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<!DOCTYPE html><html lang="zh-Hans"><head hexo-theme="https://github.com/volantis-x/hexo-theme-volantis/#6.0.3"><meta name="generator" content="Hexo 8.1.2"><meta name="Volantis" content="6.0.3"><meta charset="utf-8"><meta name="robots" content="index,follow,max-image-preview:large"><link rel="canonical" href="https://blog.mhuig.top/p/483290b5/"><meta http-equiv="x-dns-prefetch-control" content="on"><link rel="dns-prefetch" href="https://static.mhuig.top"><link rel="preconnect" href="https://static.mhuig.top" crossorigin=""><meta name="renderer" content="webkit"><meta name="force-rendering" content="webkit"><meta http-equiv="X-UA-Compatible" content="IE=Edge,chrome=1"><meta name="HandheldFriendly" content="True"><meta name="mobile-web-app-capable" content="yes"><meta name="viewport" content="width=device-width,initial-scale=1,maximum-scale=5"><meta content="black-translucent" name="apple-mobile-web-app-status-bar-style"><meta content="telephone=no" 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type="application/xml" title="MHuiG Blog Site Map" href="https://blog.mhuig.top/sitemap.xml"><link rel="author" href="https://mhuig.top"><meta name="author" content="MHuiG"><meta name="creator" content="MHuiG"><link rel="archives" href="https://blog.mhuig.top/archives/"><link rel="preload" href="/css/style.css" as="style"><link rel="preload" href="https://static.mhuig.top/npm/volantis-static@0.0.1660614606622/media/fonts/VarelaRound/VarelaRound-Regular.ttf" as="font" type="font/ttf" crossorigin="anonymous"><link rel="preload" href="https://static.mhuig.top/npm/volantis-static@0.0.1660614606622/media/fonts/VarelaRound/VarelaRound-Regular.ttf" as="font" type="font/ttf" crossorigin="anonymous"><link rel="alternate" href="/atom.xml" title="Magicland" type="application/atom+xml"><link rel="alternate" href="/rss2.xml" title="Magicland" type="application/rss+xml"><title>特征和分类器 - Magicland</title><meta name="keywords" content="机器学习, 机器视觉,MHuiG, @MHuiG, Blog, 博客, Magicland, 魔法世界"><meta desc="" name="description" content="本文系统阐述计算机视觉中特征与分类器的核心原理。特征作为图像独特属性，需满足同类样本相似、异类样本差异的特性，分为全局与局部两类，后者（如HOG、SIFT）可有效处理遮挡。分类器基于特征向量实现图像分类，但受噪声、样本量等因素限制难以完美。文中详述HOG通过梯度方向直方图编码对象形状，SIFT通过尺度空间极值检测实现尺度旋转不变性，为视觉识别提供关键技术支撑。 - MHuiG - Magicland"><meta property="og:type" content="article"><meta property="og:title" content="特征和分类器"><meta property="og:url" content="https://blog.mhuig.top/p/483290b5/"><meta property="og:site_name" content="Magicland"><meta property="og:description" content="本文系统阐述计算机视觉中特征与分类器的核心原理。特征作为图像独特属性，需满足同类样本相似、异类样本差异的特性，分为全局与局部两类，后者（如HOG、SIFT）可有效处理遮挡。分类器基于特征向量实现图像分类，但受噪声、样本量等因素限制难以完美。文中详述HOG通过梯度方向直方图编码对象形状，SIFT通过尺度空间极值检测实现尺度旋转不变性，为视觉识别提供关键技术支撑。"><meta property="og:locale"><meta property="og:image" content="https://blog.mhuig.top/lib/favicon/android-chrome-192x192.png"><meta property="article:published_time" content="2019-09-12T03:19:00.000Z"><meta property="article:modified_time" content="2025-11-20T10:18:00.000Z"><meta property="article:author" content="MHuiG"><meta 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itemscope="" itemtype="http://schema.org/CreativeWork"><meta itemprop="name" content="特征和分类器"><meta itemprop="description" content="本文系统阐述计算机视觉中特征与分类器的核心原理。特征作为图像独特属性，需满足同类样本相似、异类样本差异的特性，分为全局与局部两类，后者（如HOG、SIFT）可有效处理遮挡。分类器基于特征向量实现图像分类，但受噪声、样本量等因素限制难以完美。文中详述HOG通过梯度方向直方图编码对象形状，SIFT通过尺度空间极值检测实现尺度旋转不变性，为视觉识别提供关键技术支撑。"></span><span hidden=""><meta itemprop="image" content="/lib/favicon/android-chrome-192x192.png"></span><div class="article-meta" id="top"><h1 class="title" itemprop="name headline"> 特征和分类器</h1><div class="new-meta-box"><div class="new-meta-item author" itemprop="author" itemscope="" itemtype="http://schema.org/Person"> <a itemprop="url" class="author" target="_blank" href="https://mhuig.top/" rel="nofollow noopener" alt="author"><img itemprop="image" src="/lib/avatar/avatar-16.webp" class="lazyload" data-srcset="/lib/avatar/avatar-16.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw=="><p itemprop="name">MHuiG</p></a></div><div class="new-meta-item wordcount"><a class="notlink"><i class="fa-duotone fa-keyboard fa-fw" aria-hidden="true"></i><p>字数：1.4k 字</p></a></div><div class="new-meta-item readtime"><a class="notlink"><i class="fa-duotone fa-hourglass-half fa-fw" aria-hidden="true"></i><p>时长：4 分钟</p></a></div></div></div><div id="layoutHelper-page-plugins"></div><div id="post-body" itemprop="articleBody"><p>特征提取和分类是典型计算机视觉系统的两个关键阶段。</p><p>视觉系统的准确性、稳健性和效率在很大程度上取决于图像特征，和分类器的质量。因此，目标是从输入图像中提取信息丰富的、可靠的特征，以便能够开发出很大程度上独立于领域理论的分类。</p><div class="story post-story"><h2 id="特征"><a href="#特征" class="headerlink" title="特征"></a>特征</h2><p>特征是任何独特的方面或特性，用于解决与特定应用相关的计算任务。</p><p>n 个特征的组合可以表示成 n 维向量，称为特征向量。特征向量的质量取决于其区分不同类别的图像样本的能力。</p><p>来自同一类的图像样本应该有相似的特征值，来自不同类的图像应具有不同的特征值。</p></div><div class="story post-story"><h2 id="分类器"><a href="#分类器" class="headerlink" title="分类器"></a>分类器</h2><p>分类器是现代计算机视觉和模式识别的核心。</p><p>分类器的任务是使用特征向量对图像或感兴趣区域（RoI）划分类别。</p><p>分类任务的困难程度取决于来自相同类别的图像的特征值的可变性，以及相对于来自不同类别图像的特征值的差异性。</p><p>但是，完美的分类性能通常是不可能的。这主要是因为：</p><ul><li>噪声（以阴影、遮挡、透视扭曲等形式）</li><li>异常值</li><li>模糊性</li><li>缺少标签</li><li>仅有小训练样本可用</li><li>训练数据样本中正 / 负覆盖的不平衡</li></ul></div><div class="story post-story"><h2 id="传统特征描述符"><a href="#传统特征描述符" class="headerlink" title="传统特征描述符"></a>传统特征描述符</h2><p>传统（手工设计）特征提取方法可分为两大类：</p><ul><li>全局</li><li>局部</li></ul><p>全局特征提取方法定义了一组有效描述整个图像的全局特征。因此形状细节被忽略。全局特征也不适用于识别部分遮挡的对象。</p><p>局部特征提取方法提取关键点周围的局部区域，由此可以更好的处理遮挡。</p><p>检测关键点，并在他们周围构建描述符的方法：</p><p>局部描述符（如 HOG、SIFT、SURF、FREAK、ORB、BRISK、BRIEF、LIOP）</p></div><div class="story post-story"><h2 id="方向梯度直方图"><a href="#方向梯度直方图" class="headerlink" title="方向梯度直方图"></a>方向梯度直方图</h2><p>HOG 是一个特征描述符，用于自动检测图像中的对象。HOG 描述符对图像中局部部分的梯度方向的分布进行编码。</p><p>HOG 背后的想法是可以通过边缘方向的直方图来描述图像内的对象外观和形状。</p><h3 id="1-梯度计算"><a href="#1-梯度计算" class="headerlink" title="1.梯度计算"></a>1. 梯度计算</h3><p>第一步是计算梯度值。在图像的水平和垂直方向上，执行一维中心点离散微分模板。具体的说，该方法需要用以下滤波器内核处理灰度图像：</p><p><mjx-container class="MathJax" jax="SVG" overflow="overflow" display="true" width="full" style="min-width:46.413ex"><svg style="vertical-align:-.777ex;min-width:46.413ex" xmlns="http://www.w3.org/2000/svg" width="100%" height="2.685ex" role="img" focusable="false"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.0181,-0.0181) translate(0, -843.3)"><g data-mml-node="math" data-latex="f_x=[-1\ \ 0 \ \ +1] ,f_y=[-1\ \ 0\ \ +1] ^T"><g data-mml-node="mtable" data-latex="f_x=[-1\ \ 0 \ \ +1] ,f_y=[-1\ \ 0\ \ +1] ^T" transform="translate(2078,0) translate(-2078,0)"><g transform="translate(0 843.3) matrix(1 0 0 -1 0 0) scale(55.25)"><svg data-table="true" preserveAspectRatio="xMidYMid" viewBox="8179.2 -843.3 1 1186.7"><g transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mlabeledtr" transform="translate(0,-48.4)"><g data-mml-node="mtd"><g data-mml-node="msub" data-latex="f_x"><g 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683C202 684 194 676 194 659 194 649 205 644 226 644 269 644 290 639 290 630 290 625 289 620 288 615L155 82C150 60 140 47 125 42 118 40 100 39 69 39 44 39 34 38 34 15 34 5 40 0 53 0L181 3 313 0C329-1 337 7 337 23 337 39 325 39 303 39 264 39 240 37 240 53 240 58 241 65 244 75L376 602C381 623 391 636 406 641 413 643 431 644 462 644 486 644 497 645 497 667Z"></path></g></g></g></svg></mjx-container>，以下卷积操作（表示为<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:.088ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="0.957ex" role="img" focusable="false" viewBox="0 -462 500 423"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="*"><g data-mml-node="mo" data-latex="*"><path data-c="2217" d="M404 372C397 372 390 370 385 366L267 279 282 425C285 445 269 462 250 462 231 462 215 445 218 425L233 279 115 366C110 370 103 372 96 372 78 372 63 357 63 339 63 325 70 315 83 309L217 250 83 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39 303 39 264 39 240 37 240 53 240 58 241 65 244 75L376 602C381 623 391 636 406 641 413 643 431 644 462 644 486 644 497 645 497 667Z"></path></g></g></g></svg></mjx-container>在<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.025ex" xmlns="http://www.w3.org/2000/svg" width="1.294ex" height="1.025ex" role="img" focusable="false" viewBox="0 -442 572 453"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="x"><g data-mml-node="mi" data-latex="x"><path data-c="1D465" d="M527 373C527 419 482 442 432 442 389 442 355 419 329 373 308 419 273 442 222 442 173 442 133 419 101 374 74 335 60 306 60 287 60 278 65 273 75 273 84 273 90 278 92 287 111 345 153 413 220 413 253 413 269 392 269 351 269 330 251 252 216 118 199 51 169 18 126 18 112 18 99 21 88 26 114 36 127 54 127 80 127 106 114 119 87 119 54 119 29 91 29 58 29 12 76-11 125-11 167-11 201 12 228 58 247 12 283-11 335-11 383-11 423 12 455 57 482 96 496 125 496 144 496 153 491 158 481 158 472 158 467 153 464 144 447 87 402 18 337 18 304 18 287 38 287 79 287 92 292 120 303 165L337 300C356 375 387 413 431 413 445 413 458 410 469 405 442 396 429 378 429 351 429 325 443 312 470 312 502 312 527 341 527 373Z"></path></g></g></g></svg></mjx-container>和<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.464ex" xmlns="http://www.w3.org/2000/svg" width="1.109ex" height="1.464ex" role="img" focusable="false" viewBox="0 -442 490 647"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="y"><g data-mml-node="mi" data-latex="y"><path data-c="1D466" d="M163 442C118 442 83 417 58 367 39 328 29 301 29 286 29 277 34 272 45 272 59 272 60 278 64 293 87 372 119 412 160 412 173 412 180 403 180 385 180 369 175 346 164 317 126 214 107 145 107 108 107 32 154-13 231-13 264-13 295-1 323 23 288-109 233-175 158-175 124-175 101-164 89-142 129-140 149-121 149-85 149-60 136-47 109-47 72-47 50-78 50-115 50-170 100-205 158-205 273-205 367-99 392-1L486 377C489 388 490 396 490 401 490 421 479 431 458 431 442 431 429 423 420 408 414 387 409 369 406 354L342 97C332 61 279 16 234 16 196 16 177 41 177 92 177 134 194 198 227 284 240 319 247 343 247 357 247 406 212 442 163 442Z"></path></g></g></g></svg></mjx-container>方向的导数：</p><p><mjx-container class="MathJax" jax="SVG" overflow="overflow" display="true" width="full" style="min-width:31.323ex"><svg style="vertical-align:-.616ex;min-width:31.323ex" xmlns="http://www.w3.org/2000/svg" width="100%" height="2.364ex" role="img" focusable="false"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.0181,-0.0181) translate(0, -772.5)"><g data-mml-node="math" data-latex="I_x=I*f_x,I_y=I*f_y"><g data-mml-node="mtable" data-latex="I_x=I*f_x,I_y=I*f_y" transform="translate(2078,0) translate(-2078,0)"><g transform="translate(0 772.5) matrix(1 0 0 -1 0 0) 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442Z"></path></g></g></g></g></g></svg><svg data-labels="true" preserveAspectRatio="xMaxYMid" viewBox="1278 -772.5 1 1045"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:2" transform="translate(0,770.5)"><text data-id-align="true"></text><g data-idbox="true" transform="translate(0,-748)"><g data-mml-node="mtext" data-latex="\text{(2)}"><path data-c="28" d="M318-248C327-248 332-243 332-234 332-231 330-227 327-223 275-183 233-117 202-26 175 53 161 131 161 208L161 292C161 369 175 447 202 526 233 617 275 683 327 723 330 726 332 730 332 734 332 743 327 748 318 748 317 748 314 747 311 745 251 699 201 631 160 540 121 453 101 371 101 292L101 208C101 129 121 47 160-40 201-131 251-199 311-245 314-247 317-248 318-248Z"></path><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 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139-250Z"></path></g></g></g></svg></mjx-container>计算如下：</p><p><mjx-container class="MathJax" jax="SVG" overflow="overflow" display="true" width="full" style="min-width:39.141ex"><svg style="vertical-align:-2.017ex;min-width:39.141ex" xmlns="http://www.w3.org/2000/svg" width="100%" height="5.165ex" role="img" focusable="false"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.0181,-0.0181) translate(0, -1391.4)"><g data-mml-node="math" data-latex="\theta=\arctan\frac{I_y}{I_x},\vert g \vert=\sqrt[2] {I^2_x+I^2_y}"><g data-mml-node="mtable" data-latex="\theta=\arctan\frac{I_y}{I_x},\vert g \vert=\sqrt[2] {I^2_x+I^2_y}" transform="translate(2078,0) translate(-2078,0)"><g transform="translate(0 1391.4) matrix(1 0 0 -1 0 0) scale(55.25)"><svg data-table="true" preserveAspectRatio="xMidYMid" viewBox="6572.1 -1391.4 1 2282.7"><g transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mlabeledtr" transform="translate(0,-47.6)"><g data-mml-node="mtd"><g 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617 187 526 214 447 228 369 228 292L228 208C228 131 214 53 187-26 156-117 114-183 62-223 59-227 57-231 57-234 57-243 62-248 71-248 72-248 75-247 78-245Z" transform="translate(889,0)"></path></g></g></g></g></svg></g></g></g></g></svg></mjx-container></p><ul><li>CNN 也在层中使用卷积运算，然而主要区别在于不使用手工设计的滤波器，CNN 使用可训练的滤波器，使其具有高度的自适应性。</li><li>CNN 也在层中使用卷积运算，然而主要区别在于不使用手工设计的滤波器，CNN 使用可训练的滤波器，使其具有高度的自适应性。</li></ul><p><img src="https://static.mhuig.top/npm/mhgoos@0.0.1652000153902/20191220133534.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/mhgoos@0.0.1652000153902/20191220133534.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="HOG描述符"></p><h3 id="2-单元方向直方图"><a href="#2-单元方向直方图" class="headerlink" title="2.单元方向直方图"></a>2. 单元方向直方图</h3><p>第二步是计算单元直方图。首先将图像分成小的（通常是 8X8 像素）单元。每个单元都有固定数量的梯度方向区间，他们均匀分布在<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.566ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 500 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="0 -180^。"><g data-mml-node="mn" data-latex="0"><path data-c="30" d="M249-22C390-22 460 92 460 320 460 473 428 575 365 625 330 652 291 666 250 666 109 666 39 551 39 320 39 136 88-22 249-22M361 524C368 489 371 425 371 332 371 240 367 172 360 128 347 48 310 8 249 8 226 8 203 17 182 34 155 57 139 104 132 176 129 201 128 253 128 332 128 419 131 480 136 513 145 568 163 603 191 618 213 630 232 636 249 636 314 636 350 583 361 524Z"></path></g></g></g></svg><mjx-break size="3"></mjx-break><svg style="vertical-align:-.566ex" xmlns="http://www.w3.org/2000/svg" width="7.444ex" height="2.655ex" role="img" focusable="false" viewBox="0 -923.4 3290.3 1173.4"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="0 -180^。"><g 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379 515M250 14C168 14 99 73 99 153 99 220 136 274 210 315L328 240C376 209 400 174 400 134 400 62 325 14 250 14Z" transform="translate(500,0)"></path><path data-c="30" d="M249-22C390-22 460 92 460 320 460 473 428 575 365 625 330 652 291 666 250 666 109 666 39 551 39 320 39 136 88-22 249-22M361 524C368 489 371 425 371 332 371 240 367 172 360 128 347 48 310 8 249 8 226 8 203 17 182 34 155 57 139 104 132 176 129 201 128 253 128 332 128 419 131 480 136 513 145 568 163 603 191 618 213 630 232 636 249 636 314 636 350 583 361 524Z" transform="translate(1000,0)"></path></g><g data-mml-node="TeXAtom" transform="translate(1533,393.1) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mo" data-latex="。"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">。</text></g></g></g></g></g></svg></mjx-container>或<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.566ex" xmlns="http://www.w3.org/2000/svg" width="1.131ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 500 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="0-360^。"><g data-mml-node="mn" data-latex="0"><path data-c="30" d="M249-22C390-22 460 92 460 320 460 473 428 575 365 625 330 652 291 666 250 666 109 666 39 551 39 320 39 136 88-22 249-22M361 524C368 489 371 425 371 332 371 240 367 172 360 128 347 48 310 8 249 8 226 8 203 17 182 34 155 57 139 104 132 176 129 201 128 253 128 332 128 419 131 480 136 513 145 568 163 603 191 618 213 630 232 636 249 636 314 636 350 583 361 524Z"></path></g></g></g></svg><mjx-break size="3"></mjx-break><svg style="vertical-align:-.566ex" xmlns="http://www.w3.org/2000/svg" width="7.444ex" height="2.655ex" role="img" focusable="false" viewBox="0 -923.4 3290.3 1173.4"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="0-360^。"><g data-mml-node="mo" data-latex="-"><path data-c="2212" d="M698 270 80 270C64 270 56 263 56 250 56 237 64 230 80 230L698 230C714 230 722 237 722 250 722 262 710 270 698 270Z"></path></g><g data-mml-node="msup" data-latex="60^。" transform="translate(1000.2,0)"><g data-mml-node="mn" data-latex="60"><path data-c="33" d="M303 353C369 378 431 441 431 526 431 569 410 604 369 631 333 654 292 666 246 666 201 666 162 654 127 631 88 605 68 571 68 528 68 495 90 472 122 472 154 472 176 495 176 527 176 560 157 578 119 580 145 615 186 633 242 633 302 633 332 598 332 527 332 485 324 450 309 421 282 373 245 364 183 364 171 362 165 357 165 348 165 333 172 333 192 333L235 333C310 333 348 280 348 173 348 88 317 14 241 14 176 14 128 36 99 80 134 79 160 105 160 139 160 173 135 198 101 198 62 198 42 178 42 137 42 88 64 49 108 18 147-9 193-22 244-22 301-22 350-3 393 34 436 71 457 117 457 173 457 267 383 332 303 353Z"></path><path data-c="36" d="M383 504C416 504 432 521 432 555 432 627 378 666 304 666 221 666 155 627 106 548 63 480 42 403 42 316 42 189 65 100 112 47 152 1 198-22 251-22 312-22 362 1 401 47 438 91 457 144 457 205 457 266 439 318 403 361 365 407 316 431 257 431 205 431 165 402 138 346L138 352C138 465 166 561 226 605 252 624 279 633 306 633 342 633 368 623 385 602 351 602 334 583 334 553 334 525 355 504 383 504M344 340C355 317 361 272 361 206 361 141 356 98 345 76 325 35 294 14 251 14 222 14 200 24 184 44 171 60 162 74 158 85 146 116 140 163 140 227 140 255 144 282 151 308 164 355 201 399 256 399 295 399 325 379 344 340Z" transform="translate(500,0)"></path><path data-c="30" d="M249-22C390-22 460 92 460 320 460 473 428 575 365 625 330 652 291 666 250 666 109 666 39 551 39 320 39 136 88-22 249-22M361 524C368 489 371 425 371 332 371 240 367 172 360 128 347 48 310 8 249 8 226 8 203 17 182 34 155 57 139 104 132 176 129 201 128 253 128 332 128 419 131 480 136 513 145 568 163 603 191 618 213 630 232 636 249 636 314 636 350 583 361 524Z" transform="translate(1000,0)"></path></g><g data-mml-node="TeXAtom" transform="translate(1533,393.1) scale(0.707)" data-mjx-texclass="ORD"><g data-mml-node="mo" data-latex="。"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">。</text></g></g></g></g></g></svg></mjx-container>之间，具体取决于梯度是有符号的还是无符号的。</p><p>单元内的每一个像素基于该像素处梯度的模对每一个梯度方向区间偷加权票。对于投票权重，可以是梯度大小，梯度大小的平方根或梯度大小的平方。</p><h3 id="3-描述符块"><a href="#3-描述符块" class="headerlink" title="3.描述符块"></a>3. 描述符块</h3><p>为了处理光照和对比度的变化，通过将单元组合在一起形成更大的空间上相连的块，局部的归一化梯度强度。然后，HOG 描述符是来自所有块区域内的、归一化的单元直方图部件的向量。</p><h3 id="4-块的归一化"><a href="#4-块的归一化" class="headerlink" title="4.块的归一化"></a>4. 块的归一化</h3><p>最后一步是块描述符的归一化。设 v 是包含给定块中所有直方图的非归一化向量，‖为它的 (k) 阶范数（(k = 1,2) ），(\epsilon) 是一个小常量。归一化因子可以是如下之一：</p><p><mjx-container class="MathJax" jax="SVG" overflow="overflow" display="true" width="full" style="min-width:34.461ex"><svg style="vertical-align:-2.759ex;min-width:34.461ex" xmlns="http://www.w3.org/2000/svg" width="100%" height="6.649ex" role="img" focusable="false"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.0181,-0.0181) translate(0, -1719.5)"><g data-mml-node="math" data-latex="L2范数:v=\frac{v}{\sqrt{\|v\|^2_2+\epsilon^2} } "><g data-mml-node="mtable" data-latex="L2范数:v=\frac{v}{\sqrt{\|v\|^2_2+\epsilon^2} } " transform="translate(2078,0) translate(-2078,0)"><g transform="translate(0 1719.5) matrix(1 0 0 -1 0 0) scale(55.25)"><svg data-table="true" preserveAspectRatio="xMidYMid" viewBox="5537.8 -1719.5 1 2939"><g transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mlabeledtr" transform="translate(0,601.5)"><g data-mml-node="mtd"><g data-mml-node="mi" data-latex="L"><path data-c="1D43F" d="M520 667C520 678 513 683 500 683L354 680 223 683C208 684 200 676 200 659 200 652 203 647 209 646 218 645 226 644 231 644 262 643 279 641 284 640 289 639 292 636 292 631 292 629 291 623 288 613L156 82C150 60 140 47 125 42 119 40 101 39 70 39 49 39 39 31 39 15 39 5 49 0 70 0L527 0C552 0 554 0 561 19L639 233C642 240 643 245 643 248 643 258 638 263 627 263 617 263 612 254 607 240 588 191 570 154 555 131 518 75 455 39 363 39L270 39C259 39 252 39 249 40 242 40 239 42 239 45 239 47 241 54 244 67L377 601C383 624 396 637 415 642 421 643 442 644 478 644 506 644 520 644 520 667Z"></path></g><g data-mml-node="mn" data-latex="2" transform="translate(681,0)"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g><g data-mml-node="mi" data-latex="范" transform="translate(1181,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">范</text></g><g data-mml-node="mi" data-latex="数" transform="translate(2181,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">数</text></g><g data-mml-node="mo" data-latex=":" transform="translate(3458.8,0)"><path data-c="3A" d="M192 375C192 405 169 431 139 431 109 431 86 405 86 375 86 345 109 319 139 319 169 319 192 345 192 375M192 56C192 86 169 112 139 112 109 112 86 86 86 56 86 26 109 0 139 0 169 0 192 26 192 56Z"></path></g><g data-mml-node="mi" data-latex="v" transform="translate(4014.6,0)"><path data-c="1D463" d="M369 391C369 383 378 370 394 350 410 330 418 307 418 281 418 252 404 203 375 134 354 86 306 18 247 18 201 18 178 45 178 100 178 139 197 208 235 307 243 328 247 345 247 357 247 407 213 442 163 442 119 442 84 417 59 367 39 326 29 300 29 287 29 278 34 273 45 273 58 273 60 279 64 293 87 373 119 413 160 413 173 413 180 404 180 385 180 369 175 347 164 318 127 219 108 152 108 115 108 64 125 29 159 10 186-4 214-11 243-11 332-11 394 85 420 162 452 256 468 325 468 369 468 418 452 442 421 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18 178 45 178 100 178 139 197 208 235 307 243 328 247 345 247 357 247 407 213 442 163 442 119 442 84 417 59 367 39 326 29 300 29 287 29 278 34 273 45 273 58 273 60 279 64 293 87 373 119 413 160 413 173 413 180 404 180 385 180 369 175 347 164 318 127 219 108 152 108 115 108 64 125 29 159 10 186-4 214-11 243-11 332-11 394 85 420 162 452 256 468 325 468 369 468 418 452 442 421 442 396 442 369 416 369 391Z"></path></g><g data-mml-node="msubsup" data-latex="\|^2_2" transform="translate(883,0)"><g data-mml-node="mo" data-latex="\|"><path data-c="2016" d="M264-250C279-250 287-242 287-226L287 726C287 742 279 750 264 750 249 750 241 742 241 726L241-226C241-242 249-250 264-250M134-250C149-250 157-242 157-226L157 726C157 742 149 750 134 750 119 750 111 742 111 726L111-226C111-242 119-250 134-250Z"></path></g><g data-mml-node="mn" transform="translate(431,353.6) scale(0.707)" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g><g data-mml-node="mn" transform="translate(431,-297.3) scale(0.707)" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g></g><g data-mml-node="mo" data-latex="+" transform="translate(1939.8,0)"><path data-c="2B" d="M698 274 413 274 413 559C413 575 405 583 389 583 373 583 365 575 365 559L365 274 80 274C64 274 56 266 56 250 56 234 64 226 80 226L365 226 365-59C365-75 373-83 389-83 405-83 413-75 413-59L413 226 698 226C714 226 722 234 722 250 722 263 711 274 698 274Z"></path></g><g data-mml-node="msup" data-latex="\epsilon^2" transform="translate(2940,0)"><g data-mml-node="mi" data-latex="\epsilon"><path data-c="1D716" d="M228-11C268-11 305 0 339 22 352 31 358 38 358 43 358 55 353 61 344 61L330 54C293 30 260 18 230 18 163 18 128 72 128 142 128 168 131 195 138 222L296 222C321 222 333 229 333 242 333 254 322 260 301 260L148 260C175 349 229 393 310 393L340 393C364 393 376 400 376 413 376 425 365 431 343 431L309 431C238 431 176 407 124 358 72 309 47 250 47 179 47 71 120-11 228-11Z"></path></g><g data-mml-node="mn" transform="translate(439,289) scale(0.707)" data-latex="2"><path data-c="32" d="M237 666C186 666 143 648 106 612 69 576 50 534 50 483 50 449 75 424 106 424 136 424 161 450 161 480 161 513 137 536 105 536 102 536 100 536 98 535 117 584 161 627 224 627 306 627 352 556 352 470 352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0 450 180 417 180C409 129 402 100 396 91 391 86 361 84 306 84L139 84 236 179C304 243 390 312 419 365 439 400 449 435 449 470 449 588 357 666 237 666Z"></path></g></g></g><rect width="3782.6" height="60" x="1020" y="1171.6"></rect></g><rect width="5002.6" height="60" x="120" y="220"></rect></g></g></g></g></svg><svg data-labels="true" preserveAspectRatio="xMaxYMid" viewBox="1278 -1719.5 1 2939"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:4" transform="translate(0,1349.5)"><text data-id-align="true"></text><g data-idbox="true" transform="translate(0,-748)"><g data-mml-node="mtext" data-latex="\text{(4)}"><path data-c="28" d="M318-248C327-248 332-243 332-234 332-231 330-227 327-223 275-183 233-117 202-26 175 53 161 131 161 208L161 292C161 369 175 447 202 526 233 617 275 683 327 723 330 726 332 730 332 734 332 743 327 748 318 748 317 748 314 747 311 745 251 699 201 631 160 540 121 453 101 371 101 292L101 208C101 129 121 47 160-40 201-131 251-199 311-245 314-247 317-248 318-248Z"></path><path data-c="34" d="M353 677C344 677 336 672 330 663L28 199 28 163 289 163 289 81C289 63 285 51 278 46 271 41 252 39 219 39L194 39 194 0C223 2 269 3 331 3 393 3 439 2 468 0L468 39 443 39C410 39 391 41 384 46 377 51 373 63 373 81L373 163 471 163 471 202 373 202 373 660C373 670 366 677 353 677M295 553 295 202 67 202Z" transform="translate(389,0)"></path><path data-c="29" d="M78-245C138-199 188-131 229-40 268 47 288 129 288 208L288 292C288 371 268 453 229 540 188 631 138 699 78 745 75 747 72 748 71 748 62 748 57 743 57 734 57 730 59 726 62 723 114 683 156 617 187 526 214 447 228 369 228 292L228 208C228 131 214 53 187-26 156-117 114-183 62-223 59-227 57-231 57-234 57-243 62-248 71-248 72-248 75-247 78-245Z" transform="translate(889,0)"></path></g></g></g></g></svg></g></g></g></g></svg></mjx-container><br>或者</p><p><mjx-container class="MathJax" jax="SVG" overflow="overflow" display="true" width="full" style="min-width:31.165ex"><svg style="vertical-align:-1.785ex;min-width:31.165ex" xmlns="http://www.w3.org/2000/svg" width="100%" height="4.701ex" role="img" focusable="false"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.0181,-0.0181) translate(0, -1289)"><g data-mml-node="math" data-latex="L1范数:v=\frac{v}{\|v\|_1+\epsilon}"><g data-mml-node="mtable" data-latex="L1范数:v=\frac{v}{\|v\|_1+\epsilon}" transform="translate(2078,0) translate(-2078,0)"><g transform="translate(0 1289) matrix(1 0 0 -1 0 0) scale(55.25)"><svg data-table="true" preserveAspectRatio="xMidYMid" viewBox="4809.6 -1289 1 2078"><g transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mlabeledtr" transform="translate(0,171)"><g data-mml-node="mtd"><g data-mml-node="mi" data-latex="L"><path data-c="1D43F" d="M520 667C520 678 513 683 500 683L354 680 223 683C208 684 200 676 200 659 200 652 203 647 209 646 218 645 226 644 231 644 262 643 279 641 284 640 289 639 292 636 292 631 292 629 291 623 288 613L156 82C150 60 140 47 125 42 119 40 101 39 70 39 49 39 39 31 39 15 39 5 49 0 70 0L527 0C552 0 554 0 561 19L639 233C642 240 643 245 643 248 643 258 638 263 627 263 617 263 612 254 607 240 588 191 570 154 555 131 518 75 455 39 363 39L270 39C259 39 252 39 249 40 242 40 239 42 239 45 239 47 241 54 244 67L377 601C383 624 396 637 415 642 421 643 442 644 478 644 506 644 520 644 520 667Z"></path></g><g data-mml-node="mn" data-latex="1" transform="translate(681,0)"><path data-c="31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47 195 42 170 39 130 39L95 39 95 0C120 2 174 3 257 3 340 3 394 2 419 0L419 39 384 39C343 39 318 42 310 47 302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></g><g data-mml-node="mi" data-latex="范" transform="translate(1181,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">范</text></g><g data-mml-node="mi" data-latex="数" transform="translate(2181,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">数</text></g><g data-mml-node="mo" data-latex=":" transform="translate(3458.8,0)"><path data-c="3A" d="M192 375C192 405 169 431 139 431 109 431 86 405 86 375 86 345 109 319 139 319 169 319 192 345 192 375M192 56C192 86 169 112 139 112 109 112 86 86 86 56 86 26 109 0 139 0 169 0 192 26 192 56Z"></path></g><g data-mml-node="mi" data-latex="v" transform="translate(4014.6,0)"><path data-c="1D463" d="M369 391C369 383 378 370 394 350 410 330 418 307 418 281 418 252 404 203 375 134 354 86 306 18 247 18 201 18 178 45 178 100 178 139 197 208 235 307 243 328 247 345 247 357 247 407 213 442 163 442 119 442 84 417 59 367 39 326 29 300 29 287 29 278 34 273 45 273 58 273 60 279 64 293 87 373 119 413 160 413 173 413 180 404 180 385 180 369 175 347 164 318 127 219 108 152 108 115 108 64 125 29 159 10 186-4 214-11 243-11 332-11 394 85 420 162 452 256 468 325 468 369 468 418 452 442 421 442 396 442 369 416 369 391Z"></path></g><g data-mml-node="mo" data-latex="=" transform="translate(4777.3,0)"><path data-c="3D" d="M698 367 80 367C64 367 56 359 56 344 56 329 64 321 80 321L698 321C714 321 722 329 722 344 722 356 711 367 698 367M698 179 80 179C64 179 56 171 56 156 56 141 64 133 80 133L698 133C714 133 722 141 722 156 722 169 711 179 698 179Z"></path></g><g data-mml-node="mfrac" data-latex="\frac{v}{\|v\|_1+\epsilon}" transform="translate(5833.1,0)"><g data-mml-node="mi" data-latex="v" transform="translate(1650.5,676)"><path data-c="1D463" d="M369 391C369 383 378 370 394 350 410 330 418 307 418 281 418 252 404 203 375 134 354 86 306 18 247 18 201 18 178 45 178 100 178 139 197 208 235 307 243 328 247 345 247 357 247 407 213 442 163 442 119 442 84 417 59 367 39 326 29 300 29 287 29 278 34 273 45 273 58 273 60 279 64 293 87 373 119 413 160 413 173 413 180 404 180 385 180 369 175 347 164 318 127 219 108 152 108 115 108 64 125 29 159 10 186-4 214-11 243-11 332-11 394 85 420 162 452 256 468 325 468 369 468 418 452 442 421 442 396 442 369 416 369 391Z"></path></g><g data-mml-node="mrow" data-latex="\|v\|_1 +\epsilon" transform="translate(220,-710)"><g data-mml-node="mo" data-latex="\|"><path data-c="2016" d="M264-250C279-250 287-242 287-226L287 726C287 742 279 750 264 750 249 750 241 742 241 726L241-226C241-242 249-250 264-250M134-250C149-250 157-242 157-226L157 726C157 742 149 750 134 750 119 750 111 742 111 726L111-226C111-242 119-250 134-250Z"></path></g><g data-mml-node="mi" data-latex="v" transform="translate(398,0)"><path data-c="1D463" d="M369 391C369 383 378 370 394 350 410 330 418 307 418 281 418 252 404 203 375 134 354 86 306 18 247 18 201 18 178 45 178 100 178 139 197 208 235 307 243 328 247 345 247 357 247 407 213 442 163 442 119 442 84 417 59 367 39 326 29 300 29 287 29 278 34 273 45 273 58 273 60 279 64 293 87 373 119 413 160 413 173 413 180 404 180 385 180 369 175 347 164 318 127 219 108 152 108 115 108 64 125 29 159 10 186-4 214-11 243-11 332-11 394 85 420 162 452 256 468 325 468 369 468 418 452 442 421 442 396 442 369 416 369 391Z"></path></g><g data-mml-node="msub" data-latex="\|_1" transform="translate(883,0)"><g data-mml-node="mo" data-latex="\|"><path data-c="2016" d="M264-250C279-250 287-242 287-226L287 726C287 742 279 750 264 750 249 750 241 742 241 726L241-226C241-242 249-250 264-250M134-250C149-250 157-242 157-226L157 726C157 742 149 750 134 750 119 750 111 742 111 726L111-226C111-242 119-250 134-250Z"></path></g><g data-mml-node="mn" transform="translate(431,-150) scale(0.707)" data-latex="1"><path data-c="31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47 195 42 170 39 130 39L95 39 95 0C120 2 174 3 257 3 340 3 394 2 419 0L419 39 384 39C343 39 318 42 310 47 302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></g></g><g data-mml-node="mo" data-latex="+" transform="translate(1939.8,0)"><path data-c="2B" d="M698 274 413 274 413 559C413 575 405 583 389 583 373 583 365 575 365 559L365 274 80 274C64 274 56 266 56 250 56 234 64 226 80 226L365 226 365-59C365-75 373-83 389-83 405-83 413-75 413-59L413 226 698 226C714 226 722 234 722 250 722 263 711 274 698 274Z"></path></g><g data-mml-node="mi" data-latex="\epsilon" transform="translate(2940,0)"><path data-c="1D716" d="M228-11C268-11 305 0 339 22 352 31 358 38 358 43 358 55 353 61 344 61L330 54C293 30 260 18 230 18 163 18 128 72 128 142 128 168 131 195 138 222L296 222C321 222 333 229 333 242 333 254 322 260 301 260L148 260C175 349 229 393 310 393L340 393C364 393 376 400 376 413 376 425 365 431 343 431L309 431C238 431 176 407 124 358 72 309 47 250 47 179 47 71 120-11 228-11Z"></path></g></g><rect width="3546" height="60" x="120" y="220"></rect></g></g></g></g></svg><svg data-labels="true" preserveAspectRatio="xMaxYMid" viewBox="1278 -1289 1 2078"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:5" transform="translate(0,919)"><text data-id-align="true"></text><g data-idbox="true" transform="translate(0,-748)"><g data-mml-node="mtext" data-latex="\text{(5)}"><path data-c="28" d="M318-248C327-248 332-243 332-234 332-231 330-227 327-223 275-183 233-117 202-26 175 53 161 131 161 208L161 292C161 369 175 447 202 526 233 617 275 683 327 723 330 726 332 730 332 734 332 743 327 748 318 748 317 748 314 747 311 745 251 699 201 631 160 540 121 453 101 371 101 292L101 208C101 129 121 47 160-40 201-131 251-199 311-245 314-247 317-248 318-248Z"></path><path data-c="35" d="M118 315C123 315 129 319 134 326 164 371 205 393 257 393 292 393 319 373 337 332 348 305 354 264 354 209 354 146 346 102 331 76 306 35 272 14 229 14 162 14 109 62 91 114 94 113 96 114 100 114 130 114 155 137 155 167 155 198 130 219 100 219 65 219 50 200 50 163 50 63 131-22 231-22 292-22 344 0 386 44 428 88 449 141 449 202 449 260 432 310 398 353 361 400 315 423 259 423 212 423 171 408 138 378L138 556C165 548 191 544 218 544 264 544 304 555 338 578 369 597 390 616 402 634 408 642 411 648 411 651 411 661 406 666 396 666 341 645 294 634 256 634 211 634 168 643 127 662 122 664 118 665 114 665 105 665 100 656 100 637L100 345C100 324 100 315 118 315Z" transform="translate(389,0)"></path><path data-c="29" d="M78-245C138-199 188-131 229-40 268 47 288 129 288 208L288 292C288 371 268 453 229 540 188 631 138 699 78 745 75 747 72 748 71 748 62 748 57 743 57 734 57 730 59 726 62 723 114 683 156 617 187 526 214 447 228 369 228 292L228 208C228 131 214 53 187-26 156-117 114-183 62-223 59-227 57-231 57-234 57-243 62-248 71-248 72-248 75-247 78-245Z" transform="translate(889,0)"></path></g></g></g></g></svg></g></g></g></g></svg></mjx-container><br>或者</p><p><mjx-container class="MathJax" jax="SVG" overflow="overflow" display="true" width="full" style="min-width:40.26ex"><svg style="vertical-align:-2.218ex;min-width:40.26ex" xmlns="http://www.w3.org/2000/svg" width="100%" height="5.568ex" role="img" focusable="false"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(0.0181,-0.0181) translate(0, -1480.5)"><g data-mml-node="math" data-latex="L1范数平方根:v=\sqrt{\frac{v}{\|v\|_1+\epsilon} } "><g data-mml-node="mtable" data-latex="L1范数平方根:v=\sqrt{\frac{v}{\|v\|_1+\epsilon} } " transform="translate(2078,0) translate(-2078,0)"><g transform="translate(0 1480.5) matrix(1 0 0 -1 0 0) scale(55.25)"><svg data-table="true" preserveAspectRatio="xMidYMid" viewBox="6819.6 -1480.5 1 2461"><g transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mlabeledtr" transform="translate(0,25.8)"><g data-mml-node="mtd"><g data-mml-node="mi" data-latex="L"><path data-c="1D43F" d="M520 667C520 678 513 683 500 683L354 680 223 683C208 684 200 676 200 659 200 652 203 647 209 646 218 645 226 644 231 644 262 643 279 641 284 640 289 639 292 636 292 631 292 629 291 623 288 613L156 82C150 60 140 47 125 42 119 40 101 39 70 39 49 39 39 31 39 15 39 5 49 0 70 0L527 0C552 0 554 0 561 19L639 233C642 240 643 245 643 248 643 258 638 263 627 263 617 263 612 254 607 240 588 191 570 154 555 131 518 75 455 39 363 39L270 39C259 39 252 39 249 40 242 40 239 42 239 45 239 47 241 54 244 67L377 601C383 624 396 637 415 642 421 643 442 644 478 644 506 644 520 644 520 667Z"></path></g><g data-mml-node="mn" data-latex="1" transform="translate(681,0)"><path data-c="31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47 195 42 170 39 130 39L95 39 95 0C120 2 174 3 257 3 340 3 394 2 419 0L419 39 384 39C343 39 318 42 310 47 302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></g><g data-mml-node="mi" data-latex="范" transform="translate(1181,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">范</text></g><g data-mml-node="mi" data-latex="数" transform="translate(2181,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">数</text></g><g data-mml-node="mi" data-latex="平" transform="translate(3181,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">平</text></g><g data-mml-node="mi" data-latex="方" transform="translate(4181,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">方</text></g><g data-mml-node="mi" data-latex="根" transform="translate(5181,0)"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">根</text></g><g data-mml-node="mo" data-latex=":" transform="translate(6458.8,0)"><path data-c="3A" d="M192 375C192 405 169 431 139 431 109 431 86 405 86 375 86 345 109 319 139 319 169 319 192 345 192 375M192 56C192 86 169 112 139 112 109 112 86 86 86 56 86 26 109 0 139 0 169 0 192 26 192 56Z"></path></g><g data-mml-node="mi" data-latex="v" transform="translate(7014.6,0)"><path data-c="1D463" d="M369 391C369 383 378 370 394 350 410 330 418 307 418 281 418 252 404 203 375 134 354 86 306 18 247 18 201 18 178 45 178 100 178 139 197 208 235 307 243 328 247 345 247 357 247 407 213 442 163 442 119 442 84 417 59 367 39 326 29 300 29 287 29 278 34 273 45 273 58 273 60 279 64 293 87 373 119 413 160 413 173 413 180 404 180 385 180 369 175 347 164 318 127 219 108 152 108 115 108 64 125 29 159 10 186-4 214-11 243-11 332-11 394 85 420 162 452 256 468 325 468 369 468 418 452 442 421 442 396 442 369 416 369 391Z"></path></g><g data-mml-node="mo" data-latex="=" transform="translate(7777.3,0)"><path data-c="3D" d="M698 367 80 367C64 367 56 359 56 344 56 329 64 321 80 321L698 321C714 321 722 329 722 344 722 356 711 367 698 367M698 179 80 179C64 179 56 171 56 156 56 141 64 133 80 133L698 133C714 133 722 141 722 156 722 169 711 179 698 179Z"></path></g><g data-mml-node="msqrt" data-latex="\sqrt{\frac{v}{\|v\|_1+\epsilon} }" transform="translate(8833.1,0)"><g data-mml-node="mo" transform="translate(0,-55.3)"><path data-c="221A" d="M467-733 254 260 119 47C114 40 111 36 111 33 111 29 117 22 130 11L194 113 422-950C461-950 464-951 471-921L1016 1404C1019 1416 1020 1423 1020 1426 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249 750 241 742 241 726L241-226C241-242 249-250 264-250M134-250C149-250 157-242 157-226L157 726C157 742 149 750 134 750 119 750 111 742 111 726L111-226C111-242 119-250 134-250Z"></path></g><g data-mml-node="mi" data-latex="v" transform="translate(398,0)"><path data-c="1D463" d="M369 391C369 383 378 370 394 350 410 330 418 307 418 281 418 252 404 203 375 134 354 86 306 18 247 18 201 18 178 45 178 100 178 139 197 208 235 307 243 328 247 345 247 357 247 407 213 442 163 442 119 442 84 417 59 367 39 326 29 300 29 287 29 278 34 273 45 273 58 273 60 279 64 293 87 373 119 413 160 413 173 413 180 404 180 385 180 369 175 347 164 318 127 219 108 152 108 115 108 64 125 29 159 10 186-4 214-11 243-11 332-11 394 85 420 162 452 256 468 325 468 369 468 418 452 442 421 442 396 442 369 416 369 391Z"></path></g><g data-mml-node="msub" data-latex="\|_1" transform="translate(883,0)"><g data-mml-node="mo" data-latex="\|"><path data-c="2016" d="M264-250C279-250 287-242 287-226L287 726C287 742 279 750 264 750 249 750 241 742 241 726L241-226C241-242 249-250 264-250M134-250C149-250 157-242 157-226L157 726C157 742 149 750 134 750 119 750 111 742 111 726L111-226C111-242 119-250 134-250Z"></path></g><g data-mml-node="mn" transform="translate(431,-150) scale(0.707)" data-latex="1"><path data-c="31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47 195 42 170 39 130 39L95 39 95 0C120 2 174 3 257 3 340 3 394 2 419 0L419 39 384 39C343 39 318 42 310 47 302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"></path></g></g><g data-mml-node="mo" data-latex="+" transform="translate(1939.8,0)"><path data-c="2B" d="M698 274 413 274 413 559C413 575 405 583 389 583 373 583 365 575 365 559L365 274 80 274C64 274 56 266 56 250 56 234 64 226 80 226L365 226 365-59C365-75 373-83 389-83 405-83 413-75 413-59L413 226 698 226C714 226 722 234 722 250 722 263 711 274 698 274Z"></path></g><g data-mml-node="mi" data-latex="\epsilon" transform="translate(2940,0)"><path data-c="1D716" d="M228-11C268-11 305 0 339 22 352 31 358 38 358 43 358 55 353 61 344 61L330 54C293 30 260 18 230 18 163 18 128 72 128 142 128 168 131 195 138 222L296 222C321 222 333 229 333 242 333 254 322 260 301 260L148 260C175 349 229 393 310 393L340 393C364 393 376 400 376 413 376 425 365 431 343 431L309 431C238 431 176 407 124 358 72 309 47 250 47 179 47 71 120-11 228-11Z"></path></g></g><rect width="3546" height="60" x="120" y="220"></rect></g></g><rect width="3786" height="60" x="1020" y="1334.7"></rect></g></g></g></g></svg><svg data-labels="true" preserveAspectRatio="xMaxYMid" viewBox="1278 -1480.5 1 2461"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:6" transform="translate(0,773.8)"><text data-id-align="true"></text><g data-idbox="true" transform="translate(0,-748)"><g data-mml-node="mtext" data-latex="\text{(6)}"><path data-c="28" d="M318-248C327-248 332-243 332-234 332-231 330-227 327-223 275-183 233-117 202-26 175 53 161 131 161 208L161 292C161 369 175 447 202 526 233 617 275 683 327 723 330 726 332 730 332 734 332 743 327 748 318 748 317 748 314 747 311 745 251 699 201 631 160 540 121 453 101 371 101 292L101 208C101 129 121 47 160-40 201-131 251-199 311-245 314-247 317-248 318-248Z"></path><path data-c="36" d="M383 504C416 504 432 521 432 555 432 627 378 666 304 666 221 666 155 627 106 548 63 480 42 403 42 316 42 189 65 100 112 47 152 1 198-22 251-22 312-22 362 1 401 47 438 91 457 144 457 205 457 266 439 318 403 361 365 407 316 431 257 431 205 431 165 402 138 346L138 352C138 465 166 561 226 605 252 624 279 633 306 633 342 633 368 623 385 602 351 602 334 583 334 553 334 525 355 504 383 504M344 340C355 317 361 272 361 206 361 141 356 98 345 76 325 35 294 14 251 14 222 14 200 24 184 44 171 60 162 74 158 85 146 116 140 163 140 227 140 255 144 282 151 308 164 355 201 399 256 399 295 399 325 379 344 340Z" transform="translate(389,0)"></path><path data-c="29" d="M78-245C138-199 188-131 229-40 268 47 288 129 288 208L288 292C288 371 268 453 229 540 188 631 138 699 78 745 75 747 72 748 71 748 62 748 57 743 57 734 57 730 59 726 62 723 114 683 156 617 187 526 214 447 228 369 228 292L228 208C228 131 214 53 187-26 156-117 114-183 62-223 59-227 57-231 57-234 57-243 62-248 71-248 72-248 75-247 78-245Z" transform="translate(889,0)"></path></g></g></g></g></svg></g></g></g></g></svg></mjx-container><br>还有另一个归一化因子 L2-Hys, 它通过削减 v 的 L2 范数得到（将 v 的最大值限制为 0.2），然后重新归一化。</p><p>最终的图像 / RoI 描述符是通过连接所有归一化的块描述符而形成的。</p><p>L2 范数、L2-Hys 和 L1 范数平方根（L1-sqrt）归一化方法提供了类似的性能，而 L1 范数提供了可靠性稍差的性能。</p></div><div class="story post-story"><h2 id="尺度不变特征变换"><a href="#尺度不变特征变换" class="headerlink" title="尺度不变特征变换"></a>尺度不变特征变换</h2><p>SIFT [Lowe,2004] 提供了一组对象的特征，这些特征对于对象缩放和旋转是健壮的。</p><p>SIFT 算法由四个主要步骤组成。</p><h3 id="1-尺度空间的极值侦测"><a href="#1-尺度空间的极值侦测" class="headerlink" title="1.尺度空间的极值侦测"></a>1. 尺度空间的极值侦测</h3><p>第一步旨在确定对缩放和方向不变的潜在关键点。</p><p>SIFT 使用高斯差分（DoG）来检测尺度空间中关键点中的位置。</p><p>高斯差分是将两个不同尺度的图像（其中一个尺度为<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.025ex" xmlns="http://www.w3.org/2000/svg" width="1.292ex" height="1ex" role="img" focusable="false" viewBox="0 -431 571 442"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\sigma"><g data-mml-node="mi" data-latex="\sigma"><path data-c="1D70E" d="M525 431 300 431C252 431 207 416 166 385 102 336 38 250 38 148 38 58 100-11 190-11 257-11 317 18 368 76 417 132 441 194 441 263 441 304 432 338 414 366L515 366C550 366 567 378 567 403 567 426 550 431 525 431M107 121C107 180 121 234 150 282 184 338 228 366 283 366 341 366 370 336 370 275 370 250 365 221 355 187 335 116 302 66 256 39 233 25 211 18 191 18 136 18 107 63 107 121Z"></path></g></g></g></svg></mjx-container>,另一个是其 k 倍，即<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align:-.566ex" xmlns="http://www.w3.org/2000/svg" width="1.179ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 521 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="k\times\sigma"><g data-mml-node="mi" data-latex="k"><path data-c="1D458" d="M409 353C409 327 423 314 450 314 485 314 508 345 508 379 508 418 476 445 437 445 392 445 344 415 291 356 250 311 217 282 190 269L291 679C289 688 287 694 274 694 242 694 166 685 154 684 139 682 132 675 132 660 132 650 141 645 159 645 178 645 204 646 204 632L59 43C56 32 55 25 55 21 55 0 66-11 87-11 104-11 117-3 124 12 129 21 147 92 179 226 231 221 286 196 286 146 286 131 279 101 279 91 279 34 316-11 373-11 431-11 470 41 490 145 490 154 485 159 475 159 466 159 460 152 457 138 435 59 408 19 375 19 357 19 348 33 348 61 348 77 360 131 360 147 360 204 314 239 221 253 244 269 270 292 298 322 326 352 346 371 359 382 386 404 412 415 435 415 445 415 453 413 459 409 432 404 409 379 409 353Z"></path></g></g></g></svg><mjx-break size="3"></mjx-break><svg style="vertical-align:-.566ex" xmlns="http://www.w3.org/2000/svg" width="3.555ex" height="2.262ex" role="img" focusable="false" viewBox="0 -750 1571.2 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="k\times\sigma"><g data-mml-node="mo" data-latex="\times"><path data-c="D7" d="M630 32C630 39 628 44 623 49L422 250 623 451C628 456 630 461 630 468 630 481 620 491 607 491 600 491 595 489 590 484L389 283 188 484C183 489 178 491 171 491 158 491 148 481 148 468 148 461 150 456 155 451L356 250 155 49C150 44 148 39 148 32 148 19 158 9 171 9 178 9 183 11 188 16L389 217 590 16C595 11 600 9 607 9 620 9 630 19 630 32Z"></path></g><g data-mml-node="mi" data-latex="\sigma" transform="translate(1000.2,0)"><path data-c="1D70E" d="M525 431 300 431C252 431 207 416 166 385 102 336 38 250 38 148 38 58 100-11 190-11 257-11 317 18 368 76 417 132 441 194 441 263 441 304 432 338 414 366L515 366C550 366 567 378 567 403 567 426 550 431 525 431M107 121C107 180 121 234 150 282 184 338 228 366 283 366 341 366 370 336 370 275 370 250 365 221 355 187 335 116 302 66 256 39 233 25 211 18 191 18 136 18 107 63 107 121Z"></path></g></g></g></svg></mjx-container>）的高斯模糊进行差分得到的。</p><h3 id="2-关键点精确定位"><a href="#2-关键点精确定位" class="headerlink" title="2.关键点精确定位"></a>2. 关键点精确定位</h3><h3 id="3-方向定位"><a href="#3-方向定位" class="headerlink" title="3.方向定位"></a>3. 方向定位</h3><h3 id="4-关键点描述符"><a href="#4-关键点描述符" class="headerlink" title="4.关键点描述符"></a>4. 关键点描述符</h3></div></div><div class="footer"><div class="copyright license"><div class="license-title">特征和分类器</div><div class="license-link"><a href="https://blog.mhuig.top/p/483290b5/">https://blog.mhuig.top/p/483290b5/</a></div><div class="license-meta"><div class="license-meta-item"><div class="license-meta-title">本文作者</div><div class="license-meta-text">MHuiG</div></div><div class="license-meta-item"><div class="license-meta-title">发布于</div><div class="license-meta-text">Sep 12, 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class="content">ZooKeeper是高性能分布式协调服务，基于ZAB协议实现数据一致性，提供配置管理、服务发现等核心功能。采用Leader-Follower-Observer架构，支持分布式锁、命名服务等场景，通过树形ZNode存储节点数据，客户端可监听节点变化实现实时同步。</p></a><a class="next" href="/p/9bc3b11e/"><p class="title">图像导数<i class="fa-solid fa-chevron-right" aria-hidden="true"></i></p><p class="content">图像导数通过一阶导数识别边缘（大响应对应边缘像素）和二阶导数分析细节（如细线、噪声），可判断边缘过渡方向。实际应用中需先平滑图像以降低噪声干扰，是Sobel算子等边缘检测算法的核心原理。</p></a></div><div class="recommended-article"><div class="recommended-article-header"><i class="fa-solid fa-bookmark fa-fw" aria-hidden="true"></i> <span>推荐阅读</span></div><div class="recommended-article-group"> <a class="recommended-article-item" href="/p/9bc3b11e/" title="图像导数" rel="bookmark"><img src="https://static.mhuig.top/npm/imbox@0.0.15/c/12.webp" class="lazyload" data-srcset="https://static.mhuig.top/npm/imbox@0.0.15/c/12.webp" srcset="data:image/gif;base64,R0lGODlhAQABAIAAAP///////yH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==" alt="图像导数"> <span class="title">图像导数</span></a> <a 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href="#%E4%BC%A0%E7%BB%9F%E7%89%B9%E5%BE%81%E6%8F%8F%E8%BF%B0%E7%AC%A6"><span class="toc-text">传统特征描述符</span></a></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E6%96%B9%E5%90%91%E6%A2%AF%E5%BA%A6%E7%9B%B4%E6%96%B9%E5%9B%BE"><span class="toc-text">方向梯度直方图</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#1-%E6%A2%AF%E5%BA%A6%E8%AE%A1%E7%AE%97"><span class="toc-text">1. 梯度计算</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#2-%E5%8D%95%E5%85%83%E6%96%B9%E5%90%91%E7%9B%B4%E6%96%B9%E5%9B%BE"><span class="toc-text">2. 单元方向直方图</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#3-%E6%8F%8F%E8%BF%B0%E7%AC%A6%E5%9D%97"><span class="toc-text">3. 描述符块</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#4-%E5%9D%97%E7%9A%84%E5%BD%92%E4%B8%80%E5%8C%96"><span class="toc-text">4. 块的归一化</span></a></li></ol></li><li class="toc-item toc-level-2"><a class="toc-link" href="#%E5%B0%BA%E5%BA%A6%E4%B8%8D%E5%8F%98%E7%89%B9%E5%BE%81%E5%8F%98%E6%8D%A2"><span class="toc-text">尺度不变特征变换</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#1-%E5%B0%BA%E5%BA%A6%E7%A9%BA%E9%97%B4%E7%9A%84%E6%9E%81%E5%80%BC%E4%BE%A6%E6%B5%8B"><span class="toc-text">1. 尺度空间的极值侦测</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#2-%E5%85%B3%E9%94%AE%E7%82%B9%E7%B2%BE%E7%A1%AE%E5%AE%9A%E4%BD%8D"><span class="toc-text">2. 关键点精确定位</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#3-%E6%96%B9%E5%90%91%E5%AE%9A%E4%BD%8D"><span class="toc-text">3. 方向定位</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#4-%E5%85%B3%E9%94%AE%E7%82%B9%E6%8F%8F%E8%BF%B0%E7%AC%A6"><span class="toc-text">4. 关键点描述符</span></a></li></ol></li></ol></div></section></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div class="pjax"></div><div 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