TBM rock breaking efficiency evaluation method based on image fractal dimension

Abstract

The invention discloses a TBM rock breaking efficiency evaluation method based on an image fractal dimension, and relates to the technical field of TBM construction evaluation research, and the method comprises the following steps: building a shooting platform for obtaining a rock slag image, and carrying out the preprocessing of the obtained rock slag image; according to the basic principle of a Sandbox method, improvement is carried out on the basis of an original model for rock ballast image characteristics, a calculation program of image fractal dimensions is written based on a Matlab platform, and images are imported into the calculation program to obtain the image fractal dimensions; designing a shooting height, comparing the performance and application conditions of the fractal dimension of the image obtained in the previous step, and comparing with a traditional box counting method; analyzing the correlation between the fractal dimension of the image and the specific energy and roughness index to determine the relationship between the fractal dimension of the image and the TBM rock breaking efficiency; the rock breaking efficiency evaluation method can be used for evaluating the rock breaking efficiency in a certain project, whether the rock breaking efficiency is increased or decreased is compared, and then the construction strategy is adjusted.

Description

Technical Field

[0001] The invention relates to the technical field of TBM construction evaluation research, and in particular to a TBM rock breaking efficiency evaluation method based on image fractal dimension. Background Art

[0002] As the development of underground space in my country continues to increase, the difficulty of construction is also gradually increasing. In comparison, TBM has the advantages of fast construction speed, low construction cost, good construction quality and excellent safety, making it the preferred method for tunnel construction. How to improve excavation efficiency while ensuring safe construction and reduce tool wear has become one of the most concerned issues in the field of shield construction. The rock debris generated during TBM excavation contains rich information, which can comprehensively feedback the surrounding rock conditions and TBM rock breaking efficiency.

[0003] Fractal theory has broad application prospects in the field of rock crushing research. Similar to blasting rock and weathered rock flakes, shield tunneling rock slag also has significant self-similarity, irregularity and nonlinearity, which shows that rock slag is an ideal research object for fractals. The fuzzy rock slag characteristics can be quantified by using appropriate fractal dimension calculation methods, which provides a theoretical basis for fractal research on rock slag.

[0004] For example, Xu Zemin et al. analyzed the rock breaking state of the cutter based on the distribution of rock ballast particle size, and believed that the excavation efficiency can be judged based on the relative content of rock blocks and rock powder in the ballast; in order to accurately predict the rock breaking efficiency and optimize the excavation parameters, the academic community proposed several quantitative indicators to describe the overall particle size distribution of rock ballast, and analyzed the correlation between these indicators and the energy consumption evaluation index and excavation parameters of the excavator. Matsui et al. found through indoor impact tests that the larger the fractal dimension of the broken rock, the more energy is consumed. Yan Changbin et al. screened the rock ballast, explored the changes in the roughness index under different rock strength and rock wear resistance conditions, and used the roughness index to predict the optimal excavation thrust range. The roughness index pays too much attention to the proportion of large-size rock ballast and ignores the distribution of smaller-size rock ballast. At the same time, the shape, size, number and level of the sieve holes all affect the screening results to a certain extent. In addition, the long time and labor-intensive characteristics of the screening test also limit the analysis efficiency of the roughness index.

[0005] The existing extraction and utilization of rock slag information in tunnel excavation has the following problems: the qualitative analysis is not practical, the quantitative analysis of the rock slag particle size mass distribution index is single, and there is a lack of a quantitative index that can quickly and accurately evaluate the rock slag mass distribution, so as to optimize the excavation efficiency and excavation parameters more accurately. Therefore, it is urgent to develop a multi-index quantitative analysis method for the rock slag particle size mass distribution, so as to quickly and efficiently evaluate the TBM rock breaking efficiency. Summary of the invention

[0006] To solve the above problems, the purpose of the present invention is to provide a TBM rock breaking efficiency evaluation method based on image fractal dimension, so as to provide a new idea for TBM rock breaking efficiency prediction.

[0007] In order to achieve the above object, the present invention is implemented through the following technical solutions:

[0008] A TBM rock breaking efficiency evaluation method based on image fractal dimension includes the following steps:

[0009] Step 1: Building a shooting platform for acquiring rock slag images and preprocessing the acquired rock slag images;

[0010] Step 2: According to the basic principle of the Sandbox method, the original model is improved based on the characteristics of rock ballast images, and a calculation program for the image fractal dimension is written based on the Matlab platform. The image is imported into the calculation program to obtain the image fractal dimension D;

[0011] Step 3, design a shooting height comparison experiment to test the performance and applicable conditions of the fractal dimension of the image in step 2, and compare it with the traditional box counting method;

[0012] Step 4: Analyze the correlation between the image fractal dimension D and the specific energy SE and the roughness index CI to determine their relationship with the TBM rock breaking efficiency.

[0013] Preferably, the preprocessing in step 1 includes graying the image, image smoothing and sharpening, binarization and morphological operations.

[0014] Preferably, the shooting device used by the shooting platform in step 1 is a 16.0MP small sensor super zoom camera.

[0015] Preferably, in step 2, according to the basic principle of the Sandbox method, the specific steps of improving the original model based on the characteristics of the rock ballast image include:

[0016] The basic calculation formula of the Sandbox method is:

[0017] N(L)=CL D ;

[0018] Where L is a box of size L established with the center point of the image; N(L) is the statistical value of the number of pixels of the fractal in the box; C is a constant related to the characteristics of the fractal, and D is the fractal dimension value of the Sandbox method;

[0019] Taking the logarithm of the above formula gives:

[0020] lgN(L)=lgC+DlgL;

[0021] N(L) and L are linearly fitted in the double logarithmic coordinate system using the least squares method, and the slope of the fitting line is the Sandbox fractal dimension.

[0022] Preferably, the specific steps of writing a calculation program for the image fractal dimension based on the Matlab platform in step 2 include:

[0023] Step 2-1: Collect input parameters, including the rock slag contour image saved in binary form and with redundant information removed, and the number of divisions of the target rectangular frame;

[0024] Step 2-2: Calculate the geometric center of the fractal image and find the minimum distance L1_min from the image boundary to it;

[0025] Step 2-3: Adaptively obtain candidate regions and count the coordinates of each center point in the region;

[0026] Step 2-4: Select the target box size using the logarithmic rule;

[0027] Step 2-5: traverse each center point position and count the number of foreground pixels;

[0028] Step 2-6: Take the mean of the number of pixels and fit.

[0029] Preferably, in step 2-3, a while loop structure is added to determine the size of the candidate area based on the original method of indenting the center point candidate area into the image based on the minimum boundary distance. If the area of ​​the candidate rectangular box accounts for less than 13-17% of the original image, the original candidate area is expanded in units of k and detected again.

[0030] Preferably, in the shooting height comparison experiment in step 3, 8 different shooting heights of 30 cm, 60 cm, 90 cm, 120 cm, 150 cm, 180 cm, 210 cm and 240 cm are set, and a shooting height standard suitable for the present invention is proposed through comparative analysis.

[0031] Further preferably, 120 cm is selected as the standard observation height.

[0032] Preferably, in step 4, the correlation between the image fractal dimension D and the specific energy SE and the roughness index CI is analyzed to determine the relationship between the fractal dimension D and the rock breaking efficiency of the TBM, which specifically includes the following steps:

[0033] As the roughness index CI increases, the image fractal dimension D gradually decreases, and the two are roughly in a logarithmic relationship; without considering the surrounding rock level, the correlation between the fractal dimension D of the rock chip image and SE is not obvious, and the overall distribution of the data is relatively discrete. Under the same surrounding rock level, as the fractal dimension D of the rock chip image increases, SE gradually increases, and the two are in a logarithmic relationship. The rationality of using the image fractal dimension to evaluate the rock breaking efficiency is determined based on the degree of linear correlation.

[0034] Preferably, the fitting correlation coefficient between the roughness index CI and the image fractal dimension D is between 0.76 and 0.80, and more preferably, the fitting correlation coefficient between the roughness index CI and the image fractal dimension D is 0.78.

[0035] Compared with the prior art, the present invention has the following advantages:

[0036] The TBM rock breaking efficiency evaluation method based on image fractal dimension of the present invention analyzes the relationship between image fractal dimension and specific energy and roughness index, explores the feasibility of evaluating TBM rock breaking efficiency based on image fractal dimension, and provides a new idea for predicting TBM excavation performance; quantitatively analyzing the indicators of rock slag particle size quality distribution are diverse, and the rock slag quality distribution can be quickly and accurately evaluated, thereby accurately optimizing the excavation efficiency and excavation parameters.

[0037] The present invention analyzes the correlation between the fractal dimension D of rock ballast image and the roughness index CI and specific energy SE at different surrounding rock levels and finds that: as CI increases, the image fractal dimension D gradually decreases, the two are roughly in a logarithmic relationship, and the fitting correlation coefficient is around 0.78; without considering the surrounding rock level, the correlation between the fractal dimension D of rock ballast image and SE is not obvious, and the overall data distribution is relatively discrete. Under the same surrounding rock level, as the fractal dimension D of rock ballast image increases, SE gradually increases, and the two are in a logarithmic relationship. The rationality of evaluating rock breaking efficiency by image fractal dimension can be determined according to the degree of linear correlation. The present invention can be used to evaluate rock breaking efficiency in a certain project, compare whether the rock breaking efficiency has increased or decreased, and then adjust the construction strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is the overall picture of the shooting platform in Example 2;

[0039] Figure 2 The effect diagram of rock ballast image preprocessing, where (a) is the original image and (b) is the image after preprocessing.

[0040] Figure 3 The effect of different shooting heights on the fractal dimension D of the image;

[0041] Figure 4 The calculation method obtained in Example 2 and the influence of the input image size on the image fractal dimension D;

[0042] Figure 5 The relationship between the fractal dimension D and CI of the rock ballast images of different surrounding rock levels obtained in Example 2;

[0043] Figure 6 The relationship between the fractal dimension D and SE of the rock chip images of different surrounding rock levels obtained in Example 2. DETAILED DESCRIPTION

[0044] The purpose of the present invention is to provide a method for evaluating the rock breaking efficiency of a TBM based on image fractal dimension. The present invention will be further described below in conjunction with specific embodiments.

[0045] Example 1

[0046] A TBM rock breaking efficiency evaluation method based on image fractal dimension includes the following steps:

[0047] Step 1, build a shooting platform for obtaining rock slag images. The shooting equipment used is a 16.0MP small sensor super zoom camera. The specific device is mainly composed of a tripod, a column, a camera hoisting crossbar, an inclined support rod and a counterweight. The hoisting crossbar, the column and the inclined support rod can be freely extended and retracted to preprocess the obtained rock slag image; the preprocessing includes graying the image, smoothing and sharpening the image, binarization and morphological operations; eliminating a large amount of information including redundant background, image noise, rock slag surface texture and fractal calculation irrelevant information.

[0048] Step 2: According to the basic principle of the Sandbox method, the original model is improved based on the characteristics of rock ballast images, and a calculation program for the image fractal dimension is written based on the Matlab platform. The image is imported into the calculation program to obtain the image fractal dimension D;

[0049] The basic calculation formula of the Sandbox method is:

[0050] N(L)=CL D ;

[0051] Where L is a box of size L established with the center point of the image; N(L) is the statistical value of the number of pixels of the fractal in the box; C is a constant related to the characteristics of the fractal, and D is the fractal dimension value of the Sandbox method;

[0052] Taking the logarithm of the above formula gives:

[0053] lgN(L)=lgC+DlgL;

[0054] N(L) and L are linearly fitted in a double logarithmic coordinate system using the least squares method. The slope of the fitted line is the Sandbox fractal dimension.

[0055] The specific steps of writing a calculation program for image fractal dimension based on Matlab platform include:

[0056] Step 2-1: Collect input parameters, including the rock slag contour image saved in binary form and with redundant information removed, and the number of divisions of the target rectangular frame;

[0057] Step 2-2: Calculate the geometric center of the fractal image and find the minimum distance L1_min from the image boundary to it;

[0058] Step 2-3: Adaptively obtain the candidate area and count the coordinates of each center point in the area; In the past, the model often used the minimum boundary distance as the standard to indent into the image to establish the center point candidate area. At this time, the distance L1_min between the area and the boundaries of the image is large, resulting in the candidate area being too small and unable to search for foreground pixels. On the basis of the original method of indenting the center point candidate area into the image based on the minimum boundary distance as the standard, a while loop structure is added to determine the size of the candidate area. If the proportion of the candidate rectangular box area to the original image is less than 13-17%, the preferred proportion is less than 15%, and the original candidate area is expanded in units of k and detected again;

[0059] Step 2-4: Select the target box size using the logarithmic rule;

[0060] Step 2-5: traverse each center point position and count the number of foreground pixels;

[0061] Step 2-6: Take the mean of the number of pixels and fit.

[0062] Step 3, design a shooting height comparison experiment to test the performance and applicable conditions of the fractal dimension of the image in step 2, and compare it with the traditional box-counting method to highlight the benefits of the Sandbox method;

[0063] First, the rock slag sieved with standard square holes with nominal diameters of 2.5, 5, 10, 16, 25, 31.5, 40, and 50 mm was remixed according to a certain mass ratio from each particle size interval to study the influence of shooting height on fractal dimension. In the shooting height comparison experiment, 8 different shooting heights of 30cm, 60cm, 90cm, 120cm, 150cm, 180cm, 210cm and 240cm were set, and a shooting height standard suitable for the present invention was proposed through comparative analysis; preferably, 120cm was selected as the standard observation height.

[0064] Step 4: Analyze the correlation between the image fractal dimension D and the specific energy SE and the roughness index CI to determine their relationship with the TBM rock breaking efficiency.

[0065] The larger the roughness index CI, the smaller the specific energy SE, and the higher the TBM rock breaking efficiency. The larger the fractal dimension D of the rock debris image, the lower the TBM rock breaking efficiency. The present invention is a method for quantitatively evaluating the TBM rock breaking efficiency by the image fractal dimension D, and is not a method for qualitatively evaluating the TBM rock breaking efficiency. In addition, there is no absolute quantitative distinction between high and low in TBM rock breaking efficiency, only a relative distinction between high and low, and there is no absolute quantitative standard for distinguishing high or low rock breaking efficiency. The present invention can be used to evaluate the rock breaking efficiency in a certain project, compare whether the rock breaking efficiency has increased or decreased, and then adjust the construction strategy.

[0066] The present invention also found that as the roughness index CI increases, the image fractal dimension D gradually decreases, the two are roughly in a logarithmic relationship, and the fitting correlation coefficient is between 0.76 and 0.80. It is further preferred that the fitting correlation coefficient of the roughness index CI and the image fractal dimension D is 0.78; without considering the surrounding rock level, the correlation between the fractal dimension D and SE of the rock chip image is not obvious, and the overall distribution of the data is relatively discrete. Under the same surrounding rock level, with the increase of the fractal dimension D of the rock chip image, SE gradually increases, and the two are in a logarithmic relationship. The rationality of using the image fractal dimension to evaluate the rock breaking efficiency is determined based on the degree of linear correlation.

[0067] Example 2

[0068] For the three working conditions of the XX City Heping Avenue South Extension Project, the XX Bay Undersea Tunnel Project, and the XX Mouth Tunnel Project of the Shenzhen-Jiangmen Railway, a TBM rock breaking efficiency evaluation method based on image fractal dimension described in Example 1 is adopted, and the specific steps are as follows:

[0069] S1, first collect the required rock slag from the construction site, and then spread it evenly on the test site, taking care not to pile it up, and take pictures of the image with the built shooting platform. The whole picture of the complete test platform can be seen Figure 1 The rock slag image is preprocessed according to the steps of graying, image smoothing and sharpening, binarization and morphological operation to eliminate a large amount of information including redundant background, image noise, rock slag surface texture and fractal calculation irrelevant information. Figure 2 ;

[0070] The shooting device used is a 16.0MP small sensor super zoom camera;

[0071] S2, the image saved in binary form is input into the program written based on the Matlab platform to obtain the image fractal dimension. Before testing the performance and applicable conditions of the image fractal dimension, the rock ballast sample must be re-prepared. The mass distribution of the newly configured rock ballast mixture is shown in Table 1.

[0072] Table 1 Mass proportion of new rock slag mixture in different particle size ranges

[0073]

[0074] S3, according to the data in Table 1, under the condition of ensuring sufficient light and the shooting angle perpendicular to the sample surface, 8 different shooting heights of 30cm, 60cm, 90cm, 120cm, 150cm, 180cm, 210cm and 240cm were set. The full-size rock chip images were cropped by changing the shooting height and the fractal dimension of the images was calculated by the Sandbox method. The results are shown in Table 2 and the trend of change is shown in Figure 3 , comprehensive analysis shows that 120cm is a more standard shooting height.

[0075] Table 2 Statistics of fractal dimension of rock ballast images at different shooting heights

[0076]

[0077] Furthermore, the traditional box counting method (boxcount method) and the Sandbox method are compared and analyzed. The box counting method is a commonly used method for calculating fractal dimension. The basic principle of the algorithm is as follows: Use a grid of size L to cover the fractal figure, record the number of grids containing all graphic pixels as N(L), reduce the grid size L, cover the fractal body with the grid again and count all non-empty boxes until the grid size reaches 1 pixel length, and finally obtain a set of data of different grid sizes L and the number of non-empty boxes N(L) at this scale. The number of non-empty boxes N(L) and the grid size L satisfy the following power law relationship:

[0078] N(L)=kL -D

[0079] Where: k is the scale constant, D is the box count fractal dimension value. Taking the logarithm of both sides of (1) we get:

[0080] lgN(L)=lgK-DlgL

[0081] According to the data in Table 1, the rock ballast surface contour image was obtained at a shooting height of 120 cm, and the original image was cropped using a sliding window. According to the data in Table 3, the influence of the input image size and fractal algorithm on the fractal dimension D of the shield rock ballast image was analyzed. Figure 4 shown.

[0082] Table 3 Statistics of fractal dimensions of rock ballast images under different image sizes and fractal algorithms

[0083]

[0084]

[0085] S4, respectively, samples were collected from 30th ring to 620th ring of XX Heping Avenue South Extension Project, 520th ring to 700th ring of XX Bay Undersea Tunnel Project, and 400th ring to 1220th ring of XX Mouth Tunnel Project of Shenzhen-Jiangmen Railway, involving four surrounding rock levels, and a total of 136 groups of rock slag samples were obtained, of which 11% were grade II, 28% were grade III, 31% were grade IV, and 30% were grade V. According to the standard process, each group of rock slag collected at the construction site was photographed, and each group of rock slag was screened to obtain the particle size distribution, which was substituted into the roughness index calculation formula. At the same time, the image was preprocessed and imported into the Matlab program to obtain the image fractal dimension of each group of samples. The calculation results and key excavation parameters are statistically shown in Table 4. According to the data in Table 4, the specific surface area, specific energy, and roughness index were fitted and analyzed respectively, and the fitting image is shown in Table 4. Figure 5 and Figure 6 .like Figure 5 and Figure 6 It can be seen that: no matter what level of surrounding rock conditions, with the increase of CI, the image fractal dimension D gradually decreases, and the two are roughly in a logarithmic relationship, and the polynomial fitting correlation coefficient is around 0.78. Without considering the surrounding rock level, the correlation between the fractal dimension D of the rock slag image and SE is not obvious, and the overall distribution of the data is relatively discrete; under the same surrounding rock level, with the increase of the fractal dimension D of the rock slag image, SE gradually increases, and the two are in a logarithmic relationship. When the surrounding rock level changes from level II to level V, the correlation coefficient gradually decreases, and the mean value is around 0.82.

[0086] Table 4 Statistics of rock ballast image fractal dimension and key shield tunneling parameters

[0087]

[0088]

[0089] The essential meaning of specific energy SE is the energy consumption required to break a unit volume of rock mass, which is a way to express rock breaking efficiency. The higher the linear correlation between fractal dimension D and specific energy SE, the more it proves that fractal dimension D can reflect the size of specific energy SE and thus evaluate the size of rock breaking efficiency. Therefore, the higher the linear correlation, the more accurate the use of fractal dimension D to evaluate rock breaking efficiency.

[0090] In the three engineering examples listed in the present invention, the relationship fitting analysis was performed on the fractal dimension of the rock slag image at each surrounding rock level, the roughness index CI and the specific energy SE, and all of them showed good fitting relationships. The roughness index CI and the specific energy SE themselves can be used to evaluate the TBM excavation efficiency. Therefore, this also verifies the rationality and reliability of the present invention using the graphic fractal dimension of rock slag to evaluate the TBM excavation efficiency.

Claims

1. A TBM rock breaking efficiency evaluation method based on image fractal dimension, characterized by: The following steps are involved: Step 1: Building a shooting platform for acquiring rock slag images and preprocessing the acquired rock slag images; Step 2: According to the basic principle of the Sandbox method, the original model is improved based on the characteristics of rock ballast images, and a calculation program for the image fractal dimension is written based on the Matlab platform. The image is imported into the calculation program to obtain the image fractal dimension D; Step 3, design a shooting height comparison experiment to test the performance and applicable conditions of the fractal dimension of the image in step 2, and compare it with the traditional box counting method; Step 4: Analyze the correlation between the image fractal dimension D and the specific energy SE and the roughness index CI to determine their relationship with the TBM rock breaking efficiency.

2. The method for evaluating TBM rock breaking efficiency based on image fractal dimension according to claim 1 is characterized by: The preprocessing in step 1 includes graying the image, image smoothing and sharpening, binarization and morphological operations.

3. The method for evaluating TBM rock breaking efficiency based on image fractal dimension according to claim 1 is characterized by: The shooting device used by the shooting platform in step 1 is a 16.0MP small sensor super zoom camera.

4. The method for evaluating TBM rock breaking efficiency based on image fractal dimension according to claim 1, characterized in that: In step 2, according to the basic principles of the Sandbox method, the specific steps of improving the original model based on the characteristics of rock ballast images include: The basic calculation formula of the Sandbox method is: N(L)=CL D ; Where L is a box of size L established with the center point of the image; N(L) is the statistical value of the number of pixels of the fractal in the box; C is a constant related to the characteristics of the fractal, and D is the fractal dimension value of the Sandbox method; Taking the logarithm of the above formula gives: lgN(L)=lgC+DlgL; N(L) and L are linearly fitted in the double logarithmic coordinate system using the least squares method, and the slope of the fitting line is the Sandbox fractal dimension.

5. The method for evaluating TBM rock breaking efficiency based on image fractal dimension according to claim 1, characterized in that: The specific steps of writing the image fractal dimension calculation program based on the Matlab platform in step 2 include: Step 2-1: Collect input parameters, including the rock slag contour image saved in binary form and without redundant information, and the number of divisions of the target rectangular box. Step 2-2: Calculate the geometric center of the fractal image and find the minimum distance L1_min from the image boundary to it; Step 2-3: Adaptively obtain candidate regions and count the coordinates of each center point in the region; Step 2-4: Select the target box size using the logarithmic rule; Step 2-5: traverse each center point position and count the number of foreground pixels; Step 2-6: Take the mean of the number of pixels and fit.

6. The method for evaluating TBM rock breaking efficiency based on image fractal dimension according to claim 5 is characterized by: In step 2-3, a while loop structure is added to determine the size of the candidate area based on the original method of indenting the center point candidate area into the image based on the minimum boundary distance. If the area of ​​the candidate rectangular box accounts for less than 13-17% of the original image, the original candidate area is expanded in units of k and detected again.

7. The method for evaluating TBM rock breaking efficiency based on image fractal dimension according to claim 1, characterized in that: In the shooting height comparison experiment in step 3, 8 different shooting heights of 30 cm, 60 cm, 90 cm, 120 cm, 150 cm, 180 cm, 210 cm and 240 cm were set, and a shooting height standard suitable for the present invention was proposed through comparative analysis.

8. The method for evaluating TBM rock breaking efficiency based on image fractal dimension according to claim 7 is characterized by: 120cm was selected as the standard observation height.

9. The method for evaluating TBM rock breaking efficiency based on image fractal dimension according to claim 1, characterized in that: In step 4, the correlation between the image fractal dimension D and the specific energy SE and the roughness index CI is analyzed to determine its relationship with the rock breaking efficiency of the TBM, which specifically includes the following steps: As the roughness index CI increases, the image fractal dimension D gradually decreases, and the two are roughly in a logarithmic relationship; without considering the surrounding rock level, the correlation between the fractal dimension D of the rock chip image and SE is not obvious, and the overall distribution of the data is relatively discrete. Under the same surrounding rock level, with the increase of the fractal dimension D of the rock chip image, SE gradually increases, and the two are in a logarithmic relationship. The rationality of using the image fractal dimension to evaluate the rock breaking efficiency is determined based on the degree of linear correlation.

10. The method for evaluating TBM rock breaking efficiency based on image fractal dimension according to claim 9, characterized in that: The fitting correlation coefficient between the roughness index CI and the image fractal dimension D is between 0.76 and 0.80.

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