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摘要: 圖像分割是計算機視覺領域中的重要分支，旨在將圖像分成若干個特定的、具有獨特性質的區域。隨著計算機硬件計算能力的提高和計算方法的進步，大量基于不同理論的圖像分割算法獲得了長足的發展。因而選擇合適的評估方法對分割結果的準確性和適用性進行綜合評估，從而選擇最優分割算法，成為圖像分割研究中的必要環節。在綜述14種圖像分割評估指標的基礎上，將其分成基于像素的評估方法、基于類內重合度的評估方法、基于邊界的評估方法、基于聚類的評估方法和基于實例的評估方法五大類。在材料顯微圖像分析的應用背景下，通過實驗討論了不同分割方法和不同典型噪聲在不同評估方法中的表現。最終，討論了各種評估方法的優勢和適用性。Abstract: Material microstructure data are an important type of data in building intrinsic relationships between compositions, structures, processes, and properties, which are fundamental to material design. Therefore, the quantitative analysis of microstructures is essential for effective control of the material properties and performances of metals or alloys in various industrial applications. Microscopic images are often used to understand the important structures of a material, which are related to certain properties of interest. One of the key steps during material design process is the extraction of useful information from images through microscopic image processing using computational algorithms and tools. For example, image segmentation, which is a task that divides the image into several specific and unique regions, can detect and separate each microstructure to quantitatively analyze its size and shape distribution. This technique is commonly used in extracting significant information from microscopic images in material structure characterization field. With great improvement in computing power and methods, a large number of image segmentation methods based on different theories have made great progress, especially deep learning-based image segmentation method. Therefore selecting an appropriate evaluation method to assess the accuracy and applicability of segmentation results to properly select the optimal segmentation methods and their indications on the direction of future improvement is necessary. In this work, 14 evaluation metrics of image segmentation were summarized and discussed. The metrics were divided into five categories: pixel, intra class coincidence, edge, clustering, and instance based. In the application of material microscopic image analysis, we collected two classical datasets (Al–La alloy and polycrystalline images) to conduct quantitative experiment. The performance of different segmentation methods and different typical noises in different evaluation metrics were then compared and discussed. Finally, we discussed the advantages and applicability of various evaluation metrics in the field of microscopic image processing.
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圖 2 評估指標示意圖。（a）IoU指標示意圖；（b）VI指標示意圖
Figure 2. Schematics of evaluation metrics: (a) IoU metric diagram; (b) VI metric diagram
Note: VI(P,T) means variation of information; I(T,P) denotes mutual information; H(P/T) and H(T/P) denote conditional entropy.
圖 3 邊緣檢測匹配示意圖。（a）令預測邊界與真值邊界進行匹配；（b）令真值邊界與預測邊界進行匹配
Figure 3. Matching schematics of edge detection：(a) matching ground truth with prediction skeleton; (b) matching prediction with ground truth skeleton
圖 4 多晶純鐵晶粒組織及鋁鑭合金枝晶組織圖像在不同分割算法結果的可視化對比
Figure 4. Visualization results of different segmentation methods for polycrystalline iron and Al–La alloy microscopic image
圖 5 兩種圖像數據引入不同種類噪聲的結果。（a）多晶純鐵晶粒圖像；（b）圖（a）的真值結果；（c）在（b）中隨機引入500像素的噪聲點；（d）在（b）中引入500像素的劃痕噪聲；（e）在（b）中引入500像素的消失晶界噪聲；（f）鋁鑭合金枝晶圖像；（g）圖（f）的真值結果；（h）在（g）中隨機引入500像素的噪聲點；（i）在（g）中引入500像素的劃痕噪聲
Figure 5. Two microscopic images with different noises: (a) polycrystalline iron; (b) ground truth of (a); (c) random noises with 500 pixels in (b); (d) scratch noises with 500 pixels in (b); (e) missing boundaries with 500 pixels in (b); (f) Al la alloy; (g) ground truth of (f); (h) random noises with 500 pixels in (g); (i) scratch noises with 500 pixels in (g)
表 1 基于聚類任務的列聯表
Table 1. Contingency table
Union ${P_1}$ ${P_2}$ … ${P_s}$ Sums ${T_1}$ ${n_{11}}$ ${n_{12}}$ … ${n_{1s}}$ ${a_1}$ ${T_2}$ ${n_{21}}$ ${n_{22}}$ … ${n_{2s}}$ ${a_2}$ … … … … … … ${T_r}$ ${n_{r1}}$ ${n_{r2}}$ … ${n_{rs}}$ ${a_r}$ Sums ${b_1}$ ${b_2}$ … ${b_s}$ 
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表 2 各指標的簡要概括
Table 2. Brief description of different evaluation methods
Properties Pixel based evaluation methods Intra class coincidence based
evaluation methodsEdge based evaluation methods Pixel accuracy Mean accuracy MIoU FWIoU Dice score Figure of merit Completeness Correctness Value range [0, 1] [0, 1] [0, 1] [0, 1] [0, 1] [0, 1] [0, 1] [0, 1] tendency $ \uparrow $ $ \uparrow $ $ \uparrow $ $ \uparrow $ $ \uparrow $ $ \uparrow $ $ \uparrow $ $ \uparrow $
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表 3 材料顯微圖像數據集參數
Table 3. Description of two material micrographic image datasets
ID Microstructure Image size Image number 1 Polycrystalline iron 1024×1024 296 2 Al–La alloy 1024×1024 50
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表 4 多晶純鐵晶粒組織圖像不同分割算法下評估結果
Table 4. Evaluation results under different segmentation algorithms for polycrystalline iron image
Segmentation algorithm Pixel based evaluation methods Intra class coincidence based
evaluation methodsEdge based evaluation methods Pixel accuracy Mean accuracy MIoU FWIoU Dice score Figure of merit Completeness Correctness OTSU 0.9443 0.7800 0.7226 0.8979 0.9696 0.6593 0.8298 0.9146 Canny 0.9145 0.6364 0.5811 0.8468 0.9540 0.4085 0.7007 0.9156 Watershed 0.9017 0.5613 0.5109 0.8236 0.9476 0.2009 0.4516 0.6537 K?means 0.5739 0.5469 0.4331 0.5307 0.5771 0.4906 0.8598 0.5796 Random walker 0.9447 0.7925 0.7293 0.8994 0.9697 0.6963 0.8445 0.9059 Unet 0.9311 0.9423 0.7510 0.8898 0.9605 0.8933 0.9784 0.8562
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表 5 鋁鑭合金枝晶組織圖像不同分割算法下評估結果
Table 5. Evaluation of different segmentation results for Al–La microscopic image
Segmentation algorithm Pixel based evaluation methods Intra class coincidence based evaluation methods Clustering based evaluation methods Pixel accuracy Mean accuracy MIoU FWIoU Dice score RI OTSU 0.6263 0.7025 0.4538 0.4441 0.6573 0.6981 Canny 0.5259 0.6126 0.3497 0.3315 0.5890 0.4780 Watershed 0.4199 0.5426 0.2373 0.1974 0.5557 0.5902 K-means 0.5078 0.5098 0.3287 0.3482 0.3434 0.5210 Random walker 0.5110 0.4027 0.2559 0.3249 0.0024 0.3552 Unet 0.9850 0.9854 0.9684 0.9706 0.9796 0.9810
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表 6 多晶純鐵晶粒圖像在不同噪聲下各評估方法的結果
Table 6. Results of different evaluation methods for polycrystalline iron image under different noises
Noise type Pixel based evaluation methods Intra class coincidence based
evaluation methodsEdge based evaluation methods Pixel accuracy Mean accuracy MIoU FWIoU Dice score Figure of merit Completeness Correctness Random noises 0.9980
(?0.0020)0.9989
(?0.0011)0.9833
(?0.0167)0.9961
(?0.0039)0.9989
(?0.0011)0.9790
(?0.0011)1.0000
(?0.0000)0.9737
(?0.0263)Scratch noises 0.9980
(?0.0020)0.9989
(?0.0011)0.9833
(?0.0167)0.9961
(?0.0039)0.9989
(?0.0011)0.9739
(?0.0261)1.0000
(?0.0000)0.9702
(?0.0298)Missing boundaries 0.9964
(?0.0036)0.9713
(?0.0287)0.9694
(?0.0306)0.9929
(?0.0071)0.9981
(?0.0019)0.9426
(?0.0574)0.9465
(?0.0535)1.0000
(?0.0298)
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表 7 鋁鑭合金枝晶圖像在不同噪聲下各評估方法的結果
Table 7. Results of different evaluation methods for Al La alloy under different noises
Noise type Pixel based evaluation methods Intra class coincidence based evaluation methods Clustering based evaluation methods Pixel accuracy Mean accuracy MIoU FWIoU Dice score RI Random noises 0.9980(?0.0020) 0.9974(?0.0026) 0.9958(?0.0042) 0.9960(?0.0040) 0.9974(?-0.0026) 0.9974(?0.0026) Scratch noises 0.9980(?0.0020) 0.9974(?0.0026) 0.9958(?0.0042) 0.9960(?0.0040) 0.9974(?0.0026) 0.9966(?0.0034)
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