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[P27–35](/course/pages/l3-r2-p27.html) 和 [LAB 10 的图像到框训练](https://deepnote.com/project/38755e4e-23f6-4f5f-8c68-8a2e4114b1c1/notebook/a14237bfa9dd413d959ab4e458e11f42)。先按自己的问题读一段，不必在运行模型前读完全部。","sha256":"8560cc92f5ba742f1c60ed74ecfdb4342af5e340aef761676c2308d0b54f08bc","chapter":{"id":"course","title":"四个数怎样指向图像里的同一区域"},"unit":{"id":"notebook-blocks/9264aa76ab44410a94ba0c31731e50ef","title":"四个数怎样指向图像里的同一区域"},"page":{"id":"reading-opening","title":"四个数怎样指向图像里的同一区域","number":1},"sectionTitle":"四个数怎样指向图像里的同一区域","currentQuestion":"四个数怎样指向图像里的同一区域","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-9e6d2032b50c9e7a49b39112","nextBlock":"b-74558a1ed4e692b67b8c48c7","prerequisites":[{"id":"b-d7c538c45ff54e04e07a2ada","url":"#b-d7c538c45ff54e04e07a2ada","role":"section-title"},{"id":"b-a4c631765d1c583520bd762b","url":"#b-a4c631765d1c583520bd762b","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-74558a1ed4e692b67b8c48c7","type":"ul","scope":"document","url":"https://codingai-lec03.pages.dev/course/notebook-blocks/9264aa76ab44410a94ba0c31731e50ef.html#b-74558a1ed4e692b67b8c48c7","content":"- 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与评价匹配](/course/blocks/nms-versus-matching.html)。","sha256":"d2c2e5495e53ef8a3f1ca587b170cd2deadae52ef91b4508655dad4f24e8253e","chapter":{"id":"course","title":"四个数怎样指向图像里的同一区域"},"unit":{"id":"notebook-blocks/9264aa76ab44410a94ba0c31731e50ef","title":"四个数怎样指向图像里的同一区域"},"page":{"id":"reading-opening","title":"四个数怎样指向图像里的同一区域","number":1},"sectionTitle":"四个数怎样指向图像里的同一区域","currentQuestion":"四个数怎样指向图像里的同一区域","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-bd43b86624cc65ba2e604f85","nextBlock":"b-eecf41b0cc87ac3910c6d682","prerequisites":[{"id":"b-d7c538c45ff54e04e07a2ada","url":"#b-d7c538c45ff54e04e07a2ada","role":"section-title"},{"id":"b-a4c631765d1c583520bd762b","url":"#b-a4c631765d1c583520bd762b","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-eecf41b0cc87ac3910c6d682","type":"li","scope":"document","url":"https://codingai-lec03.pages.dev/course/notebook-blocks/9264aa76ab44410a94ba0c31731e50ef.html#b-eecf41b0cc87ac3910c6d682","content":"- 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重复框如何影响结果：[NMS 与评价匹配](/course/blocks/nms-versus-matching.html)。","sha256":"f242c7ee4328040c119d646550367cf3a3d8f45a7a7d5b769edcec25309f4975","chapter":{"id":"course","title":"四个数怎样指向图像里的同一区域"},"unit":{"id":"notebook-blocks/9264aa76ab44410a94ba0c31731e50ef","title":"四个数怎样指向图像里的同一区域"},"page":{"id":"reading-opening","title":"四个数怎样指向图像里的同一区域","number":1},"sectionTitle":"四个数怎样指向图像里的同一区域","currentQuestion":"四个数怎样指向图像里的同一区域","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-b1b4f752fa887053b5ea072c","nextBlock":"b-cad4958ce6383ff03ab7a389","prerequisites":[{"id":"b-d7c538c45ff54e04e07a2ada","url":"#b-d7c538c45ff54e04e07a2ada","role":"section-title"},{"id":"b-a4c631765d1c583520bd762b","url":"#b-a4c631765d1c583520bd762b","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-cad4958ce6383ff03ab7a389","type":"p","scope":"document","url":"https://codingai-lec03.pages.dev/course/notebook-blocks/9264aa76ab44410a94ba0c31731e50ef.html#b-cad4958ce6383ff03ab7a389","content":"读完后选一个预测，指出它被判错是因为重复、定位不足还是背景，并写明阈值和匹配协议。要亲手改坐标/分数，到附属工作台 [LAB 09](https://deepnote.com/project/38755e4e-23f6-4f5f-8c68-8a2e4114b1c1/notebook/90d213b4e1e04c7e889ee6fc042b2358)；要理解模型在何处出错，回到 [检测学习证据](/course/blocks/detector-learning-evidence.html)。","sha256":"5824845f2bd25d6b85eb2bedeb7fde8bbdc2adbd87bd830bf65b0450fb73702c","chapter":{"id":"course","title":"四个数怎样指向图像里的同一区域"},"unit":{"id":"notebook-blocks/9264aa76ab44410a94ba0c31731e50ef","title":"四个数怎样指向图像里的同一区域"},"page":{"id":"reading-opening","title":"四个数怎样指向图像里的同一区域","number":1},"sectionTitle":"四个数怎样指向图像里的同一区域","currentQuestion":"四个数怎样指向图像里的同一区域","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-83c5cb8cdbeddd39d3dd01ba","nextBlock":"b-dcfb560fc657b6fb0cc5274e","prerequisites":[{"id":"b-d7c538c45ff54e04e07a2ada","url":"#b-d7c538c45ff54e04e07a2ada","role":"section-title"},{"id":"b-a4c631765d1c583520bd762b","url":"#b-a4c631765d1c583520bd762b","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-dcfb560fc657b6fb0cc5274e","type":"p","scope":"document","url":"https://codingai-lec03.pages.dev/course/notebook-blocks/9264aa76ab44410a94ba0c31731e50ef.html#b-dcfb560fc657b6fb0cc5274e","content":"“这张图有杯子”可以由一个整图类别分数回答；“两只杯子分别在哪里”需要对象数、类别和位置。分类器即便准确，也没有被要求把分数分配给具体区域。全局平均池化还可能把左右位置汇总掉。检测因此要改变输出参数化、训练目标和评价协议，而不是给分类结果补画一个框。","sha256":"4069e14c5ad08dc619a5598db00977a4c0e0de429f00c9ecd0091eb7d58b8a1c","chapter":{"id":"course","title":"四个数怎样指向图像里的同一区域"},"unit":{"id":"notebook-blocks/9264aa76ab44410a94ba0c31731e50ef","title":"四个数怎样指向图像里的同一区域"},"page":{"id":"reading-opening","title":"四个数怎样指向图像里的同一区域","number":1},"sectionTitle":"四个数怎样指向图像里的同一区域","currentQuestion":"四个数怎样指向图像里的同一区域","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-cad4958ce6383ff03ab7a389","nextBlock":"b-0c8e41bdc9d0b7f56db72fee","prerequisites":[{"id":"b-d7c538c45ff54e04e07a2ada","url":"#b-d7c538c45ff54e04e07a2ada","role":"section-title"},{"id":"b-a4c631765d1c583520bd762b","url":"#b-a4c631765d1c583520bd762b","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-0c8e41bdc9d0b7f56db72fee","type":"h2","scope":"document","url":"https://codingai-lec03.pages.dev/course/notebook-blocks/9264aa76ab44410a94ba0c31731e50ef.html#b-0c8e41bdc9d0b7f56db72fee","content":"## 四个数怎样指向图像里的同一区域","sha256":"0fe74dbe6635492abd693709fe30045ffdc781ab4cdbe8186bf03ddf8cbaf1fc","chapter":{"id":"course","title":"四个数怎样指向图像里的同一区域"},"unit":{"id":"notebook-blocks/9264aa76ab44410a94ba0c31731e50ef","title":"四个数怎样指向图像里的同一区域"},"page":{"id":"reading-opening","title":"四个数怎样指向图像里的同一区域","number":1},"sectionTitle":"四个数怎样指向图像里的同一区域","currentQuestion":"四个数怎样指向图像里的同一区域","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-dcfb560fc657b6fb0cc5274e","nextBlock":"b-55e03279602450ba68c7ccd9","prerequisites":[{"id":"b-d7c538c45ff54e04e07a2ada","url":"#b-d7c538c45ff54e04e07a2ada","role":"section-title"},{"id":"b-a4c631765d1c583520bd762b","url":"#b-a4c631765d1c583520bd762b","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-55e03279602450ba68c7ccd9","type":"p","scope":"document","url":"https://codingai-lec03.pages.dev/course/notebook-blocks/9264aa76ab44410a94ba0c31731e50ef.html#b-55e03279602450ba68c7ccd9","content":"轴对齐框可表示为 $(x_{\\min},y_{\\min},x_{\\max},y_{\\max})$，也可表示为中心与宽高 $(c_x,c_y,w,h)$。本册用连续边界、右下边界不额外加 1 的约定，并把坐标除以图像宽高归一化到 $[0,1]$。这与“像素编号含两端”的面积算法不同，混用会让小框 IoU 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IoU=0.6；右表是一类、两个真值对象的排序算例，第二个预测虽也盖住对象，却因重复而算假阳性。","sha256":"9098789457bdb4955ec4f933dc2f9e3ba5366f7356882e102ee2309a78302040","chapter":{"id":"course","title":"四个数怎样指向图像里的同一区域"},"unit":{"id":"notebook-blocks/9264aa76ab44410a94ba0c31731e50ef","title":"四个数怎样指向图像里的同一区域"},"page":{"id":"reading-opening","title":"四个数怎样指向图像里的同一区域","number":1},"sectionTitle":"四个数怎样指向图像里的同一区域","currentQuestion":"四个数怎样指向图像里的同一区域","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-2c86c729b299892831820309","nextBlock":"b-4d4b2386ba2d12c313acd095","prerequisites":[{"id":"b-0c8e41bdc9d0b7f56db72fee","url":"#b-0c8e41bdc9d0b7f56db72fee","role":"section-title"},{"id":"b-a4c631765d1c583520bd762b","url":"#b-a4c631765d1c583520bd762b","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-4d4b2386ba2d12c313acd095","type":"h2","scope":"document","url":"https://codingai-lec03.pages.dev/course/notebook-blocks/9264aa76ab44410a94ba0c31731e50ef.html#b-4d4b2386ba2d12c313acd095","content":"## 锚框先给坐标一个起点，匹配再赋予训练身份","sha256":"8e6b0c8407cefcaeb3b9a235195b40b038695cddb1c3461c819b19ec767f0650","chapter":{"id":"course","title":"四个数怎样指向图像里的同一区域"},"unit":{"id":"notebook-blocks/9264aa76ab44410a94ba0c31731e50ef","title":"四个数怎样指向图像里的同一区域"},"page":{"id":"reading-opening","title":"四个数怎样指向图像里的同一区域","number":1},"sectionTitle":"四个数怎样指向图像里的同一区域","currentQuestion":"四个数怎样指向图像里的同一区域","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-f31d329fd99bf40d39fa4887","nextBlock":"b-6a4fb9c87f0042941adc131a","prerequisites":[{"id":"b-0c8e41bdc9d0b7f56db72fee","url":"#b-0c8e41bdc9d0b7f56db72fee","role":"section-title"},{"id":"b-a4c631765d1c583520bd762b","url":"#b-a4c631765d1c583520bd762b","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-6a4fb9c87f0042941adc131a","type":"p","scope":"document","url":"https://codingai-lec03.pages.dev/course/notebook-blocks/9264aa76ab44410a94ba0c31731e50ef.html#b-6a4fb9c87f0042941adc131a","content":"锚框是预设位置、尺度和长宽比的参考框，不是模型已经检测出的结果。输出头为每个锚框预测类别或 objectness，以及相对坐标改变量。一种不加额外尺度系数的参数化是","sha256":"39e9d99c41a61b16e0edc703daef9d3075d4e5c7b18009e2090e7a4dfc508443","chapter":{"id":"course","title":"四个数怎样指向图像里的同一区域"},"unit":{"id":"notebook-blocks/9264aa76ab44410a94ba0c31731e50ef","title":"四个数怎样指向图像里的同一区域"},"page":{"id":"reading-opening","title":"四个数怎样指向图像里的同一区域","number":1},"sectionTitle":"四个数怎样指向图像里的同一区域","currentQuestion":"四个数怎样指向图像里的同一区域","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-4d4b2386ba2d12c313acd095","nextBlock":"b-91f1dfbf3a4d2f01d5c32ce7","prerequisites":[{"id":"b-4d4b2386ba2d12c313acd095","url":"#b-4d4b2386ba2d12c313acd095","role":"section-title"},{"id":"b-a4c631765d1c583520bd762b","url":"#b-a4c631765d1c583520bd762b","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-91f1dfbf3a4d2f01d5c32ce7","type":"p","scope":"document","url":"https://codingai-lec03.pages.dev/course/notebook-blocks/9264aa76ab44410a94ba0c31731e50ef.html#b-91f1dfbf3a4d2f01d5c32ce7","content":"$t_x=(c_x^g-c_x^a)/w^a,\\quad t_y=(c_y^g-c_y^a)/h^a,\\quad\nt_w=\\log(w^g/w^a),\\quad t_h=\\log(h^g/h^a).$","sha256":"f2e92753771abbafbcb6b78618e928db0d86d334070ed63cd8ae3c084e0a19f5","chapter":{"id":"course","title":"四个数怎样指向图像里的同一区域"},"unit":{"id":"notebook-blocks/9264aa76ab44410a94ba0c31731e50ef","title":"四个数怎样指向图像里的同一区域"},"page":{"id":"reading-opening","title":"四个数怎样指向图像里的同一区域","number":1},"sectionTitle":"四个数怎样指向图像里的同一区域","currentQuestion":"四个数怎样指向图像里的同一区域","sourceSlides":[],"knowledgeBlock":null,"formulas":[{"latex":"t_x=(c_x^g-c_x^a)/w^a,\\quad t_y=(c_y^g-c_y^a)/h^a,\\quad\nt_w=\\log(w^g/w^a),\\quad t_h=\\log(h^g/h^a).","definitionContext":"四个数怎样指向图像里的同一区域"}],"previousBlock":"b-6a4fb9c87f0042941adc131a","nextBlock":"b-ebd526548278d2589b85606e","prerequisites":[{"id":"b-4d4b2386ba2d12c313acd095","url":"#b-4d4b2386ba2d12c313acd095","role":"section-title"},{"id":"b-a4c631765d1c583520bd762b","url":"#b-a4c631765d1c583520bd762b","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-ebd526548278d2589b85606e","type":"p","scope":"document","url":"https://codingai-lec03.pages.dev/course/notebook-blocks/9264aa76ab44410a94ba0c31731e50ef.html#b-ebd526548278d2589b85606e","content":"锚框中心 $(0.4,0.4)$、宽高均为 0.4，真值中心移到 $(0.45,0.4)$ 且大小不变，目标就是 $(0.125,0,0,0)$。解码时用 $c_x^p=c_x^a+w^at_x$、$w^p=w^a\\exp(t_w)$ 等逆运算。具体实现可能乘 10、5 等尺度因子，例如 D2L 的一套约定；编码和解码必须成对，不可只复制一边公式。","sha256":"40858ec0f600a17096cc7466a4f922b9540d5c1a169226cf8af91498a8a711e3","chapter":{"id":"course","title":"四个数怎样指向图像里的同一区域"},"unit":{"id":"notebook-blocks/9264aa76ab44410a94ba0c31731e50ef","title":"四个数怎样指向图像里的同一区域"},"page":{"id":"reading-opening","title":"四个数怎样指向图像里的同一区域","number":1},"sectionTitle":"四个数怎样指向图像里的同一区域","currentQuestion":"四个数怎样指向图像里的同一区域","sourceSlides":[],"knowledgeBlock":null,"formulas":[{"latex":"(0.4,0.4)","definitionContext":"四个数怎样指向图像里的同一区域"},{"latex":"(0.45,0.4)","definitionContext":"四个数怎样指向图像里的同一区域"},{"latex":"(0.125,0,0,0)","definitionContext":"四个数怎样指向图像里的同一区域"},{"latex":"c_x^p=c_x^a+w^at_x","definitionContext":"四个数怎样指向图像里的同一区域"},{"latex":"w^p=w^a\\exp(t_w)","definitionContext":"四个数怎样指向图像里的同一区域"}],"previousBlock":"b-91f1dfbf3a4d2f01d5c32ce7","nextBlock":"b-1ab59e5622e37d0557c024a3","prerequisites":[{"id":"b-4d4b2386ba2d12c313acd095","url":"#b-4d4b2386ba2d12c313acd095","role":"section-title"},{"id":"b-a4c631765d1c583520bd762b","url":"#b-a4c631765d1c583520bd762b","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-1ab59e5622e37d0557c024a3","type":"p","scope":"document","url":"https://codingai-lec03.pages.dev/course/notebook-blocks/9264aa76ab44410a94ba0c31731e50ef.html#b-1ab59e5622e37d0557c024a3","content":"训练时要把锚框分配为正例、负例或忽略项。常见方案先保障每个真值有匹配，再按 IoU 阈值增加正例，把远离真值的锚框设为背景，中间区域可忽略。两阈值的具体值是协议选择，不是 IoU 的定义。位置回归只对正例计损失；背景没有“应该回归到哪里”的真值。若一幅图没有对象，仍应通过负例分类损失学会不报框，回归项则安全地归零，避免除以零。","sha256":"072c7fcb91f010db36447b5f7636ad481ddad26681f26397e6b7e7661508f502","chapter":{"id":"course","title":"四个数怎样指向图像里的同一区域"},"unit":{"id":"notebook-blocks/9264aa76ab44410a94ba0c31731e50ef","title":"四个数怎样指向图像里的同一区域"},"page":{"id":"reading-opening","title":"四个数怎样指向图像里的同一区域","number":1},"sectionTitle":"四个数怎样指向图像里的同一区域","currentQuestion":"四个数怎样指向图像里的同一区域","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-ebd526548278d2589b85606e","nextBlock":"b-7ebd16c0ead1bd83ff1e0496","prerequisites":[{"id":"b-4d4b2386ba2d12c313acd095","url":"#b-4d4b2386ba2d12c313acd095","role":"section-title"},{"id":"b-a4c631765d1c583520bd762b","url":"#b-a4c631765d1c583520bd762b","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-7ebd16c0ead1bd83ff1e0496","type":"p","scope":"document","url":"https://codingai-lec03.pages.dev/course/notebook-blocks/9264aa76ab44410a94ba0c31731e50ef.html#b-7ebd16c0ead1bd83ff1e0496","content":"写成 $L=L_{cls}+\\lambda L_{box}$ 仍不够：两个分母怎样归一化、负例是否筛选、ignore 如何 mask，都决定了优化问题。大量背景锚框可能淹没少数正例；hard-negative mining 和 focal loss 是改变贡献权重的不同办法。学生可以沿 [D2L §14.4 锚框分配/偏移](https://d2l.ai/chapter_computer-vision/anchor.html) 与 [§14.7 TinySSD](https://d2l.ai/chapter_computer-vision/ssd.html) 核对输出张量、分类标签和回归 mask。","sha256":"842f4305a9f2d8fe7fb3192c4b4b2ff23e7ab466c311abaad3889acebfb6dd58","chapter":{"id":"course","title":"四个数怎样指向图像里的同一区域"},"unit":{"id":"notebook-blocks/9264aa76ab44410a94ba0c31731e50ef","title":"四个数怎样指向图像里的同一区域"},"page":{"id":"reading-opening","title":"四个数怎样指向图像里的同一区域","number":1},"sectionTitle":"四个数怎样指向图像里的同一区域","currentQuestion":"四个数怎样指向图像里的同一区域","sourceSlides":[],"knowledgeBlock":null,"formulas":[{"latex":"L=L_{cls}+\\lambda 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