{"id":54,"date":"2024-10-27T10:56:22","date_gmt":"2024-10-27T02:56:22","guid":{"rendered":"https:\/\/aimc.skyate.com\/?p=54"},"modified":"2024-10-27T13:20:19","modified_gmt":"2024-10-27T05:20:19","slug":"%e5%9f%ba%e4%ba%8eopencv%e7%9a%84%e7%9b%b8%e6%9c%ba%e6%a0%87%e5%ae%9a","status":"publish","type":"post","link":"https:\/\/aimc.skyate.com\/index.php\/2024\/10\/27\/%e5%9f%ba%e4%ba%8eopencv%e7%9a%84%e7%9b%b8%e6%9c%ba%e6%a0%87%e5%ae%9a\/","title":{"rendered":"\u57fa\u4e8eopencv\u7684\u76f8\u673a\u6807\u5b9a"},"content":{"rendered":"\n

0 \u53c2\u8003\u6587\u732e<\/h1>\n\n\n\n

[1] c++opencv\u76f8\u673a\u6807\u5b9a\uff08calibrateCamera\uff09\u8be6\u89e3<\/a><\/p>\n\n\n\n

[2] Python OpenCV \u76f8\u673a\u6807\u5b9a\u4e0e\u9e1f\u77b0\u56fe\u8f6c\u6362<\/a><\/p>\n\n\n\n

1 \u57fa\u672c\u539f\u7406<\/h1>\n\n\n\n

\u76f8\u673a\u6210\u50cf\u7684\u8fc7\u7a0b\u5373\u771f\u5b9e\u4e09\u7ef4\u4e16\u754c\u5728\u76f8\u673a\u4f20\u611f\u5668\u5e73\u9762\u7684\u6295\u5f71\u8fc7\u7a0b\u3002\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e2a\u6570\u5b66\u6a21\u578b\u5c06\u771f\u5b9e\u7269\u4f53\u7684\u4e09\u7ef4\u5750\u6807\u4e0e\u56fe\u50cf\u4e2d\u7684\u4e8c\u7ef4\u5750\u6807\u4e00\u4e00\u5bf9\u5e94\uff0c\u8fd9\u4e2a\u6570\u5b66\u6a21\u578b\uff08\u76f8\u673a\u77e9\u9635\uff09\u7684\u6c42\u53d6\u8ba1\u7b97\u8fc7\u7a0b\u5c31\u662f\u76f8\u673a\u6807\u5b9a\u3002\u5982\u56fe1\u6240\u793a \"a06161da4dfd61fe0d629d71d6e7fa56.png\" \u56fe1 \u76f8\u673a\u77e9\u9635<\/p>\n\n\n\n

\u4ece\u4e09\u7ef4\u5750\u6807\uff08\u4e16\u754c\u5750\u6807\u7cfb\uff09\u5230\u4e8c\u7ef4\u5750\u6807\uff08\u56fe\u50cf\u5750\u6807\u7cfb\uff09\u53c8\u53ef\u4ee5\u5206\u4e3a\u4e09\u4e2a\u6b65\u9aa4\uff1a<\/p>\n\n\n\n

\uff081\uff09\u4ece\u4e16\u754c\u5750\u6807\u8f6c\u6362\u5230\u76f8\u673a\u5750\u6807\uff1b \uff082\uff09\u4ece\u76f8\u673a\u5750\u6807\u8f6c\u6362\u5230\u56fe\u50cf\u5750\u6807\uff1b \uff083\uff09\u4ece\u56fe\u50cf\u5750\u6807\u8f6c\u6362\u5230\u50cf\u7d20\u5750\u6807\u3002 \"d20a7ca3429ccc43737c3e6283e44607.png\" \u56fe2 \u4e16\u754c\u5750\u6807\u3001\u76f8\u673a\u5750\u6807\u3001\u56fe\u50cf\u5750\u6807\u3001\u50cf\u7d20\u5750\u6807<\/p>\n\n\n\n

\u5982\u56fe2\u6240\u793a\uff1a \uff081\uff09\u5750\u6807\u7cfb\uff08Xw, Yw, Zw\uff09\u4e3a\u4e16\u754c\u5750\u6807\u7cfb\uff1b \uff082\uff09\u5750\u6807\u7cfb\uff08Xc, Yc, Zc\uff09\u4e3a\u76f8\u673a\u5750\u6807\u7cfb\uff1b \uff083\uff09\u5750\u6807\u7cfb\uff08x, y\uff09\u4e3a\u56fe\u50cf\u5750\u6807\u7cfb\uff1b \uff084\uff09\u5750\u6807\u7cfb\uff08u, v\uff09\u4e3a\u50cf\u7d20\u5750\u6807\u7cfb\uff1b<\/p>\n\n\n\n

1.1 \u4ece\u4e16\u754c\u5750\u6807\u7cfb\u5230\u76f8\u673a\u5750\u6807\u7cfb<\/h2>\n\n\n\n

\u5982\u56fe2\u6240\u793a\uff0c\u70b9P\u4ece\u4e16\u754c\u5750\u6807\uff08Xpw, Ypw, Zpw\uff09\u5230\u76f8\u673a\u5750\u6807\uff08Xpc, Ypc, Zpc\uff09\u7684\u53d8\u6362\u5305\u542b\u4e86\u4e00\u4e2a\u4e09\u7ef4\u7684\u65cb\u8f6c\u53d8\u6362R\u4ee5\u53ca\u4e00\u4e2a\u5e73\u79fb\u53d8\u6362t\uff0c\u9f50\u6b21\u8868\u8fbe\u5f0f\u4e3a\uff1a \"ae3a9a0b46d15d3b0f0ce3613a79d843.png\"<\/p>\n\n\n\n

\u5176\u4e2dR\u4e3a3\u00d73\u5927\u5c0f\u7684\u65cb\u8f6c\u77e9\u9635\uff0ct\u4e3a3\u00d71\u7684\u5e73\u79fb\u77e9\u9635\uff0c\u53d8\u6362\u77e9\u9635P\u4e3a3\u00d74\u5927\u5c0f\u7684\u77e9\u9635\uff1a \"b6d7a9c199b48c300ce3dab1609aac5f.png\"<\/p>\n\n\n\n

1.2 \u4ece\u76f8\u673a\u5750\u6807\u5230\u56fe\u50cf\u5750\u6807<\/h2>\n\n\n\n

\"86c6872a14250dcf2eaf162dcd820535.png\" \u56fe3 \u5c0f\u5b54\u6210\u50cf\u6a21\u578b<\/p>\n\n\n\n

\u5982\u56fe3\u6240\u793a\u4e3a\u5c0f\u5b54\u6210\u50cf\u6a21\u578b\uff0c\u5219\u6709P\u7684\u76f8\u673a\u5750\u6807\uff08Xpc, Ypc, Zpc\uff09\u5230\u56fe\u50cf\u5750\u6807\uff08xp, yp\uff09\u6709\uff1a \"9e8e676705ebad67f72a5b5ebf96b7ce.png\" \u8f6c\u6362\u4e3a\u77e9\u9635\u4e3a\uff1a \"5215b1eea5c8278f9ed7d2a198202f5a.png\" fx, fy\u5206\u522b\u4e3ax, y\u65b9\u5411\u4e0a\u7684\u7126\u8ddd\u3002<\/p>\n\n\n\n

1.3 \u4ece\u56fe\u50cf\u5750\u6807\u8f6c\u6362\u5230\u50cf\u7d20\u5750\u6807<\/h2>\n\n\n\n

\u5982\u56fe2\u6240\u793a\uff0c\u56fe\u50cf\u5750\u6807\u7cfb\u5e73\u9762\u53ef\u4ee5\u8ba4\u4e3a\u662f\u7406\u60f3\u7684\u6210\u50cf\u9762\uff0c\u50cf\u7d20\u5750\u6807\u7cfb\u5219\u662f\u76f8\u673a\u4f20\u611f\u5668\u5e73\u9762\uff0c\u7406\u60f3\u60c5\u51b5\u4e0b\u56fe\u50cf\u5750\u6807\u5e73\u9762\u548c\u50cf\u7d20\u5750\u6807\u5e73\u9762\u5728\u540c\u4e00\u5e73\u9762<\/strong>\uff0c\u5219\u4ece\u56fe\u50cf\u5750\u6807\u8f6c\u6362\u5230\u50cf\u7d20\u5750\u6807\u6709\u4e24\u4e2a\u6b65\u9aa4\uff1a<\/p>\n\n\n\n

\uff081\uff09\u7f29\u653e\uff0c\u5728\u524d\u9762\u7684\u5750\u6807\u7cfb\u4e2d\uff0c\u5750\u6807\u7cfb\u5355\u4f4d\u662f\u7edf\u4e00\u7684\u5b9e\u9645\u8ddd\u79bb\u5355\u4f4d\uff0c\u4f46\u662f\u50cf\u7d20\u5750\u6807\u7cfb\u7684\u5355\u4f4d\u4e0d\u4e00\u6837\uff0c\u56e0\u6b64\u8981\u7f29\u653e\uff0c\u6362\u7b97\u5230\u50cf\u7d20\u5750\u6807\u7cfb\uff1b<\/p>\n\n\n\n

\uff082\uff09\u5e73\u79fb\uff0c\u4ece\u56fe\u50cf\u5750\u6807\u7cfb\u539f\u70b9\u5230\u50cf\u7d20\u5750\u6807\u7cfb\u539f\u70b9\u3002<\/p>\n\n\n\n

\u5219\u53d8\u6362\u4e3a\uff1a \"482e676a516cb16ed7c40d48c7b52cea.png\"<\/p>\n\n\n\n

\u5176\u4e2dsx\u548csy\u4e3a\u5355\u4f4d\u957f\u5ea6\u7684\u50cf\u7d20\u6570\u3002<\/p>\n\n\n\n

\u4ee5\u4e0a\u662f\u7406\u8bba\u60c5\u51b5\u4e0b\uff0c\u4f46\u662f\u5728\u5b9e\u9645\u4e2d\u53ef\u80fd\u7531\u4e8e\u76f8\u673a\u4f20\u611f\u5668\u7684\u95ee\u9898\u5bfc\u81f4\u56fe\u50cf\u8f74\u4e0d\u5782\u76f4\u7684\u60c5\u51b5\uff0c\u5982\u4e0b\u56fe4 \"049fe7eb80838854664f625af6e48706.png\" \u56fe4 \u56fe\u50cf\u8f74\u4e0d\u5782\u76f4 \u53ef\u4ee5\u8ba4\u4e3a\u5728y\u65b9\u5411\u5750\u6807\u4e0d\u53d8\uff0cx\u65b9\u5411\u5750\u6807\u5b58\u5728\u504f\u79fb\uff0c\u5219\u6709 \"52ba6ab3a2ae63843d7d48e64830aaec.png\" \u5176\u4e2dc\u4e3a\u504f\u79fb\u7cfb\u6570\u3002<\/p>\n\n\n\n

1.4 \u76f8\u673a\u5185\u53c2\u3001\u5916\u53c2<\/h2>\n\n\n\n

\u75311.1, 1.2, 1.3\u5c0f\u7ed3\uff0c\u5f97\u5230\u6700\u7ec8\u7684\u7531\u4e16\u754c\u5750\u6807\u5230\u50cf\u7d20\u5750\u6807\u8f6c\u6362\u5173\u7cfb\uff1a \"fdbc2b72783011dc1abc4d80c0064e15.png\" \u5373\uff1a \"0a15894c029fcd655cfa657e63690107.png\" \u5f97\u5230\uff1a \"9fc5a63f111be381724e75490f1d66ef.png\" 1.5 \u955c\u5934\u7578\u53d8\u7cfb\u6570 \u9664\u4e86\u76f8\u673a\u786c\u4ef6\u7684\u53c2\u6570\u5916\uff0c\u955c\u5934\u4e5f\u4e0d\u4f1a\u662f\u7406\u60f3\u4e2d\u7684\u5b8c\u7f8e\u955c\u5934\uff0c\u7531\u4e8e\u955c\u5934\u7684\u7f3a\u9677\u4e5f\u4f1a\u5bfc\u81f4\u5750\u6807\u6362\u7b97\u51fa\u73b0\u8bef\u5dee\uff0c\u56e0\u6b64\u9700\u8981\u8003\u8651\u955c\u5934\u5e26\u6765\u7684\u56fe\u50cf\u5931\u771f\u3002\u955c\u5934\u5e26\u6765\u7684\u7578\u53d8\u5305\u62ec\u5f84\u5411\u7578\u53d8\u548c\u5207\u5411\u7578\u53d8\u4e24\u79cd\u3002<\/p>\n\n\n\n

1.5.1 \u5f84\u5411\u7578\u53d8<\/h3>\n\n\n\n

\u5f53\u5149\u7ebf\u5728\u955c\u5934\u8fb9\u7f18\u9644\u8fd1\u6bd4\u5728\u5176\u5149\u5b66\u4e2d\u5fc3\u5f2f\u66f2\u5f97\u66f4\u591a\u65f6\uff0c\u5c31\u4f1a\u53d1\u751f\u5f84\u5411\u7578\u53d8\u3002\u955c\u5934\u8d8a\u5c0f\uff0c\u7578\u53d8\u8d8a\u5927\u3002\u5305\u542b\u6795\u5f62\uff08pincushion\uff09\u3001\u6876\u5f62\uff08barrel\uff09\u4e24\u79cd\uff1a \"6e573e13a61e45132f96f184bd105394.png\" \u56fe5 \u955c\u5934\u7578\u53d8<\/p>\n\n\n\n

\u5f84\u5411\u7578\u53d8\u901a\u8fc7\u5f84\u5411\u7578\u53d8\u7cfb\u6570\u6a21\u578b\u8868\u793a\u5e76\u6821\u6b63\uff1a \"4353ca14ba10b1e9920dd42fb1910ea6.png\" \u5176\u4e2d\uff1a<\/p>\n\n\n\n

x, y\u4e3a\u672a\u53d1\u751f\u7578\u53d8\u7684\u50cf\u7d20\u4f4d\u7f6e\uff1b<\/p>\n\n\n\n

k1, k2, k3\u4e3a\u5f84\u5411\u7578\u53d8\u7cfb\u6570\uff0c\u4e00\u822c\u4e24\u4e2a\u7cfb\u6570\u5c31\u8db3\u591f\u6821\u51c6\uff0c\u4f46\u662f\u5bf9\u4e8e\u5927\u7578\u53d8\u5982\u5e7f\u89d2\u955c\u5934\u5c31\u9700\u8981\u4e09\u4e2a\u7cfb\u6570\uff1b<\/p>\n\n\n\n

r^2 = x^2 + y^2.<\/p>\n\n\n\n

1.5.2 \u5207\u5411\u7578\u53d8<\/h3>\n\n\n\n

\u5f53\u955c\u5934\u548c\u50cf\u5e73\u9762\u4e0d\u5e73\u884c\u65f6\u4f1a\u53d1\u751f\u5207\u5411\u7578\u53d8\uff1a \"01aa7afee07baeafcb4e95e2b9503475.png\" \u56fe6 \u5207\u5411\u7578\u53d8 \u5207\u5411\u7578\u53d8\u901a\u8fc7\u5207\u5411\u7578\u53d8\u7cfb\u6570\u6a21\u578b\u8868\u793a\u5e76\u6821\u6b63\uff1a \"c1e44181b8aaf198d4dfca3007fb90e0.png\" x, y\u4e3a\u672a\u53d1\u751f\u7578\u53d8\u7684\u50cf\u7d20\u4f4d\u7f6e\uff1b<\/p>\n\n\n\n

k1, k2\u4e3a\u5207\u5411\u7578\u53d8\u7cfb\u6570\uff1b<\/p>\n\n\n\n

r^2 = x^2 + y^2.<\/p>\n\n\n\n

1.6 \u5c0f\u7ed3<\/h2>\n\n\n\n

\u76f8\u673a\u6807\u5b9a\u4e3b\u8981\u8ba1\u7b97\uff1a<\/p>\n\n\n\n

\uff081\uff09\u76f8\u673a\u5916\u53c2\uff1a\u4e16\u754c\u5750\u6807\u7cfb\u5230\u76f8\u673a\u5750\u6807\u7cfb\u7684\u53d8\u6362\u77e9\u9635\uff08\u4e09\u8f74\u65cb\u8f6c\u89d2\u5ea6+\u4e09\u8f74\u5e73\u79fb\u91cf\u603b\u51716\u4e2a\u53c2\u6570\uff09<\/p>\n\n\n\n

\uff082\uff09\u76f8\u673a\u5185\u53c2\uff1a\u7126\u8ddd\uff08fx, fy\uff09\uff0c\u5149\u5fc3\/\u4e3b\u70b9\uff08cx, cy\uff09\uff0c\u503e\u659c\u7cfb\u6570\uff08c\uff09\uff085\u4e2a\u53c2\u6570\uff09<\/p>\n\n\n\n

\uff083\uff09\u955c\u5934\u7578\u53d8\u7cfb\u6570\uff1a\u5f84\u5411\u7578\u53d8\u7cfb\u6570\u548c\u5207\u5411\u7578\u53d8\u7cfb\u6570\uff08k1, k2, p1, p2\uff0c4\u4e2a\u53c2\u6570\uff09<\/p>\n\n\n\n

2 \u5f20\u6b63\u53cb\u6807\u5b9a\u6cd5<\/h1>\n\n\n\n

\u300c\u5f20\u6c0f\u6807\u5b9a\u6cd5\u300d\u662f\u5f20\u6b63\u53cb\u535a\u58eb\u57281999\u5e74\u53d1\u8868\u5728\u56fd\u9645\u9876\u7ea7\u4f1a\u8baeICCV\u4e0a\u7684\u8bba\u6587\u300aFlexible Camera Calibration By Viewing a Plane From Unknown Orientations\u300b\u4e2d\uff0c\u63d0\u51fa\u7684\u4e00\u79cd\u5229\u7528\u5e73\u9762\u68cb\u76d8\u683c\u8fdb\u884c\u76f8\u673a\u6807\u5b9a\u7684\u5b9e\u7528\u65b9\u6cd5\u3002<\/p>\n\n\n\n

2.1 \u5355\u5e94\u6027\u3001\u5355\u5e94\u6027\u77e9\u9635\u3001\u9f50\u6b21\u5750\u6807<\/h2>\n\n\n\n

\u5355\u5e94\u6027\uff1a<\/strong> \u5e73\u9762\u7684\u5355\u5e94\u6027\u88ab\u5b9a\u4e49\u4e3a\u4ece\u4e00\u4e2a\u5e73\u9762\u5230\u53e6\u4e00\u4e2a\u5e73\u9762\u7684\u6295\u5f71\u6620\u5c04\uff0c\u5355\u5e94\u6027\u53d8\u6362\u6216\u6295\u5f71\u53d8\u6362\uff1b<\/p>\n\n\n\n

\u5355\u5e94\u6027\u77e9\u9635\uff1a<\/strong> \u4e24\u4e2a\u6295\u5f71\u5e73\u9762\u7684\u53d8\u6362\u77e9\u9635\uff0c\u6295\u5f71\u53d8\u6362\u77e9\u9635\uff1b<\/p>\n\n\n\n

\u9f50\u6b21\u5750\u6807\uff1a<\/strong> \u7c7b\u4f3c\u5b9a\u4e49\u4e09\u7ef4\u7a7a\u95f4\u5750\u6807\u7cfb\u7684\u7b1b\u5361\u5c14\u5750\u6807\u7cfb\uff0c\u9f50\u6b21\u5750\u6807\u7cfb\u5b9a\u4e49\u6295\u5f71\u7a7a\u95f4\uff0c\u9f50\u6b21\u5750\u6807\u4e0e\u7b1b\u5361\u5c14\u5750\u6807\u8f6c\u6362\u5173\u7cfb\u5982\u4e0b\uff1a \u4e8c\u7ef4\u5e73\u9762\uff1a \"bf94657611f76e1bddb76ecca77b14cc.png\" \u4e09\u7ef4\u7a7a\u95f4\uff1a \"97b63a7bb6d2d72ac70328d45a44fad1.png\"<\/p>\n\n\n\n

2.2 \u5f20\u6b63\u53cb\u6807\u5b9a\u6cd5\u6570\u5b66\u6a21\u578b<\/h2>\n\n\n\n

2.2.1 \u57fa\u672c\u65b9\u7a0b<\/h3>\n\n\n\n

\u5728\u4e0d\u8003\u8651\u955c\u5934\u7578\u53d8\u65f6\uff0c\u6a21\u578b\u70b9\u5230\u56fe\u50cf\u70b9\u7684\u53d8\u6362\u5173\u7cfb\u8868\u793a\u4e3a\uff1a \"c9a7d310c4e64609de637adb197fe119.png\" \u5047\u8bbe\u6a21\u578b\u5e73\u9762\u5728\u4e16\u754c\u5750\u6807\u7cfb\u7684Z = 0\uff08\u6807\u5b9a\u65f6\u5c06\u68cb\u76d8\u683c\u4f5c\u4e3a\u4e16\u754c\u5750\u6807\u7cfb\u539f\u70b9\uff0c\u5219Z=0\uff09\u4e0a\u3002\u8ba9\u6211\u4eec\u7528ri\u8868\u793a\u65cb\u8f6c\u77e9\u9635R\u7684\u7b2ci\u5217,\u5219\u7531\uff081\uff09\u6709\uff1a \"4f76379921984f3bdfcfe1061e1e5cab.png\" \u5176\u4e2d\uff1a \"cfc01cd9011534bd59d3617624777c5b.png\" H\u662f\u4e00\u4e2a3\u00d73\u7684\u7cfb\u6570\u77e9\u9635\uff08\u5355\u5e94\u6027\u77e9\u9635\uff09\uff1a \"b1e96da9661ac208add68649f3421878.png\" \u5bf9\u4e8e\u9f50\u6b21\u5750\u6807\u7cfb\u4e2d\u7684H\u6709\u6027\u8d28\uff1a<\/p>\n\n\n\n

\u8fd9\u91cc\u4f7f\u7528\u7684\u662f\u9f50\u6b21\u5750\u6807\u7cfb\uff0c\u4e5f\u5c31\u662f\u8bf4\u53ef\u4ee5\u8fdb\u884c\u4efb\u610f\u5c3a\u5ea6\u7684\u7f29\u653e\uff08s\u4e3a\u5c3a\u5ea6\u56e0\u5b50\uff09\uff0c\u4e5f\u5c31\u662f\u8bf4\u628aH\u4e58\u4ee5\u4efb\u610f\u4e00\u4e2a\u975e\u96f6\u5e38\u6570k\u5e76\u4e0d\u6539\u53d8\u4e0a\u5f0f\u7ed3\u679c\uff0c\u65e0\u975e\u5c31\u662f\u5c3a\u5ea6\u56e0\u5b50s\u6709\u6240\u6539\u53d8\u3002<\/p>\n\n\n\n

\u4f8b\u5982\u5c06H\u4e58\u4ee51\/h33\uff1a \"7479530d924c4c932c016e268a8667d7.png\" H\u2019\u4e0eH\u5e26\u5165\u516c\u5f0f\uff082\uff09\u5f97\u5230\u7684\u8ba1\u7b97\u7ed3\u679cu, v\u76f8\u7b49\u3002\u56e0\u6b64\u53ef\u4ee5\u8ba4\u4e3aH\u53ea\u67098\u4e2a\u81ea\u7531\u5ea6\u3002<\/p>\n\n\n\n

2.2.2 \u5185\u5728\u53c2\u6570\u7684\u7ea6\u675f\u6761\u4ef6<\/h3>\n\n\n\n

\u4ee4 H = [h1 h2 h3]\uff0c\u5219\u7531\u516c\u5f0f\uff083\uff09\u6709\uff1a \"78e4f26ac142ad2d715cfa05d76c98a3.png\" \u5176\u4e2dk\u4e3a\u4efb\u610f\u7684\u5c3a\u5ea6\u56e0\u5b50\u3002\u7531\u4e8e\u65cb\u8f6c\u77e9\u9635\u662f\u4e00\u4e2a\u6807\u51c6\u7684\u6b63\u4ea4\u77e9\u5f62\uff0c\u56e0\u6b64r1\u548cr2\u4e3a\u6b63\u4ea4\u7684\u5355\u4f4d\u5411\u91cf\uff0c\u6709\uff1a \"72693862e09973647038f27d444a07e3.png\" \u6709\u516c\u5f0f\uff084\uff09\u6709\uff1a \"aeeb1038c7640306089abaf187d996f7.png\" \u8fdb\u4e00\u6b65\u7531\u516c\u5f0f\uff086\uff09\u5f97\u5230\uff1a \"873b0f031aae68910c6855995f1f4861.png\" \u7ed3\u5408\u516c\u5f0f\uff085\uff09\u548c\uff087\uff09\u6709\uff1a \"a40c5d5591f00510fbd08d40317b4edd.png\" \u5f97\u5230\uff088\uff09\uff089\uff09\u4e24\u4e2a\u7ea6\u675f\u3002<\/p>\n\n\n\n

2.2.3 \u53c2\u6570\u6c42\u89e3<\/h3>\n\n\n\n

\u53c2\u6570\u6c42\u89e3\u8fc7\u7a0b\uff1a<\/p>\n\n\n\n

\uff081\uff09\u7ed9\u51fa\u4e00\u4e2a\u5c01\u95ed\u89e3<\/p>\n\n\n\n

\uff082\uff09\u6839\u636e\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\u7ed9\u51fa\u975e\u7ebf\u6027\u7684\u6700\u4f18\u5316\u89e3<\/p>\n\n\n\n

\uff083\uff09\u8003\u8651\u955c\u5934\u7684\u5f84\u5411\u7578\u53d8\uff08\u5f20\u6b63\u53cb\u6807\u5b9a\u6cd5\u4e0d\u8003\u8651\u5207\u5411\u7578\u53d8\uff09\uff0c\u7ed9\u51fa\u89e3\u6790\u89e3\u548c\u975e\u7ebf\u6027\u89e3<\/p>\n\n\n\n

2.2.3.1 \u5c01\u95ed\u89e3<\/h4>\n\n\n\n

\u6709\uff1a \"f762e8a3500771a68778aa12f8b29c9d.png\" \u4ee4\uff1a \"93e1b777bddc2ed9556578d8f598e9eb.png\" \u5176\u4e2dB\u662f\u4e00\u4e2a\u5bf9\u79f0\u77e9\u9635\uff0c\u8bbe\u4e00\u4e2a\u516d\u7ef4\u5411\u91cfb\uff1a \"cefc8094ba46aa301599b05f1ce782e1.png\" \u8bbeH\u7684\u7b2ci\u5217\u5411\u91cf\u4e3a \"99bbe07c001bbf8215d774e6a3356e6b.png\" \u6709\uff1a \"bbd9d19a3b4adccdede8551be396ad74.png\" \u5176\u4e2d\uff1a \"cccd539d3094659a8f6571c0e0134187.png\" \u7ea6\u675f\u516c\u5f0f\uff088\uff09\uff089\uff09\u53ef\u4ee5\u91cd\u5199\u4e3a\uff1a \"ef3f8660c53d153c1693407dc9d812b9.png\" \u7531\u4e0a\u9762\u4e24\u5f0f\u5f97\u5230\uff1a \"48344b3b0dd81b124c1c67946b732964.png\" \u516c\u5f0f\uff0813\uff09\u4e3a\u4e00\u4e2a\u7ed9\u5b9a\u5355\u5e94\u6027\u4e2d\u7684\u4e24\u4e2a\u57fa\u672c\u7ea6\u675f\u6761\u4ef6\uff0c\u5373\u6807\u5b9a\u4e00\u5f20\u56fe\u50cf\u5c31\u7ed9\u51fa\u4e0a\u9762\u4e24\u4e2a\u7ea6\u675f\u3002\u901a\u8fc7\u6807\u5b9an\u5f20\u56fe\u50cf\uff0c\u5219\u6709n\u4e2a\u516c\u5f0f\uff0813\uff09\uff0c\u53e0\u52a0\u8868\u793a\u5f97\u5230\uff1a \"dfacbb560b20b0fea25d6f6cd0e424e0.png\" \u5176\u4e2dV\u662f\u4e00\u4e2a2n*6\u7684\u77e9\u9635\u3002 \u56e0\u4e3ab\u662f\u4e00\u4e2a6\u7ef4\u5411\u91cf\uff0c\u56e0\u6b64\u6700\u5c11\u67096\u4e2a\u65b9\u7a0b\u5c31\u53ef\u4ee5\u6c42\u89e3\u8fd96\u4e2a\u672a\u77e5\u91cf\uff0c\u6bcf\u5f20\u56fe\u50cf\u53ef\u4ee5\u63d0\u4f9b\u4e24\u4e2a\u7ea6\u675f\u65b9\u7a0b\u3002\u82e5\u67093\u5f20\u56fe\u50cf\u5219\u53ef\u4ee5\u89e3\u51fa\u7ed9\u5b9a\u6bd4\u4f8b\u56e0\u5b50\u76846\u7ef4\u5411\u91cfb\u7684\u89e3\u3002<\/p>\n\n\n\n

\u82e5\u53ea\u67092\u5f20\u56fe\u50cf\uff0c\u53ef\u4ee5\u65bd\u52a0\u65e0\u503e\u659c\u7cfb\u6570\u7684\u7ea6\u675f\uff0c\u5373c=0\uff0c\u6709\uff1a \"3bc0965d86d61eeff76db3879a0ab02b.png\" \u5c06\u4e0a\u5f0f\u4ee3\u5165\uff0813\uff09\u4f5c\u4e3a\u989d\u5916\u7ea6\u675f\u3002<\/p>\n\n\n\n

\u5f97\u5230b\u7684\u89e3\u540e\uff0c\u5373\u5f97\u5230B\uff0c\u5e76\u89e3\u51fa\u76f8\u673a\u5185\u53c2A\u3002\u89e3\u51faA\uff0c\u5219\u80fd\u591f\u89e3\u51fa\u76f8\u673a\u5916\u53c2\u3002<\/p>\n\n\n\n

\u5f97\u5230B\u540e\u3002\u76f8\u673a\u5185\u53c2A\u8ba1\u7b97\u5982\u4e0b\uff1a \"d61c7f138bd1a779a05289b409f3c9a9.png\" \u6839\u636e\u4e0a\u5f0f\u8ba1\u7b97\u5f97\u5230A\u540e\uff0c\u53ef\u4ee5\u8ba1\u7b97\u76f8\u673a\u5916\u53c2\uff1a \"88e901dff07a258c8be7096cd1488fa3.png\" \u8fd9\u91cc\u8ba1\u7b97\u5f97\u5230\u7684R\u6bd4\u4e00\u5b9a\u6ee1\u8db3\u6807\u51c6\u65cb\u8f6c\u77e9\u9635\u7684\u6027\u8d28\uff0c\u9700\u8981\u4f18\u5316\u3002<\/p>\n\n\n\n

2.2.3.2 \u6700\u5927\u4f3c\u7136\u4f30\u8ba1<\/h4>\n\n\n\n

\u4e0a\u8ff0\u89e3\u662f\u901a\u8fc7\u6700\u5c0f\u5316\u4e00\u4e2a\u6ca1\u6709\u7269\u7406\u610f\u4e49\u7684\u4ee3\u6570\u8ddd\u79bb\u800c\u5f97\u5230\u7684\u3002\u53ef\u4ee5\u901a\u8fc7\u6700\u5927\u4f3c\u7136\u63a8\u7406\u6765\u6539\u8fdb\u5b83\u3002<\/p>\n\n\n\n

\u82e5\u7ed9\u51fa\u6a21\u578b\u5e73\u9762\u4e0an\u5f20\u56fe\u50cf\uff0c\u6a21\u578b\u5e73\u9762\u4e0a\u6709m\u4e2a\u70b9\uff0c\u5047\u8bbe\u56fe\u50cf\u70b9\u88ab\u72ec\u7acb\u4e14\u540c\u5206\u5e03\u7684\u566a\u58f0\u7834\u574f\u3002\u6700\u5927\u4f3c\u7136\u4f30\u8ba1\u53ef\u4ee5\u901a\u8fc7\u6700\u5c0f\u5316\u4ee5\u4e0b\u51fd\u6570\u6765\u5f97\u5230\uff1a \"5e2a496972c3d6b56830405f2ac33f46.png\" \u4e00\u4e2a\u65cb\u8f6cR\u7531\u4e00\u4e2a\u5305\u542b3\u4e2a\u53c2\u6570\u7684\u5411\u91cf\u53c2\u6570\u5316\uff0c\u7528r\u8868\u793a\uff0c\u5b83\u5e73\u884c\u4e8e\u65cb\u8f6c\u8f74\uff0c\u5176\u5927\u5c0f\u7b49\u4e8e\u65cb\u8f6c\u89d2\u3002R\u548cr\u7531\u7f57\u5fb7\u91cc\u683c\u65af\u516c\u5f0f\u76f8\u5173\u8054\u3002\u6700\u5c0f\u5316\u516c\u5f0f\uff0814\uff09\u662f\u4e00\u4e2a\u975e\u7ebf\u6027\u6700\u5c0f\u5316\u95ee\u9898\uff0c\u5b83\u53ef\u4ee5\u7528\u5728Minpack\u4e2d\u5b9e\u73b0\u7684LM\u7b97\u6cd5\u6765\u6c42\u89e3\u3002\u5b83\u9700\u8981\u4e00\u4e2a\u521d\u59cb\u53c2\u6570\u503c\uff1aA\uff0c{Ri\uff0cti|i=1\u2026\u8fd9\u4e2a\u521d\u59cb\u53c2\u6570\u5219\u53ef\u4ee5\u4f7f\u75282.2.3.1\u4e2d\u6240\u6c42\u7684\u53c2\u6570\u89e3\u3002<\/p>\n\n\n\n

2.2.3.3 \u5904\u7406\u955c\u5934\u5f84\u5411\u7578\u53d8<\/h4>\n\n\n\n

\u5728\u524d\u97621.5.1\u4e2d\u5b9a\u4e49\u4e86\u56fe\u50cf\u7684\u5f84\u5411\u7578\u53d8\u7cfb\u6570\u6a21\u578b\uff1a \"1958e54d2323f7ccce704c8879c2102b.png\" \u5728\u5f20\u6b63\u53cb\u6570\u5b66\u6a21\u578b\u4e2d\u53ea\u8003\u8651k1,k2\uff1a \"754d4626d15d17ec50ce5f757f3f1ac2.png\" \u5c06\u4e0a\u5f0f\u4ece\u56fe\u50cf\u5750\u6807\u7cfb\u8f6c\u5230\u50cf\u7d20\u5750\u6807\u7cfb\u6709\uff1a \"8cb12f00ba0a009bcc3ce20ac466f7ee.png\" \u5c06\u4e0a\u5f0f\u8f6c\u6362\u5230\u77e9\u9635\u5f62\u5f0f\uff1a \"130100442bbc5e32d782b71cac92874d.png\" \u56e0\u6b64\u6bcf\u4e2a\u56fe\u50cf\u4e0a\u7684\u6a21\u578b\u70b9\u53ef\u4ee5\u63d0\u4f9b\u4e0a\u9762\u4e24\u4e2a\u65b9\u7a0b\uff0c\u5219n\u5f20\u56fe\u50cfm\u4e2a\u6a21\u578b\u70b9\u67092mn\u4e2a\u65b9\u7a0b\uff0c\u77e9\u9635\u5f62\u5f0f\u4e3a\uff1a \"6f1e9cb924fbf024a0645e4d2224efdd.png\" \u7ebf\u6027\u6700\u5c0f\u4e8c\u4e58\u89e3\u53ef\u7531\u516c\u5f0f\u5f97\u51fa\uff1a \"e1099e8d5a75b1b2df80bb908c472470.png\" \u4e00\u65e6\u4f30\u8ba1\u4e86k1\u548ck2\uff0c\u5c31\u53ef\u4ee5\u901a\u8fc7\uff0815\uff09\u6c42\u5f97\u7684\u6295\u5f71\u70b9\u5e26\u5165\u516c\u5f0f\uff0814\uff09\u6765\u7ec6\u5316\u5176\u4ed6\u53c2\u6570\u7684\u4f30\u8ba1\uff0c\u4ea4\u66ff\u4f7f\u7528\u8fd9\u4e24\u4e2a\u65b9\u6cd5\uff0c\u76f4\u5230\u6536\u655b\u4e3a\u6b62\u3002 \u5b9e\u9a8c\u7ed3\u679c\u8868\u660e\uff0c\u4e0a\u8ff0\u4ea4\u66ff\u6280\u672f\u7684\u6536\u655b\u901f\u5ea6\u8f83\u6162\u3002\u5bf9\uff0814\uff09\u7684\u4e00\u4e2a\u81ea\u7136\u6269\u5c55\u662f\u901a\u8fc7\u6700\u5c0f\u5316\u4ee5\u4e0b\u51fd\u6570\u6765\u4f30\u8ba1\u5b8c\u6574\u7684\u53c2\u6570\u96c6\uff1a \"c90ae1773562c94d2d438a663498af37.png\" \u4e0a\u5f0f\u4f7f\u7528LM\u7b97\u6cd5\u6765\u6c42\u89e3\u3002\u9700\u8981\u7684\u521d\u59cb\u53c2\u6570\u503c\uff1aA\uff0c{Ri\uff0cti|i=1\u2026\u53ef\u4ee5\u4f7f\u75282.2.3.1\u4e2d\u6240\u6c42\u7684\u53c2\u6570\u89e3\u6216\u80052.2.3.2\u4e2d\u6240\u6c42\u7684\u53c2\u6570\u89e3\u6216\u8005\u7b80\u5355\u8bbe\u4e3a0.<\/p>\n\n\n\n

2.3 \u5f20\u6b63\u53cb\u6807\u5b9a\u6cd5\u6807\u5b9a\u6b65\u9aa4<\/h2>\n\n\n\n

\uff081\uff09\u6253\u5370\u56fe\u6848\uff08\u5982\u68cb\u76d8\u683c\uff09\u5e76\u5c06\u5176\u9644\u7740\u5230\u5e73\u9762\u8868\u9762\u4e0a\uff1b<\/p>\n\n\n\n

\uff082\uff09\u901a\u8fc7\u79fb\u52a8\u5e73\u9762\u6216\u6444\u50cf\u673a\uff0c\u62cd\u6444\u4e0d\u540c\u65b9\u5411\u7684\u56fe\u50cf\uff1b<\/p>\n\n\n\n

\uff083\uff09\u68c0\u6d4b\u56fe\u50cf\u4e2d\u7684\u7279\u5f81\u70b9\uff1b<\/p>\n\n\n\n

\uff084\uff09\u5229\u75282.2.3.1\u6240\u8ff0\u7684\u5c01\u95ed\u89e3\u4f30\u8ba1\u4e94\u4e2a\u5185\u5728\u53c2\u6570\u548c\u6240\u6709\u5916\u90e8\u53c2\u6570\u3002<\/p>\n\n\n\n

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\uff086\uff09\u901a\u8fc7\u6700\u5c0f\u5316\u6765\u7ec6\u5316\u6240\u6709\u53c2\u6570\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

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