{"version":2,"relationshipURLBase":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p42.html","relationshipResolution":"Resolve relative relationship URLs against relationshipURLBase; complete records and absolute URLs are in blocks.","title":"连续位置的数值，怎样从四个邻点得到？","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p42.html","markdown":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p42.md","pages":[{"id":"roi-bilinear-point","title":"从四个邻点实际算出 2.5","unit":"区域采样怎样保住几何对应？","unitId":"roi-alignment-and-evidence","chapter":"II","number":1},{"id":"roi-alignment-paper-comparison","title":"在同一设置下比较 RoIPool、RoIWarp 与 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2.5。两步插值与四项加权是同一运算。读完算例后，接着看[原论文的对照：对齐改善了哪些指标](/course/blocks/roi-align-paper-evidence.html)，区分“使用双线性插值”和“保持坐标对齐”的作用。","sha256":"185d6570689468f3c523e1d63cc5d2dd507c9b0ff60f2af36bd85b2834d7978e","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"roi-alignment-and-evidence","title":"区域采样怎样保住几何对应？"},"page":{"id":"roi-bilinear-point","title":"从四个邻点实际算出 2.5","number":1},"sectionTitle":"从四个邻点实际算出 2.5","currentQuestion":"从坐标、四邻插值到局部目标，再检查论文中的同条件证据。","sourceSlides":["l3-r2-p42"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-7e195c5cb5b0d5cd9a75d17a","nextBlock":"b-bd1174ff1f8c27a23778f2a5","prerequisites":[{"id":"b-7e195c5cb5b0d5cd9a75d17a","url":"#b-7e195c5cb5b0d5cd9a75d17a","role":"section-title"}],"relatedBlocks":[{"id":"b-bd1174ff1f8c27a23778f2a5","url":"#b-bd1174ff1f8c27a23778f2a5","relation":"figure-and-explanation"}]},{"id":"b-bd1174ff1f8c27a23778f2a5","type":"figure","scope":"document","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p42.html#b-bd1174ff1f8c27a23778f2a5","content":"图内标签与数值：Lecture 03 课堂图解 P42；F = [[0,2],[4,6]]；x 向右，y 向下；0；2；4；6；(.25, .5)；x；y；上行：¾×0 + ¼×2 = 0.5；下行：¾×4 + ¼×6 = 4.5；再取两行中间值；½×0.5 + ½×4.5 = 2.5；四邻点权重：⅜，⅛，⅜，⅛；权重和 = 1；结果 = 2.5；一个连续采样点的双线性算例；完整 RoIAlign 还要组织分格、多个采样点与汇总。\n\nF=[[0,2],[4,6]] 的四邻点与 (.25,.5) 采样点，横向两次插值和纵向一次插值连接到 2.5。\n\n- F = [[0,2],[4,6]]；x 向右，y 向下\n- 0\n- 2\n- 4\n- 6\n- (.25, .5)\n- x\n- y\n- 上行：¾×0 + ¼×2 = 0.5\n- 下行：¾×4 + ¼×6 = 4.5\n- 再取两行中间值\n- ½×0.5 + ½×4.5 = 2.5\n- 四邻点权重：⅜，⅛，⅜，⅛\n- 权重和 = 1；结果 = 2.5\n- 一个连续采样点的双线性算例；完整 RoIAlign 还要组织分格、多个采样点与汇总。F=[[0,2],[4,6]] 的四邻点与 (.25,.5) 采样点，横向两次插值和纵向一次插值连接到 2.5。 [查看对应图解状态](/#/l3-r2-p42/1)[查看完整图解](/course/figures/l3-r2-p42-1.html)","sha256":"7cfd12e8a6fb39b6b584051658e0572333ea554fe1d4b1890a3eac4903d1e548","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"roi-alignment-and-evidence","title":"区域采样怎样保住几何对应？"},"page":{"id":"roi-bilinear-point","title":"从四个邻点实际算出 2.5","number":1},"sectionTitle":"从四个邻点实际算出 2.5","currentQuestion":"从坐标、四邻插值到局部目标，再检查论文中的同条件证据。","sourceSlides":["l3-r2-p42"],"knowledgeBlock":null,"formulas":[],"figure":{"caption":"F=[[0,2],[4,6]] 的四邻点与 (.25,.5) 采样点，横向两次插值和纵向一次插值连接到 2.5。 查看对应图解状态","labels":["F = [[0,2],[4,6]]；x 向右，y 向下","0","2","4","6","(.25, .5)","x","y","上行：¾×0 + ¼×2 = 0.5","下行：¾×4 + ¼×6 = 4.5","再取两行中间值","½×0.5 + ½×4.5 = 2.5","四邻点权重：⅜，⅛，⅜，⅛","权重和 = 1；结果 = 2.5","一个连续采样点的双线性算例；完整 RoIAlign 还要组织分格、多个采样点与汇总。"],"description":"F=[[0,2],[4,6]] 的四邻点与 (.25,.5) 采样点，横向两次插值和纵向一次插值连接到 2.5。F = [[0,2],[4,6]]；x 向右，y 向下0246(.25, .5)xy上行：¾×0 + ¼×2 = 0.5下行：¾×4 + ¼×6 = 4.5再取两行中间值½×0.5 + ½×4.5 = 2.5四邻点权重：⅜，⅛，⅜，⅛权重和 = 1；结果 = 2.5一个连续采样点的双线性算例；完整 RoIAlign 还要组织分格、多个采样点与汇总。","evidenceIdentity":"F=[[0,2],[4,6]] 的四邻点与 (.25,.5) 采样点，横向两次插值和纵向一次插值连接到 2.5。 查看对应图解状态","images":[]},"previousBlock":"b-f7b25c3229af6ac083bd9bf2","nextBlock":"b-5934a96ea42b8a8d7b111646","prerequisites":[{"id":"b-7e195c5cb5b0d5cd9a75d17a","url":"#b-7e195c5cb5b0d5cd9a75d17a","role":"section-title"},{"id":"b-f7b25c3229af6ac083bd9bf2","url":"#b-f7b25c3229af6ac083bd9bf2","role":"problem-context"}],"relatedBlocks":[]},{"id":"b-5934a96ea42b8a8d7b111646","type":"h2","scope":"narrative","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p42.html#b-5934a96ea42b8a8d7b111646","content":"## 课堂讲述","sha256":"786ce10a6b32a492259a3dccd0a54e61cd41d28a34382fb7b5386c5f03b7ad69","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"roi-alignment-and-evidence","title":"区域采样怎样保住几何对应？"},"page":{"id":"roi-bilinear-point","title":"从四个邻点实际算出 2.5","number":1},"sectionTitle":"从四个邻点实际算出 2.5","currentQuestion":"从坐标、四邻插值到局部目标，再检查论文中的同条件证据。","sourceSlides":["l3-r2-p42"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-bd1174ff1f8c27a23778f2a5","nextBlock":"b-d67608f74d980c651b1ca8c3","prerequisites":[{"id":"b-7e195c5cb5b0d5cd9a75d17a","url":"#b-7e195c5cb5b0d5cd9a75d17a","role":"section-title"},{"id":"b-f7b25c3229af6ac083bd9bf2","url":"#b-f7b25c3229af6ac083bd9bf2","role":"problem-context"}],"relatedBlocks":[{"id":"b-bd1174ff1f8c27a23778f2a5","url":"#b-bd1174ff1f8c27a23778f2a5","relation":"figure-and-explanation"}]},{"id":"b-d67608f74d980c651b1ca8c3","type":"p","scope":"narrative","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p42.html#b-d67608f74d980c651b1ca8c3","content":"这四个相邻位置的值分别是零、二、四、六。我们要读的位置在横向四分之一、纵向一半处，不正好落在其中任何一个整数点上。\n先在上面一行按横向位置插值，得到零点五；下面一行同样插值得到四点五；再在两行的中间取值，得到二点五。也可以一次写成四个邻点的加权和，结果相同。\n这段计算不是让你背四个权重，而是看清连续采样没有创造一张新图：它在已有特征之间，按指定位置构造读出。RoIAlign 会在区域的分格中组织这类采样与聚合。保持坐标对应，对需要细轮廓的任务就特别重要。","sha256":"dc4ea7cd3e6bb02ae42889df64f7cfced896437d94ce4b1c6535f820400fe2d7","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"roi-alignment-and-evidence","title":"区域采样怎样保住几何对应？"},"page":{"id":"roi-bilinear-point","title":"从四个邻点实际算出 2.5","number":1},"sectionTitle":"从四个邻点实际算出 2.5","currentQuestion":"从坐标、四邻插值到局部目标，再检查论文中的同条件证据。","sourceSlides":["l3-r2-p42"],"knowledgeBlock":null,"formulas":[],"previousBlock":"b-5934a96ea42b8a8d7b111646","nextBlock":"b-e40c5d52d8b8e006e7839424","prerequisites":[{"id":"b-5934a96ea42b8a8d7b111646","url":"#b-5934a96ea42b8a8d7b111646","role":"section-title"},{"id":"b-f7b25c3229af6ac083bd9bf2","url":"#b-f7b25c3229af6ac083bd9bf2","role":"problem-context"}],"relatedBlocks":[{"id":"b-bd1174ff1f8c27a23778f2a5","url":"#b-bd1174ff1f8c27a23778f2a5","relation":"figure-and-explanation"}]},{"id":"b-e40c5d52d8b8e006e7839424","type":"h3","scope":"bilinear-four-neighbors","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p42.html#b-e40c5d52d8b8e006e7839424","content":"### 四个邻点如何读出 2.5","sha256":"c8b573b98a7fa194bf937b9a406747425138e4b74e7ca487215523d704aff87c","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"roi-alignment-and-evidence","title":"区域采样怎样保住几何对应？"},"page":{"id":"roi-bilinear-point","title":"从四个邻点实际算出 2.5","number":1},"sectionTitle":"四个邻点如何读出 2.5","currentQuestion":"从坐标、四邻插值到局部目标，再检查论文中的同条件证据。","sourceSlides":["l3-r2-p42"],"knowledgeBlock":"bilinear-four-neighbors","formulas":[],"previousBlock":"b-d67608f74d980c651b1ca8c3","nextBlock":"b-90f6c096efe9ae5f53f9e9dd","prerequisites":[{"id":"b-5934a96ea42b8a8d7b111646","url":"#b-5934a96ea42b8a8d7b111646","role":"section-title"},{"id":"b-f7b25c3229af6ac083bd9bf2","url":"#b-f7b25c3229af6ac083bd9bf2","role":"problem-context"}],"relatedBlocks":[{"id":"b-bd1174ff1f8c27a23778f2a5","url":"#b-bd1174ff1f8c27a23778f2a5","relation":"figure-and-explanation"},{"id":"b-90f6c096efe9ae5f53f9e9dd","url":"#b-90f6c096efe9ae5f53f9e9dd","relation":"same-reasoning"},{"id":"b-44274492d8f6e8ca95cfb223","url":"#b-44274492d8f6e8ca95cfb223","relation":"same-reasoning"},{"id":"b-fca28abad0df2325f0762e0b","url":"#b-fca28abad0df2325f0762e0b","relation":"same-reasoning"},{"id":"b-fac45115c8ce2736a005838c","url":"#b-fac45115c8ce2736a005838c","relation":"same-reasoning"},{"id":"b-b6db1d489d32ff848bd71bc8","url":"#b-b6db1d489d32ff848bd71bc8","relation":"same-reasoning"},{"id":"b-4a4e17fcc23248e5e929a0fb","url":"#b-4a4e17fcc23248e5e929a0fb","relation":"same-reasoning"}]},{"id":"b-90f6c096efe9ae5f53f9e9dd","type":"p","scope":"bilinear-four-neighbors","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p42.html#b-90f6c096efe9ae5f53f9e9dd","content":"把左上、右上、左下、右下值依次记为 0、2、4、6。要读取的点相对左上角横向走了 α=1/4、纵向走了 β=1/2。上排插值为 $(1-α)0+α2=.5$，下排为 $(1-α)4+α6=4.5$，再纵向插值得 $(1-β).5+β4.5=2.5$。","sha256":"9068ee93532c027ce4a75a59639e005de9272ab4f6cedc3e1e4e0f6ab8dad0e6","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"roi-alignment-and-evidence","title":"区域采样怎样保住几何对应？"},"page":{"id":"roi-bilinear-point","title":"从四个邻点实际算出 2.5","number":1},"sectionTitle":"四个邻点如何读出 2.5","currentQuestion":"从坐标、四邻插值到局部目标，再检查论文中的同条件证据。","sourceSlides":["l3-r2-p42"],"knowledgeBlock":"bilinear-four-neighbors","formulas":[{"latex":"(1-α)0+α2=.5","definitionContext":"把左上、右上、左下、右下值依次记为 0、2、4、6。要读取的点相对左上角横向走了 α=1/4、纵向走了 β=1/2。上排插值为 $(1-α)0+α2=.5$，下排为 $(1-α)4+α6=4.5$，再纵向插值得 $(1-β).5+β4.5=2.5$。\n也可直接写四点加权和：\n$\nv=(1-α)(1-β)F_{00}+α(1-β)F_{10}+(1-α)βF_{01}+αβF_{11}.\n$\n对应权重为 3/8、1/8、3/8、1/8，总和为 1。代入得 $0+2/8+12/8+6/8=2.5$。离左边更近，所以两项左邻的总权重是 3/4；纵向正好一半，上下各占 1/2。这些比例直接来自几何，而不是学出来的四个自由参数。\nRoIAlign 在每个 bin 内组织多个这种连续采样点，再按实现聚合。它用原有特征构造位置相关读数，没有查到原图中的隐藏真值。改变特征图分辨率、RoI 或采样数量时，应重新计算位置；不能沿用旧邻点却声称只是换了 stride。\n读完算例后，接着看[原论文的对照：对齐改善了哪些指标](/course/blocks/roi-align-paper-evidence.html)，区分“使用双线性插值”和“保持坐标对齐”的作用。"},{"latex":"(1-α)4+α6=4.5","definitionContext":"把左上、右上、左下、右下值依次记为 0、2、4、6。要读取的点相对左上角横向走了 α=1/4、纵向走了 β=1/2。上排插值为 $(1-α)0+α2=.5$，下排为 $(1-α)4+α6=4.5$，再纵向插值得 $(1-β).5+β4.5=2.5$。\n也可直接写四点加权和：\n$\nv=(1-α)(1-β)F_{00}+α(1-β)F_{10}+(1-α)βF_{01}+αβF_{11}.\n$\n对应权重为 3/8、1/8、3/8、1/8，总和为 1。代入得 $0+2/8+12/8+6/8=2.5$。离左边更近，所以两项左邻的总权重是 3/4；纵向正好一半，上下各占 1/2。这些比例直接来自几何，而不是学出来的四个自由参数。\nRoIAlign 在每个 bin 内组织多个这种连续采样点，再按实现聚合。它用原有特征构造位置相关读数，没有查到原图中的隐藏真值。改变特征图分辨率、RoI 或采样数量时，应重新计算位置；不能沿用旧邻点却声称只是换了 stride。\n读完算例后，接着看[原论文的对照：对齐改善了哪些指标](/course/blocks/roi-align-paper-evidence.html)，区分“使用双线性插值”和“保持坐标对齐”的作用。"},{"latex":"(1-β).5+β4.5=2.5","definitionContext":"把左上、右上、左下、右下值依次记为 0、2、4、6。要读取的点相对左上角横向走了 α=1/4、纵向走了 β=1/2。上排插值为 $(1-α)0+α2=.5$，下排为 $(1-α)4+α6=4.5$，再纵向插值得 $(1-β).5+β4.5=2.5$。\n也可直接写四点加权和：\n$\nv=(1-α)(1-β)F_{00}+α(1-β)F_{10}+(1-α)βF_{01}+αβF_{11}.\n$\n对应权重为 3/8、1/8、3/8、1/8，总和为 1。代入得 $0+2/8+12/8+6/8=2.5$。离左边更近，所以两项左邻的总权重是 3/4；纵向正好一半，上下各占 1/2。这些比例直接来自几何，而不是学出来的四个自由参数。\nRoIAlign 在每个 bin 内组织多个这种连续采样点，再按实现聚合。它用原有特征构造位置相关读数，没有查到原图中的隐藏真值。改变特征图分辨率、RoI 或采样数量时，应重新计算位置；不能沿用旧邻点却声称只是换了 stride。\n读完算例后，接着看[原论文的对照：对齐改善了哪些指标](/course/blocks/roi-align-paper-evidence.html)，区分“使用双线性插值”和“保持坐标对齐”的作用。"}],"previousBlock":"b-e40c5d52d8b8e006e7839424","nextBlock":"b-44274492d8f6e8ca95cfb223","prerequisites":[{"id":"b-e40c5d52d8b8e006e7839424","url":"#b-e40c5d52d8b8e006e7839424","role":"section-title"},{"id":"b-f7b25c3229af6ac083bd9bf2","url":"#b-f7b25c3229af6ac083bd9bf2","role":"problem-context"}],"relatedBlocks":[{"id":"b-bd1174ff1f8c27a23778f2a5","url":"#b-bd1174ff1f8c27a23778f2a5","relation":"figure-and-explanation"},{"id":"b-e40c5d52d8b8e006e7839424","url":"#b-e40c5d52d8b8e006e7839424","relation":"same-reasoning"},{"id":"b-44274492d8f6e8ca95cfb223","url":"#b-44274492d8f6e8ca95cfb223","relation":"same-reasoning"},{"id":"b-fca28abad0df2325f0762e0b","url":"#b-fca28abad0df2325f0762e0b","relation":"same-reasoning"},{"id":"b-fac45115c8ce2736a005838c","url":"#b-fac45115c8ce2736a005838c","relation":"same-reasoning"},{"id":"b-b6db1d489d32ff848bd71bc8","url":"#b-b6db1d489d32ff848bd71bc8","relation":"same-reasoning"},{"id":"b-4a4e17fcc23248e5e929a0fb","url":"#b-4a4e17fcc23248e5e929a0fb","relation":"same-reasoning"}]},{"id":"b-44274492d8f6e8ca95cfb223","type":"p","scope":"bilinear-four-neighbors","url":"https://codingai-lec03.pages.dev/course/pages/l3-r2-p42.html#b-44274492d8f6e8ca95cfb223","content":"也可直接写四点加权和：","sha256":"6098132f38143db98713510c6df60aa2a55dfc48b17b0637c5e2592782dbb6c0","chapter":{"id":"II","title":"区域、像素与实例"},"unit":{"id":"roi-alignment-and-evidence","title":"区域采样怎样保住几何对应？"},"page":{"id":"roi-bilinear-point","title":"从四个邻点实际算出 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