*3.2. Estimation of Segmentation Accuracy*

*3.2. Estimation of Segmentation Accuracy*  The area (px) of the regions surrounded by contours in the segmented images were counted, and the cumulative area distribution was calculated. Suppose ଵ, ଶ, …, are areas of the regions enclosed by the particle segmentation contours in a processed image. Among ଵ, ଶ, …, , areas of the regions that are smaller than the specified values are ଵ , ଶ , …, . The cumulative area distribution () is computed using the following equation: The area (px) of the regions surrounded by contours in the segmented images were counted, and the cumulative area distribution was calculated. Suppose *x*1, *x*2, . . . , *x<sup>n</sup>* are areas of the regions enclosed by the particle segmentation contours in a processed image. Among *x*1, *x*2, . . . , *xn*, areas of the regions that are smaller than the specified values are *y*1, *y*2, . . . , *ym*. The cumulative area distribution (*C*) is computed using the following equation:

$$\mathbf{C} = \frac{\sum\_{i=1}^{m} y\_i}{\sum\_{j=1}^{n} x\_j} \quad (m \le n) \tag{4}$$

We use the cumulative area distribution to evaluate the segmentation accuracy of algorithms. The specified value used to calculate the cumulative area distribution is called the area filter (px). If the number of pixels in the region surrounded by the contour is less than the area filter, the region can pass the area filter; otherwise, the region cannot pass. The contourArea function from the Python OpenCV library (version 4.1.1) was adopted to get the number of pixels in the region surrounded by We use the cumulative area distribution to evaluate the segmentation accuracy of algorithms. The specified value used to calculate the cumulative area distribution is called the area filter (px). If the number of pixels in the region surrounded by the contour is less than the area filter, the region can pass the area filter; otherwise, the region cannot pass. The contourArea function from the Python OpenCV library (version 4.1.1) was adopted to get the number of pixels in the region surrounded by the contour.

1

=

*j*

the contour. The cumulative area distributions of the segmentation results of the empty belt image,

The cumulative area distributions of the segmentation results of the empty belt image, mixed material image, and coarse material image are quite different; therefore, different area filters were used for calculating the cumulative area distribution of the segmented images. The empty belt images were evaluated using 2000, 4000, 8000, 10,000, 20,000, 40,000, 80,000, and 100,000 px area filters. The mixed material images were evaluated using 2000, 4000, 6000, 8000, 10,000, 20,000, 30,000, and 40,000 px area filters. The coarse material images were evaluated using 5000, 10,000, 15,000, 20,000, 25,000, 30,000, 35,000, and 40,000 px area filters. The cumulative area distribution and the number of segmentation contours of the image segmented by the PCS system, CIS, and FIS, respectively, were compared with the segmentation result of the manual segmentation image. The segmentation result of the algorithm, which was close to the manual segmentation result, was evaluated as accurate.

#### **4. Experimental Results and Discussions**

#### *4.1. The Segmentation Result Analysis of Di*ff*erent Algorithms*

Images in Figure 9a were segmented using manual segmentation, PCS, CIS, and FIS, respectively, providing results as shown in Figure 9b–e. By counting the number of segmentation contours in the segmented images, the results are shown in Table 1. By calculating the cumulative area distribution of the segmented images, the results are shown in Figure 10. Table 1 shows that the segmentation contour counts of the empty belt image by the PCS system, CIS algorithm and FIS algorithm, respectively, are 371, 51, 92. Figure 10a and Table 1 demonstrate that no algorithm can accurately segment the empty belt images. Due to many disturbing factors such as small particles, dirt, and water on the surface of the empty belts, the segmentation algorithms always segments the empty belt images. We only require to recognize and need not segment the empty belt images. Table 2 shows our method alarms all three empty belt images from groups 2 to 4. Table 2 indicates that using the training model based on the convolutional neural network to process the empty belt images shows better performance and accuracy. From Figure 10c and Table 1, it is observed that the PCS system shows serious over-segmentation in processing the coarse material images, and the segmentation accuracy of the FIS algorithm is found to be between that of the CIS algorithm and the PCS system. The outlines of massive rocks are obvious as compared to those of granular particles and fine material. Many disturbing factors, such as edges and corners, uneven color distribution, shadow, and so on, are found on the surface of massive rocks. An algorithm that can accurately segment the coarse material images must overcome the above interferences, however, the blur and denoise operations used cannot weaken the outlines of coarse ores too much. Figure 9 shows that the CIS algorithm has obvious advantages for segmenting the coarse material images. The blur, denoise, and smooth operations of the CIS algorithm weaken the outlines of ores; therefore, there is a serious under-segmentation in processing mixed material images, especially the fine material images (see Figures 9 and 10b). We classified the images in the original dataset, which are neither coarse material images nor empty belt images, as mixed material images.


**Table 1.** The segmentation contour count of various algorithms.

**Table 2.** The results of empty belt images from groups 2 to 4, as processed by our method.


**Figure 10.** The results of raw images by segmenting group 1 using manual segmentation, PCS, CIS, and FIS, respectively: empty belt (**a**), mixed materials (**b**), and coarse materials (**c**). **Figure 10.** The results of raw images by segmenting group 1 using manual segmentation, PCS, CIS, and FIS, respectively: empty belt (**a**), mixed materials (**b**), and coarse materials (**c**).

As the number of images in the original dataset is very high, it is not feasible to count the particle size distribution of materials on conveyor belts. The method of distinguishing empty, mixed materials, and coarse materials is based on artificial classification. An image that is full of massive ores is classified as a coarse material image. The accurate segmentation of mixed material images is most difficult to achieve. The massive ores show a greater impact on the grinding process. The results calculated by the under-segmentation of fine material images are found to be much coarser than the actual results. Fewer morphological operations enable the FIS algorithm to retain the outlines of granular particles and fine materials. More denoise operations enable the FIS algorithm to remove the interferences on the surface of the massive ores as much as possible. Figure 10b shows that the FIS algorithm shows accurate segmentation in processing mixed material images, especially the fine material images. As the FIS algorithm cannot remove the large non-edge features on the surface of massive rocks such as edges, corners, and color blocks, the FIS algorithm does not show as accurate results as the CIS algorithm in processing the coarse material images (see Figure 10c and Table 1). It As the number of images in the original dataset is very high, it is not feasible to count the particle size distribution of materials on conveyor belts. The method of distinguishing empty, mixed materials, and coarse materials is based on artificial classification. An image that is full of massive ores is classified as a coarse material image. The accurate segmentation of mixed material images is most difficult to achieve. The massive ores show a greater impact on the grinding process. The results calculated by the under-segmentation of fine material images are found to be much coarser than the actual results. Fewer morphological operations enable the FIS algorithm to retain the outlines of granular particles and fine materials. More denoise operations enable the FIS algorithm to remove the interferences on the surface of the massive ores as much as possible. Figure 10b shows that the FIS algorithm shows accurate segmentation in processing mixed material images, especially the fine material images. As the FIS algorithm cannot remove the large non-edge features on the surface of massive rocks such as edges, corners, and color blocks, the FIS algorithm does not show as accurate results as the CIS algorithm in processing the coarse material images (see Figure 10c and Table 1). It is more accurate and reasonable

to classify images first and then use different algorithms for processing rather than to process all images with the same algorithm.
