Measurement of rock joint width based on digital image processing technology

The measurement of rock mass joint fissure width is widely used in many engineering fields such as geological exploration, mining engineering, highway and railway construction, and nuclear power engineering. However, due to the diversity of the causes of fissure formation, its measurement and research are extremely difficult. One of the simplest ways to measure the width is to use calipers (caliper gauges) to measure the vertical distance between the fracture surfaces of the rock mass on both sides of the joint fissure. This method is greatly affected by human factors and instrument accuracy, and the results are unstable and the data is inaccurate. For the measurement of rock mass microcracks, it can only be done under a microscope. The general method is: first sample the target rock mass and collect digital image information from it, then use the traditional manual measurement method to measure the target object in the image, and finally obtain the measurement result. This method only improves the accuracy during data collection, but due to the lack of application of existing image analysis technology during the measurement process, the measurement results are not ideal. At present, the commonly used image analysis technologies are mainly some image measurement algorithms, including: equivalent circle diameter algorithm, equivalent ellipse length and short axis algorithm, etc. They can all measure the graphics under certain conditions stably and accurately, but using one algorithm alone has limitations. The diameter of a circle with equal area to the joints and fissures is used to calculate the width of the fissure (equivalent circle diameter algorithm). This method is simple to implement but has a limited scope of application. It requires that the boundary of the measured object has large fluctuations to achieve satisfactory results. The short axis of an ellipse with equal area to the joints and fissures is used to calculate the width of the fissure (referred to as the ellipse algorithm). This method is very complicated to implement, but the effect is good and it is still used in practice. In addition, the simple Ferret algorithm (also known as the Ferret Box algorithm) [1] uses the method of measuring the distance between two parallel lines tangent to the target object to determine the length, width and other geometric features of the irregular figure. However, due to the lack of determination of the measurement direction, this method makes the width value unstable and needs further improvement.

Based on the simple Ferret algorithm, this paper introduces its improved algorithm. Through the introduction of the actual measurement process of a rock joint and crack and the analysis of the measurement results, the advantages and disadvantages of the improved Ferret algorithm and the currently commonly used measurement algorithms are compared.

1 Digital Image Processing Principles and Algorithms

In digital image processing technology, polygonal approximation methods are often used to measure irregular two-dimensional geometric figures[2]. For complex irregular two-dimensional geometric figures, regular geometric figures are usually used to approximate them, thereby obtaining the geometric feature values ​​of the measured target figure. It should be noted that before measuring the target object in the image, the original image is generally binarized[2], and then the measurement analysis is performed based on the binary image.

1.1 Principle of Simple Ferret Algorithm

The simple Ferret algorithm first selects a point from the boundary of the binary image and makes a tangent line through this point. Take a straight line parallel to the tangent line and make it tangent to the boundary of the other side of the image. When the vertical distance between the two tangent lines is the largest, the distance at this time is the length value of the measured image; when the vertical distance reaches the minimum, it is the width value of the measured image. The schematic diagram of measuring the width of an irregular image using a Ferret Box is shown in Figure 1. In the figure, Fm is the maximum value.

It can be seen that this algorithm is simple but has defects. The reason is: in order to find the maximum and minimum values ​​of the vertical distance, it is necessary to take values ​​and compare them many times, which is very cumbersome for graphics with frequent boundary changes. Moreover, this method is more suitable for convex polygons. It is difficult to determine the tangent for concave polygons, especially for complex graphics with large boundary changes such as joints and fissures, which will affect the accuracy of the measurement. The following will introduce a relatively stable algorithm for measuring width based on the simple Ferret algorithm - the improved Ferret algorithm.

1.2 Principle of the Improved Ferret Algorithm

The improved Ferret algorithm makes full use of the rotation invariance principle of two-dimensional geometric figures and makes up for the defect that the simple Ferret algorithm is not easy to measure concave polygons. The principle steps are as follows.

(1) Using the method of finding the minimum second-order moment, the reference direction for measuring the width of the irregular figure is uniquely determined.

(2) Taking the determined reference direction as the reference, the Ferret Box method is used to obtain the length and width of the figure.

It can be seen that the improved Ferret algorithm mainly adds a method for determining the direction, which makes the width measurement result tend to be stable.

The method of using the least second-order moment to determine the reference direction is shown in Figure 2. In the figure, the dotted line is an arbitrary straight line passing through the center of mass of the object, the equation of the binary graph curve is f(x, y), and the vertical distance R from the point (x, y) to the dotted line is the rotation radius, and the moment of inertia equation can be obtained:

According to Figure 2, we can get:

2 Legend Application

2.1 Collection of rock joint images

First, obtain rock samples. Drill holes in the rock mass to be studied and place radioactive material into the holes. After a week of radiation, the radioactive material fills all accessible cracks in the rock mass. Then, cut the rock. Use a 10-50x microscope to collect original color images of representative joints. The magnification ratio used in this example to collect samples is set to: the actual length represented by a light spot is 0.004mm. Due to the use of a relatively large magnification ratio, the physical characteristics of the micro-joints are more prominent, and the scale of the picture is also larger. During the collection process, the entire joint fissure was divided into 34 independent images and photographed separately. The size of each image is 760×230 pixels. For the sake of simplicity, this article selects one of the pictures in this group for processing and compares and analyzes various measurement methods and results.
2.2 Image processing process

First, the collected original color image is binarized. In order to facilitate the measurement comparison of various algorithms and reduce accidental errors, the analyzed image is divided into 7 equal parts by the average segmentation method. The segmented image is measured using the improved Ferret algorithm. Figures 3 and 4 are the original image of the crack and the image segmented after binarization. This crack has complex changes and large fluctuations. There are holes (or filling materials) in the middle of the crack and "smoke" on the boundary, which will affect the accuracy of the measurement. Therefore, the threshold method is used to remove the boundary noise before measurement. The effect diagram after processing by the improved Ferret algorithm is shown in Figure 5, and the measurement results are shown in Table 1.

2.3 Statistical analysis

Since the ellipse algorithm is widely used and has ideal results, it is used as a benchmark for comparative analysis. The comparison of the width measurement results of the three algorithms is shown in Figure 6. It can be seen from the figure that for the measurement of segments 3, 4, and 7, the results obtained by the equivalent circle diameter algorithm and the ellipse algorithm are relatively close. It can also be seen from Figure 4 that the length and width differences of the cracks in segments 3, 4, and 7 are similar. In this case, the Ferret algorithm does not show a good superiority; while for the measurement of segments 5 and 6, the results of the ellipse algorithm and the Ferret algorithm are relatively close, but the length and width difference between segments 5 and 6 is large. It can be seen that the Ferret algorithm can be used to measure irregular figures with a large length and width difference. This requires that when using the Ferret algorithm for actual measurement, attention should be paid to the segmentation scale before measurement, so that there is a certain gap between the length and width, and the ideal effect can be achieved by using the Ferret algorithm.

A large number of experimental comparisons of width measurements show that the Ferret algorithm has achieved ideal results in measuring irregular shapes, especially those with large length-width differences.

3. Conclusion

A large number of digital image processing technologies are applied in engineering measurement. Due to their heterogeneity, facing many measurement algorithms, a lot of comparative studies are needed to select a suitable algorithm. For regular measured figures, the equivalent circle algorithm and the equivalent ellipse algorithm can basically meet the needs, while the Ferret algorithm shows good adaptability in the measurement of a large number of irregular figures with large length and width differences, and achieves satisfactory results. This paper analyzes the principle of the simple Ferret algorithm, proposes an improved Ferret algorithm, and gives an example process of rock joint width measurement based on the improved Ferret algorithm. However, in actual measurement, the length selected when segmenting the image, the middle hole of the non-real crack, and the boundary noise will have a certain impact on the width measurement, which will be the problems to be solved in the future.