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anchor，避免某个对象完全收不到位置监督。强制匹配服务于学习，评价时不能为了“每个对象都匹配一次”照搬这条规则。","sha256":"9950be4406a476d8d766763df53ea513bbe7eed02f34aff4f837c30a3d045b5c","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"learnable-box-prediction","title":"类别与位置怎样成为可学习的区域目标？"},"page":{"id":"anchor-training-targets","title":"给正例、背景和忽略项分配任务","number":1},"sectionTitle":"为什么要有正例、背景和忽略项","currentQuestion":"候选、训练匹配和框偏移分别承担哪一步？","sourceSlides":["l3-r2-p32","l3-r2-p33"],"knowledgeBlock":"anchor-training-assignment","formulas":[],"previousBlock":"b-0e16adaadfc51be7ff259377","nextBlock":"b-083d33345765a7eb0ae41c54","prerequisites":[{"id":"b-ab433d65e7661c16e1a0cdbc","url":"#b-ab433d65e7661c16e1a0cdbc","role":"section-title"},{"id":"b-70702901ba6667d77e936f9e","url":"#b-70702901ba6667d77e936f9e","role":"problem-context"}],"relatedBlocks":[{"id":"b-ab433d65e7661c16e1a0cdbc","url":"#b-ab433d65e7661c16e1a0cdbc","relation":"same-reasoning"},{"id":"b-0e16adaadfc51be7ff259377","url":"#b-0e16adaadfc51be7ff259377","relation":"same-reasoning"},{"id":"b-083d33345765a7eb0ae41c54","url":"#b-083d33345765a7eb0ae41c54","relation":"same-reasoning"},{"id":"b-d3c4cd97a8c258a60bf1b037","url":"#b-d3c4cd97a8c258a60bf1b037","relation":"same-reasoning"}]},{"id":"b-083d33345765a7eb0ae41c54","type":"p","scope":"anchor-training-assignment","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p33.html#b-083d33345765a7eb0ae41c54","content":"空图同样是有效训练输入。所有参考框都应学背景，回归项没有正例便归零。如果只训练总有物体的图片，模型可能从未被要求学会空输出。","sha256":"157cb5eec4f8576589386132685fedffe3cc7d7ba664168060367d6e5a58232b","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"learnable-box-prediction","title":"类别与位置怎样成为可学习的区域目标？"},"page":{"id":"anchor-training-targets","title":"给正例、背景和忽略项分配任务","number":1},"sectionTitle":"为什么要有正例、背景和忽略项","currentQuestion":"候选、训练匹配和框偏移分别承担哪一步？","sourceSlides":["l3-r2-p32","l3-r2-p33"],"knowledgeBlock":"anchor-training-assignment","formulas":[],"previousBlock":"b-2ad9675dfc5bfe77f50a82e7","nextBlock":"b-d3c4cd97a8c258a60bf1b037","prerequisites":[{"id":"b-ab433d65e7661c16e1a0cdbc","url":"#b-ab433d65e7661c16e1a0cdbc","role":"section-title"},{"id":"b-70702901ba6667d77e936f9e","url":"#b-70702901ba6667d77e936f9e","role":"problem-context"}],"relatedBlocks":[{"id":"b-ab433d65e7661c16e1a0cdbc","url":"#b-ab433d65e7661c16e1a0cdbc","relation":"same-reasoning"},{"id":"b-0e16adaadfc51be7ff259377","url":"#b-0e16adaadfc51be7ff259377","relation":"same-reasoning"},{"id":"b-2ad9675dfc5bfe77f50a82e7","url":"#b-2ad9675dfc5bfe77f50a82e7","relation":"same-reasoning"},{"id":"b-d3c4cd97a8c258a60bf1b037","url":"#b-d3c4cd97a8c258a60bf1b037","relation":"same-reasoning"}]},{"id":"b-d3c4cd97a8c258a60bf1b037","type":"p","scope":"anchor-training-assignment","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p33.html#b-d3c4cd97a8c258a60bf1b037","content":"负例远多于正例时，本实验选难负例参与分类损失，最多正例数的三倍、每图至少十二个。阅读代码时应看 loss 的掩码与归一化，而不只看 $L=L_{cls}+\\lambda L_{box}$ 这一行总公式。","sha256":"767e9cdba079c3d5360d01ca6637ff47b625f805ea988b0a945b3600317d283c","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"learnable-box-prediction","title":"类别与位置怎样成为可学习的区域目标？"},"page":{"id":"anchor-training-targets","title":"给正例、背景和忽略项分配任务","number":1},"sectionTitle":"为什么要有正例、背景和忽略项","currentQuestion":"候选、训练匹配和框偏移分别承担哪一步？","sourceSlides":["l3-r2-p32","l3-r2-p33"],"knowledgeBlock":"anchor-training-assignment","formulas":[{"latex":"L=L_{cls}+\\lambda L_{box}","definitionContext":"给定参考框与真值的 IoU 矩阵，匹配规则把参考框变成训练样本。例如课堂教学阈值若设正例至少 0.7、背景小于 0.3，则 IoU 为 0.8、0.4、0.1 的三个框分别是正例、忽略、背景。只有正例有对应的框回归目标。忽略的用途是暂不把模糊覆盖强行当正或负，而不是悄悄改成背景。\n真实 LAB10 使用另一组公开写明的阈值：正例至少 0.45，背景低于 0.25，中间忽略；再用逐次最大 IoU 为每个真值保留一个不同 anchor，避免某个对象完全收不到位置监督。强制匹配服务于学习，评价时不能为了“每个对象都匹配一次”照搬这条规则。\n空图同样是有效训练输入。所有参考框都应学背景，回归项没有正例便归零。如果只训练总有物体的图片，模型可能从未被要求学会空输出。\n负例远多于正例时，本实验选难负例参与分类损失，最多正例数的三倍、每图至少十二个。阅读代码时应看 loss 的掩码与归一化，而不只看 $L=L_{cls}+\\lambda L_{box}$ 这一行总公式。"}],"previousBlock":"b-083d33345765a7eb0ae41c54","nextBlock":null,"prerequisites":[{"id":"b-ab433d65e7661c16e1a0cdbc","url":"#b-ab433d65e7661c16e1a0cdbc","role":"section-title"},{"id":"b-70702901ba6667d77e936f9e","url":"#b-70702901ba6667d77e936f9e","role":"problem-context"}],"relatedBlocks":[{"id":"b-ab433d65e7661c16e1a0cdbc","url":"#b-ab433d65e7661c16e1a0cdbc","relation":"same-reasoning"},{"id":"b-0e16adaadfc51be7ff259377","url":"#b-0e16adaadfc51be7ff259377","relation":"same-reasoning"},{"id":"b-2ad9675dfc5bfe77f50a82e7","url":"#b-2ad9675dfc5bfe77f50a82e7","relation":"same-reasoning"},{"id":"b-083d33345765a7eb0ae41c54","url":"#b-083d33345765a7eb0ae41c54","relation":"same-reasoning"}]},{"id":"b-286b2081cb409e08f960be00","type":"h2","scope":"box-offset-encode-decode","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p33.html#b-286b2081cb409e08f960be00","content":"## 把目标框编码，再原样解码回来","sha256":"3e71ded799f4f9396a5fa036b4399a37ce7df50f9d6417c2b153ae4815f0be0c","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"learnable-box-prediction","title":"类别与位置怎样成为可学习的区域目标？"},"page":{"id":"box-offset-encode-decode","title":"把目标框编码，再原样解码回来","number":2},"sectionTitle":"把目标框编码，再原样解码回来","currentQuestion":"候选、训练匹配和框偏移分别承担哪一步？","sourceSlides":["l3-r2-p33"],"knowledgeBlock":null,"formulas":[],"previousBlock":null,"nextBlock":"b-4023eec9c013b807da425eaa","prerequisites":[{"id":"b-c096477a5c0755b653e82033","url":"#b-c096477a5c0755b653e82033","role":"problem-context"}],"relatedBlocks":[{"id":"b-27b20ba175569c35dc80b6d9","url":"#b-27b20ba175569c35dc80b6d9","relation":"figure-and-explanation"}]},{"id":"b-4023eec9c013b807da425eaa","type":"h2","scope":"explanation","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p33.html#b-4023eec9c013b807da425eaa","content":"## 解释、算例与证据","sha256":"d71cf15e707c8a3674b4c90a599efee783cb84da5b8c8236a1d01c3add7b4958","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"learnable-box-prediction","title":"类别与位置怎样成为可学习的区域目标？"},"page":{"id":"box-offset-encode-decode","title":"把目标框编码，再原样解码回来","number":2},"sectionTitle":"把目标框编码，再原样解码回来","currentQuestion":"候选、训练匹配和框偏移分别承担哪一步？","sourceSlides":["l3-r2-p33"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-286b2081cb409e08f960be00","nextBlock":"b-c21d2dda80d8e1d46dfb6dfa","prerequisites":[{"id":"b-286b2081cb409e08f960be00","url":"#b-286b2081cb409e08f960be00","role":"section-title"},{"id":"b-c096477a5c0755b653e82033","url":"#b-c096477a5c0755b653e82033","role":"problem-context"}],"relatedBlocks":[{"id":"b-27b20ba175569c35dc80b6d9","url":"#b-27b20ba175569c35dc80b6d9","relation":"figure-and-explanation"}]},{"id":"b-c21d2dda80d8e1d46dfb6dfa","type":"h1","scope":"document","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p33.html#b-c21d2dda80d8e1d46dfb6dfa","content":"# P33 · 位置怎样成为可学习的目标？","sha256":"eb19007089ea3c75b5251859ba803bfbf8b9c26ea5f5a375689dcdea66a386da","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"learnable-box-prediction","title":"类别与位置怎样成为可学习的区域目标？"},"page":{"id":"box-offset-encode-decode","title":"把目标框编码，再原样解码回来","number":2},"sectionTitle":"把目标框编码，再原样解码回来","currentQuestion":"候选、训练匹配和框偏移分别承担哪一步？","sourceSlides":["l3-r2-p33"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-4023eec9c013b807da425eaa","nextBlock":"b-c096477a5c0755b653e82033","prerequisites":[{"id":"b-4023eec9c013b807da425eaa","url":"#b-4023eec9c013b807da425eaa","role":"section-title"},{"id":"b-c096477a5c0755b653e82033","url":"#b-c096477a5c0755b653e82033","role":"problem-context"}],"relatedBlocks":[{"id":"b-27b20ba175569c35dc80b6d9","url":"#b-27b20ba175569c35dc80b6d9","relation":"figure-and-explanation"}]},{"id":"b-c096477a5c0755b653e82033","type":"p","scope":"document","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p33.html#b-c096477a5c0755b653e82033","content":"把“位置回归”算到四个具体目标：.2、−.1、ln1.2、0；再逆变换回目标框。归一化、坐标格式与尺度因子必须成对。下方匹配说明哪些参考框具有位置目标，背景和忽略项为什么不能照样回归。","sha256":"448faa09c6c73221ba6a7a9dd9726ee3f487b4c173d8143c0741d8efe22d30d0","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"learnable-box-prediction","title":"类别与位置怎样成为可学习的区域目标？"},"page":{"id":"box-offset-encode-decode","title":"把目标框编码，再原样解码回来","number":2},"sectionTitle":"把目标框编码，再原样解码回来","currentQuestion":"候选、训练匹配和框偏移分别承担哪一步？","sourceSlides":["l3-r2-p33"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-c21d2dda80d8e1d46dfb6dfa","nextBlock":"b-27b20ba175569c35dc80b6d9","prerequisites":[{"id":"b-c21d2dda80d8e1d46dfb6dfa","url":"#b-c21d2dda80d8e1d46dfb6dfa","role":"section-title"}],"relatedBlocks":[{"id":"b-27b20ba175569c35dc80b6d9","url":"#b-27b20ba175569c35dc80b6d9","relation":"figure-and-explanation"}]},{"id":"b-27b20ba175569c35dc80b6d9","type":"figure","scope":"document","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p33.html#b-27b20ba175569c35dc80b6d9","content":"图内标签与数值：Lecture 03 课堂图解 P33；参考框与目标框（连续坐标，无 +1）；0；10；20；30；40；50；60；70；80；参考 (20,20,60,60)；中心 (40,40) · 宽40 · 高40；目标 (24,16,72,56)；中心 (48,36) · 宽48 · 高40；tₓ = (48−40)/40 = 0.2；tᵧ = (36−40)/40 = −0.1；t_w = ln(48/40) ≈ 0.1823；t_h = ln(40/40) = 0；本课程坐标算例；展示常见框参数化，不代表所有检测器。\n\n连续坐标网格上的参考框 (20,20,60,60) 与目标框 (24,16,72,56)，中心位移和四项回归目标逐项对应。\n\n- 参考框与目标框（连续坐标，无 +1）\n- 0\n- 10\n- 20\n- 30\n- 40\n- 50\n- 60\n- 70\n- 80\n- 参考 (20,20,60,60)\n- 中心 (40,40) · 宽40 · 高40\n- 目标 (24,16,72,56)\n- 中心 (48,36) · 宽48 · 高40\n- tₓ = (48−40)/40 = 0.2\n- tᵧ = (36−40)/40 = −0.1\n- t_w = ln(48/40) ≈ 0.1823\n- t_h = ln(40/40) = 0\n- 本课程坐标算例；展示常见框参数化，不代表所有检测器。连续坐标网格上的参考框 (20,20,60,60) 与目标框 (24,16,72,56)，中心位移和四项回归目标逐项对应。 [查看对应图解状态](/#/l3-r2-p33/1)[查看完整图解](/course/figures/l3-r2-p33-1.html)","sha256":"8d0cbec15b96368db38a95495ff285c35c846ec28196ffcb1cf556836227eb59","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"learnable-box-prediction","title":"类别与位置怎样成为可学习的区域目标？"},"page":{"id":"box-offset-encode-decode","title":"把目标框编码，再原样解码回来","number":2},"sectionTitle":"把目标框编码，再原样解码回来","currentQuestion":"候选、训练匹配和框偏移分别承担哪一步？","sourceSlides":["l3-r2-p33"],"knowledgeBlock":null,"formulas":[],"figure":{"caption":"连续坐标网格上的参考框 (20,20,60,60) 与目标框 (24,16,72,56)，中心位移和四项回归目标逐项对应。 查看对应图解状态","labels":["参考框与目标框（连续坐标，无 +1）","0","10","20","30","40","50","60","70","80","参考 (20,20,60,60)","中心 (40,40) · 宽40 · 高40","目标 (24,16,72,56)","中心 (48,36) · 宽48 · 高40","tₓ = (48−40)/40 = 0.2","tᵧ = (36−40)/40 = −0.1","t_w = ln(48/40) ≈ 0.1823","t_h = ln(40/40) = 0","本课程坐标算例；展示常见框参数化，不代表所有检测器。"],"description":"连续坐标网格上的参考框 (20,20,60,60) 与目标框 (24,16,72,56)，中心位移和四项回归目标逐项对应。参考框与目标框（连续坐标，无 +1）01020304050607080参考 (20,20,60,60)中心 (40,40) · 宽40 · 高40目标 (24,16,72,56)中心 (48,36) · 宽48 · 高40tₓ = (48−40)/40 = 0.2tᵧ = (36−40)/40 = −0.1t_w = ln(48/40) ≈ 0.1823t_h = ln(40/40) = 0本课程坐标算例；展示常见框参数化，不代表所有检测器。","evidenceIdentity":"连续坐标网格上的参考框 (20,20,60,60) 与目标框 (24,16,72,56)，中心位移和四项回归目标逐项对应。 查看对应图解状态","images":[]},"previousBlock":"b-c096477a5c0755b653e82033","nextBlock":"b-61061e4885e1f407aa125f1a","prerequisites":[{"id":"b-c21d2dda80d8e1d46dfb6dfa","url":"#b-c21d2dda80d8e1d46dfb6dfa","role":"section-title"},{"id":"b-c096477a5c0755b653e82033","url":"#b-c096477a5c0755b653e82033","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-61061e4885e1f407aa125f1a","type":"h2","scope":"narrative","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p33.html#b-61061e4885e1f407aa125f1a","content":"## 课堂讲述","sha256":"786ce10a6b32a492259a3dccd0a54e61cd41d28a34382fb7b5386c5f03b7ad69","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"learnable-box-prediction","title":"类别与位置怎样成为可学习的区域目标？"},"page":{"id":"box-offset-encode-decode","title":"把目标框编码，再原样解码回来","number":2},"sectionTitle":"把目标框编码，再原样解码回来","currentQuestion":"候选、训练匹配和框偏移分别承担哪一步？","sourceSlides":["l3-r2-p33"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-27b20ba175569c35dc80b6d9","nextBlock":"b-9488d47253afecf94151ddaa","prerequisites":[{"id":"b-c21d2dda80d8e1d46dfb6dfa","url":"#b-c21d2dda80d8e1d46dfb6dfa","role":"section-title"},{"id":"b-c096477a5c0755b653e82033","url":"#b-c096477a5c0755b653e82033","role":"problem-context"}],"relatedBlocks":[{"id":"b-27b20ba175569c35dc80b6d9","url":"#b-27b20ba175569c35dc80b6d9","relation":"figure-and-explanation"}]},{"id":"b-9488d47253afecf94151ddaa","type":"p","scope":"narrative","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p33.html#b-9488d47253afecf94151ddaa","content":"类别可以用一个标签训练，框的位置怎样训练？先看这两个具体框。参考框中心是四十、四十，宽高都是四十；目标框中心是四十八、三十六，宽变成四十八，高不变。\n网络可以学习相对这个起点的修正：中心往右多少、往上多少，宽高怎样改变。横向移动八个单位，相对于原宽度就是零点二；纵向移动负四个单位，相对于原高度就是负零点一。宽高常用比例的对数来表示，完整计算放在说明里。\n这页只要把抽象的“回归”落到对象上。网络并不是突然输出一个完美矩形，而是在明确坐标约定和监督目标下学习几何关系。类别正确但位置错误，因而完全可能发生。","sha256":"315a6026a49c44b75d9fbb1bce2a56cefee61f48c75a834c8b0133089e8c77a8","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"learnable-box-prediction","title":"类别与位置怎样成为可学习的区域目标？"},"page":{"id":"box-offset-encode-decode","title":"把目标框编码，再原样解码回来","number":2},"sectionTitle":"把目标框编码，再原样解码回来","currentQuestion":"候选、训练匹配和框偏移分别承担哪一步？","sourceSlides":["l3-r2-p33"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-61061e4885e1f407aa125f1a","nextBlock":"b-4dea0ffeee603c5187371eaf","prerequisites":[{"id":"b-61061e4885e1f407aa125f1a","url":"#b-61061e4885e1f407aa125f1a","role":"section-title"},{"id":"b-c096477a5c0755b653e82033","url":"#b-c096477a5c0755b653e82033","role":"problem-context"}],"relatedBlocks":[{"id":"b-27b20ba175569c35dc80b6d9","url":"#b-27b20ba175569c35dc80b6d9","relation":"figure-and-explanation"}]},{"id":"b-4dea0ffeee603c5187371eaf","type":"h3","scope":"box-offset-roundtrip","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p33.html#b-4dea0ffeee603c5187371eaf","content":"### 框回归的四个数怎样编码与还原","sha256":"ff108d3562e4d180fab3f2009627ac445cc3883a4cff7458c92f32b7f85bb530","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"learnable-box-prediction","title":"类别与位置怎样成为可学习的区域目标？"},"page":{"id":"box-offset-encode-decode","title":"把目标框编码，再原样解码回来","number":2},"sectionTitle":"框回归的四个数怎样编码与还原","currentQuestion":"候选、训练匹配和框偏移分别承担哪一步？","sourceSlides":["l3-r2-p33"],"knowledgeBlock":"box-offset-roundtrip","formulas":[],"previousBlock":"b-9488d47253afecf94151ddaa","nextBlock":"b-7b0dc4e9a5d3edc4a336e7a4","prerequisites":[{"id":"b-61061e4885e1f407aa125f1a","url":"#b-61061e4885e1f407aa125f1a","role":"section-title"},{"id":"b-c096477a5c0755b653e82033","url":"#b-c096477a5c0755b653e82033","role":"problem-context"}],"relatedBlocks":[{"id":"b-27b20ba175569c35dc80b6d9","url":"#b-27b20ba175569c35dc80b6d9","relation":"figure-and-explanation"},{"id":"b-7b0dc4e9a5d3edc4a336e7a4","url":"#b-7b0dc4e9a5d3edc4a336e7a4","relation":"same-reasoning"},{"id":"b-171e36ae8a402033cc3703e2","url":"#b-171e36ae8a402033cc3703e2","relation":"same-reasoning"},{"id":"b-f96d9e4f04d8acdc6d1d42ad","url":"#b-f96d9e4f04d8acdc6d1d42ad","relation":"same-reasoning"},{"id":"b-7667661163843d7c969793b3","url":"#b-7667661163843d7c969793b3","relation":"same-reasoning"},{"id":"b-8e825c99e59cb4d4dfad109d","url":"#b-8e825c99e59cb4d4dfad109d","relation":"same-reasoning"}]},{"id":"b-7b0dc4e9a5d3edc4a336e7a4","type":"p","scope":"box-offset-roundtrip","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p33.html#b-7b0dc4e9a5d3edc4a336e7a4","content":"用中心和宽高记参考框 $a=(40,40,40,40)$，目标框 $g=(48,36,48,40)$。采用不加额外缩放因子的约定：","sha256":"b3bbbbc3e614e11be62c2d2ae8f3e2cd050bc3ce13ba03cd8827d23a0f3fab71","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"learnable-box-prediction","title":"类别与位置怎样成为可学习的区域目标？"},"page":{"id":"box-offset-encode-decode","title":"把目标框编码，再原样解码回来","number":2},"sectionTitle":"框回归的四个数怎样编码与还原","currentQuestion":"候选、训练匹配和框偏移分别承担哪一步？","sourceSlides":["l3-r2-p33"],"knowledgeBlock":"box-offset-roundtrip","formulas":[{"latex":"a=(40,40,40,40)","definitionContext":"用中心和宽高记参考框 $a=(40,40,40,40)$，目标框 $g=(48,36,48,40)$。采用不加额外缩放因子的约定：\n$\nt_x=(g_x-a_x)/a_w=0.2,\\quad t_y=(g_y-a_y)/a_h=-0.1,\n$\n$\nt_w=\\log(g_w/a_w)=\\log(1.2)\\approx0.18232,\\quad t_h=0.\n$\n中心偏移除以参考框宽高，把绝对位移变为相对比例。宽高用对数比值，则放大和缩小可以由正负实数表示；解码通过指数确保宽高为正。将四个数还原：中心 $40+40\\times0.2=48$、$40-4=36$，宽 $40e^{\\log1.2}=48$，高 40。\n由中心宽高变回连续 `xyxy`，参考框是 `(20,20,60,60)`，目标是 `(24,16,72,56)`。这一来一回检查的是坐标约定相容。网络实际输出只是对四个目标数的估计，偏移接近也不代表每个小目标的 IoU 同样好。\n有些实现对偏移再乘 10 或 5 等尺度系数；应同时阅读 encode 与 decode。LAB10 的成对函数没有这些额外系数，不能从另一教材复制半套公式混用。"},{"latex":"g=(48,36,48,40)","definitionContext":"用中心和宽高记参考框 $a=(40,40,40,40)$，目标框 $g=(48,36,48,40)$。采用不加额外缩放因子的约定：\n$\nt_x=(g_x-a_x)/a_w=0.2,\\quad t_y=(g_y-a_y)/a_h=-0.1,\n$\n$\nt_w=\\log(g_w/a_w)=\\log(1.2)\\approx0.18232,\\quad t_h=0.\n$\n中心偏移除以参考框宽高，把绝对位移变为相对比例。宽高用对数比值，则放大和缩小可以由正负实数表示；解码通过指数确保宽高为正。将四个数还原：中心 $40+40\\times0.2=48$、$40-4=36$，宽 $40e^{\\log1.2}=48$，高 40。\n由中心宽高变回连续 `xyxy`，参考框是 `(20,20,60,60)`，目标是 `(24,16,72,56)`。这一来一回检查的是坐标约定相容。网络实际输出只是对四个目标数的估计，偏移接近也不代表每个小目标的 IoU 同样好。\n有些实现对偏移再乘 10 或 5 等尺度系数；应同时阅读 encode 与 decode。LAB10 的成对函数没有这些额外系数，不能从另一教材复制半套公式混用。"}],"previousBlock":"b-4dea0ffeee603c5187371eaf","nextBlock":"b-171e36ae8a402033cc3703e2","prerequisites":[{"id":"b-4dea0ffeee603c5187371eaf","url":"#b-4dea0ffeee603c5187371eaf","role":"section-title"},{"id":"b-c096477a5c0755b653e82033","url":"#b-c096477a5c0755b653e82033","role":"problem-context"}],"relatedBlocks":[{"id":"b-27b20ba175569c35dc80b6d9","url":"#b-27b20ba175569c35dc80b6d9","relation":"figure-and-explanation"},{"id":"b-4dea0ffeee603c5187371eaf","url":"#b-4dea0ffeee603c5187371eaf","relation":"same-reasoning"},{"id":"b-171e36ae8a402033cc3703e2","url":"#b-171e36ae8a402033cc3703e2","relation":"same-reasoning"},{"id":"b-f96d9e4f04d8acdc6d1d42ad","url":"#b-f96d9e4f04d8acdc6d1d42ad","relation":"same-reasoning"},{"id":"b-7667661163843d7c969793b3","url":"#b-7667661163843d7c969793b3","relation":"same-reasoning"},{"id":"b-8e825c99e59cb4d4dfad109d","url":"#b-8e825c99e59cb4d4dfad109d","relation":"same-reasoning"}]},{"id":"b-171e36ae8a402033cc3703e2","type":"p","scope":"box-offset-roundtrip","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p33.html#b-171e36ae8a402033cc3703e2","content":"$\nt_x=(g_x-a_x)/a_w=0.2,\\quad t_y=(g_y-a_y)/a_h=-0.1,\n$\n$\nt_w=\\log(g_w/a_w)=\\log(1.2)\\approx0.18232,\\quad t_h=0.\n$","sha256":"187af0c6d48210fd01d2ac309e925ddaecae1b6bfaab9b3bd08c2894ae3d9713","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"learnable-box-prediction","title":"类别与位置怎样成为可学习的区域目标？"},"page":{"id":"box-offset-encode-decode","title":"把目标框编码，再原样解码回来","number":2},"sectionTitle":"框回归的四个数怎样编码与还原","currentQuestion":"候选、训练匹配和框偏移分别承担哪一步？","sourceSlides":["l3-r2-p33"],"knowledgeBlock":"box-offset-roundtrip","formulas":[{"latex":"\nt_x=(g_x-a_x)/a_w=0.2,\\quad t_y=(g_y-a_y)/a_h=-0.1,\n","definitionContext":"用中心和宽高记参考框 $a=(40,40,40,40)$，目标框 $g=(48,36,48,40)$。采用不加额外缩放因子的约定：\n$\nt_x=(g_x-a_x)/a_w=0.2,\\quad t_y=(g_y-a_y)/a_h=-0.1,\n$\n$\nt_w=\\log(g_w/a_w)=\\log(1.2)\\approx0.18232,\\quad t_h=0.\n$\n中心偏移除以参考框宽高，把绝对位移变为相对比例。宽高用对数比值，则放大和缩小可以由正负实数表示；解码通过指数确保宽高为正。将四个数还原：中心 $40+40\\times0.2=48$、$40-4=36$，宽 $40e^{\\log1.2}=48$，高 40。\n由中心宽高变回连续 `xyxy`，参考框是 `(20,20,60,60)`，目标是 `(24,16,72,56)`。这一来一回检查的是坐标约定相容。网络实际输出只是对四个目标数的估计，偏移接近也不代表每个小目标的 IoU 同样好。\n有些实现对偏移再乘 10 或 5 等尺度系数；应同时阅读 encode 与 decode。LAB10 的成对函数没有这些额外系数，不能从另一教材复制半套公式混用。"},{"latex":"\nt_w=\\log(g_w/a_w)=\\log(1.2)\\approx0.18232,\\quad t_h=0.\n","definitionContext":"用中心和宽高记参考框 $a=(40,40,40,40)$，目标框 $g=(48,36,48,40)$。采用不加额外缩放因子的约定：\n$\nt_x=(g_x-a_x)/a_w=0.2,\\quad t_y=(g_y-a_y)/a_h=-0.1,\n$\n$\nt_w=\\log(g_w/a_w)=\\log(1.2)\\approx0.18232,\\quad t_h=0.\n$\n中心偏移除以参考框宽高，把绝对位移变为相对比例。宽高用对数比值，则放大和缩小可以由正负实数表示；解码通过指数确保宽高为正。将四个数还原：中心 $40+40\\times0.2=48$、$40-4=36$，宽 $40e^{\\log1.2}=48$，高 40。\n由中心宽高变回连续 `xyxy`，参考框是 `(20,20,60,60)`，目标是 `(24,16,72,56)`。这一来一回检查的是坐标约定相容。网络实际输出只是对四个目标数的估计，偏移接近也不代表每个小目标的 IoU 同样好。\n有些实现对偏移再乘 10 或 5 等尺度系数；应同时阅读 encode 与 decode。LAB10 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