*5.6. Confusion Matrix and Visualization*

Table 3 lists the detailed classification of test set of DNST-GLCM-KSR scheme. The accuracy of positive sample (crack defect) is 95.50%; the accuracy of negative sample is 97.08%. There are four pseudo-defects misclassified as crack defects, and five crack defects are misclassified as pseudo-defects. This was due to the fact that inter-class defects have similar aspects in appearance. The false alarm rate of cracks is 4/110 = 3.64%, and the missing alarm rate is 5/111 = 4.5%. The above metrics meet the needs of engineering application of continuous casting slabs.

**Table 3.** The confusion matrix of discrete nonseparable shearlet transform gray-level co-occurrence matrix kernel spectral regression (DNST-GLCM-KSR) scheme.


Figure 6 shows the visualization of the DNST-GLCM-KSR test set. The result is a straight line, because the number of the feature dimensionality is 1. The pink circle represents the positive sample, the blue one represents the negative sample, and the upper left corner is a local enlargement image. The result of Figure 6 is consistent with that of Table 3, namely that four pseudo-defects are misclassified as crack and five crack defects are misclassified as pseudo-defects. From the graph, we can see that the DNST-GLCM-KSR features truly reflect the similarity between defect images. The intra-class scatter is small, and the inter-class scatter is large. The above analysis shows the method proposed can effectively recognize crack defects of continuous casting slabs in complex background images and interference factors.

**Figure 6.** Visualization results.

#### **6. Conclusions**

According to the direction and texture information of surface defects of the continuous casting slabs with complex backgrounds, a new feature extraction approach DNST-GLCM-KSR is proposed, which combines multi-scale and multi-directional DNST features with GLCM texture features and uses KSR technology to reduce dimensionality. The experimental results are as follows.

(1) The DNST feature obtained the highest average accuracy and the best accuracy. It can better characterize defects of continuous casting slabs than that of Contourlet, DST, wavelet, and GLCM.


**Author Contributions:** K.X. contributed to the methodology of the study and investigation. X.L. contributed significantly to formal analysis and manuscript writing. P.Z. and H.L. helped perform the analysis with constructive discussions.

**Funding:** This research was funded by the National Natural Science Foundation of China (grant number 51674031 and 51874022) and the Fundamental Research Finds for the Central Universities under Grant FRF-TP-18-009A2.

**Conflicts of Interest:** The authors declare there is no conflicts of interest regarding the publication of this paper.
