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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" 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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><div class="article-meta" id="top"><h1 class="title allow-select" 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==" alt="author"><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: -0.777ex; min-width: 46.413ex;" xmlns="http://www.w3.org/2000/svg" width="100%" height="2.685ex" role="img" 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55C188 44 154 39 94 39C63 39 49 42 49 16C49 5 56 0 69 0C120 0 192 4 235 3L317 2C331 2 386 0 403 0C420 0 428 8 428 24C428 34 416 39 391 39C339 39 309 41 300 46C297 48 295 52 295 58L430 603C433 617 436 626 439 629C443 635 467 638 511 638C566 638 604 634 623 625C642 616 652 595 652 561C652 543 649 517 644 483C642 475 641 469 641 464C641 453 646 447 657 447C666 447 672 456 675 473L702 645C703 650 704 656 704 662C704 672 694 677 673 677L125 677C99 677 97 674 89 655L30 481C27 472 25 466 24 462C24 452 29 447 40 447C48 447 55 455 60 470C85 543 110 588 133 607C159 628 209 638 282 638L321 638C332 638 344 639 344 631Z"/></g></g></g></g></g></svg><svg data-labels="true" preserveaspectratio="xMaxYMid" viewbox="1278 -843.3 1 1186.7"><g data-labels="true" transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mtd" id="mjx-eqn:1" transform="translate(0,699.6)"><text data-id-align="true"/><g data-idbox="true" transform="translate(0,-748)"><g data-mml-node="mtext" data-latex="\text{(}"><path data-c="28" d="M318-248C327-248 332-243 332-234C332-231 330-227 327-223C275-183 233-117 202-26C175 53 161 131 161 208L161 292C161 369 175 447 202 526C233 617 275 683 327 723C330 726 332 730 332 734C332 743 327 748 318 748C317 748 314 747 311 745C251 699 201 631 160 540C121 453 101 371 101 292L101 208C101 129 121 47 160-40C201-131 251-199 311-245C314-247 317-248 318-248Z"/></g><g data-mml-node="mtext" data-latex="\text{1}" transform="translate(389,0)"><path data-c="31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"/></g><g data-mml-node="mtext" data-latex="\text{)}" transform="translate(889,0)"><path data-c="29" d="M78-245C138-199 188-131 229-40C268 47 288 129 288 208L288 292C288 371 268 453 229 540C188 631 138 699 78 745C75 747 72 748 71 748C62 748 57 743 57 734C57 730 59 726 62 723C114 683 156 617 187 526C214 447 228 369 228 292L228 208C228 131 214 53 187-26C156-117 114-183 62-223C59-227 57-231 57-234C57-243 62-248 71-248C72-248 75-247 78-245Z"/></g></g></g></g></svg></g></g></g></g></svg></mjx-container></p><p>因此给定一个图像<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align: -0.002ex;" xmlns="http://www.w3.org/2000/svg" width="1.124ex" height="1.55ex" role="img" focusable="false" viewbox="0 -684 497 685"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="I"><g data-mml-node="mi" data-latex="I"><path data-c="1D43C" d="M497 667C497 678 491 683 478 683L349 680L218 683C202 684 194 676 194 659C194 649 205 644 226 644C269 644 290 639 290 630C290 625 289 620 288 615L155 82C150 60 140 47 125 42C118 40 100 39 69 39C44 39 34 38 34 15C34 5 40 0 53 0L181 3L313 0C329-1 337 7 337 23C337 39 325 39 303 39C264 39 240 37 240 53C240 58 241 65 244 75L376 602C381 623 391 636 406 641C413 643 431 644 462 644C486 644 497 645 497 667Z"/></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: 0.088ex;" 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 279L282 425C285 445 269 462 250 462C231 462 215 445 218 425L233 279L115 366C110 370 103 372 96 372C78 372 63 357 63 339C63 325 70 315 83 309L217 250L83 191C70 185 63 175 63 161C63 143 78 128 96 128C103 128 110 130 115 134L233 221L218 75C215 55 231 39 250 39C269 39 285 55 282 75L267 221L385 134C390 130 397 128 404 128C415 128 424 133 431 142C446 162 435 183 417 191L283 250L417 309C430 315 437 325 437 339C437 357 422 372 404 372Z"/></g></g></g></svg></mjx-container>）得出图像<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align: -0.002ex;" xmlns="http://www.w3.org/2000/svg" width="1.124ex" height="1.55ex" role="img" focusable="false" viewbox="0 -684 497 685"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="I"><g data-mml-node="mi" data-latex="I"><path data-c="1D43C" d="M497 667C497 678 491 683 478 683L349 680L218 683C202 684 194 676 194 659C194 649 205 644 226 644C269 644 290 639 290 630C290 625 289 620 288 615L155 82C150 60 140 47 125 42C118 40 100 39 69 39C44 39 34 38 34 15C34 5 40 0 53 0L181 3L313 0C329-1 337 7 337 23C337 39 325 39 303 39C264 39 240 37 240 53C240 58 241 65 244 75L376 602C381 623 391 636 406 641C413 643 431 644 462 644C486 644 497 645 497 667Z"/></g></g></g></svg></mjx-container>在<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align: -0.025ex;" 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 442C389 442 355 419 329 373C308 419 273 442 222 442C173 442 133 419 101 374C74 335 60 306 60 287C60 278 65 273 75 273C84 273 90 278 92 287C111 345 153 413 220 413C253 413 269 392 269 351C269 330 251 252 216 118C199 51 169 18 126 18C112 18 99 21 88 26C114 36 127 54 127 80C127 106 114 119 87 119C54 119 29 91 29 58C29 12 76-11 125-11C167-11 201 12 228 58C247 12 283-11 335-11C383-11 423 12 455 57C482 96 496 125 496 144C496 153 491 158 481 158C472 158 467 153 464 144C447 87 402 18 337 18C304 18 287 38 287 79C287 92 292 120 303 165L337 300C356 375 387 413 431 413C445 413 458 410 469 405C442 396 429 378 429 351C429 325 443 312 470 312C502 312 527 341 527 373Z"/></g></g></g></svg></mjx-container>和<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align: -0.464ex;" 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 367C39 328 29 301 29 286C29 277 34 272 45 272C59 272 60 278 64 293C87 372 119 412 160 412C173 412 180 403 180 385C180 369 175 346 164 317C126 214 107 145 107 108C107 32 154-13 231-13C264-13 295-1 323 23C288-109 233-175 158-175C124-175 101-164 89-142C129-140 149-121 149-85C149-60 136-47 109-47C72-47 50-78 50-115C50-170 100-205 158-205C273-205 367-99 392-1L486 377C489 388 490 396 490 401C490 421 479 431 458 431C442 431 429 423 420 408C414 387 409 369 406 354L342 97C332 61 279 16 234 16C196 16 177 41 177 92C177 134 194 198 227 284C240 319 247 343 247 357C247 406 212 442 163 442Z"/></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: -0.616ex; min-width: 31.323ex;" xmlns="http://www.w3.org/2000/svg" width="100%" height="2.364ex" role="img" focusable="false" data-mjx-viewbox="0 -772.5 13844.6 1045"><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) scale(55.25)"><svg data-table="true" preserveaspectratio="xMidYMid" viewbox="4844.3 -772.5 1 1045"><g transform="matrix(1 0 0 -1 0 0)"><g data-mml-node="mlabeledtr" transform="translate(0,22.5)"><g data-mml-node="mtd"><g data-mml-node="msub" 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d="M78-245C138-199 188-131 229-40C268 47 288 129 288 208L288 292C288 371 268 453 229 540C188 631 138 699 78 745C75 747 72 748 71 748C62 748 57 743 57 734C57 730 59 726 62 723C114 683 156 617 187 526C214 447 228 369 228 292L228 208C228 131 214 53 187-26C156-117 114-183 62-223C59-227 57-231 57-234C57-243 62-248 71-248C72-248 75-247 78-245Z"/></g></g></g></g></svg></g></g></g></g></svg></mjx-container></p><p>因此，梯度的方向<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align: -0.025ex;" xmlns="http://www.w3.org/2000/svg" width="1.061ex" height="1.62ex" role="img" focusable="false" viewbox="0 -705 469 716"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\theta"><g data-mml-node="mi" data-latex="\theta"><path data-c="1D703" d="M164-11C209-11 256 16 302 70C382 163 455 335 455 498C455 539 448 582 434 625C416 678 382 705 333 705C288 705 243 678 196 624C116 532 42 360 42 196C42 94 75-11 164-11M332 675C365 675 382 637 382 560C382 517 372 452 352 367L155 367C180 460 204 529 229 574C266 641 301 675 332 675M145 327L341 327C322 246 299 181 274 132C235 57 199 19 164 19C131 19 115 58 115 135C115 185 125 249 145 327Z"/></g></g></g></svg></mjx-container>和梯度的大小<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align: -0.566ex;" xmlns="http://www.w3.org/2000/svg" width="2.337ex" height="2.262ex" role="img" focusable="false" viewbox="0 -750 1033 1000"><g stroke="currentColor" fill="currentColor" stroke-width="0" transform="scale(1,-1)"><g data-mml-node="math" data-latex="\vert g \vert"><g data-mml-node="mo" data-latex="\vert"><path data-c="7C" d="M139-250C152-250 159-242 159-226L159 726C159 742 152 750 139 750C126 750 119 742 119 726L119-226C119-242 126-250 139-250Z"/></g><g data-mml-node="mi" data-latex="g" transform="translate(278,0)"><path data-c="1D454" d="M15-141C15-184 60-205 150-205C197-205 241-193 280-170C324-144 351-109 362-66L471 373C473 383 474 389 474 392C474 412 463 422 442 422C420 422 406 410 399 387C377 424 347 442 310 442C246 442 189 410 140 346C95 286 72 223 72 158C72 71 123-3 207-3C246-3 282 14 315 47L285-71C256-140 211-175 148-175C122-175 100-173 82-169C103-158 113-141 113-118C113-93 99-80 72-80C40-80 15-109 15-141M356 392C376 371 386 351 386 331C386 330 385 325 383 318L336 129C330 106 313 82 286 60C259 38 233 27 210 27C170 27 150 56 150 114C150 169 184 291 204 327C235 384 270 412 311 412C329 412 344 405 356 392Z"/></g><g data-mml-node="mo" data-latex="\vert" transform="translate(755,0)"><path data-c="7C" d="M139-250C152-250 159-242 159-226L159 726C159 742 152 750 139 750C126 750 119 742 119 726L119-226C119-242 126-250 139-250Z"/></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%" 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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 320C460 473 428 575 365 625C330 652 291 666 250 666C109 666 39 551 39 320C39 136 88-22 249-22M361 524C368 489 371 425 371 332C371 240 367 172 360 128C347 48 310 8 249 8C226 8 203 17 182 34C155 57 139 104 132 176C129 201 128 253 128 332C128 419 131 480 136 513C145 568 163 603 191 618C213 630 232 636 249 636C314 636 350 583 361 524Z"/></g></g></g></svg><mjx-break size="3"> </mjx-break><svg style="vertical-align: -0.566ex;" 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 data-mml-node="mo" data-latex="-"><path data-c="2212" d="M698 270L80 270C64 270 56 263 56 250C56 237 64 230 80 230L698 230C714 230 722 237 722 250C722 262 710 270 698 270Z"/></g><g data-mml-node="msup" data-latex="180^。" transform="translate(1000.2,0)"><g data-mml-node="mn" data-latex="180"><path data-c="31" d="M269 666C228 624 168 603 89 603L89 564C141 564 184 572 217 588L217 82C217 64 213 52 204 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"/><path data-c="38" d="M250 666C201 666 158 650 122 618C86 586 68 546 68 497C68 456 83 419 113 386C120 378 142 361 179 335C88 288 42 227 42 153C42 100 64 57 107 24C147-7 194-22 249-22C305-22 354-4 395 32C436 68 457 115 457 170C457 216 441 257 408 294C396 307 365 330 316 361C393 402 431 454 431 515C431 606 344 666 250 666M379 515C379 463 348 418 286 381L167 459C136 479 120 505 120 536C120 596 185 633 249 633C318 633 379 584 379 515M250 14C168 14 99 73 99 153C99 220 136 274 210 315L328 240C376 209 400 174 400 134C400 62 325 14 250 14Z" transform="translate(500,0)"/><path data-c="30" d="M249-22C390-22 460 92 460 320C460 473 428 575 365 625C330 652 291 666 250 666C109 666 39 551 39 320C39 136 88-22 249-22M361 524C368 489 371 425 371 332C371 240 367 172 360 128C347 48 310 8 249 8C226 8 203 17 182 34C155 57 139 104 132 176C129 201 128 253 128 332C128 419 131 480 136 513C145 568 163 603 191 618C213 630 232 636 249 636C314 636 350 583 361 524Z" transform="translate(1000,0)"/></g><g data-mml-node="mo" transform="translate(1533,393.1) scale(0.707)" data-latex="。"><text data-variant="normal" transform="scale(1,-1)" font-size="884px" font-family="serif">。</text></g></g></g></g></svg></mjx-container>或<mjx-container class="MathJax" jax="SVG" overflow="overflow"><svg style="vertical-align: -0.566ex;" 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 320C460 473 428 575 365 625C330 652 291 666 250 666C109 666 39 551 39 320C39 136 88-22 249-22M361 524C368 489 371 425 371 332C371 240 367 172 360 128C347 48 310 8 249 8C226 8 203 17 182 34C155 57 139 104 132 176C129 201 128 253 128 332C128 419 131 480 136 513C145 568 163 603 191 618C213 630 232 636 249 636C314 636 350 583 361 524Z"/></g></g></g></svg><mjx-break size="3"> </mjx-break><svg style="vertical-align: -0.566ex;" 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 270L80 270C64 270 56 263 56 250C56 237 64 230 80 230L698 230C714 230 722 237 722 250C722 262 710 270 698 270Z"/></g><g data-mml-node="msup" data-latex="360^。" transform="translate(1000.2,0)"><g data-mml-node="mn" data-latex="360"><path data-c="33" d="M303 353C369 378 431 441 431 526C431 569 410 604 369 631C333 654 292 666 246 666C201 666 162 654 127 631C88 605 68 571 68 528C68 495 90 472 122 472C154 472 176 495 176 527C176 560 157 578 119 580C145 615 186 633 242 633C302 633 332 598 332 527C332 485 324 450 309 421C282 373 245 364 183 364C171 362 165 357 165 348C165 333 172 333 192 333L235 333C310 333 348 280 348 173C348 88 317 14 241 14C176 14 128 36 99 80C134 79 160 105 160 139C160 173 135 198 101 198C62 198 42 178 42 137C42 88 64 49 108 18C147-9 193-22 244-22C301-22 350-3 393 34C436 71 457 117 457 173C457 267 383 332 303 353Z"/><path data-c="36" d="M383 504C416 504 432 521 432 555C432 627 378 666 304 666C221 666 155 627 106 548C63 480 42 403 42 316C42 189 65 100 112 47C152 1 198-22 251-22C312-22 362 1 401 47C438 91 457 144 457 205C457 266 439 318 403 361C365 407 316 431 257 431C205 431 165 402 138 346L138 352C138 465 166 561 226 605C252 624 279 633 306 633C342 633 368 623 385 602C351 602 334 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font-family="serif">。</text></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" data-mjx-viewbox="0 -1719.5 15231.7 2939"><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 680L223 683C208 684 200 676 200 659C200 652 203 647 209 646C218 645 226 644 231 644C262 643 279 641 284 640C289 639 292 636 292 631C292 629 291 623 288 613L156 82C150 60 140 47 125 42C119 40 101 39 70 39C49 39 39 31 39 15C39 5 49 0 70 0L527 0C552 0 554 0 561 19L639 233C642 240 643 245 643 248C643 258 638 263 627 263C617 263 612 254 607 240C588 191 570 154 555 131C518 75 455 39 363 39L270 39C259 39 252 39 249 40C242 40 239 42 239 45C239 47 241 54 244 67L377 601C383 624 396 637 415 642C421 643 442 644 478 644C506 644 520 644 520 667Z"/></g><g data-mml-node="mn" data-latex="2" transform="translate(681,0)"><path data-c="32" d="M237 666C186 666 143 648 106 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"/></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 431C109 431 86 405 86 375C86 345 109 319 139 319C169 319 192 345 192 375M192 56C192 86 169 112 139 112C109 112 86 86 86 56C86 26 109 0 139 0C169 0 192 26 192 56Z"/></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 350C410 330 418 307 418 281C418 252 404 203 375 134C354 86 306 18 247 18C201 18 178 45 178 100C178 139 197 208 235 307C243 328 247 345 247 357C247 407 213 442 163 442C119 442 84 417 59 367C39 326 29 300 29 287C29 278 34 273 45 273C58 273 60 279 64 293C87 373 119 413 160 413C173 413 180 404 180 385C180 369 175 347 164 318C127 219 108 152 108 115C108 64 125 29 159 10C186-4 214-11 243-11C332-11 394 85 420 162C452 256 468 325 468 369C468 418 452 442 421 442C396 442 369 416 369 391Z"/></g><g data-mml-node="mo" data-latex="=" transform="translate(4777.3,0)"><path data-c="3D" d="M698 367L80 367C64 367 56 359 56 344C56 329 64 321 80 321L698 321C714 321 722 329 722 344C722 356 711 367 698 367M698 179L80 179C64 179 56 171 56 156C56 141 64 133 80 133L698 133C714 133 722 141 722 156C722 169 711 179 698 179Z"/></g><g data-mml-node="mfrac" data-latex="\frac{v}{\sqrt{\|v\|^2_2+\epsilon^2} }" transform="translate(5833.1,0)"><g data-mml-node="mi" data-latex="v" transform="translate(2378.8,676)"><path data-c="1D463" d="M369 391C369 383 378 370 394 350C410 330 418 307 418 281C418 252 404 203 375 134C354 86 306 18 247 18C201 18 178 45 178 100C178 139 197 208 235 307C243 328 247 345 247 357C247 407 213 442 163 442C119 442 84 417 59 367C39 326 29 300 29 287C29 278 34 273 45 273C58 273 60 279 64 293C87 373 119 413 160 413C173 413 180 404 180 385C180 369 175 347 164 318C127 219 108 152 108 115C108 64 125 29 159 10C186-4 214-11 243-11C332-11 394 85 420 162C452 256 468 325 468 369C468 418 452 442 421 442C396 442 369 416 369 391Z"/></g><g data-mml-node="msqrt" data-latex="\sqrt{\|v\|^2_2+\epsilon^2}" 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373 119 413 160 413C173 413 180 404 180 385C180 369 175 347 164 318C127 219 108 152 108 115C108 64 125 29 159 10C186-4 214-11 243-11C332-11 394 85 420 162C452 256 468 325 468 369C468 418 452 442 421 442C396 442 369 416 369 391Z"/></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 750C249 750 241 742 241 726L241-226C241-242 249-250 264-250M134-250C149-250 157-242 157-226L157 726C157 742 149 750 134 750C119 750 111 742 111 726L111-226C111-242 119-250 134-250Z"/></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 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 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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 22C352 31 358 38 358 43C358 55 353 61 344 61L330 54C293 30 260 18 230 18C163 18 128 72 128 142C128 168 131 195 138 222L296 222C321 222 333 229 333 242C333 254 322 260 301 260L148 260C175 349 229 393 310 393L340 393C364 393 376 400 376 413C376 425 365 431 343 431L309 431C238 431 176 407 124 358C72 309 47 250 47 179C47 71 120-11 228-11Z"/></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 612C69 576 50 534 50 483C50 449 75 424 106 424C136 424 161 450 161 480C161 513 137 536 105 536C102 536 100 536 98 535C117 584 161 627 224 627C306 627 352 556 352 470C352 403 318 331 250 255L62 43C49 28 50 29 50 0L421 0L450 180L417 180C409 129 402 100 396 91C391 86 361 84 306 84L139 84L236 179C304 243 390 312 419 365C439 400 449 435 449 470C449 588 357 666 237 666Z"/></g></g></g><rect width="3782.6" height="60" x="1020" y="1171.6"/></g><rect width="5002.6" height="60" x="120" y="220"/></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"/><g data-idbox="true" transform="translate(0,-748)"><g data-mml-node="mtext" data-latex="\text{(}"><path data-c="28" d="M318-248C327-248 332-243 332-234C332-231 330-227 327-223C275-183 233-117 202-26C175 53 161 131 161 208L161 292C161 369 175 447 202 526C233 617 275 683 327 723C330 726 332 730 332 734C332 743 327 748 318 748C317 748 314 747 311 745C251 699 201 631 160 540C121 453 101 371 101 292L101 208C101 129 121 47 160-40C201-131 251-199 311-245C314-247 317-248 318-248Z"/></g><g data-mml-node="mtext" data-latex="\text{4}" transform="translate(389,0)"><path data-c="34" d="M353 677C344 677 336 672 330 663L28 199L28 163L289 163L289 81C289 63 285 51 278 46C271 41 252 39 219 39L194 39L194 0C223 2 269 3 331 3C393 3 439 2 468 0L468 39L443 39C410 39 391 41 384 46C377 51 373 63 373 81L373 163L471 163L471 202L373 202L373 660C373 670 366 677 353 677M295 553L295 202L67 202Z"/></g><g data-mml-node="mtext" data-latex="\text{)}" transform="translate(889,0)"><path data-c="29" d="M78-245C138-199 188-131 229-40C268 47 288 129 288 208L288 292C288 371 268 453 229 540C188 631 138 699 78 745C75 747 72 748 71 748C62 748 57 743 57 734C57 730 59 726 62 723C114 683 156 617 187 526C214 447 228 369 228 292L228 208C228 131 214 53 187-26C156-117 114-183 62-223C59-227 57-231 57-234C57-243 62-248 71-248C72-248 75-247 78-245Z"/></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" data-mjx-viewbox="0 -1289 13775.1 2078"><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 680L223 683C208 684 200 676 200 659C200 652 203 647 209 646C218 645 226 644 231 644C262 643 279 641 284 640C289 639 292 636 292 631C292 629 291 623 288 613L156 82C150 60 140 47 125 42C119 40 101 39 70 39C49 39 39 31 39 15C39 5 49 0 70 0L527 0C552 0 554 0 561 19L639 233C642 240 643 245 643 248C643 258 638 263 627 263C617 263 612 254 607 240C588 191 570 154 555 131C518 75 455 39 363 39L270 39C259 39 252 39 249 40C242 40 239 42 239 45C239 47 241 54 244 67L377 601C383 624 396 637 415 642C421 643 442 644 478 644C506 644 520 644 520 667Z"/></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 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"/></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 431C109 431 86 405 86 375C86 345 109 319 139 319C169 319 192 345 192 375M192 56C192 86 169 112 139 112C109 112 86 86 86 56C86 26 109 0 139 0C169 0 192 26 192 56Z"/></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 350C410 330 418 307 418 281C418 252 404 203 375 134C354 86 306 18 247 18C201 18 178 45 178 100C178 139 197 208 235 307C243 328 247 345 247 357C247 407 213 442 163 442C119 442 84 417 59 367C39 326 29 300 29 287C29 278 34 273 45 273C58 273 60 279 64 293C87 373 119 413 160 413C173 413 180 404 180 385C180 369 175 347 164 318C127 219 108 152 108 115C108 64 125 29 159 10C186-4 214-11 243-11C332-11 394 85 420 162C452 256 468 325 468 369C468 418 452 442 421 442C396 442 369 416 369 391Z"/></g><g data-mml-node="mo" data-latex="=" transform="translate(4777.3,0)"><path data-c="3D" d="M698 367L80 367C64 367 56 359 56 344C56 329 64 321 80 321L698 321C714 321 722 329 722 344C722 356 711 367 698 367M698 179L80 179C64 179 56 171 56 156C56 141 64 133 80 133L698 133C714 133 722 141 722 156C722 169 711 179 698 179Z"/></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 350C410 330 418 307 418 281C418 252 404 203 375 134C354 86 306 18 247 18C201 18 178 45 178 100C178 139 197 208 235 307C243 328 247 345 247 357C247 407 213 442 163 442C119 442 84 417 59 367C39 326 29 300 29 287C29 278 34 273 45 273C58 273 60 279 64 293C87 373 119 413 160 413C173 413 180 404 180 385C180 369 175 347 164 318C127 219 108 152 108 115C108 64 125 29 159 10C186-4 214-11 243-11C332-11 394 85 420 162C452 256 468 325 468 369C468 418 452 442 421 442C396 442 369 416 369 391Z"/></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 750C249 750 241 742 241 726L241-226C241-242 249-250 264-250M134-250C149-250 157-242 157-226L157 726C157 742 149 750 134 750C119 750 111 742 111 726L111-226C111-242 119-250 134-250Z"/></g><g data-mml-node="mi" data-latex="v" transform="translate(398,0)"><path data-c="1D463" d="M369 391C369 383 378 370 394 350C410 330 418 307 418 281C418 252 404 203 375 134C354 86 306 18 247 18C201 18 178 45 178 100C178 139 197 208 235 307C243 328 247 345 247 357C247 407 213 442 163 442C119 442 84 417 59 367C39 326 29 300 29 287C29 278 34 273 45 273C58 273 60 279 64 293C87 373 119 413 160 413C173 413 180 404 180 385C180 369 175 347 164 318C127 219 108 152 108 115C108 64 125 29 159 10C186-4 214-11 243-11C332-11 394 85 420 162C452 256 468 325 468 369C468 418 452 442 421 442C396 442 369 416 369 391Z"/></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 750C249 750 241 742 241 726L241-226C241-242 249-250 264-250M134-250C149-250 157-242 157-226L157 726C157 742 149 750 134 750C119 750 111 742 111 726L111-226C111-242 119-250 134-250Z"/></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 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"/></g></g><g data-mml-node="mo" data-latex="+" transform="translate(1939.8,0)"><path data-c="2B" d="M698 274L413 274L413 559C413 575 405 583 389 583C373 583 365 575 365 559L365 274L80 274C64 274 56 266 56 250C56 234 64 226 80 226L365 226L365-59C365-75 373-83 389-83C405-83 413-75 413-59L413 226L698 226C714 226 722 234 722 250C722 263 711 274 698 274Z"/></g><g data-mml-node="mi" data-latex="\epsilon" transform="translate(2940,0)"><path data-c="1D716" d="M228-11C268-11 305 0 339 22C352 31 358 38 358 43C358 55 353 61 344 61L330 54C293 30 260 18 230 18C163 18 128 72 128 142C128 168 131 195 138 222L296 222C321 222 333 229 333 242C333 254 322 260 301 260L148 260C175 349 229 393 310 393L340 393C364 393 376 400 376 413C376 425 365 431 343 431L309 431C238 431 176 407 124 358C72 309 47 250 47 179C47 71 120-11 228-11Z"/></g></g><rect width="3546" height="60" x="120" y="220"/></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"/><g data-idbox="true" transform="translate(0,-748)"><g data-mml-node="mtext" data-latex="\text{(}"><path data-c="28" d="M318-248C327-248 332-243 332-234C332-231 330-227 327-223C275-183 233-117 202-26C175 53 161 131 161 208L161 292C161 369 175 447 202 526C233 617 275 683 327 723C330 726 332 730 332 734C332 743 327 748 318 748C317 748 314 747 311 745C251 699 201 631 160 540C121 453 101 371 101 292L101 208C101 129 121 47 160-40C201-131 251-199 311-245C314-247 317-248 318-248Z"/></g><g data-mml-node="mtext" data-latex="\text{5}" transform="translate(389,0)"><path data-c="35" d="M118 315C123 315 129 319 134 326C164 371 205 393 257 393C292 393 319 373 337 332C348 305 354 264 354 209C354 146 346 102 331 76C306 35 272 14 229 14C162 14 109 62 91 114C94 113 96 114 100 114C130 114 155 137 155 167C155 198 130 219 100 219C65 219 50 200 50 163C50 63 131-22 231-22C292-22 344 0 386 44C428 88 449 141 449 202C449 260 432 310 398 353C361 400 315 423 259 423C212 423 171 408 138 378L138 556C165 548 191 544 218 544C264 544 304 555 338 578C369 597 390 616 402 634C408 642 411 648 411 651C411 661 406 666 396 666C341 645 294 634 256 634C211 634 168 643 127 662C122 664 118 665 114 665C105 665 100 656 100 637L100 345C100 324 100 315 118 315Z"/></g><g data-mml-node="mtext" data-latex="\text{)}" transform="translate(889,0)"><path data-c="29" d="M78-245C138-199 188-131 229-40C268 47 288 129 288 208L288 292C288 371 268 453 229 540C188 631 138 699 78 745C75 747 72 748 71 748C62 748 57 743 57 734C57 730 59 726 62 723C114 683 156 617 187 526C214 447 228 369 228 292L228 208C228 131 214 53 187-26C156-117 114-183 62-223C59-227 57-231 57-234C57-243 62-248 71-248C72-248 75-247 78-245Z"/></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" data-mjx-viewbox="0 -1480.5 17795.1 2461"><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 680L223 683C208 684 200 676 200 659C200 652 203 647 209 646C218 645 226 644 231 644C262 643 279 641 284 640C289 639 292 636 292 631C292 629 291 623 288 613L156 82C150 60 140 47 125 42C119 40 101 39 70 39C49 39 39 31 39 15C39 5 49 0 70 0L527 0C552 0 554 0 561 19L639 233C642 240 643 245 643 248C643 258 638 263 627 263C617 263 612 254 607 240C588 191 570 154 555 131C518 75 455 39 363 39L270 39C259 39 252 39 249 40C242 40 239 42 239 45C239 47 241 54 244 67L377 601C383 624 396 637 415 642C421 643 442 644 478 644C506 644 520 644 520 667Z"/></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 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"/></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 431C109 431 86 405 86 375C86 345 109 319 139 319C169 319 192 345 192 375M192 56C192 86 169 112 139 112C109 112 86 86 86 56C86 26 109 0 139 0C169 0 192 26 192 56Z"/></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 350C410 330 418 307 418 281C418 252 404 203 375 134C354 86 306 18 247 18C201 18 178 45 178 100C178 139 197 208 235 307C243 328 247 345 247 357C247 407 213 442 163 442C119 442 84 417 59 367C39 326 29 300 29 287C29 278 34 273 45 273C58 273 60 279 64 293C87 373 119 413 160 413C173 413 180 404 180 385C180 369 175 347 164 318C127 219 108 152 108 115C108 64 125 29 159 10C186-4 214-11 243-11C332-11 394 85 420 162C452 256 468 325 468 369C468 418 452 442 421 442C396 442 369 416 369 391Z"/></g><g data-mml-node="mo" data-latex="=" transform="translate(7777.3,0)"><path data-c="3D" d="M698 367L80 367C64 367 56 359 56 344C56 329 64 321 80 321L698 321C714 321 722 329 722 344C722 356 711 367 698 367M698 179L80 179C64 179 56 171 56 156C56 141 64 133 80 133L698 133C714 133 722 141 722 156C722 169 711 179 698 179Z"/></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="M467-733L254 260L119 47C114 40 111 36 111 33C111 29 117 22 130 11L194 113L422-950C461-950 464-951 471-921L1016 1404C1019 1416 1020 1423 1020 1426C1020 1442 1012 1450 996 1450C984 1450 976 1440 971 1420Z"/></g><g transform="translate(1020,0)"><g data-mml-node="mfrac" data-latex="\frac{v}{\|v\|_1+\epsilon}"><g data-mml-node="mi" data-latex="v" transform="translate(1650.5,676)"><path data-c="1D463" d="M369 391C369 383 378 370 394 350C410 330 418 307 418 281C418 252 404 203 375 134C354 86 306 18 247 18C201 18 178 45 178 100C178 139 197 208 235 307C243 328 247 345 247 357C247 407 213 442 163 442C119 442 84 417 59 367C39 326 29 300 29 287C29 278 34 273 45 273C58 273 60 279 64 293C87 373 119 413 160 413C173 413 180 404 180 385C180 369 175 347 164 318C127 219 108 152 108 115C108 64 125 29 159 10C186-4 214-11 243-11C332-11 394 85 420 162C452 256 468 325 468 369C468 418 452 442 421 442C396 442 369 416 369 391Z"/></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 750C249 750 241 742 241 726L241-226C241-242 249-250 264-250M134-250C149-250 157-242 157-226L157 726C157 742 149 750 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750 111 742 111 726L111-226C111-242 119-250 134-250Z"/></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 47C195 42 170 39 130 39L95 39L95 0C120 2 174 3 257 3C340 3 394 2 419 0L419 39L384 39C343 39 318 42 310 47C302 52 297 64 297 82L297 636C297 660 295 666 269 666Z"/></g></g><g data-mml-node="mo" data-latex="+" transform="translate(1939.8,0)"><path data-c="2B" d="M698 274L413 274L413 559C413 575 405 583 389 583C373 583 365 575 365 559L365 274L80 274C64 274 56 266 56 250C56 234 64 226 80 226L365 226L365-59C365-75 373-83 389-83C405-83 413-75 413-59L413 226L698 226C714 226 722 234 722 250C722 263 711 274 698 274Z"/></g><g data-mml-node="mi" data-latex="\epsilon" transform="translate(2940,0)"><path data-c="1D716" d="M228-11C268-11 305 0 339 22C352 31 358 38 358 43C358 55 353 61 344 61L330 54C293 30 260 18 230 18C163 18 128 72 128 142C128 168 131 195 138 222L296 222C321 222 333 229 333 242C333 254 322 260 301 260L148 260C175 349 229 393 310 393L340 393C364 393 376 400 376 413C376 425 365 431 343 431L309 431C238 431 176 407 124 358C72 309 47 250 47 179C47 71 120-11 228-11Z"/></g></g><rect width="3546" height="60" x="120" y="220"/></g></g><rect width="3786" height="60" x="1020" y="1334.7"/></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"/><g data-idbox="true" transform="translate(0,-748)"><g data-mml-node="mtext" data-latex="\text{(}"><path data-c="28" d="M318-248C327-248 332-243 332-234C332-231 330-227 327-223C275-183 233-117 202-26C175 53 161 131 161 208L161 292C161 369 175 447 202 526C233 617 275 683 327 723C330 726 332 730 332 734C332 743 327 748 318 748C317 748 314 747 311 745C251 699 201 631 160 540C121 453 101 371 101 292L101 208C101 129 121 47 160-40C201-131 251-199 311-245C314-247 317-248 318-248Z"/></g><g data-mml-node="mtext" data-latex="\text{6}" transform="translate(389,0)"><path data-c="36" d="M383 504C416 504 432 521 432 555C432 627 378 666 304 666C221 666 155 627 106 548C63 480 42 403 42 316C42 189 65 100 112 47C152 1 198-22 251-22C312-22 362 1 401 47C438 91 457 144 457 205C457 266 439 318 403 361C365 407 316 431 257 431C205 431 165 402 138 346L138 352C138 465 166 561 226 605C252 624 279 633 306 633C342 633 368 623 385 602C351 602 334 583 334 553C334 525 355 504 383 504M344 340C355 317 361 272 361 206C361 141 356 98 345 76C325 35 294 14 251 14C222 14 200 24 184 44C171 60 162 74 158 85C146 116 140 163 140 227C140 255 144 282 151 308C164 355 201 399 256 399C295 399 325 379 344 340Z"/></g><g data-mml-node="mtext" data-latex="\text{)}" transform="translate(889,0)"><path data-c="29" d="M78-245C138-199 188-131 229-40C268 47 288 129 288 208L288 292C288 371 268 453 229 540C188 631 138 699 78 745C75 747 72 748 71 748C62 748 57 743 57 734C57 730 59 726 62 723C114 683 156 617 187 526C214 447 228 369 228 292L228 208C228 131 214 53 187-26C156-117 114-183 62-223C59-227 57-231 57-234C57-243 62-248 71-248C72-248 75-247 78-245Z"/></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: -0.025ex;" 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 431L300 431C252 431 207 416 166 385C102 336 38 250 38 148C38 58 100-11 190-11C257-11 317 18 368 76C417 132 441 194 441 263C441 304 432 338 414 366L515 366C550 366 567 378 567 403C567 426 550 431 525 431M107 121C107 180 121 234 150 282C184 338 228 366 283 366C341 366 370 336 370 275C370 250 365 221 355 187C335 116 302 66 256 39C233 25 211 18 191 18C136 18 107 63 107 121Z"/></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: -0.566ex;" 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 314C485 314 508 345 508 379C508 418 476 445 437 445C392 445 344 415 291 356C250 311 217 282 190 269L291 679C289 688 287 694 274 694C242 694 166 685 154 684C139 682 132 675 132 660C132 650 141 645 159 645C178 645 204 646 204 632L59 43C56 32 55 25 55 21C55 0 66-11 87-11C104-11 117-3 124 12C129 21 147 92 179 226C231 221 286 196 286 146C286 131 279 101 279 91C279 34 316-11 373-11C431-11 470 41 490 145C490 154 485 159 475 159C466 159 460 152 457 138C435 59 408 19 375 19C357 19 348 33 348 61C348 77 360 131 360 147C360 204 314 239 221 253C244 269 270 292 298 322C326 352 346 371 359 382C386 404 412 415 435 415C445 415 453 413 459 409C432 404 409 379 409 353Z"/></g></g></g></svg><mjx-break size="3"> </mjx-break><svg style="vertical-align: -0.566ex;" 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 250L623 451C628 456 630 461 630 468C630 481 620 491 607 491C600 491 595 489 590 484L389 283L188 484C183 489 178 491 171 491C158 491 148 481 148 468C148 461 150 456 155 451L356 250L155 49C150 44 148 39 148 32C148 19 158 9 171 9C178 9 183 11 188 16L389 217L590 16C595 11 600 9 607 9C620 9 630 19 630 32Z"/></g><g data-mml-node="mi" data-latex="\sigma" transform="translate(1000.2,0)"><path data-c="1D70E" d="M525 431L300 431C252 431 207 416 166 385C102 336 38 250 38 148C38 58 100-11 190-11C257-11 317 18 368 76C417 132 441 194 441 263C441 304 432 338 414 366L515 366C550 366 567 378 567 403C567 426 550 431 525 431M107 121C107 180 121 234 150 282C184 338 228 366 283 366C341 366 370 336 370 275C370 250 365 221 355 187C335 116 302 66 256 39C233 25 211 18 191 18C136 18 107 63 107 121Z"/></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, 2019</div></div><div class="license-meta-item"><div class="license-meta-title">更新于</div><div class="license-meta-text">Nov 20, 2025</div></div><div 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aria-hidden="true"></i><p>机器视觉</p></a></div> <span hidden itemprop="keywords">机器视觉</span><div class="new-meta-item date" itemprop="dateCreated datePublished" datetime="2019-09-12T11:19:00+08:00"><a class="notlink"><i class="fa-duotone fa-calendar-alt fa-fw" aria-hidden="true"></i><p>发布于：Sep 12, 2019</p></a></div><div class="new-meta-item date" itemprop="dateModified" datetime="2025-11-20T18:18:00+08:00"><a class="notlink"><i class="fa-duotone fa-edit fa-fw" aria-hidden="true"></i><p>更新于：Nov 20, 2025</p></a></div></div></div><div class="prev-next"><a class="prev" href="/p/notes-zookeeper/"><p class="title"><i class="fa-solid fa-chevron-left" aria-hidden="true"></i>Zookeeper 系列专题</p><p 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 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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="widget pjax"></div><div class="widget pjax"></div><div class="widget pjax"></div><div class="widget pjax"></div><div class="widget pjax"></div><div class="widget pjax"></div><div class="widget pjax"></div><div 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