Extraction of complex grain boundaries in multiphase grain image analysis
Source: Application of Electronic Technology: Zhang Yiqiong Xia Wei TENG Qi-zhi HE Xiao-hai Abstract: effective method of extracting complex multiphase grain boundaries in the crystal image analysis proposed. By pretreatment eliminates the effect of grain internal grayness difference and scratches on boundary extraction; introduced into a blurred theory discrimination and tracking boundary, the characteristics of the fuzzy edge detection algorithm are not required to determine the threshold, with strong adaptiveness Finally, refine the grain boundary to obtain a single pixel width.
Keywords: grain boundary extraction grayscale transformation neighboring smoothing blur theoretical reflex
The grain boundary is often taken to extract the grain boundaries in multiphase grain image analysis to perform measurement and calculation of various parameters. For simple and clear images, you can achieve better results by direct processing of a common Sobel operator, Roberts operator, Laplace operator. However, the large number of images encountered in the project due to the impact of the material itself or the natural factor, there is a certain extent of the internal grayscale distribution uneven, boundary blurry or scratches, and directly extract the grain boundary with the above operator. The result is mainly manifested in two aspects: (1) There is a number of pseudo boundaries internally in the crystal grains, which affects the primary stop research on the image; (2) Partial main boundary is lost, the loss is large. In this paper, for the above, a method of complex multiphase grain image grain boundary extract is proposed, effectively overcoming the above disadvantages to obtain a relatively ideal grain boundary.
1 pretreatment
1.1 grayscale transformation
For a multi-phase grain image, there is often a case where the grayscale is dark, hot or inventive. If the change detection boundary is directly utilized, some main boundaries will be lost because the grayscale changes. Use a power-free transform to increase the contrast of the region of interest. The basic form of power-transfer transformation is:
The R and S are the input grayscale and output grayscale level, C, and β are normal. According to the actual situation of the image, the value of the adjustment parameter C can change the gray dynamic range of the image, and the value of the adjustment β can enhance the contrast of the region of interest in the image. In the case where the C value is unchanged, as the change in β value will simply obtain a family conversion curve, as shown in Figure 1.
As can be seen from FIG. 1, when the transformation is mapped to the broadband output value when the input narrow strip value is introduced, and the value of the β <1 and the curve generated by the value of β <1 have an opposite effect. Due to the large boundary of the extracted image, the gradation variation is more obvious boundary, while the internal gradation is absent, but the gradation difference is small, the change is relatively stable, so the parameter C is appropriately compressed image The grayscale dynamic range, thereby smoothing images, which is conducive to the back border extraction. 1.2 Neighborhood Smooth 2.3 Decision Function
1.2.1 median filtering
Since the crystal grains contain impurities, scratches, the grayscale release is uneven, the median filtering of different scales can be selected to be smoothed. Medium value filtering can smooth the image while protecting the edge profile well. However, block blurring occurs when using large-scale median filtering.
1.2.2 Adaptive filtering
After grayscale transform and median filtering, the adaptive filter is further smoothed with adaptive filtering without obtaining a satisfactory smoothed image. The basic form of adaptive smoothing is:
Where g (i, j) is an input image, g (i, j) and the mean and variance of the local image of the M × N neighborhood, and σ2 is a mean value of the local variance of the entire image, f (i, j) is Output image after smoothing. The recovery coefficient is:
For an image σ2 is fixed, the recovery coefficient k will vary with local statistical variance. In the flat area of the image, the relatively small, the K value is small, and the formula (2) is smaller, and the local value is smaller, or not recover (k = 0); and corresponding to the gray change The large area, σ2 (i, j) is large, the K value is also large, and the local value is large. This is the principle of adaptive smoothing, and the price is the edge blur. 2 blur detection
In the edge detection algorithm, a grayscale threshold is usually determined in advance, and then the gradation value of each pixel point is compared to the threshold, the pixel point greater than the threshold is confirmed as an edge point. If you use a certain edge operator (such as a Sobel Operator) to detect the edge, there are two difficulties: if you take a small threshold, the resulting edge point contains many false edges; if you take a large threshold Value, then the edge is very discontinuous. The gradient-based fuzzy edge detection algorithm can automatically determine the threshold, eliminating the huge impact on the edge due to the selection of different thresholds.
2.1 definition of a fuzzy subset
When the aroma is a limited set, the fuzzy subset F is defined as:
Where uf: [0, 1] is the membership function of F, uf (xj) represents the degree of XJ belongs to the collection F. When the value domain of u (x) is {0,1}, f is degraded into a general (non-blur) collection. That is, ordinary collections can be seen as a special blurred set, which is 0 or 1. In order to obtain the boundary of the image, the set of gradients is defined as the gradient, and XJ is defined as the gradient of the image; UF (xj) indicates the degree of pixel point of the gradient XJ is the degree of boundary point.
2.2 Edge membership function
In actual image processing, whether the membership function is appropriate is the key to successful use of the fuzzy collection. The problem now is the edge detection of the multiphase grain image, processing a grayscale image, which uses a blurred statistical method to determine the membership function. Through a large number of experiments, the gradient histogram of different multiphase grain images is very similar, as shown in FIG. As can be seen from Figure 2, the gradient histogram is mainly concentrated in a low value area. This is because each pixel point internally internally is different from the gradation value of the domain pixel point, and the gradation value of the pixel point between the particles and the particles is large, and the number of the former is much more than the latter. The shape of the statistical affiliate function is approximately shown in Figure 3. Therefore, select the subordinate function:
u (x) = (x-n) / (m-n) (5)
Where X is the gradient value, M and N of the image, the maximum value and minimum of the image gradient, respectively.
After introducing the blur theory, the math expectation of the fuzzy set can be used as a threshold for edge detection, with strong adaptiveness. Math expectations of fuzzy set f are:
In Formula 6, u (xj) represents the image edge membership function, and P (xj) represents the probability of the edge subordinate function u (xj) appearing in the image, that is, the gradient probability of the gradient value when the gradient value is XJ in the image gradient diagram.
2.4 Edge Tracking Algorithm
The edge tracking algorithm is as follows:
(1) Scan the image in any coordinate axis, find a non-bound point;
(2) Calculate the membership of this point, if u is greater than e (f), then the point is the boundary point, record its row, column number, performed (3), otherwise returns (1);
(3) Looking for U the largest point in the 8 neighborhood of this point, if it is a point of tracking, returns (1), otherwise (4);
(4) If the image is not scanned, return (2); if all points are scanned, the end. After the tracking is over, re-assign the recorded boundary point to get the boundary line.
3 post-processing
The boundary lines are burr and have a certain width in the two-value image obtained by the above method, and the grain calculation is used to perform crystal grain calculations directly, it is necessary to smooth and refine the extracted boundary.
3.1 Smooth edge
Detaching the extracted boundary will produce a lot of branch shortlines due to many burrs in the edge. The edges can be performed using the mathematical morphology opening and closing operation. The operation generally makes the profile of the image smooth, disconnects narrow interruption and eliminates fine protrusions. The closed operation makes the outline more smooth, but it is opposite to the operation, it usually eliminates the fine hole, fill the break in the contour.
3.2 Refining
Refine processing of the smooth boundary image to obtain a boundary image of the single pixel width. When there is a projection in the edge of the strip, it must be removed after the short lines formed in the protrusions and the short-branch of the sporadic pseudo-boundary fine. First, the length threshold value of the short line is set, if the line length is greater than the threshold L, it is considered that the line is a line in the original line diagram; if its value is less than or equal to the threshold L, it is considered that the line is excess short line. It is removed. 4 experimental results
As an experimental picture, as shown in Fig. 4 (a), it is used as an experimental original view. Fig. 4 (b) is a boundary diagram obtained with a Sobel operator. With a fuzzy edge detection algorithm, the detected boundary is shown in Fig. 4 (c), and the grain boundary obtained after the deposition treatment is shown in Fig. 4 (d). Comparison FIG. 4 (b) and Fig. 4 (D) can be seen that the algorithm effectively suppresses the generation of the pseudo-boundary, extracts a more complete grain boundary.
The grain boundary extraction is an important part of grain granular image analysis. In this paper, a simple and effective grain boundary extraction method is proposed for the defects of the conventional multiphase grain image analysis. Advanced in advance (grayscale transform, neighbor smoothing), and then fuzzy edge detection, and extracting a relatively ideal grain boundary while effectively suppressing pseudo borders. Through experiments, the effectiveness of the algorithm is verified, and since there is a discontinuity of the grain boundary image, the automatic repair of the grain boundary is the next research direction.
