{"version":2,"relationshipURLBase":"https://codingai-lec03.pages.dev/course/blocks/box-offset-roundtrip.html","relationshipResolution":"Resolve relative relationship URLs against relationshipURLBase; complete records and absolute URLs are in blocks.","title":"框回归的四个数怎样编码与还原","url":"https://codingai-lec03.pages.dev/course/blocks/box-offset-roundtrip.html","markdown":"https://codingai-lec03.pages.dev/course/blocks/box-offset-roundtrip.md","pages":[{"id":"reading-opening","title":"框回归的四个数怎样编码与还原","unit":"类别与位置怎样成为可学习的区域目标？","unitId":"learnable-box-prediction","chapter":"II","number":1}],"aliases":[{"oldId":"b-27ad5b11c29511da30795613","targetId":"b-27ad5b11c29511da30795613","page":"reading-opening","operation":"move","beforeSHA256":"50d3cef58b8c8ede994027e8fdee0c315b85937f4d59df8ee7bdb59e72bd607e","afterSHA256":"50d3cef58b8c8ede994027e8fdee0c315b85937f4d59df8ee7bdb59e72bd607e","reason":"Same source body in authored semantic page"},{"oldId":"b-f5ce4811d5a11d9fc14cbc43","targetId":"b-f5ce4811d5a11d9fc14cbc43","page":"reading-opening","operation":"move","beforeSHA256":"448faa09c6c73221ba6a7a9dd9726ee3f487b4c173d8143c0741d8efe22d30d0","afterSHA256":"448faa09c6c73221ba6a7a9dd9726ee3f487b4c173d8143c0741d8efe22d30d0","reason":"Same source body in authored semantic page"},{"oldId":"b-c99b3f946cad7c067738a8b8","targetId":"b-c99b3f946cad7c067738a8b8","page":"reading-opening","operation":"move","beforeSHA256":"b3bbbbc3e614e11be62c2d2ae8f3e2cd050bc3ce13ba03cd8827d23a0f3fab71","afterSHA256":"b3bbbbc3e614e11be62c2d2ae8f3e2cd050bc3ce13ba03cd8827d23a0f3fab71","reason":"Same source body in authored semantic page"},{"oldId":"b-0133c43282ffa169b028ad83","targetId":"b-0133c43282ffa169b028ad83","page":"reading-opening","operation":"move","beforeSHA256":"187af0c6d48210fd01d2ac309e925ddaecae1b6bfaab9b3bd08c2894ae3d9713","afterSHA256":"187af0c6d48210fd01d2ac309e925ddaecae1b6bfaab9b3bd08c2894ae3d9713","reason":"Same source body in authored semantic page"},{"oldId":"b-0054a6f868ada4ff3fc0476f","targetId":"b-0054a6f868ada4ff3fc0476f","page":"reading-opening","operation":"move","beforeSHA256":"d7444e338e1c0d15c5c34eabc3e423969240480386582c8b37df49c582126e18","afterSHA256":"d7444e338e1c0d15c5c34eabc3e423969240480386582c8b37df49c582126e18","reason":"Same source body in authored semantic page"},{"oldId":"b-5f9622a7ce4f30da9b4e065f","targetId":"b-5f9622a7ce4f30da9b4e065f","page":"reading-opening","operation":"move","beforeSHA256":"9c0c5495f55e57dc54960b56bd2d9557d4aec07533a830446b1d8a6c16c7efbc","afterSHA256":"9c0c5495f55e57dc54960b56bd2d9557d4aec07533a830446b1d8a6c16c7efbc","reason":"Same source body in authored semantic page"},{"oldId":"b-84ca8e5ad26a3db9908eccb7","targetId":"b-84ca8e5ad26a3db9908eccb7","page":"reading-opening","operation":"move","beforeSHA256":"1cfcbe05dfe96197283ba9302d29281e1bf77664d8975d9c7ed6c3244a89a659","afterSHA256":"1cfcbe05dfe96197283ba9302d29281e1bf77664d8975d9c7ed6c3244a89a659","reason":"Same source body in authored semantic page"},{"oldId":"b-71c9f427dded530984286ed7","targetId":"b-71c9f427dded530984286ed7","page":"reading-opening","operation":"rewrite","beforeSHA256":"49ab4f838c92e6ff96334e8881214fb8b9d8a335c85898e6f3f85e1935e30d59","afterSHA256":"7d2a29b19e1cd1a196823c364b84e894681651b53fc6ce2c26f81c883424ee89","reason":"Same source identity with figure semantics or reading context enriched"},{"oldId":"b-6c850eeec525f98ae14bf94e","targetId":"b-6c850eeec525f98ae14bf94e","page":"reading-opening","operation":"move","beforeSHA256":"2b9ccef7e1220e2250cceff1abd8bdd736b42f8da5a223f26b029f44b962e807","afterSHA256":"2b9ccef7e1220e2250cceff1abd8bdd736b42f8da5a223f26b029f44b962e807","reason":"Same source body in authored semantic page"}],"blocks":[{"id":"b-27ad5b11c29511da30795613","type":"h1","scope":"box-offset-roundtrip","url":"https://codingai-lec03.pages.dev/course/blocks/box-offset-roundtrip.html#b-27ad5b11c29511da30795613","content":"# 框回归的四个数怎样编码与还原","sha256":"50d3cef58b8c8ede994027e8fdee0c315b85937f4d59df8ee7bdb59e72bd607e","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":"reading-opening","title":"框回归的四个数怎样编码与还原","number":1},"sectionTitle":"框回归的四个数怎样编码与还原","currentQuestion":"框回归的四个数怎样编码与还原","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":null,"nextBlock":"b-f5ce4811d5a11d9fc14cbc43","prerequisites":[{"id":"b-f5ce4811d5a11d9fc14cbc43","url":"#b-f5ce4811d5a11d9fc14cbc43","role":"problem-context"}],"relatedBlocks":[{"id":"b-71c9f427dded530984286ed7","url":"#b-71c9f427dded530984286ed7","relation":"figure-and-explanation"}]},{"id":"b-f5ce4811d5a11d9fc14cbc43","type":"p","scope":"box-offset-roundtrip","url":"https://codingai-lec03.pages.dev/course/blocks/box-offset-roundtrip.html#b-f5ce4811d5a11d9fc14cbc43","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":"reading-opening","title":"框回归的四个数怎样编码与还原","number":1},"sectionTitle":"框回归的四个数怎样编码与还原","currentQuestion":"框回归的四个数怎样编码与还原","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-27ad5b11c29511da30795613","nextBlock":"b-c99b3f946cad7c067738a8b8","prerequisites":[{"id":"b-27ad5b11c29511da30795613","url":"#b-27ad5b11c29511da30795613","role":"section-title"}],"relatedBlocks":[{"id":"b-71c9f427dded530984286ed7","url":"#b-71c9f427dded530984286ed7","relation":"figure-and-explanation"}]},{"id":"b-c99b3f946cad7c067738a8b8","type":"p","scope":"box-offset-roundtrip","url":"https://codingai-lec03.pages.dev/course/blocks/box-offset-roundtrip.html#b-c99b3f946cad7c067738a8b8","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":"reading-opening","title":"框回归的四个数怎样编码与还原","number":1},"sectionTitle":"框回归的四个数怎样编码与还原","currentQuestion":"框回归的四个数怎样编码与还原","sourceSlides":[],"knowledgeBlock":null,"formulas":[{"latex":"a=(40,40,40,40)","definitionContext":"框回归的四个数怎样编码与还原"},{"latex":"g=(48,36,48,40)","definitionContext":"框回归的四个数怎样编码与还原"}],"previousBlock":"b-f5ce4811d5a11d9fc14cbc43","nextBlock":"b-0133c43282ffa169b028ad83","prerequisites":[{"id":"b-27ad5b11c29511da30795613","url":"#b-27ad5b11c29511da30795613","role":"section-title"},{"id":"b-f5ce4811d5a11d9fc14cbc43","url":"#b-f5ce4811d5a11d9fc14cbc43","role":"problem-context"}],"relatedBlocks":[{"id":"b-71c9f427dded530984286ed7","url":"#b-71c9f427dded530984286ed7","relation":"figure-and-explanation"}]},{"id":"b-0133c43282ffa169b028ad83","type":"p","scope":"box-offset-roundtrip","url":"https://codingai-lec03.pages.dev/course/blocks/box-offset-roundtrip.html#b-0133c43282ffa169b028ad83","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":"reading-opening","title":"框回归的四个数怎样编码与还原","number":1},"sectionTitle":"框回归的四个数怎样编码与还原","currentQuestion":"框回归的四个数怎样编码与还原","sourceSlides":[],"knowledgeBlock":null,"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":"框回归的四个数怎样编码与还原"},{"latex":"\nt_w=\\log(g_w/a_w)=\\log(1.2)\\approx0.18232,\\quad t_h=0.\n","definitionContext":"框回归的四个数怎样编码与还原"}],"previousBlock":"b-c99b3f946cad7c067738a8b8","nextBlock":"b-0054a6f868ada4ff3fc0476f","prerequisites":[{"id":"b-27ad5b11c29511da30795613","url":"#b-27ad5b11c29511da30795613","role":"section-title"},{"id":"b-f5ce4811d5a11d9fc14cbc43","url":"#b-f5ce4811d5a11d9fc14cbc43","role":"problem-context"}],"relatedBlocks":[{"id":"b-71c9f427dded530984286ed7","url":"#b-71c9f427dded530984286ed7","relation":"figure-and-explanation"}]},{"id":"b-0054a6f868ada4ff3fc0476f","type":"p","scope":"box-offset-roundtrip","url":"https://codingai-lec03.pages.dev/course/blocks/box-offset-roundtrip.html#b-0054a6f868ada4ff3fc0476f","content":"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。","sha256":"d7444e338e1c0d15c5c34eabc3e423969240480386582c8b37df49c582126e18","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":"reading-opening","title":"框回归的四个数怎样编码与还原","number":1},"sectionTitle":"框回归的四个数怎样编码与还原","currentQuestion":"框回归的四个数怎样编码与还原","sourceSlides":[],"knowledgeBlock":null,"formulas":[{"latex":"40+40\\times0.2=48","definitionContext":"框回归的四个数怎样编码与还原"},{"latex":"40-4=36","definitionContext":"框回归的四个数怎样编码与还原"},{"latex":"40e^{\\log1.2}=48","definitionContext":"框回归的四个数怎样编码与还原"}],"previousBlock":"b-0133c43282ffa169b028ad83","nextBlock":"b-5f9622a7ce4f30da9b4e065f","prerequisites":[{"id":"b-27ad5b11c29511da30795613","url":"#b-27ad5b11c29511da30795613","role":"section-title"},{"id":"b-f5ce4811d5a11d9fc14cbc43","url":"#b-f5ce4811d5a11d9fc14cbc43","role":"problem-context"}],"relatedBlocks":[{"id":"b-71c9f427dded530984286ed7","url":"#b-71c9f427dded530984286ed7","relation":"figure-and-explanation"}]},{"id":"b-5f9622a7ce4f30da9b4e065f","type":"p","scope":"box-offset-roundtrip","url":"https://codingai-lec03.pages.dev/course/blocks/box-offset-roundtrip.html#b-5f9622a7ce4f30da9b4e065f","content":"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。","sha256":"9c0c5495f55e57dc54960b56bd2d9557d4aec07533a830446b1d8a6c16c7efbc","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":"reading-opening","title":"框回归的四个数怎样编码与还原","number":1},"sectionTitle":"框回归的四个数怎样编码与还原","currentQuestion":"框回归的四个数怎样编码与还原","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-0054a6f868ada4ff3fc0476f","nextBlock":"b-84ca8e5ad26a3db9908eccb7","prerequisites":[{"id":"b-27ad5b11c29511da30795613","url":"#b-27ad5b11c29511da30795613","role":"section-title"},{"id":"b-f5ce4811d5a11d9fc14cbc43","url":"#b-f5ce4811d5a11d9fc14cbc43","role":"problem-context"}],"relatedBlocks":[{"id":"b-71c9f427dded530984286ed7","url":"#b-71c9f427dded530984286ed7","relation":"figure-and-explanation"}]},{"id":"b-84ca8e5ad26a3db9908eccb7","type":"p","scope":"box-offset-roundtrip","url":"https://codingai-lec03.pages.dev/course/blocks/box-offset-roundtrip.html#b-84ca8e5ad26a3db9908eccb7","content":"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。","sha256":"1cfcbe05dfe96197283ba9302d29281e1bf77664d8975d9c7ed6c3244a89a659","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":"reading-opening","title":"框回归的四个数怎样编码与还原","number":1},"sectionTitle":"框回归的四个数怎样编码与还原","currentQuestion":"框回归的四个数怎样编码与还原","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-5f9622a7ce4f30da9b4e065f","nextBlock":"b-71c9f427dded530984286ed7","prerequisites":[{"id":"b-27ad5b11c29511da30795613","url":"#b-27ad5b11c29511da30795613","role":"section-title"},{"id":"b-f5ce4811d5a11d9fc14cbc43","url":"#b-f5ce4811d5a11d9fc14cbc43","role":"problem-context"}],"relatedBlocks":[{"id":"b-71c9f427dded530984286ed7","url":"#b-71c9f427dded530984286ed7","relation":"figure-and-explanation"}]},{"id":"b-71c9f427dded530984286ed7","type":"figure","scope":"box-offset-roundtrip","url":"https://codingai-lec03.pages.dev/course/blocks/box-offset-roundtrip.html#b-71c9f427dded530984286ed7","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同一坐标单位下，位移目标与框图对应。 查看对应图解状态\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。同一坐标单位下，位移目标与框图对应。 [查看对应图解状态](/#/l3-r2-p33/1)[查看完整图解](/#/l3-r2-p33/1)","sha256":"7d2a29b19e1cd1a196823c364b84e894681651b53fc6ce2c26f81c883424ee89","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":"reading-opening","title":"框回归的四个数怎样编码与还原","number":1},"sectionTitle":"框回归的四个数怎样编码与还原","currentQuestion":"框回归的四个数怎样编码与还原","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"figure":{"caption":"同一坐标单位下，位移目标与框图对应。 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":"同一坐标单位下，位移目标与框图对应。 查看对应图解状态参考框与目标框（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":"同一坐标单位下，位移目标与框图对应。 查看对应图解状态","images":[]},"previousBlock":"b-84ca8e5ad26a3db9908eccb7","nextBlock":"b-6c850eeec525f98ae14bf94e","prerequisites":[{"id":"b-27ad5b11c29511da30795613","url":"#b-27ad5b11c29511da30795613","role":"section-title"},{"id":"b-f5ce4811d5a11d9fc14cbc43","url":"#b-f5ce4811d5a11d9fc14cbc43","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-6c850eeec525f98ae14bf94e","type":"h2","scope":"box-offset-roundtrip","url":"https://codingai-lec03.pages.dev/course/blocks/box-offset-roundtrip.html#b-6c850eeec525f98ae14bf94e","content":"## 继续阅读与实验","sha256":"2b9ccef7e1220e2250cceff1abd8bdd736b42f8da5a223f26b029f44b962e807","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":"reading-opening","title":"框回归的四个数怎样编码与还原","number":1},"sectionTitle":"框回归的四个数怎样编码与还原","currentQuestion":"框回归的四个数怎样编码与还原","sourceSlides":[],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-71c9f427dded530984286ed7","nextBlock":null,"prerequisites":[{"id":"b-27ad5b11c29511da30795613","url":"#b-27ad5b11c29511da30795613","role":"section-title"},{"id":"b-f5ce4811d5a11d9fc14cbc43","url":"#b-f5ce4811d5a11d9fc14cbc43","role":"problem-context"}],"relatedBlocks":[{"id":"b-71c9f427dded530984286ed7","url":"#b-71c9f427dded530984286ed7","relation":"figure-and-explanation"}]}]}