Pattern Matching Fusion Reconstruction Method Based on Point Layout

Abstract

The present invention discloses a pattern matching fusion reconstruction method based on point distribution. It is proposed that in the case of known three-dimensional high- and low-resolution core images, first, the position information of large and small pore structures in the high-resolution image is extracted, and this information is used to distribute points in the interpolated and enlarged low-resolution image. Then, a pattern dictionary is established using the pattern information of the small pore structures in the high-resolution image. Subsequently, based on the point distribution positions in the low-resolution image, the small pore structures are reconstructed in the low-resolution image by means of a cross-correlation function pattern matching strategy. The present invention can perform fusion reconstruction on three-dimensional high- and low-resolution heterogeneous core images of different scales, thereby constructing a more complete three-dimensional pore structure to improve the accuracy of subsequent feature analysis and physical property research.

Description

Technical Field

[0001] The present invention relates to a method for fusing and reconstructing three-dimensional core images at different scales, and particularly to a pattern matching fusion and reconstruction method based on point distribution, belonging to the technical field of three-dimensional image reconstruction. Background Technique

[0002] Digital core imaging often has a contradiction between the field of view and the resolution. If directly scanning a large-scale (such as centimeter-scale plunger-shaped) core, the obtained core image has a large field of view but low resolution, making it difficult to capture small pore information; if scanning a cut small-scale (such as millimeter-scale) core sample, the imaging resolution is high, but the corresponding field of view is limited. Therefore, it is necessary to study how to use high- and low-resolution core images at different scales to construct a more complete large-scale high-resolution three-dimensional pore structure in a way of fusion and reconstruction.

[0003] The digital reconstruction technology in the core field is to obtain two-dimensional or three-dimensional information of the core image and apply mathematical methods to model it to construct the three-dimensional structure of the core. At present, the reconstruction algorithms based on mathematical modeling often assume that the reconstructed structure is isotropic and take homogeneous core images, that is, images with relatively uniform pore distribution, as the research object. The theoretical development of such algorithms has been relatively mature. However, in practical engineering applications, there are still a certain number of heterogeneous core images, which often have various shapes and non-uniform pore distributions. In recent years, the three-dimensional reconstruction of heterogeneous core images has gradually attracted the attention of scholars. The fusion and reconstruction algorithm based on prior point distribution pattern matching proposed by the present invention uses the pore position distribution information in the high-resolution image to guide the reconstruction of the small pore structure in the background of the low-resolution large pore structure, and then solves the problem of the fusion and reconstruction of heterogeneous core images. Summary of the Invention

[0004] The main purpose of the present invention is to extract the morphology and position information of pores in a small-scale three-dimensional high-resolution core image, and use the interpolated and enlarged large-scale three-dimensional low-resolution core image as the background to fuse and reconstruct a large-scale three-dimensional high-resolution core image that simultaneously has large pore structures and small pore structures, and the pore spatial distribution is consistent with that of the small-scale high-resolution image.

[0005] The present invention realizes the above object through the following technical solutions:

[0006] The pattern matching fusion and reconstruction method based on point distribution includes the following steps:

[0007] (1) Given a three-dimensional high-resolution core image and a three-dimensional low-resolution core image, unify their resolutions by interpolating and enlarging the low-resolution image;

[0008] (2) Initialize the image to be fused and reconstructed with a three-dimensional low-resolution core image, where the pore points are fixed points;

[0009] (3) Statistically analyze the pore size distribution of the three-dimensional high-resolution core image, and only retain the pores with pore sizes smaller than the smallest pore size in the low-resolution image as the small-pore training image;

[0010] (4) Determine the optimal template size for scanning the small-pore training image based on the first-order difference of the information entropy;

[0011] (5) Scan the small-pore training image according to the optimal template determined in step (4), establish an ordered pattern dictionary, and store it as a fixed file;

[0012] (6) Perform constrained point placement in the image to be fused and reconstructed according to the position distribution information of the pore structure contained in the three-dimensional high-resolution core image;

[0013] (7) According to the number of placed points, randomly select the corresponding number of initial patterns from the ordered pattern dictionary and place them at the placed-point positions in the image to be fused and reconstructed;

[0014] (8) According to the cross-correlation function distance metric method, search for the best matching pattern of the pattern to be matched at the placed-point position in the ordered pattern dictionary, and translate the template by one step in any direction in the form of a sliding window to obtain a new pattern to be matched. Repeat the above steps until the porosity of the reconstructed small-pore structure is the same as that of the small-pore structure in the high-resolution image.

[0015] In step (4), by scanning the small-pore training image with three-dimensional templates of different sizes (N×N×N) in a raster path, three-dimensional pattern blocks corresponding to the image are obtained. If the three-dimensional pattern block contains pore points, the set of pixel points contained in the three-dimensional pattern block at this time is called a pattern. The frequency of each pattern is statistically analyzed, and the information entropy is calculated. The formula for the information entropy is defined as:

[0016]

[0017] where K represents the number of pattern types, p iDenote the occurrence frequency of the \(i\)-th pattern. The larger \(H\) is, the richer the pattern information extracted by the template of this size is. For heterogeneous core images, due to their strong anisotropy and high complexity, \(H\) will continuously increase as the template size increases. When the template size is small, the change of \(H\) is very obvious and increases sharply as the template size increases; when the template size increases to a certain critical value, the growth rate of \(H\) slows down. It can be considered that the pattern set obtained by the template through scanning has the characteristics of statistical stationarity. Therefore, calculate the first-order difference of \(H\) to obtain the optimal template size. The first-order difference can represent the change amplitude of \(H\). When the change amplitude tends to be stable, it means that the pattern information entropy scanned by the template tends to be stable. It is defined as:

[0018] \(\Delta H = H\) l \(-H\) l-1 (2)

[0019] where \(l\) represents the size of the template. Considering that applying the information entropy to the selection of the template size is to determine the minimum information required to reproduce the pattern information of the training image, and a too large template size will increase the additional computational burden. Therefore, the template size corresponding to the peak of the first-order difference is taken as the optimal template size.

[0020] In the step (5) above, the ordered pattern dictionary is to establish a pattern set of the small-hole training image with the optimal template. Based on the proportion of pore points in the pattern, that is, the proportion of the number of pore points in each pattern to the total number of pixels, the pattern set is divided. Patterns with the same proportion of pore points are stored in the same sub-pattern set, establishing a one-to-many mapping relationship between the proportion of pore points and multiple patterns to form a pattern dictionary. Then, each pattern is encoded in binary code, and each sub-pattern set is sorted based on the encoding to form an ordered pattern dictionary and store it as a fixed file for ordered search during the reconstruction process.

[0021] In the step (6) above, the specific steps of the constrained point layout strategy are as follows: First, calculate the pore sizes in the three-dimensional high- and low-resolution core images respectively. Let the pore size range of the low-resolution image be \(D\) min \(\sim D\) max , and the pore size range of the high-resolution image be \(d\) min \(\sim d\) max , where \(d\) max \(\sim D\) min . Mark the pore structure with a pore size range of \(d\) min \(\sim D\) min in the high-resolution image as a small-hole structure, and the pore size range of \(D\) min \(\sim d\) maxThe pore structure is marked as the macropore structure. Then, based on the central coordinates of the micropore structure, using the optimal template size determined in step (4) as the search radius, search for pixel points of the macropore structure within the neighborhood of the micropore structure. Traverse each micropore structure in the three-dimensional high-resolution image and calculate the distribution point ratio λ:

[0022]

[0023] where m a is the number of micropores with macropore structures in the neighborhood, and m b is the number of micropores without macropore structures in the neighborhood. Based on this, further calculate the number of distribution points n p :

[0024]

[0025] where size L represents the size of the low-resolution core image after interpolation and magnification, represents the porosity of the micropore structure in the high-resolution image, and p represents the distribution point probability.

[0026] In step (8), when searching for the best matching pattern from the pattern dictionary, first calculate the proportion of pore points of the pattern to be matched, then find the subset of sub-patterns with the corresponding pore point proportion in the pattern dictionary, and calculate the matching degree between the pattern to be matched and all patterns in the subset of sub-patterns using the cross-correlation function matching method:

[0027]

[0028] where N is the template size, pat rec and pat n represent the pattern to be matched in the fused reconstruction image and the nth matched pattern in the subset of sub-patterns respectively, m is the total number of patterns in the subset of sub-patterns, (x, y, z) is the coordinate of the first pixel point of the pattern to be matched, pat rec (x + i, y + j, z + k) is the pixel value of this point, and i, j, and k represent the moving distances along the x, y, and z directions, and ⊙ represents the exclusive OR operator. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 are the three-dimensional high-resolution core image (left) and the three-dimensional low-resolution core image (right) in the embodiments of the present invention;

[0030] Figure 2 is the aperture distribution relationship diagram of the three-dimensional high-resolution core image and the three-dimensional low-resolution core image in the embodiments of the present invention;

[0031] Figure 3 is the result of the fused reconstruction in the embodiments of the present invention;

[0032] Figure 4 This is the pore size comparison between the fused and reconstructed image and the real high-resolution core image in the embodiments of the present invention. Specific implementation manners

[0033] The present invention will be described in more detail below with specific embodiments in conjunction with the accompanying drawings. However, the described embodiments are only a specific and detailed description of the implementation method of the present invention, and should not be construed as any limitation to the protected content of the present invention.

[0034] (1) Figure 1 These are the three-dimensional high- and low-resolution core images after unifying the resolution, with a resolution of 1 μm / pixel. The left figure is the high-resolution core image with a size of 512×512×512, and the right figure is the interpolated and enlarged low-resolution core image with a size of 1000×1000×1000.

[0035] (2) Use Figure 1 The interpolated and enlarged low-resolution image (right) as the initial image to be fused and reconstructed, and the pore points therein are the points that cannot be changed during the fusion process.

[0036] (3) Calculate the pore size ranges of the three-dimensional high-resolution image and the interpolated and enlarged three-dimensional low-resolution image. The pore size relationship between the two is as Figure 2 shown. In this example, d min ~d max is 0.78~158.49 μm, D min ~D max is 12.88~291.53 μm. Then, in the high-resolution image, the pores with pore sizes between 12.88~158.49 μm are marked as large pore structures, and the pores with pore sizes less than 12.88 μm are marked as small pore structures. Only the small pore structures in the three-dimensional high-resolution image are retained as the small pore training images for establishing the pattern dictionary.

[0037] (4) By scanning the small pore training image with three-dimensional templates of different sizes, obtain the three-dimensional pattern blocks corresponding to the small pore structures, count the frequency of each pattern, calculate the information entropy according to formula (1), and calculate the pattern size 8 corresponding to the maximum first-order difference of the sample information entropy according to formula (2) as the optimal template size.

[0038] (5) Scan the small-hole training images to extract patterns using a template of the optimal size (8×8×8 in this example). Divide the pattern set based on the proportion of pore points, that is, the ratio of the number of pore points to the total number of pixels in each pattern. Store the patterns with the same pore-point proportion in the same sub-pattern set, establishing a one-to-many mapping relationship between the pore-point proportion and multiple patterns to form a pattern dictionary. Encode each pattern in binary code, sort each sub-pattern set based on the encoding, form an ordered pattern dictionary, and store it as a fixed file for ordered searching during the reconstruction process.

[0039] (6) Based on the central coordinates of the small-hole structures in the three-dimensional high-resolution core image, with the optimal template size (8 in this example) as the search radius, search for pixel points of large-hole structures in the neighborhood of the small-hole structures. Statistically analyze the ratio of the number of small-hole structures close to and far from the large-hole structures in the three-dimensional high-resolution core image, obtaining λ as 72%. Determine the number of distribution points n close to the large-hole structures according to formula (4). p , and the parameter values in this example are shown in Table 1.

[0040] Table 1

[0041]

[0042] (7) According to the cross-correlation function distance metric method, search for the best-matching pattern of the pattern to be matched at the distribution point position in the ordered pattern dictionary, and translate the template in any direction by one step length in a sliding window form to obtain a new pattern to be matched. Repeat the above steps until the porosity of the reconstructed small-hole structure is consistent with the porosity of the small-hole structure in the high-resolution image.

[0043] (8) Figure 3 For the result of the fusion reconstruction and the display of its local magnification, where the light gray pixel points represent the large-hole structures that remain unchanged in the low-resolution image, and the dark gray pixel points represent the reconstructed small-hole structures. To illustrate that the fusion result effectively utilizes the complementary nature of the pore structure information in the high- and low-resolution images, supplementing the small-hole structure information relative to the three-dimensional low-resolution core image and supplementing the large-hole structure information relative to the three-dimensional high-resolution core image, we statistically analyzed the pore size range of the images before and after fusion, and the results are shown in Table 2.

[0044] Table 2

[0045]

[0046] As can be seen from the table, the fused reconstructed image contains the pore size information of both high- and low-resolution images. The maximum pore size in the figure is larger than that in the low-resolution three-dimensional structure. This is because although the reconstructed small pore structure cannot change the position distribution of the real large pore structure, it can connect with it and enrich its detailed information, rather than existing in isolation. Therefore, the size of the large pore structure will also increase to some extent.

[0047] To quantitatively compare the pore size distributions of the fused reconstructed images, the pore size comparisons between the fused reconstructed images and the real high-resolution core images are shown in Figure 4 . It can be seen that the pore size range of the fused reconstructed images is larger than that of the real high-resolution images, indicating that more large pore structure information can be captured. And the pore size distributions within the same pore size range are consistent, indicating that the pore structure information of the high-resolution images is also maintained simultaneously.

[0048] Table 3

[0049]

[0050] To further analyze the effectiveness of the reconstructed small pore structure, the reconstructed small pore structure in the fusion result is separately extracted here, and its morphological parameters are compared with those of the small pore structure in the real high-resolution image. The results are shown in Table 3.

[0051] By observing and comparing the data in Table 3, the parameter errors of the morphological parameters of the reconstructed small pore structure and those of the real small pore structure are relatively small, indicating that the present invention can also better reproduce the morphological characteristics of the real pore structure.

[0052] The above embodiments are only the preferred embodiments of the present invention and do not limit the technical solutions described in the present invention. Any technical solutions that can be achieved on the basis of the above embodiments without creative labor shall be regarded as falling within the protection scope of the present invention.

Claims

1. A pattern matching fusion reconstruction method based on dot distribution, characterized in that: It includes the following steps: (1) Given a three-dimensional high-resolution core image and a three-dimensional low-resolution core image, unify their resolutions by interpolating and magnifying the low-resolution image. (2) Initialize the image to be fused and reconstructed with the interpolated and magnified three-dimensional low-resolution core image as the background, and take the pore points therein as fixed points. (3) Statistically analyze the pore size distribution of the three-dimensional high-resolution core image, and only retain the pores with pore sizes smaller than the smallest pore size in the low-resolution image in this image as the small-pore training image for establishing the pattern dictionary. (4) Determine the optimal template size for scanning the small-pore training image according to the first-order difference of information entropy. (5) Scan the small-pore training image according to the optimal template established in step (4), establish an ordered pattern dictionary, and store it as a fixed file. (6) Perform constrained point placement in the image to be fused and reconstructed according to the spatial distribution information of the pore structure contained in the three-dimensional high-resolution core image. (7) Randomly select an initial pattern from the ordered pattern dictionary according to the number of placed points and place it at the placed point position in the image to be fused and reconstructed. (8) According to the cross-correlation function distance metric method, search for the best matching pattern of the pattern to be matched at the placed point position in the ordered pattern dictionary, and translate the template by one step length in any direction in the form of a sliding window to obtain a new pattern to be matched. Repeat the above steps until the porosity of the reconstructed small-pore structure is the same as that of the small-pore structure in the high-resolution image.

2. The pattern matching fusion reconstruction method based on dot distribution according to claim 1, characterized in that In step (4), scan the three-dimensional high-resolution training image with templates of different sizes, obtain the corresponding three-dimensional pattern blocks of the image, statistically analyze the frequency of each pattern, and calculate the information entropy corresponding to the template of this size. The formula is: where K represents the number of pattern types, and p i represents the occurrence frequency of the i-th pattern. The larger the information entropy, the richer the pattern information extracted by the template of this size. The first-order difference of the information entropy can represent its change amplitude. On the premise of balancing the reconstruction accuracy and speed, the template size corresponding to the peak of the first-order difference of the information entropy is taken as the optimal template size.

3. The pattern matching fusion reconstruction method based on dot distribution according to claim 1, characterized in that In step (5), convert the patterns extracted using the optimal size template obtained in step (4) into corresponding binary codes, classify them into multiple sub-pattern sets according to the proportion of pore points in the patterns, and then sort the patterns in each sub-pattern set according to the coding values and store them as a fixed file.

4. The pattern matching fusion reconstruction method based on dot distribution according to claim 1, characterized in that In step (6), in order to better guide the reconstruction of the small hole structure in the space to be fused, a constrained point distribution strategy is proposed. The specific steps are as follows. First, calculate the pore diameters in the three-dimensional high-resolution core image and the three-dimensional low-resolution core image respectively. Let the pore diameter range of the pore structure in the low-resolution image be D min ~D max , and the pore diameter range of the pore structure in the high-resolution image be d min ~d max , where d max >D min . Then, the pore diameter range of the small hole structure in the high-resolution image is d min ~D min , and the pore diameter range of the large hole structure is D min ~d max . Then, taking the center coordinates of the small hole structure as the benchmark and the optimal template size determined in step (4) as the search radius, search whether there are pixel points of the large hole structure in the neighborhood of the small hole structure, traverse each small hole structure in the three-dimensional high-resolution core image, and calculate the point distribution ratio λ: where m a is the number of small holes with macroporous structures in the neighborhood, and m b is the number of small holes without macroporous structures in the neighborhood. According to the sampling ratio λ and the porosity of the small hole structure in the high-resolution image sampling is performed around the macroporous structures in the image to be fused and reconstructed, and the number of sampling points n p is as follows: Among them, size L represents the size of the macropore structure of the three-dimensional low-resolution core image, represents the porosity of the micropore structure in the high-resolution image, and p represents the point distribution probability.

5. The pattern matching fusion reconstruction method based on dot distribution according to claim 1, characterized in that In step (8), calculate the matching degree R between the pattern to be matched and all patterns in the sub-pattern set using the cross-correlation function matching method: where N is the template size, pat rec and pat n represent the pattern to be matched and the n-th matched pattern in the subset of sub-patterns in the fused reconstruction image respectively, m is the total number of patterns in the subset of sub-patterns, (x, y, z) is the coordinate of the first pixel of the pattern to be matched, pat rec (x + i, y + j, z + k) is the pixel value at this point, i, j, and k represent the moving distances along the x, y, and z directions, and ⊙ represents the operator for exclusive NOR operation.

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