealing algorithm, greatly shortens the system updating time, remarkably improves the reconstruction efficiency of porous medium images, and particularly has higher accuracy and higher efficiency than the conventional simulated annealing algorithm, and the reconstruction of large-scale three-dimensional images is improved.
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 scheme of the invention is further described below with reference to the accompanying drawings and examples.
In three-dimensional image reconstruction, the simulated annealing algorithm comprises 5 steps: (1) acquiring and preprocessing a reference image; (2) generating a reference image and an initial reconstructed image; (3) selecting and calculating a statistical function; (4) calculating and updating system energy; (5) and (5) finishing the temperature cooling and reconstruction. The specific flow is shown in figure 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 conversion on an original RGB color image according to the formula gray=0.299×R+0.587×G+0.114×B to obtain a Gray image of a medium; dividing a gray value into a low part, a medium part and a high part based on a gray digital image, and carrying out contrast adjustment according to a 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, replacing the pixel to obtain a replaced histogram based on the gradient, and dividing the gray level in the following modes:
[0.255]＝[0,G P ]+[G P ,G V ]+[G V ,255]；
wherein G is P ,G V Gray values at the highest crest at the left side and the lowest trough at the middle part of the gradient histogram are respectively obtained; taking the optimal threshold value as T * ＝(G P +G V ) And (2) carrying out threshold segmentation on the original image to obtain a reference binary image of the simulated annealing algorithm.
Step 2, counting the porosity of the reference image according to the single-point probability function, randomly generating an initial reconstructed image, and extracting and characterizing the contribution information about the pore structure of the reference image obtained in the step 1 by using a two-point probability function and a linear path function; the single-point probability function, the two-point probability function and the linear path function expression are respectively as follows:
wherein I (x) is an attribute value of a pixel point at an x position in the image, a pore is 1, and a matrix is 0; r is the statistical distance of the distance between two pixels in the image; and (4) carrying out average operation on the internal calculated value of the image.
And 3, taking a 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 reconstructed image as an initial energy value C, wherein the weighted sum is expressed as follows:
wherein R is the statistical distance between two pixels in the image, R is the maximum statistical distance between two pixels, alpha and beta are weight coefficients,α+β=1, S (r), L (r) being the two-point probability function value and the linear path function value of the system to be reconstructed, S 0 (r),L 0 (r) two-point probability function values and linear path function values of the reference image, respectively;
and 4, because the reconstruction system for simulating the annealing method is carried out by utilizing a random algorithm, the most time-consuming part is the calculation of the statistical function value of the reconstruction system, when a pore pixel or a matrix pixel is randomly selected in the reconstruction system to carry out pixel exchange, the system enters a new state, the system energy value is changed along with the new state, and the process is the energy update 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 steps:
randomly selecting the pore and matrix pixel point positions for exchange, updating energy in a mode of performing incremental calculation in a specific direction of an exchange pixel center, searching pixels in the specific direction of a 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 C ini And C new The amount of change in the system statistical function value caused by the pixel position exchange can be calculated by the following formula, corresponding to the contribution values of the selected pixel points (pore phase or matrix phase) to the statistical function before and after the pixel position exchange of the reconstructed image respectively:
△C＝C new -C ini
the updated statistical function value of the system can be easily calculated according to the calculated statistical function increment; thus, incremental computation of the statistical function is a key to improving the simulated annealing algorithm.
The incremental calculation method of the two-point probability function and the linear path function will be described in detail below.
A first part: and calculating the contribution value of the pore pixel to the two-point probability function.
(1) As in the 2D image shown in fig. 2, the correlation is expressed as follows when the contribution value of the pore pixel point to the whole system is twice as large as the contribution value thereof:
C total ＝2C ind
in the above, C total A total contribution to the overall system for the presence of aperture pixels at the selected locations; c (C) ind Individual contributions of aperture pixels to the system at selected locations.
(2) As shown in fig. 3, a two-point probability function increment calculation is performed. Uplink in the figure: a one-dimensional example image having a pore phase and a matrix phase; and (3) downlink: each pixel considers only its own contribution value; pixel contribution values as shown in fig. 3, the distance r=1 between the system pixels, the individual contribution of the selected aperture to the system being 2; since the calculation of the two-point probability function requires traversing each pixel point of the line, the contribution of the existence of the pore phase at the selected position to the pore phases located at both sides of the pore phase is respectively 1; 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 single 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 pixel position exchange can be expressed as:
in the above-mentioned method, the step of,and->And the individual contribution values of the pore phase pixel points at the selected positions before and after pixel position exchange to the two-point statistical function of the system are respectively corresponding to the pixel positions.
A second part: and (5) calculating the increment of the linear path function.
(1) The linear path function calculation method of the continuous adjacent pore phase is given according to the connectivity information of the pores in the system contained in the linear path function, as shown in fig. 4. Uplink in the figure: continuously adjacent pore phases; leftmost column: different distances r between two arbitrary pixels in the system; rightmost column: each pixel in the system sums the contributions of the linear path functions at different distances r.
FIG. 4 shows the relationship between the linear path function and the distance r, and the sum C of the contribution values of all the pores in the system relative to the linear path function at a given statistical distance r for N successive adjacent pore phases present in the selected calculation direction sum Can be expressed as follows:
(2) Incremental calculation of linear path function: searching for the pore pixels along four directions (taking 2D image reconstruction as an example) respectively by taking the pixel point (pore or matrix) at the selected position as a center, and taking the matrix pixels as the searching boundary; further counting the number of pore pixels in the searching process to finally obtain the number of pore pixels continuously adjacent in four directions, wherein the matrix pixels are respectively marked as N 0-u 、N 0-d 、N 0-l And N 0-r The aperture pixels are respectively denoted as N 1-u 、N 1-d 、N 1-l And N 1-r The method comprises the steps of carrying out a first treatment on the surface of the Finally, the total number of consecutive adjacent apertures centered on the selected aperture and the matrix pixel is calculated in the same row and column directions, respectively.
For the initial system before pixel location exchange, the total number of consecutive adjacent pore phases in the row and column directions can be calculated by the following equation:
in the middle ofAnd->The number of the total continuous adjacent pore phases in the row and column directions of the initial system before pixel position exchange is respectively;
for the update system after pixel location exchange, the initial pore phase is updated to be the matrix phase, the pore connectivity may be weakened, and the initial matrix phase is updated to be the pore phase, the pore connectivity may be enhanced, so that the above formula needs to be modified to calculate the total number of consecutive adjacent pore phases of the update system in the row and column directions, which is specifically as follows:
in the middle ofAnd->The total number of the continuous adjacent pore phases in the row and column directions of the updating system after pixel position exchange is respectively;
finally, linear path function increment of the updating system is obtained:
step 5, based on Metropolis criterion, the acceptance criterion of the updating of the reconstruction system is P more than or equal to rand (0, 1), P is the acceptance probability of the new system, if the criterion is met, the replacement of the positions of the pores and the matrix pixel points is accepted, and the original system is updated; otherwise, refusing the exchange of the positions of the pores and the matrix pixels, keeping the original system unchanged, and returning to the step 4 to continue the exchange of the pores and the matrix pixels at other positions; the probability of acceptance is calculated as follows:
wherein T is the temperature used in the simulated annealing process;
step 6, under the same temperature condition, continuously repeating the iterative process of the pixel exchange probability judgment acceptance/rejection of 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; along with the gradual decrease of the system temperature, the energy of the system is gradually reduced, and generally, 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 by comprising the following steps of: the method comprises the following steps:
step 1, carrying out gray level conversion on an original image to obtain a gray level image; calculating the gradient amplitude of a pixel by using a Sobel operator, replacing the pixel to obtain a replaced histogram based on the gradient, dividing the gray level, and performing threshold segmentation on an original gray level image to obtain 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 reconstructed image, and extracting and characterizing the contribution information about the pore structure of the reference image obtained in the step 1 by using a two-point probability function and a linear path function;
and 3, taking a 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 reconstructed image as an initial energy value C, wherein the weighted sum is expressed as follows:
wherein R is the statistical distance between two pixels in the image, R is the maximum statistical distance between two pixels,alpha and beta are weight coefficients, alpha+beta=1, S (r), L (r) are respectively the two-point probability function value and the linear path function value of the system to be reconstructed, S 0 (r),L 0 (r) two-point probability function values and linear path function values of the reference image, respectively;
step 4, randomly selecting the positions of the pores and the matrix pixel points for exchanging, updating energy in a mode of performing incremental calculation in a specific direction of exchanging pixel centers, searching the pixels in the specific direction of the pores when pixel exchanging occurs, and performing incremental delta C calculation according to a two-point probability function and a linear path function respectively;
let C ini And C new The contribution values of the selected pixel points to the statistical function before and after pixel position exchange of the reconstructed image are respectively corresponding to the reconstructed image;
searching pore pixels along the up-down, left-right and left-right directions by taking the pixel point at the selected position as the center, and taking the matrix pixels as the searching boundary;
counting the number of pore pixels in the searching process to finally obtain the number of pore pixels continuously adjacent in four directions, wherein the matrix pixels are respectively marked as N 0-u 、N 0-d 、N 0-l And N 0-r The aperture pixels are respectively denoted as N 1-u 、N 1-d 、N 1-l And N 1-r ；
Finally, calculating the total number of continuous adjacent pores centering on the selected pores and the matrix pixels according to the same row and column directions;
the amount of change in the system statistics function value caused by this pixel location exchange is calculated by:
wherein r is the distance between two arbitrary pixels in the system;and->The total number of consecutive adjacent pore phases in the row and column directions of the initial system before pixel position exchange; />And->The total number of the continuous adjacent pore phases in the row and column directions of the updating system after pixel position exchange;
step 5, based on Metropolis criterion, the acceptance criterion of the updating of the reconstruction system is P more than or equal to rand (0, 1), P is the acceptance probability of the new system, if the criterion is met, the replacement of the positions of the pores and the matrix pixel points is accepted, and the original system is updated; otherwise, refusing the exchange of the positions of the pores and the matrix pixels, keeping the original system unchanged, and returning to the step 4 to continue the exchange of the pores and the matrix pixels at other positions; the probability of acceptance is calculated as follows:
wherein T is the temperature used in the simulated annealing process;
step 6, continuously repeating the iterative processes of the steps 4 to 5 under the same temperature condition until the reconstruction system reaches a stable equilibrium state; then cooling according to a certain cooling rule, so that the system can reach a balance under any temperature condition; when the temperature or energy of the system is lower than a certain critical value, the system is rebuilt, and a rebuilt 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 according to claim 1, wherein: in the step 1, selecting a threshold value, adopting a gray scale division form, and acquiring a reference image of a simulated annealing method through a mean value taking segmentation technology; dividing gray level into the following modes:
[0.255]＝[0,G P ]+[G P ,G V ]+[G V ,255]；
wherein G is P ,G V Gray values at the highest crest at the left side and the lowest trough at the middle part of the gradient histogram are respectively obtained; taking the optimal threshold value as T * ＝(G P +G V ) And (2) carrying out threshold segmentation on the original image to obtain a reference binary image of the simulated annealing algorithm.
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