{"id":74149,"date":"2026-02-09T08:33:27","date_gmt":"2026-02-09T00:33:27","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/74149.html"},"modified":"2026-02-09T08:33:27","modified_gmt":"2026-02-09T00:33:27","slug":"yolov1%e6%8d%9f%e5%a4%b1%e5%87%bd%e6%95%b0","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/74149.html","title":{"rendered":"YOLOv1\u635f\u5931\u51fd\u6570"},"content":{"rendered":"

\u6211\u4eec\u6765\u9010\u9879\u3001\u9010\u7b26\u53f7\u3001\u7528\u901a\u4fd7\u8bed\u8a00+\u4f8b\u5b50，\u5f7b\u5e95\u8bb2\u6e05\u695a YOLOv1 \u7684\u635f\u5931\u51fd\u6570（Loss Function）\u5230\u5e95\u5728\u7b97\u4ec0\u4e48\u3001\u4e3a\u4ec0\u4e48\u8fd9\u6837\u8bbe\u8ba1\u3002<\/p>\n

\n

🎯 \u635f\u5931\u51fd\u6570\u7684\u76ee\u6807\u662f\u4ec0\u4e48？<\/h3>\n

YOLOv1 \u8981\u540c\u65f6\u5b8c\u6210\u4e09\u4ef6\u4e8b：<\/p>\n

  • \u5b9a\u4f4d\u7269\u4f53（\u9884\u6d4b\u8fb9\u754c\u6846\u7684 x, y, w, h）<\/li>\n
  • \u5224\u65ad\u6709\u6ca1\u6709\u7269\u4f53（\u7f6e\u4fe1\u5ea6 confidence）<\/li>\n
  • \u8bc6\u522b\u7269\u4f53\u7c7b\u522b（\u5982\u201c\u72d7\u201d\u3001\u201c\u8f66\u201d）<\/li>\n

    \u6240\u4ee5\u5b83\u7684\u635f\u5931\u51fd\u6570\u5fc5\u987b\u540c\u65f6\u76d1\u7763\u8fd9\u4e09\u90e8\u5206，\u800c\u4e14\u8981\u806a\u660e\u5730\u5206\u914d\u6743\u91cd\u2014\u2014\u4e0d\u80fd\u8ba9\u67d0\u4e00\u90e8\u5206\u201c\u538b\u57ae\u201d\u5176\u4ed6\u90e8\u5206\u3002<\/p>\n

    \n

    📐 \u6574\u4f53\u7ed3\u6784：5 \u4e2a\u90e8\u5206\u76f8\u52a0<\/h3>\n

    YOLOv1 \u7684\u603b\u635f\u5931 $ \\\\mathcal{L} $ \u662f\u4ee5\u4e0b 5 \u9879\u4e4b\u548c：<\/p>\n\n\u9879\u76d1\u7763\u5185\u5bb9\u53ea\u5bf9\u54ea\u4e9b\u7f51\u683c\/\u6846\u8ba1\u7b97？<\/tr>\n\n\n\n\n\n\n
    1\ufe0f\u20e3 \u5750\u6807\u635f\u5931（x, y）<\/td>\n\u6846\u4e2d\u5fc3\u4f4d\u7f6e<\/td>\n\u6709\u7269\u4f53\u7684\u7f51\u683c\u4e2d，\u8d1f\u8d23\u9884\u6d4b\u7684\u90a3\u4e2a\u6846<\/td>\n<\/tr>\n
    2\ufe0f\u20e3 \u5c3a\u5bf8\u635f\u5931（w, h）<\/td>\n\u6846\u5bbd\u9ad8<\/td>\n\u540c\u4e0a<\/td>\n<\/tr>\n
    3\ufe0f\u20e3 \u6709\u7269\u4f53\u7684\u7f6e\u4fe1\u5ea6\u635f\u5931<\/td>\nconfidence \u5e94\u63a5\u8fd1 IoU<\/td>\n\u540c\u4e0a<\/td>\n<\/tr>\n
    4\ufe0f\u20e3 \u65e0\u7269\u4f53\u7684\u7f6e\u4fe1\u5ea6\u635f\u5931<\/td>\nconfidence \u5e94\u63a5\u8fd1 0<\/td>\n\u6240\u6709\u4e0d\u542b\u7269\u4f53\u4e2d\u5fc3\u7684\u7f51\u683c\u7684\u6240\u6709\u6846<\/td>\n<\/tr>\n
    5\ufe0f\u20e3 \u5206\u7c7b\u635f\u5931<\/td>\n\u7c7b\u522b\u6982\u7387<\/td>\n\u6709\u7269\u4f53\u7684\u7f51\u683c（\u6574\u4e2a\u7f51\u683c，\u4e0d\u662f\u6bcf\u4e2a\u6846）<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    \u2705 \u6ce8\u610f：\u53ea\u6709\u771f\u5b9e\u7269\u4f53\u4e2d\u5fc3\u6240\u5728\u7684\u90a3\u4e2a\u7f51\u683c\u624d\u7b97\u201c\u6709\u7269\u4f53\u201d\u3002<\/p>\n

    \n

    🔍 \u9010\u9879\u8be6\u89e3（\u914d\u5408\u7b26\u53f7\u8bf4\u660e）<\/h3>\n

    \u7b26\u53f7\u8bf4\u660e（\u5148\u641e\u61c2\u8fd9\u4e9b！）<\/h4>\n
      \n
    • $ S = 7 $：\u56fe\u50cf\u88ab\u5206\u6210 7\u00d77 \u7f51\u683c<\/li>\n
    • $ B = 2 $：\u6bcf\u4e2a\u7f51\u683c\u9884\u6d4b 2 \u4e2a\u8fb9\u754c\u6846<\/li>\n
    • $ i $：\u7f51\u683c\u7d22\u5f15（\u4ece 0 \u5230 S2\u22121S^2 – 1<\/span><\/span>S<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>，\u5171 49 \u4e2a）<\/li>\n
    • $ j $：\u6846\u7d22\u5f15（0 \u6216 1）<\/li>\n
    • $ \\\\mathbb{1}_{ij}^{\\\\text{obj}} $：\u6307\u793a\u51fd\u6570\n
        \n
      • \u5982\u679c\u7b2c ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u4e2a\u7f51\u683c\u4e2d\u7684\u7b2c jj<\/span><\/span>j<\/span><\/span><\/span><\/span><\/span> \u4e2a\u6846\u201c\u8d1f\u8d23\u201d\u9884\u6d4b\u67d0\u4e2a\u771f\u5b9e\u7269\u4f53 \u2192 \u503c\u4e3a 1<\/li>\n
      • \u5426\u5219\u4e3a 0<\/li>\n<\/ul>\n<\/li>\n
      • $ \\\\mathbb{1}_{i}^{\\\\text{obj}} $：\u5982\u679c\u7b2c ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u4e2a\u7f51\u683c\u5305\u542b\u67d0\u4e2a\u7269\u4f53\u7684\u4e2d\u5fc3 \u2192 \u4e3a 1（\u7528\u4e8e\u5206\u7c7b\u635f\u5931）<\/li>\n
      • $ x_i, y_i $：\u6a21\u578b\u9884\u6d4b\u7684\u6846\u4e2d\u5fc3（\u76f8\u5bf9\u4e8e\u7f51\u683c\u5de6\u4e0a\u89d2，\u5f52\u4e00\u5316\u5230 [0,1]）<\/li>\n
      • $ \\\\hat{x}_i, \\\\hat{y}_i $：\u771f\u5b9e\u503c（ground truth）<\/li>\n
      • $ w_i, h_i $：\u9884\u6d4b\u7684\u5bbd\u9ad8（\u76f8\u5bf9\u4e8e\u6574\u56fe，\u53ef >1）<\/li>\n
      • $ \\\\hat{w}_i, \\\\hat{h}_i $：\u771f\u5b9e\u5bbd\u9ad8<\/li>\n
      • $ C_i $：\u9884\u6d4b\u7684\u7f6e\u4fe1\u5ea6（confidence）<\/li>\n
      • $ \\\\hat{C}_i $：\u76ee\u6807\u7f6e\u4fe1\u5ea6（\u8bad\u7ec3\u65f6 = \u9884\u6d4b\u6846\u4e0e\u771f\u5b9e\u6846\u7684 IoU）<\/li>\n
      • $ p_i\u00a9 $：\u9884\u6d4b\u7684\u201c\u8be5\u7f51\u683c\u7269\u4f53\u5c5e\u4e8e\u7c7b\u522b c\u201d\u7684\u6982\u7387<\/li>\n
      • $ \\\\hat{p}_i\u00a9 $：\u771f\u5b9e\u6807\u7b7e（one-hot \u7f16\u7801，\u5982\u201c\u72d7\u201d=1，\u5176\u4f59=0）<\/li>\n<\/ul>\n
        \n

        \u7b2c1\u9879：\u6846\u4e2d\u5fc3\u5750\u6807\u635f\u5931（x, y）<\/h4>\n

        \u03bbcoord\u2211i=0S2\u2211j=0B1ijobj[(xi\u2212x^i)2+(yi\u2212y^i)2]
        \n\\\\lambda_{\\\\text{coord}} \\\\sum_{i=0}^{S^2} \\\\sum_{j=0}^{B} \\\\mathbb{1}_{ij}^{\\\\text{obj}} \\\\left[ (x_i – \\\\hat{x}_i)^2 + (y_i – \\\\hat{y}_i)^2 \\\\right]
        \n<\/span><\/span>\u03bb<\/span><\/span>coord<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>S<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>obj<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span><\/span>(<\/span>x<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>x<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>(<\/span>y<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span>y<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

        \u2705 \u542b\u4e49：
        \n\u53ea\u5bf9\u201c\u8d1f\u8d23\u9884\u6d4b\u771f\u5b9e\u7269\u4f53\u201d\u7684\u90a3\u4e9b\u6846，\u8ba1\u7b97\u5176\u4e2d\u5fc3\u70b9\u9884\u6d4b\u8bef\u5dee\u3002<\/p>\n

        📌 \u5173\u952e\u70b9：<\/p>\n

          \n
        • \u53ea\u6709\u4e00\u4e2a\u6846\u4f1a\u88ab\u9009\u4e2d（IoU \u66f4\u5927\u7684\u90a3\u4e2a），\u6240\u4ee5 1ijobj\\\\mathbb{1}_{ij}^{\\\\text{obj}}<\/span><\/span>1<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>obj<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u5927\u90e8\u5206\u662f 0\u3002<\/li>\n
        • \u7528 L2 \u635f\u5931（\u5e73\u65b9\u8bef\u5dee），\u60e9\u7f5a\u5927\u504f\u5dee\u3002<\/li>\n
        • \u4e58\u4ee5 \u03bbcoord=5\\\\lambda_{\\\\text{coord}} = 5<\/span><\/span>\u03bb<\/span><\/span>coord<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>5<\/span><\/span><\/span><\/span><\/span>：\u5f3a\u8c03\u5b9a\u4f4d\u5f88\u91cd\u8981！<\/li>\n<\/ul>\n

          💡 \u4e3e\u4f8b：
          \n\u771f\u5b9e\u7269\u4f53\u4e2d\u5fc3\u5728\u7f51\u683c (3,4)，\u4e24\u4e2a\u9884\u6d4b\u6846 A \u548c B\u3002
          \nA \u4e0e\u771f\u5b9e\u6846 IoU=0.6，B=0.3 \u2192 \u9009 A\u3002
          \n\u53ea\u8ba1\u7b97 A \u7684 (x,y) \u8bef\u5dee，B \u7684\u4e0d\u7b97\u3002<\/p>\n

          \n

          \u7b2c2\u9879：\u6846\u5c3a\u5bf8\u635f\u5931（w, h）\u2014\u2014\u4f46\u7528\u4e86 \u221a！<\/h4>\n

          \u03bbcoord\u2211i=0S2\u2211j=0B1ijobj[(wi\u2212w^i)2+(hi\u2212h^i)2]
          \n\\\\lambda_{\\\\text{coord}} \\\\sum_{i=0}^{S^2} \\\\sum_{j=0}^{B} \\\\mathbb{1}_{ij}^{\\\\text{obj}} \\\\left[ (\\\\sqrt{w_i} – \\\\sqrt{\\\\hat{w}_i})^2 + (\\\\sqrt{h_i} – \\\\sqrt{\\\\hat{h}_i})^2 \\\\right]
          \n<\/span><\/span>\u03bb<\/span><\/span>coord<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>S<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>obj<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>[<\/span><\/span>(<\/span><\/span>w<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>w<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>(<\/span><\/span>h<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span>h<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>]<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

          \u2705 \u542b\u4e49：\u540c\u6837\u53ea\u5bf9\u201c\u8d1f\u8d23\u6846\u201d\u8ba1\u7b97\u5bbd\u9ad8\u8bef\u5dee，\u4f46\u5bf9 w \u548c h \u5f00\u5e73\u65b9\u540e\u518d\u7b97\u8bef\u5dee\u3002<\/p>\n

          \u2753 \u4e3a\u4ec0\u4e48\u8981\u5f00\u5e73\u65b9？<\/p>\n

          👉 \u89e3\u51b3\u5c0f\u7269\u4f53\u8bef\u5dee\u88ab\u5927\u7269\u4f53\u6df9\u6ca1\u7684\u95ee\u9898\u3002<\/p>\n

            \n
          • \u5047\u8bbe\u771f\u5b9e\u5bbd = 0.1（\u5c0f\u7269\u4f53），\u9884\u6d4b = 0.2 \u2192 \u8bef\u5dee = 0.01（\u5e73\u65b9\u540e）<\/li>\n
          • \u771f\u5b9e\u5bbd = 0.9（\u5927\u7269\u4f53），\u9884\u6d4b = 1.0 \u2192 \u8bef\u5dee = 0.01（\u4e00\u6837！）<\/li>\n
          • \u4f46\u5b9e\u9645\u4e0a，\u5c0f\u7269\u4f53\u9884\u6d4b\u9519\u4e00\u500d，\u6bd4\u5927\u7269\u4f53\u9519\u4e00\u70b9\u70b9\u66f4\u4e25\u91cd！<\/li>\n<\/ul>\n

            \u5f00\u5e73\u65b9\u540e：<\/p>\n

              \n
            • \u5c0f\u7269\u4f53：\u221a0.1 \u2248 0.316，\u221a0.2 \u2248 0.447 \u2192 \u5dee \u2248 0.131 \u2192 \u5e73\u65b9 \u2248 0.017<\/li>\n
            • \u5927\u7269\u4f53：\u221a0.9 \u2248 0.949，\u221a1.0 = 1.0 \u2192 \u5dee \u2248 0.051 \u2192 \u5e73\u65b9 \u2248 0.0026<\/li>\n<\/ul>\n

              \u2192 \u5c0f\u7269\u4f53\u7684\u635f\u5931\u53d8\u5927\u4e86！\u6a21\u578b\u4f1a\u66f4\u5173\u6ce8\u5b83\u3002<\/p>\n

              \n

              \u7b2c3\u9879：\u6709\u7269\u4f53\u7684\u7f6e\u4fe1\u5ea6\u635f\u5931<\/h4>\n

              \u2211i=0S2\u2211j=0B1ijobj(Ci\u2212C^i)2
              \n\\\\sum_{i=0}^{S^2} \\\\sum_{j=0}^{B} \\\\mathbb{1}_{ij}^{\\\\text{obj}} (C_i – \\\\hat{C}_i)^2
              \n<\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>S<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>obj<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>C<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>C<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

              \u2705 \u542b\u4e49：\u8ba9\u201c\u8d1f\u8d23\u6846\u201d\u7684\u7f6e\u4fe1\u5ea6 CiC_i<\/span><\/span>C<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u63a5\u8fd1 \u5b83\u4e0e\u771f\u5b9e\u6846\u7684 IoU\u3002<\/p>\n

                \n
              • \u5982\u679c\u9884\u6d4b\u6846\u548c\u771f\u5b9e\u6846\u5b8c\u5168\u91cd\u5408 \u2192 IoU=1 \u2192 \u5e0c\u671b Ci=1C_i = 1<\/span><\/span>C<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/li>\n
              • \u5982\u679c\u91cd\u5408\u5ea6\u4f4e \u2192 IoU=0.5 \u2192 \u5e0c\u671b Ci=0.5C_i = 0.5<\/span><\/span>C<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.5<\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ul>\n

                📌 \u6ce8\u610f：\u8fd9\u4e0d\u662f\u8ba9 confidence=1，\u800c\u662f\u8ba9\u5b83\u7b49\u4e8e \u5b9a\u4f4d\u8d28\u91cf（IoU）！<\/p>\n

                \n

                \u7b2c4\u9879：\u65e0\u7269\u4f53\u7684\u7f6e\u4fe1\u5ea6\u635f\u5931（\u91cd\u70b9！）<\/h4>\n

                \u03bbnoobj\u2211i=0S2\u2211j=0B1ijnoobj(Ci\u2212C^i)2
                \n\\\\lambda_{\\\\text{noobj}} \\\\sum_{i=0}^{S^2} \\\\sum_{j=0}^{B} \\\\mathbb{1}_{ij}^{\\\\text{noobj}} (C_i – \\\\hat{C}_i)^2
                \n<\/span><\/span>\u03bb<\/span><\/span>noobj<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>S<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>j<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>B<\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>noobj<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>C<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>C<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                \u2705 \u542b\u4e49：\u8ba9\u4e0d\u8d1f\u8d23\u4efb\u4f55\u7269\u4f53\u7684\u6846\u7684\u7f6e\u4fe1\u5ea6\u8d8b\u8fd1\u4e8e 0\u3002<\/p>\n

                  \n
                • 1ijnoobj=1\u22121ijobj\\\\mathbb{1}_{ij}^{\\\\text{noobj}} = 1 – \\\\mathbb{1}_{ij}^{\\\\text{obj}}<\/span><\/span>1<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>noobj<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>obj<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n
                • \u603b\u5171\u6709 49 \u7f51\u683c \u00d7 2 \u6846 = 98 \u4e2a\u9884\u6d4b\u6846<\/li>\n
                • \u4f46\u4e00\u5f20\u56fe\u901a\u5e38\u53ea\u6709 2~5 \u4e2a\u7269\u4f53 \u2192 \u53ea\u6709 2~5 \u4e2a\u6846\u662f\u201c\u6709\u7269\u4f53\u201d\u7684<\/li>\n
                • \u5269\u4e0b 90+ \u4e2a\u6846\u90fd\u662f\u80cc\u666f！<\/li>\n<\/ul>\n

                  \u26a0\ufe0f \u95ee\u9898：\u5982\u679c\u4e0d\u5bf9\u8fd9\u4e9b\u80cc\u666f\u6846\u60e9\u7f5a，\u6a21\u578b\u4f1a\u80e1\u4e71\u9884\u6d4b\u9ad8\u7f6e\u4fe1\u5ea6\u6846（\u5168\u662f\u5047\u9633\u6027）\u3002<\/p>\n

                  🔧 \u89e3\u51b3\u65b9\u6848：<\/p>\n

                    \n
                  • \u8ba1\u7b97\u5b83\u4eec\u7684 loss（\u5e0c\u671b Ci=0C_i = 0<\/span><\/span>C<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>）<\/li>\n
                  • \u4f46\u4e58\u4ee5\u4e00\u4e2a\u5c0f\u6743\u91cd \u03bbnoobj=0.5\\\\lambda_{\\\\text{noobj}} = 0.5<\/span><\/span>\u03bb<\/span><\/span>noobj<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.5<\/span><\/span><\/span><\/span><\/span>
                    \n\u2192 \u9632\u6b62\u8d1f\u6837\u672c（\u80cc\u666f）\u4e3b\u5bfc\u603b\u635f\u5931（\u5426\u5219 loss \u5168\u88ab\u80cc\u666f\u63a7\u5236，\u7269\u4f53\u5b66\u4e0d\u597d）<\/li>\n<\/ul>\n
                    \n

                    \u7b2c5\u9879：\u5206\u7c7b\u635f\u5931<\/h4>\n

                    \u2211i=0S21iobj\u2211c\u2208classes(pi(c)\u2212p^i(c))2
                    \n\\\\sum_{i=0}^{S^2} \\\\mathbb{1}_{i}^{\\\\text{obj}} \\\\sum_{c \\\\in \\\\text{classes}} (p_i(c) – \\\\hat{p}_i(c))^2
                    \n<\/span><\/span><\/span>i<\/span>=<\/span>0<\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>S<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>1<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span>obj<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>c<\/span>\u2208<\/span>classes<\/span><\/span><\/span><\/span><\/span><\/span>\u2211<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>p<\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>c<\/span>)<\/span><\/span>\u2212<\/span><\/span><\/span><\/span><\/span>p<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>i<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>c<\/span>)<\/span>)<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

                    \u2705 \u542b\u4e49：\u53ea\u5bf9\u5305\u542b\u7269\u4f53\u4e2d\u5fc3\u7684\u7f51\u683c，\u8ba1\u7b97\u5176\u7c7b\u522b\u6982\u7387\u8bef\u5dee\u3002<\/p>\n

                      \n
                    • \u6ce8\u610f：\u8fd9\u91cc\u6ca1\u6709 j（\u6846\u7d22\u5f15）！\u56e0\u4e3a YOLOv1 \u4e2d\u4e00\u4e2a\u7f51\u683c\u53ea\u8f93\u51fa\u4e00\u7ec4\u7c7b\u522b\u6982\u7387（\u5171\u4eab\u7ed9\u4e24\u4e2a\u6846）<\/li>\n
                    • \u7528 L2 \u635f\u5931（\u4e5f\u53ef\u4ee5\u7528\u4ea4\u53c9\u71b5，\u4f46\u539f\u8bba\u6587\u7528 L2）<\/li>\n
                    • \u5982\u679c\u7f51\u683c\u6ca1\u7269\u4f53，\u4e0d\u8ba1\u7b97\u5206\u7c7b loss<\/li>\n<\/ul>\n

                      💡 \u4e3e\u4f8b：
                      \n\u7f51\u683c (2,5) \u4e2d\u5fc3\u6709\u201c\u732b\u201d \u2192 p^(cat)=1\\\\hat{p}(\\\\text{cat}) = 1<\/span><\/span><\/span>p<\/span><\/span><\/span>^<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span>(<\/span>cat<\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>，\u5176\u4ed6\u7c7b=0
                      \n\u6a21\u578b\u9884\u6d4b p(cat)=0.8p(\\\\text{cat}) = 0.8<\/span><\/span>p<\/span>(<\/span>cat<\/span><\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>0.8<\/span><\/span><\/span><\/span><\/span> \u2192 \u8bef\u5dee = (0.8 – 1)\u00b2 = 0.04<\/p>\n

                      \n

                      🧩 \u4e3a\u4ec0\u4e48\u8fd9\u6837\u8bbe\u8ba1？\u603b\u7ed3\u4e09\u5927\u667a\u6167<\/h3>\n\n\u8bbe\u8ba1\u76ee\u7684<\/tr>\n\n\n\n\n
                      \u03bbcoord=5\\\\lambda_{\\\\text{coord}} = 5<\/span><\/span>\u03bb<\/span><\/span>coord<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/td>\n\u5f3a\u8c03\u5b9a\u4f4d\u7cbe\u5ea6\u6bd4\u5206\u7c7b\u66f4\u91cd\u8981（\u68c0\u6d4b\u4efb\u52a1\u7684\u6838\u5fc3\u662f\u201c\u5728\u54ea\u201d）<\/td>\n<\/tr>\n
                      \u03bbnoobj=0.5\\\\lambda_{\\\\text{noobj}} = 0.5<\/span><\/span>\u03bb<\/span><\/span>noobj<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0.5<\/span><\/span><\/span><\/span><\/span><\/td>\n\u5e73\u8861\u6b63\u8d1f\u6837\u672c（98 \u4e2a\u6846 vs 3 \u4e2a\u7269\u4f53），\u9632\u6b62\u80cc\u666f\u566a\u58f0\u6df9\u6ca1\u4fe1\u53f7<\/td>\n<\/tr>\n
                      \u221aw, \u221ah<\/td>\n\u8ba9\u5c0f\u7269\u4f53\u548c\u5927\u7269\u4f53\u7684\u5b9a\u4f4d\u8bef\u5dee\u201c\u516c\u5e73\u7ade\u4e89\u201d，\u63d0\u5347\u5c0f\u7269\u4f53\u68c0\u6d4b\u80fd\u529b<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
                      \n

                      🖼\ufe0f \u4e3e\u4e2a\u5b8c\u6574\u4f8b\u5b50（\u4e00\u5f20\u56fe\u6709 1 \u4e2a\u7269\u4f53）<\/h3>\n
                        \n
                      • \u56fe\u50cf：448\u00d7448，\u542b 1 \u53ea\u72d7<\/li>\n
                      • \u72d7\u7684\u4e2d\u5fc3\u843d\u5728\u7f51\u683c #23（\u5373\u7b2c 23 \u4e2a\u7f51\u683c）<\/li>\n
                      • \u8be5\u7f51\u683c\u7684\u4e24\u4e2a\u9884\u6d4b\u6846：Box A（IoU=0.7），Box B（IoU=0.4）\u2192 \u9009 A \u8d1f\u8d23<\/li>\n<\/ul>\n

                        \u90a3\u4e48\u635f\u5931\u8ba1\u7b97\u5982\u4e0b：<\/p>\n\n\u635f\u5931\u9879\u662f\u5426\u8ba1\u7b97？\u8bf4\u660e<\/tr>\n\n\n\n\n\n\n\n
                        Box A \u7684 (x,y) \u8bef\u5dee<\/td>\n\u2705<\/td>\n123,0obj=1\\\\mathbb{1}_{23,0}^{\\\\text{obj}} = 1<\/span><\/span>1<\/span><\/span>23<\/span>,<\/span>0<\/span><\/span><\/span><\/span><\/span>obj<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
                        Box A \u7684 (\u221aw, \u221ah) \u8bef\u5dee<\/td>\n\u2705<\/td>\n\u540c\u4e0a<\/td>\n<\/tr>\n
                        Box A \u7684 confidence \u8bef\u5dee<\/td>\n\u2705<\/td>\n\u76ee\u6807 = 0.7<\/td>\n<\/tr>\n
                        Box B \u7684\u6240\u6709\u8bef\u5dee<\/td>\n\u274c<\/td>\n\u4e0d\u8d1f\u8d23，123,1obj=0\\\\mathbb{1}_{23,1}^{\\\\text{obj}} = 0<\/span><\/span>1<\/span><\/span>23<\/span>,<\/span>1<\/span><\/span><\/span><\/span><\/span>obj<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
                        \u7f51\u683c #23 \u7684\u5206\u7c7b\u8bef\u5dee<\/td>\n\u2705<\/td>\n123obj=1\\\\mathbb{1}_{23}^{\\\\text{obj}} = 1<\/span><\/span>1<\/span><\/span>23<\/span><\/span><\/span><\/span><\/span>obj<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n
                        \u5176\u4ed6 48 \u4e2a\u7f51\u683c\u7684 96 \u4e2a\u6846<\/td>\n\u2705（\u4ec5 confidence）<\/td>\n1ijnoobj=1\\\\mathbb{1}_{ij}^{\\\\text{noobj}} = 1<\/span><\/span>1<\/span><\/span>ij<\/span><\/span><\/span><\/span><\/span>noobj<\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span>，\u5e0c\u671b confidence\u22480<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
                        \n

                        \u2705 \u603b\u7ed3\u4e00\u53e5\u8bdd<\/h3>\n

                        YOLOv1 \u7684\u635f\u5931\u51fd\u6570\u662f\u4e00\u4e2a\u7cbe\u5fc3\u52a0\u6743\u7684\u591a\u4efb\u52a1\u56de\u5f52\u635f\u5931，\u5b83\u901a\u8fc7：<\/p>\n

                          \n
                        • \u53ea\u8ba9\u6b63\u786e\u7684\u7f51\u683c\u548c\u6846\u5b66\u4e60<\/li>\n
                        • \u653e\u5927\u5b9a\u4f4d\u548c\u5c0f\u7269\u4f53\u7684\u8bef\u5dee<\/li>\n
                        • \u6291\u5236\u80cc\u666f\u6846\u7684\u7f6e\u4fe1\u5ea6<\/li>\n<\/ul>\n

                          \u5b9e\u73b0\u4e86\u7aef\u5230\u7aef\u7684\u7edf\u4e00\u68c0\u6d4b\u8bad\u7ec3\u3002<\/p>\n

                          \u5982\u679c\u4f60\u73b0\u5728\u518d\u56de\u5934\u770b\u516c\u5f0f，\u5e94\u8be5\u80fd\u770b\u61c2\u6bcf\u4e00\u9879\u5728\u201c\u60e9\u7f5a\u8c01\u201d\u3001\u201c\u4e3a\u4ec0\u4e48\u60e9\u7f5a\u201d\u3001\u201c\u7f5a\u591a\u91cd\u201d\u4e86！<\/p>\n","protected":false},"excerpt":{"rendered":"

                          \u6211\u4eec\u6765\u9010\u9879\u3001\u9010\u7b26\u53f7\u3001\u7528\u901a\u4fd7\u8bed\u8a00\u4f8b\u5b50，\u5f7b\u5e95\u8bb2\u6e05\u695a YOLOv1 \u7684\u635f\u5931\u51fd\u6570（Loss Function）\u5230\u5e95\u5728\u7b97\u4ec0\u4e48\u3001\u4e3a\u4ec0\u4e48\u8fd9\u6837\u8bbe\u8ba1\u3002🎯 \u635f\u5931\u51fd\u6570\u7684\u76ee\u6807\u662f\u4ec0\u4e48？
                          \nYOLOv1 \u8981\u540c\u65f6\u5b8c\u6210\u4e09\u4ef6\u4e8b：
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