In order to accurately and comprehensively obtain information about coal rock mesocrack images, image processing technique based on partial differential equation (PDE) is introduced in order to expound on the active contour model without edges and overcome the deficiency of the C-V model. The improved C-V model is adopted in order to process mesoimages of coal rocks containing single and multiple cracks and obtain high-quality binary images of coal rock mesocracks and the effective characteristic parameters of coal rock mesostructures through quantitative processing, which will lay solid foundations for the follow-up research into coal rock seepage computation and damage calculation. Studies have shown that, compared to the original C-V model, the improved model achieves better image segmentation effects and more accurate quantitative information about coal rock mesostructures for coal rock mesoimages with low contrast ratios and nonuniform grayscale, a fact showing that it can be applied to the calculation of coal rock permeability and damage factors.
Underground coal mining will inevitably trigger an inner stress response of coal rock and cause the concentration or release of local stress, thus resulting in the buckling failure of coal rock. In this process, different stress states and amplitudes will bring about different forms of destruction to the rock. The material composition within coal rock and its primary physical and mechanical structure determine its stress and strain status under the external load, which further controls the macromechanical response and failure mechanism. Cracks are generated under high stress in a certain area of underground mining, and the formed cracks of the unstable coal rock in turn affect its inner stress and strain state, thus causing the deflection of local principal stress and improving or worsening the stress state of local coal rock. Research on the damage to coal rock on the mesoscale mainly focuses on the crack initiation, expansion, connection, direction, scale, and properties. These important factors provide significant guidance and design basis for the prevention and control of coal rock instability and failure.
The digital image processing technique provides an effective means for the precise measurement and quantitative analysis of the materials on the mesoscale and opens up a new way for scientists and engineers to gain a comprehensive understanding of the heterogeneity, internal structure characteristics, and morphological characteristics of each component and the corresponding mesomechanic characteristics [
Digital image processing includes the removal of noise, contrast enhancement, recovery, segmentation, and characteristic extraction of images through computers. The abovementioned literature review is based on traditional image processing methods, which can inhibit noise but possess the deficiencies of obfuscation of detailed image information, susceptibility to interference, and low accuracy. It is worth noticing that it is inaccurate to process images obtained through coal rock mesomechanic experiments that are characterized by low contrast ratios, multiple details, and weak boundary information, which restricts the fundamental research on the calculation of coal permeability, coal rock damage, and multifield crack coupling. Compared to traditional image processing methods, image processing methods based on partial differential equations (PDE) have the distinctive advantages of conserving the marginal detailed information and realizing nonlinear noise removal while eliminating image noise. PDE-based methods also utilize numerical analysis theories and PDE, which are characterized by high speed, accuracy, and stability. These methods enable analysis from the perspective of the space geometry of the image on the basis of the natural connection between the geometric images and the equation in order to establish an image processing model that is close to reality. The C-V model is a widely applied PDE image processing method. This paper introduces and explains the principle of the C-V model and proposes an improved model based on image enhancement function. With respect to coal rock mesoimages with nonuniform grayscales and low contrast ratios, the improved C-V model obtains high-quality segmentation images through processing experiments on mesoimages with single and multiple cracks. This method also obtains coal rock mesostructural information through the binary image quantization process and studies the permeability coefficient and damage variables of coal rocks containing cracks, which provides a reliable support for the in-depth research on the mesomechanic characteristics of coal rocks.
Currently, no universal segmentation theory can be applied to image segmentation technology. The proposed segmentation algorithms are mainly targeted at specific issues. When handing objectives with fuzzy boundaries or dispersed objectives in the image, the traditional segmentation technologies [
The basic concept of the image processing method based on PDE is to evolve an image, a curve, or a curved face in the PDE model and to obtain the expected result by solving this equation [
The C-V model proposed by Chan and Vese [
Variation level methods are adopted and embedded in function
Under fixed function
Under the fixed
In which,
The C-V model can effectively detect the weak or fuzzy edge of images, which testifies to the high segmentation accuracy, simple calculation, and noise immunity. These advantages have substantially expanded its applied range. However, the evolutionary velocity
In light of the aforesaid analysis, in order to enhance the utilization effect of the C-V model, it is necessary to improve the C-V model from the two perspectives of increasing the image contrast ratio and the equalization of image grayscale. By mapping the grayscale value, with a narrow grayscale distribution range, of images to be processed into a broadband output value, the contrast ratio of the target area can be effectively improved. The typical methods include logarithm transformation and power transformation. Gonzalez et al. [
This paper adopts an image enhancement function,
The aforesaid image enhancement function,
By following the C-V derivation process, the minimum value of functional
In the original C-V model, the regularized Heaviside function must be conformed to the condition
Such regularized function is an odd symmetric function. Parameter
The numerical calculation scheme of PDE includes the explicit, implicit, and semi-implicit schemes. The explicit scheme refers to the direct calculation, which can be easily understood but is prone to the accumulation and propagation of error, which testifies to its low algorithm stability. The implicit scheme has the advantage of high stability but usually gives rise to the nonlinear simultaneous algebraic equation. It is usually accompanied by more complicated calculations compared to the explicit scheme. The semi-implicit scheme usually generates a linear difference equation. Different from the nonlinear simultaneous algebraic equation, it usually requires much easier numerical calculation; at the same time, the semi-implicit scheme is also characterized by high stability, and thus, it is widely applied to PDE numerical calculation. Therefore, the semi-implicit scheme is adopted in this paper.
Parameters
Under the regularized Heaviside function, the following calculation is applied to the internal and external image grayscale averages of the current evolving curve (zero level set) in order to avoid the troubles of detecting zero level sets:
In order to verify the feasibility and superiority of the method proposed in this paper, both the C-V model and the improved C-V model were adopted to process images of coal samples with single and multiple cracks with the specific procedure that is listed below:
Original image of the coal sample containing cracks.
Segmentation of the image by the C-V model (10000 times iteration).
Single crack
Multicrack
Segmentation of the image by the improved C-V model (4000 times iteration).
Single crack
Multicrack
Table
Comparison between the effects of the C-V model and the improved C-V model.
Conditions | 1000 times iteration | 4000 times iteration | ||
---|---|---|---|---|
Effect image | Time consumption | Effect image | Time consumption | |
Single crack | ||||
C-V model | 69 s | 287 s | ||
Improved C-V model | 70 s | 261 s | ||
Multicrack | ||||
C-V model | 68 s | 280 s | ||
Improved C-V model | 69 s | 273 s |
The aforesaid segmentation image based on the improved C-V model should be further processed in order to eliminate the interference of the background and obtain more effective crack information. The original image shows that the straight line portion that connects the top and bottom in Figure
First, the improved C-V model is adopted in order to iterate image binarization for 4000 times and select the segmentation area in accordance with the original image by means of the use of the morphological function, Bwselect. A careful observation shows that the cracks in the original image have been segmented into several sections with the space between each section similar to the line connection. In this paper, the tangential direction growth method is utilized in order to reconnect the fractured cracks, as shown in Figure
Extraction of crack information.
Crack image obtained at the initial stage
Connection of crack image
Crack profile
Fill of crack profile
Crack image overlaid on the original one
The function Regionprops is adopted to obtain the regional characteristic parameters in the image and crack information, as shown in Table
Two-dimensional information of the crack (unit: pixel).
Characteristics | Crack 1 | Crack 2 | Crack 3 | Crack 4 |
---|---|---|---|---|
Single crack | ||||
Crack area | 4175 | |||
Fitted long axis | 499 | |||
Fitted short axis | 53 | |||
Azimuth (°) | -81.9 | |||
Crack perimeter | 1385 | |||
Equivalent radius | 36.5 | |||
Multicrack | ||||
Crack area | 16504 | 1888 | 277 | 1942 |
Fitted long axis | 435 | 418 | 193 | 301 |
Fitted short axis | 53 | 11 | 11 | 15 |
Azimuth (°) | -79.3 | -73.6 | 4.4 | -70.2 |
Crack perimeter | 1096 | 816 | 338 | 679 |
Equivalent radius | 72.5 | 24.5 | 9.5 | 25 |
Measurement of the multicrack space.
The mesocomposition and structure of coal rocks determine their stress-strain states under external force and control their macromechanical response and failure mechanisms. The existence and development of these mesocompositions and structures make the seepage-stress coupling of coal rock very complicated. Digital image processing technology provides an effective method of expressing the heterogeneity of coal rock from the perspective of mesophysical mechanic structure, which has made the mesoresearch on crack rock mass liquid-solid coupling more direct and efficient.
The method based on the improved C-V model is adopted in order to process the coal rock image containing cracks and obtain various two-dimensional data about cracks, such as the crack area (
In coal rock containing cracks, the cracks can be grouped according to their strike. In accordance with the model with equal-width crack, the coefficient of permeability for crack can be expressed as
Romm [
As the Darcy Law suggests,
Combining Equations (
The mesostructure of coal rock determines its damage state, which can be roughly obtained by evaluating the mesostructural characteristics of microcracks. The mesoimages obtained through the mesomechanic experiment can be used to quantitatively investigate the relationship among the initiation, expansion, and deformation response of cracks (mesostructure). In order to establish the correlation among the damage variables of mesostructures, macromechanical responses, and physical constitutive equations, variable
The effective length of a crack is calculated according to the following equation [
In order to comprehensively and accurately obtain crack information from coal rock mesoimages, this paper introduces image processing technology based on PDE and expounds on the principle of active contour models without edges. In light of the uneven grayscale distribution of the C-V model and the limitations of coal rock images with low contrast ratios, an improved C-V model based on image enhancement functions is proposed with a discretization scheme that combines forward difference and backward difference and a semi-implicit scheme for numerical calculation is adopted.
The C-V model and improved C-V model were adopted for the image processing of coal rock mesoimages. The results show that the improved C-V model achieved a better image segmentation effect and provided more accurate quantitative information about coal rock mesostructure than the C-V method for images with both single cracks and multiple cracks. This fact demonstrates that the improved C-V model is superior when it comes to processing coal rock mesoimages with nonuniform grayscales and low contrast.
The extracted binary crack images were subjected to quantitative processing in order to extract the length, azimuth, area, perimeter, and space of cracks and crack sets. The quantitative information about crack images at different experimental stages of coal rock mesostructure is used in order to conduct more in-depth research into coal rock seepage and damage mechanics.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare no conflict of interest.
This research was funded by the Beijing Natural Science Foundation (8204068).