{"id":964,"date":"2022-01-18T16:44:10","date_gmt":"2022-01-18T08:44:10","guid":{"rendered":"http:\/\/www.wayln.com\/?p=964"},"modified":"2022-01-21T10:13:50","modified_gmt":"2022-01-21T02:13:50","slug":"%e7%ac%ac%e4%b8%89%e7%ab%a0-%e7%81%b0%e5%ba%a6%e5%8f%98%e6%8d%a2%e4%b8%8e%e7%a9%ba%e9%97%b4%e6%bb%a4%e6%b3%a2","status":"publish","type":"post","link":"https:\/\/www.wayln.com\/?p=964","title":{"rendered":"\u7b2c\u4e09\u7ae0 \u7070\u5ea6\u53d8\u6362\u4e0e\u7a7a\u95f4\u6ee4\u6ce2"},"content":{"rendered":"<div id=\"toc_container\" class=\"toc_transparent no_bullets\"><p class=\"toc_title\">Contents<\/p><ul class=\"toc_list\"><li><a href=\"#31\"><span class=\"toc_number toc_depth_1\">1<\/span> 3.1 \u80cc\u666f\u77e5\u8bc6<\/a><ul><li><a href=\"#311\"><span class=\"toc_number toc_depth_2\">1.1<\/span> 3.1.1 \u7070\u5ea6\u53d8\u6362\u548c\u7a7a\u95f4\u6ee4\u6ce2\u57fa\u7840<\/a><\/li><\/ul><\/li><li><a href=\"#32\"><span class=\"toc_number toc_depth_1\">2<\/span> 3.2 \u4e00\u4e9b\u57fa\u672c\u7684\u7070\u5ea6\u53d8\u6362\u51fd\u6570<\/a><ul><li><a href=\"#321\"><span class=\"toc_number toc_depth_2\">2.1<\/span> 3.2.1 \u56fe\u50cf\u53cd\u8f6c<\/a><\/li><li><a href=\"#322\"><span class=\"toc_number toc_depth_2\">2.2<\/span> 3.2.2 \u5bf9\u6570\u53d8\u6362<\/a><\/li><li><a href=\"#323\"><span class=\"toc_number toc_depth_2\">2.3<\/span> 3.2.3 \u5e42\u5f8b\uff08\u4f3d\u9a6c\uff09\u53d8\u6362<\/a><\/li><li><a href=\"#324\"><span class=\"toc_number toc_depth_2\">2.4<\/span> 3.2.4 \u5206\u6bb5\u7ebf\u6027\u53d8\u6362\u51fd\u6570<\/a><\/li><\/ul><\/li><li><a href=\"#33\"><span class=\"toc_number toc_depth_1\">3<\/span> 3.3 \u76f4\u65b9\u56fe\u5904\u7406<\/a><ul><li><a href=\"#331\"><span class=\"toc_number toc_depth_2\">3.1<\/span> 3.3.1 \u76f4\u65b9\u56fe\u5747\u8861<\/a><\/li><li><a href=\"#332\"><span class=\"toc_number toc_depth_2\">3.2<\/span> 3.3.2 \u76f4\u65b9\u56fe\u5339\u914d\uff08\u89c4\u5b9a\u5316\uff09<\/a><\/li><li><a href=\"#334\"><span class=\"toc_number toc_depth_2\">3.3<\/span> 3.3.4 \u5728\u56fe\u50cf\u589e\u5f3a\u4e2d\u4f7f\u7528\u76f4\u65b9\u56fe\u7edf\u8ba1<\/a><\/li><\/ul><\/li><li><a href=\"#34\"><span class=\"toc_number toc_depth_1\">4<\/span> 3.4 \u7a7a\u95f4\u6ee4\u6ce2\u57fa\u7840<\/a><ul><li><a href=\"#341\"><span class=\"toc_number toc_depth_2\">4.1<\/span> 3.4.1 \u7a7a\u95f4\u6ee4\u6ce2\u673a\u7406<\/a><\/li><li><a href=\"#342\"><span class=\"toc_number toc_depth_2\">4.2<\/span> 3.4.2 \u7a7a\u95f4\u76f8\u5173\u4e0e\u5377\u79ef<\/a><\/li><li><a href=\"#343\"><span class=\"toc_number toc_depth_2\">4.3<\/span> 3.4.3 \u7ebf\u6027\u6ee4\u6ce2\u7684\u5411\u91cf\u8868\u793a<\/a><\/li><li><a href=\"#344\"><span class=\"toc_number toc_depth_2\">4.4<\/span> 3.4.4 \u7a7a\u95f4\u6ee4\u6ce2\u5668\u6a21\u677f\u7684\u4ea7\u751f<\/a><\/li><\/ul><\/li><li><a href=\"#35\"><span class=\"toc_number toc_depth_1\">5<\/span> 3.5 \u5e73\u6ed1\u7a7a\u95f4\u6ee4\u6ce2\u5668<\/a><ul><li><a href=\"#351\"><span class=\"toc_number toc_depth_2\">5.1<\/span> 3.5.1 \u5e73\u6ed1\u7ebf\u6027\u6ee4\u6ce2\u5668<\/a><\/li><li><a href=\"#363\"><span class=\"toc_number toc_depth_2\">5.2<\/span> 3.6.3 \u975e\u9510\u5316\u63a9\u853d\u548c\u9ad8\u63d0\u5347\u6ee4\u6ce2<\/a><\/li><li><a href=\"#364\"><span class=\"toc_number toc_depth_2\">5.3<\/span> 3.6.4 \u4f7f\u7528\u4e00\u9636\u5fae\u5206\u5bf9\uff08\u975e\u7ebf\u6027\uff09\u56fe\u50cf\u9510\u5316\u2014\u2014\u68af\u5ea6<\/a><\/li><\/ul><\/li><li><a href=\"#37\"><span class=\"toc_number toc_depth_1\">6<\/span> 3.7 \u6df7\u5408\u7a7a\u95f4\u589e\u5f3a\u6cd5<\/a><\/li><li><a href=\"#38\"><span class=\"toc_number toc_depth_1\">7<\/span> 3.8 \u4f7f\u7528\u6a21\u7cca\u6280\u672f\u8fdb\u884c\u7070\u5ea6\u53d8\u6362\u548c\u7a7a\u95f4\u6ee4\u6ce2<\/a><\/li><li><a href=\"#382\"><span class=\"toc_number toc_depth_1\">8<\/span> 3.8.2 \u6a21\u7cca\u5ea6\u96c6\u5408\u8bba\u539f\u7406<\/a><\/li><\/ul><\/div>\n<p>\u5f15\u8a00<br \/>\n\u53d8\u6362\u57df\u7684\u56fe\u50cf\u5904\u7406\u9996\u5148\u628a\u4e00\u5e45\u56fe\u50cf\u53d8\u6362\u5230\u53d8\u6362\u57df<\/p>\n<h1><span id=\"31\">3.1 \u80cc\u666f\u77e5\u8bc6<\/span><\/h1>\n<h2><span id=\"311\">3.1.1 \u7070\u5ea6\u53d8\u6362\u548c\u7a7a\u95f4\u6ee4\u6ce2\u57fa\u7840<\/span><\/h2>\n<p>\u7a7a\u95f4\u57df\u6280\u672f\u76f4\u63a5\u5728\u56fe\u50cf\u50cf\u7d20\u4e0a\u64cd\u4f5c\uff0c\u5bf9\u4e8e\u9891\u7387\u57df\u6765\u4e66\uff0c\u5176\u64cd\u4f5c\u5728\u56fe\u50cf\u7684\u5085\u91cc\u53f6\u53d8\u6362\u4e0a\u6267\u884c\uff0c\u800c\u4e0d\u9488\u5bf9\u56fe\u50cf\u672c\u8eab\u3002<br \/>\n\u7a7a\u95f4\u6ee4\u6ce2\u5668\uff1a\u90bb\u57df\u4e0e\u9884\u5b9a\u4e49\u7684\u64cd\u4f5c\u4e00\u8d77\u79f0\u4e3a\u7a7a\u95f4\u6ee4\u6ce2\u5668\uff08\u4e5f\u6210\u4e3a\u7a7a\u95f4\u63a9\u819c\u3001\u6838\u3001\u6a21\u677f\u6216\u7a97\u53e3\uff09<br \/>\n<strong>\u5bf9\u6bd4\u5ea6\u62c9\u4f38<\/strong>\u5bf9f\u4e2d\u6bcf\u4e00\u4e2a\u50cf\u7d20\u65bd\u4ee5\u53d8\u6362\u4ea7\u751f\u76f8\u5e94\u7684g\u7684\u50cf\u7d20\u7684\u6548\u679c\u5c06\u6bd4\u539f\u59cb\u56fe\u50cf\u6709\u66f4\u9ad8\u7684\u5bf9\u6bd4\u5ea6\uff0c\u5373\u4f4e\u4e8eK\u7684\u7070\u5ea6\u7ea7\u66f4\u6697\uff0c\u800c\u9ad8\u4e8ek\u7684\u7070\u5ea6\u7ea7\u66f4\u4eae\u3002<br \/>\n<strong>\u9608\u503c\u5904\u7406\u51fd\u6570<\/strong>\u4ea7\u751f\u4e00\u5e45\u4e24\u7ea7\uff08\u4e8c\u503c\uff09\u56fe\u50cf\u3002<\/p>\n<h1><span id=\"32\">3.2 \u4e00\u4e9b\u57fa\u672c\u7684\u7070\u5ea6\u53d8\u6362\u51fd\u6570<\/span><\/h1>\n<p>\u7070\u5ea6\u53d8\u6362\u662f\u6240\u6709\u56fe\u50cf\u5904\u7406\u6280\u672f\u4e2d\u6700\u7b80\u5355\u7684\u6280\u672f\u3002r\u548cs\u5206\u522b\u4ee3\u8868\u5904\u7406\u524d\u540e\u7684\u50cf\u7d20\u503c\u3002<\/p>\n<h2><span id=\"321\">3.2.1 \u56fe\u50cf\u53cd\u8f6c<\/span><\/h2>\n<div class=\"katex math multi-line no-emojify\">s=L-1-r\n<\/div>\n<h2><span id=\"322\">3.2.2 \u5bf9\u6570\u53d8\u6362<\/span><\/h2>\n<div class=\"katex math multi-line no-emojify\">s=clog(1+r)\n<\/div>\n<p>\u8be5\u53d8\u5316\u5c06\u8f93\u5165\u4e2d\u8303\u56f4\u8f83\u7a84\u7684\u4f4e\u7070\u5ea6\u503c\u6620\u5c04\u4e3a\u8f93\u51fa\u4e2d\u8f83\u5bbd\u8303\u56f4\u7684\u7070\u5ea6\u503c\uff0c\u76f8\u53cd\u5730\uff0c\u5bf9\u9ad8\u7684\u8f93\u5165\u7070\u5ea6\u503c\u4e5f\u662f\u5982\u6b64\u3002\u6211\u4eec\u4f7f\u7528\u8fd9\u79cd\u7c7b\u578b\u7684\u53d8\u6362\u6765\u6269\u5c55\u56fe\u50cf\u4e2d\u7684\u6309\u50cf\u7d20\u503c\uff0c\u540c\u65f6\u538b\u7f29\u66f4\u9ad8\u7070\u5ea6\u7ea7\u7684\u503c\u3002\u53cd\u5bf9\u6570\u53d8\u6362\u7684\u4f5c\u7528\u4e0e\u6b64\u76f8\u53cd\u3002<\/p>\n<h2><span id=\"323\">3.2.3 \u5e42\u5f8b\uff08\u4f3d\u9a6c\uff09\u53d8\u6362<\/span><\/h2>\n<div class=\"katex math multi-line no-emojify\">s=cr^{\\gamma}\n<\/div>\n<p>\u5176\u4e2d<span class=\"katex math inline\">c\u548c\\gamma<\/span>\u4e3a\u6b63\u5e38\u6570\uff0c\u6709\u65f6\u8003\u8651\u5230\u504f\u79fb\u91cf\uff08\u5373\u8f93\u5165\u4e3a0\u65f6\u7684\u4e00\u4e2a\u53ef\u5ea6\u91cf\u8f93\u51fa\uff09\uff0c\u53ef\u4ee5\u5199\u4e3a<\/p>\n<div class=\"katex math multi-line no-emojify\">s=c(r+\\epsilon)^{\\gamma}\n<\/div>\n<p>\u4f7f\u7528\u5e42\u5f8b\u53d8\u6362\u8fdb\u884c\u4f3d\u9a6c\u6821\u6b63\uff0c\u8fd8\u53ef\u4ee5\u8fdb\u884c\u5bf9\u6bd4\u5ea6\u589e\u5f3a<br \/>\n\u5bf9\u6bd4\u5ea6\u62c9\u4f38<br \/>\n\u7070\u5ea6\u7ea7\u5206\u5c42<br \/>\n\u6bd4\u7279\u5e73\u9762\u5206\u5c42<\/p>\n<h2><span id=\"324\">3.2.4 \u5206\u6bb5\u7ebf\u6027\u53d8\u6362\u51fd\u6570<\/span><\/h2>\n<h1><span id=\"33\">3.3 \u76f4\u65b9\u56fe\u5904\u7406<\/span><\/h1>\n<h2><span id=\"331\">3.3.1 \u76f4\u65b9\u56fe\u5747\u8861<\/span><\/h2>\n<p>\u5982\u679c<span class=\"katex math inline\">p_r(r)\u548cT(r)<\/span>\u5df2\u77e5\uff0c\u4e14\u5728\u611f\u5174\u8da3\u7684\u503c\u57df\u4e0a<span class=\"katex math inline\">T(r)<\/span>\u662f\u8fde\u7eed\u4e14\u53ef\u5fae\u7684\uff0c\u5219\u53d8\u6362\uff08\u6620\u5c04\uff09\u540e\u7684\u53d8\u91cfs\u7684PDF\u53ef\u7531\u4e0b\u9762\u7684\u7b80\u5355\u516c\u5f0f\u5f97\u5230\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">p_s(s)=p_r(r)|\\frac{dr}{ds}|\n<\/div>\n<p>\u8f93\u51fa\u7070\u5ea6\u53d8\u91cfs\u7684PDF\u5c31\u7531\u8f93\u5165\u7070\u5ea6\u7684PDF\u548c\u6240\u7528\u7684\u53d8\u6362\u51fd\u6570\u51b3\u5b9a<br \/>\n\u5728\u56fe\u50cf\u5904\u7406\u4e2d\u7279\u522b\u91cd\u8981\u7684\u53d8\u6362\u51fd\u6570\u6709\u5982\u4e0b\u5f62\u5f0f\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">s=T(r)=(L-1)\\int_0^rp_r(w)d_w\n<\/div>\n<p>\u4e00\u5e45\u6570\u5b57\u56fe\u50cf\u4e2d\u7070\u5ea6\u7ea7<span class=\"katex math inline\">r_k<\/span>\u51fa\u73b0\u7684\u6982\u7387\u8fd1\u4f3c\u4e3a<\/p>\n<div class=\"katex math multi-line no-emojify\">p_r(r_k)=\\frac{n_k}{MN},K=0,1,2,&#8230;,L-1\n<\/div>\n<p>\u5176\u4e2d\uff0cMN\u662f\u56fe\u50cf\u4e2d\u50cf\u7d20\u7684\u603b\u6570\uff0c<span class=\"katex math inline\">n_k<\/span>\u662f\u7070\u5ea6\u4e3a<span class=\"katex math inline\">r_k<\/span>\u7684\u50cf\u7d20\u4e2a\u6570\uff0cL\u662f\u56fe\u50cf\u4e2d\u53ef\u80fd\u7684\u7070\u5ea6\u7ea7\u7684\u6570\u91cf\u3002<br \/>\n\u4e0a\u9762\u8fde\u7eed\u53d8\u6362\u7684\u79bb\u6563\u5f62\u5f0f\u4e3a\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">s_k=T(r_k)=(L-1)\\sum_{j=0}^kp_r(r_j)=\\frac{L-1}{MN}\\sum_{j=0}^kn_j,\\\\ k=0,1,2,&#8230;,L-1\n<\/div>\n<p>\u53d8\u6362\uff08\u6620\u5c04\uff09<span class=\"katex math inline\">T(r_k)<\/span>\u79f0\u4e3a\u76f4\u65b9\u56fe\u5747\u8861\u6216\u76f4\u65b9\u56fe\u7ebf\u6027\u53d8\u6362<\/p>\n<h2><span id=\"332\">3.3.2 \u76f4\u65b9\u56fe\u5339\u914d\uff08\u89c4\u5b9a\u5316\uff09<\/span><\/h2>\n<p>\u8fde\u7eed\u7070\u5ea6r\u548cz,\u4ee4<span class=\"katex math inline\">p_r(r)\u548cp_z(z)<\/span>\u8868\u793a\u4ed6\u4eec\u5bf9\u5e94\u7684\u8fde\u7eed\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u3002r\u548cz\u5206\u522b\u8868\u793a\u8f93\u5165\u56fe\u50cf\u548c\u8f93\u51fa\u56fe\u50cf\u7684\u7070\u5ea6\u7ea7\u3002\u6211\u4eec\u53ef\u4ee5\u7531\u7ed9\u5b9a\u7684\u8f93\u5165\u56fe\u50cf\u4f30\u8ba1<span class=\"katex math inline\">p_r(r)<\/span>,\u800c<span class=\"katex math inline\">p_z(z)<\/span>\u662f\u6211\u4eec\u5e0c\u671b\u8f93\u5165\u56fe\u50cf\u6240\u5177\u6709\u7684\u6307\u5b9a\u6982\u7387\u5bc6\u5ea6\u51fd\u6570<br \/>\n\u4ee4s\u4e3a\u4e00\u4e2a\u6709\u5982\u4e0b\u7279\u6027\u7684\u968f\u673a\u53d8\u91cf\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">s=T(r)=(L-1)\\int^r_0p_r(w)dw  \\tag{3.3-10}\n<\/div>\n<p>\u5982\u524d\u9762\u4e00\u6837\uff0cw\u4e3a\u79ef\u5206\u5047\u53d8\u91cf\u3002<br \/>\n\u63a5\u7740,\u6211\u4eec\u5b9a\u4e49\u4e00\u4e2a\u6709\u5982\u4e0b\u7279\u6027\u7684\u968f\u673a\u53d8\u91cfz:<\/p>\n<div class=\"katex math multi-line no-emojify\">G(z)=(L-1)\\int^z_0p_z(t)dt=s  \\tag{3.3-11}\n<\/div>\n<p>\u5176\u4e2d\uff0ct\u4e3a\u79ef\u5206\u5047\u53d8\u91cf\u3002\u7531\u8fd9\u4e24\u4e2a\u7b49\u5f0f\u53ef\u5f97<span class=\"katex math inline\">G(z)=T(r)<\/span><\/p>\n<div class=\"katex math multi-line no-emojify\">z=G^{-1}[T(r)]=G^{-1}(s)  \\tag{3.3-12}\n<\/div>\n<p>\u4e00\u65e6\u7531\u8f93\u5165\u56fe\u50cf\u4f30\u8ba1\u51fa<span class=\"katex math inline\">p_r(r)<\/span>,\u53d8\u6362\u51fd\u6570<span class=\"katex math inline\">T(r)<\/span>\u5c31\u53ef\u4ee5\u7531\u5f0f<span class=\"katex math inline\">(3.3-10)<\/span>\u5f97\u5230\u3002\u7c7b\u4f3c\u5730\uff0c\u56e0\u4e3a<span class=\"katex math inline\">p_z(z)<\/span>\u5df2\u77e5\uff0c\u53d8\u6362\u51fd\u6570<span class=\"katex math inline\">G(z)<\/span>\u53ef\u7531\u5f0f<span class=\"katex math inline\">(3.3-11)<\/span>\u5f97\u5230\u3002<br \/>\n\u5f0f<span class=\"katex math inline\">(3.3-10)<\/span>\u5230\u5f0f<span class=\"katex math inline\">(3.3-12)<\/span>\u8868\u660e\uff0c\u4f7f\u7528\u4e0b\u5217\u6b65\u9aa4\uff0c\u53ef\u7531\u4e00\u5e45\u7ed9\u5b9a\u56fe\u50cf\u5f97\u5230\u4e00\u5e45\u5176\u7070\u5ea6\u7ea7\u5177\u6709\u6307\u5b9a\u6982\u7387\u5bc6\u5ea6\u51fd\u6570\u7684\u56fe\u50cf<br \/>\n1. \u7531\u8f93\u5165\u56fe\u50cf\u5f97\u5230<span class=\"katex math inline\">p_r(r)<\/span>\uff0c\u5e76\u7531\u5f0f<span class=\"katex math inline\">(3.3-10)<\/span>\u6c42\u5f97s\u7684\u503c\u3002<br \/>\n2. \u4f7f\u7528\u5f0f<span class=\"katex math inline\">(3.3-11)<\/span>\u4e2d\u6307\u5b9a\u7684PDF\u6c42\u5f97\u53d8\u6362\u51fd\u6570<span class=\"katex math inline\">G(z)<\/span><br \/>\n3. \u6c42\u5f97\u53cd\u53d8\u6362\u51fd\u6570<span class=\"katex math inline\">z=G^{-1}(s)<\/span>;\u56e0\u4e3az\u662f\u7531s\u5f97\u5230\u7684\uff0c\u6240\u4ee5\u8be5\u5904\u7406\u662fs\u5230z\u7684\u6620\u5c04\uff0c\u800c\u540e\u8005\u6b63\u5f0f\u6211\u4eec\u671f\u671b\u7684\u503c<br \/>\n4. \u9996\u5148\u7528\u5f0f<span class=\"katex math inline\">(3.3-10)<\/span>\u5bf9\u8f93\u5165\u56fe\u50cf\u8fdb\u884c\u5747\u8861\u5f97\u5230\u8f93\u51fa\u56fe\u50cf\uff1b\u8be5\u56fe\u50cf\u7684\u50cf\u7d20\u503c\u662fs\u503c\u3002\u5bf9\u5747\u8861\u540e\u7684\u56fe\u50cf\u4e2d\u5177\u6709s\u503c\u7684\u6bcf\u4e2a\u50cf\u7d20\u6267\u884c\u53cd\u6620\u5c04<span class=\"katex math inline\">z=G^{-1}(s)<\/span>,\u5f97\u5230\u8f93\u51fa\u56fe\u50cf\u4e2d\u7684\u76f8\u5e94\u50cf\u7d20\u3002\u5f53\u6240\u6709\u7684\u50cf\u7d20\u90fd\u5904\u7406\u5b8c\u540e\uff0c\u8f93\u51fa\u56fe\u50cf\u7684PDF\u5c06\u7b49\u4e8e\u6307\u5b9a\u7684PDF\u3002<\/p>\n<p>\u5728\u5904\u7406\u79bb\u6563\u91cf\u65f6\uff0c\u95ee\u9898\u53ef\u88ab\u5927\u5927\u7b80\u5316\uff0c\u5f0f<span class=\"katex math inline\">(3.3-10)<\/span>\u7684\u79bb\u6563\u5f62\u5f0f\u662f\u5f0f<span class=\"katex math inline\">(3.3-8)<\/span>\u4e2d\u76f4\u65b9\u56fe\u5747\u8861\u53d8\u6362<\/p>\n<div class=\"katex math multi-line no-emojify\">s_k=T(r_k)=(L-1)\\sum_{j=0}^kp_r(r_j)=\\frac{(L-1)}{MN}\\sum_{j=0}^kn_j,k=0,1,2,&#8230;,L-1\n<\/div>\n<div class=\"katex math multi-line no-emojify\">G(z_q)=(L-1)\\sum_{i=0}^qp_z(z_i) \\tag{3.3-14}\n<\/div>\n<p>\u5bf9\u4e00\u4e2aq\u503c\uff0c\u6709<\/p>\n<div class=\"katex math multi-line no-emojify\">G(z_q)=s_k  \\tag{3.3-15}\n<\/div>\n<p>\u5176\u4e2d\uff0c<span class=\"katex math inline\">(p_z(z_i))<\/span>\u662f\u89c4\u5b9a\u7684\u76f4\u65b9\u56fe\u7684\u7b2ci\u4e2a\u503c\u3002\u4e0e\u524d\u9762\u4e00\u6837\uff0c\u6211\u4eec\u7528\u53cd\u53d8\u6362\u627e\u5230\u671f\u671b\u7684\u503c<span class=\"katex math inline\">z_q<\/span>\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">z_q=G^{-1}(s_k) \\tag{3.3-16}\n<\/div>\n<p>\u6362\u53e5\u8bdd\u8bf4\uff0c\u8be5\u64cd\u4f5c\u5bf9\u6bcf\u4e00\u4e2as\u503c\u627e\u51fa\u4e00\u4e2az\u503c\uff1b\u8fd9\u6837\uff0c\u5c31\u5f62\u6210\u4e86\u4eces\u5230z\u7684\u4e00\u4e2a\u6620\u5c04\u3002<\/p>\n<h2><span id=\"334\">3.3.4 \u5728\u56fe\u50cf\u589e\u5f3a\u4e2d\u4f7f\u7528\u76f4\u65b9\u56fe\u7edf\u8ba1<\/span><\/h2>\n<p>r\u5173\u4e8e\u5176\u5747\u503c\u7684n\u9636\u8ddd\u5b9a\u4e49\u4e3a\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">\\mu_n(r)=\\sum_{i=0}^{L-1}(r_i-m)^np(r_i) \\tag{3.3-17}\n<\/div>\n<p>\u5176\u4e2d\uff0cm\u662fr\u7684\u5747\u503c\uff08\u5e73\u5747\u7070\u5ea6\uff0c\u5373\u56fe\u50cf\u4e2d\u50cf\u7d20\u7684\u5e73\u5747\u7070\u5ea6\uff09:<\/p>\n<div class=\"katex math multi-line no-emojify\">m=\\sum_{i=0}^{L-1}r_ip(r_i) \\tag{3.3-18}\n<\/div>\n<p>\u4e8c\u9636\u77e9\u7279\u522b\u91cd\u8981\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">\\mu_2(r)=\\sum_{i=0}^{L-1}(r_i-m)^2p(r_i)  \\tag{3.3-19}\n<\/div>\n<p>\u6211\u4eec\u5c06\u8be5\u8868\u8fbe\u5f0f\u79f0\u4e3a<strong>\u7070\u5ea6\u65b9\u5dee<\/strong>\uff0c\u901a\u5e38\u7528<span class=\"katex math inline\">\\sigma^2<\/span>\u8868\u793a(\u6807\u51c6\u5dee\u662f\u65b9\u5dee\u7684\u5e73\u65b9\u6839)\u3002\u5747\u503c\u662f\u5e73\u5747\u7070\u5ea6\u7684\u5ea6\u91cf\uff0c\u65b9\u5dee\uff08\u6216\u6807\u51c6\u5dee\uff09\u662f\u56fe\u50cf\u5bf9\u6bd4\u5ea6\u7684\u5ea6\u91cf\u3002<br \/>\n\u5728\u5904\u7406\u5747\u503c\u548c\u65b9\u5dee\u65f6\uff0c\u5b9e\u9645\u4e0a\u901a\u5e38\u76f4\u63a5\u4ece\u53d6\u6837\u503c\u6765\u4f30\u8ba1\u5b83\u4eec\uff0c\u800c\u4e0d\u5fc5\u8ba1\u7b97\u76f4\u65b9\u56fe\u3002\u8fd1\u4f3c\u7684\uff0c\u8fd9\u4e9b\u4f30\u8ba1\u79f0\u4e3a<strong>\u53d6\u6837\u5747\u503c\u548c\u53d6\u6837\u65b9\u5dee<\/strong>\uff0c\u5b83\u4eec\u53ef\u4ee5\u6839\u636e\u57fa\u672c\u7684\u7edf\u8ba1\u5b66\u6709\u4e0b\u9762\u5f62\u5f0f\u7ed9\u51fa\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">m=\\frac{1}{MN}\\sum_{x=0}^{M-1}\\sum_{y=0}^{N-1}f(x,y) \\tag{3.3-20}\n<\/div>\n<p>\u548c<\/p>\n<div class=\"katex math multi-line no-emojify\">\\sigma^2=\\frac{1}{MN}\\sum_{x=0}^{M-1}\\sum_{y=0}^{N-1}[f(x,y)-m]^2 \\tag{3.3-21}\n<\/div>\n<p>\u4ee4<span class=\"katex math inline\">(x,y)<\/span>\u8868\u793a\u7ed9\u5b9a\u56fe\u50cf\u4e2d\u4efb\u610f\u50cf\u7d20\u7684\u5750\u6807\uff0c<span class=\"katex math inline\">S_{xy}<\/span>\u8868\u793a\u89c4\u5b9a\u5927\u5c0f\u7684\u4ee5<span class=\"katex math inline\">(x,y)<\/span>\u4e3a\u4e2d\u5fc3\u7684\u90bb\u57df\uff08\u5b50\u56fe\u50cf\uff09\u3002\u8be5\u90bb\u57df\u4e2d\u50cf\u7d20\u7684\u5747\u503c\u7531\u4e0b\u5f0f\u7ed9\u51fa\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">m_{S_{xy}}=\\sum_{i=0}^{L-1}r_ip_{S_{xy}}(r_i) \\tag{3.3-22}\n<\/div>\n<p>\u5176\u4e2d<span class=\"katex math inline\">p_{S_{xy}}<\/span>\u662f\u533a\u57df<span class=\"katex math inline\">S_{xy}<\/span>\u4e2d\u50cf\u7d20\u7684\u76f4\u65b9\u56fe<br \/>\n\u7c7b\u4f3c\u7684\uff0c\u6797\u7389\u5fe0\u50cf\u7d20\u7684\u65b9\u5dee\u7531\u4e0b\u5f0f\u7ed9\u51fa<\/p>\n<div class=\"katex math multi-line no-emojify\">\\sigma^2_{S{xy}}=\\sum_{i=0}^{L-1}(r_i-m_{S_{XY}})^2P_{S_{xy}}(r_i)\n<\/div>\n<p>\u5224\u65ad\u4e00\u4e2a\u533a\u57df\u5728\u70b9<span class=\"katex math inline\">(x,y)<\/span>\u662f\u6697\u8fd8\u662f\u4eae\u7684\u65b9\u6cd5\u662f\u628a\u5c40\u90e8\u5e73\u5747\u7070\u5ea6<span class=\"katex math inline\">m_{s_{xy}}<\/span>\u4e0e\u8868\u793a\u4e3a<span class=\"katex math inline\">m_G<\/span>\u5e76\u79f0\u4e4b\u4e3a\u5168\u5c40\u5747\u503c\u7684\u5e73\u5747\u56fe\u50cf\u7070\u5ea6\u8fdb\u884c\u6bd4\u8f83\u3002\u5982\u679c<span class=\"katex math inline\">m_{s_{xy} \\leq k_0m_G}<\/span>,\u5176\u4e2d\uff0c<span class=\"katex math inline\">K_0<\/span>\u662f\u4e00\u4e2a\u503c\u5c0f\u4e8e1.0\u7684\u6b63\u5e38\u6570,\u90a3\u4e48\u6211\u4eec\u5c06\u628a\u70b9<span class=\"katex math inline\">(x,y)<\/span>\u5904\u7684\u50cf\u7d20\u8003\u8651\u4e3a\u5904\u7406\u7684\u5019\u9009\u70b9\u3002<br \/>\n\u786e\u5b9a\u4e00\u4e2a\u533a\u57df\u7684\u5bf9\u6bd4\u5ea6\u662f\u5426\u53ef\u4f5c\u4e3a\u589e\u91cf\u7684\u5019\u9009\u70b9\u7684\u5ea6\u91cf\u65b9\u6cd5\uff1a\u5982\u679c<span class=\"katex math inline\">\\sigma_{s_{xy}} \\leq k_2\\sigma_G<\/span>,\u5219\u8ba4\u4e3a\u5728\u70b9\uff08x,y\uff09\u5904\u7684\u50cf\u7d20\u662f\u589e\u5f3a\u7684\u5019\u9009\u70b9\uff0c\u5176\u4e2d<span class=\"katex math inline\">\\sigma_G<\/span>\u662f\u7531\u5f0f\uff083.3-19\uff09\u548c\uff083.3-21\uff09\u5f97\u5230\u7684\u5168\u5c40\u6807\u51c6\u5dee\uff0c<span class=\"katex math inline\">k_2<\/span>\u4e3a\u6b63\u5e38\u6570\u3002\u5982\u679c\u6211\u4eec\u611f\u5174\u8da3\u7684\u662f\u589e\u5f3a\u4eae\u533a\u57df\uff0c\u5219\u8be5\u5e38\u6570\u5927\u4e8e1\uff0c\u5bf9\u4e8e\u6697\u533a\uff0c\u5219\u5c0f\u4e8e1.<br \/>\n\u9700\u8981\u9650\u5236\u80fd\u591f\u63a5\u6536\u7684\u6700\u4f4e\u7684\u5bf9\u6bd4\u5ea6\u503c\u3002\u5426\u5219\u8be5\u8fc7\u7a0b\u4f1a\u89c6\u56fe\u589e\u5f3a\u6807\u51c6\u5dee\u4e3a\u96f6\u7684\u6052\u5b9a\u533a\u57df\u3002\u56e0\u6b64\u901a\u8fc7\u8981\u6c42<span class=\"katex math inline\">k_1\\sigma_G \\leq \\sigma_{s_xy},k1 \\leq k2<\/span>\uff0c\u5bf9\u5c40\u90e8\u6807\u51c6\u5dee\u8bbe\u7f6e\u4e00\u4e2a\u8f83\u4f4e\u7684\u9650\u5236\u503c<\/p>\n<h1><span id=\"34\">3.4 \u7a7a\u95f4\u6ee4\u6ce2\u57fa\u7840<\/span><\/h1>\n<p>\u6ee4\u6ce2\u662f\u6307\u63a5\u6536\u6216\u62d2\u7edd\u4e00\u5b9a\u7684\u9891\u7387\u5206\u91cf\u3002<\/p>\n<h2><span id=\"341\">3.4.1 \u7a7a\u95f4\u6ee4\u6ce2\u673a\u7406<\/span><\/h2>\n<p>\u5982\u679c\u5728\u56fe\u50cf\u50cf\u7d20\u4e0a\u6267\u884c\u7684\u662f\u7ebf\u6027\u64cd\u4f5c\uff0c\u5219\u8be5\u6ee4\u6ce2\u5668\u79f0\u4e3a\u7ebf\u6027\u7a7a\u95f4\u6ee4\u6ce2\u5668\u3002\u5426\u5219\uff0c\u6ee4\u6ce2\u5668\u5c31\u79f0\u4e3a\u975e\u7ebf\u6027\u7a7a\u95f4\u6ee4\u6ce2\u5668\u3002<br \/>\n\u4f7f\u7528\u5927\u5c0f\u4e3amxn\u7684\u6ee4\u6ce2\u5668\u5bf9\u5927\u5c0f\u4e3aMXN\u7684\u56fe\u50cf\u8fdb\u884c\u7ebf\u6027\u7a7a\u95f4\u6ee4\u6ce2\uff0c\u53ef\u7531\u4e0b\u5f0f\u8868\u793a\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">g(x,y)=\\sum_{s=-a}^{a}\\sum_{t=-b}^{b}w(s,t)f(x+s,y+t)\n<\/div>\n<p>\u5176\u4e2d\uff0cx\u548cy\u662f\u53ef\u53d8\u7684\uff0c\u4ee5\u4fbfw\u4e2d\u7684\u6bcf\u4e2a\u50cf\u7d20\u53ef\u8bbf\u95eef\u4e2d\u7684\uff0c\u6bcf\u4e2a\u50cf\u7d20\u3002<\/p>\n<h2><span id=\"342\">3.4.2 \u7a7a\u95f4\u76f8\u5173\u4e0e\u5377\u79ef<\/span><\/h2>\n<p><strong>\u76f8\u5173\uff1a<\/strong>\u662f\u6ee4\u6ce2\u5668\u6a21\u677f\u79fb\u52a8\u8fc7\u56fe\u50cf\u5e76\u8ba1\u7b97\u6bcf\u4e2a\u4f4d\u7f6e\u4e58\u79ef\u4e4b\u548c\u7684\u5904\u7406\u3002<br \/>\n<strong>\u5377\u79ef\uff1a<\/strong>\u673a\u7406\u4e0e\u76f8\u5173\u7c7b\u4f3c\uff0c\u4f46\u6ee4\u6ce2\u5668\u8981\u65cb\u8f6c180\u00b0\u3002\u65cb\u8f6c180\u00b0\u7b49\u4e8e\u6c34\u5e73\u7ffb\u8f6c\u8be5\u51fd\u6570\uff0c\u5728\u4e8c\u7ef4\u60c5\u51b5\u4e0b\uff0c\u65cb\u8f6c180\u00b0\u7b49\u540c\u4e8e\u6cbf\u4e00\u4e2a\u5750\u6807\u8f74\u7ffb\u8f6c\u6a21\u677f\uff0c\u7136\u540e\u6cbf\u53e6\u4e00\u4e2a\u5750\u6807\u8f74\u518d\u6b21\u7ffb\u8f6c\u6a21\u677f\u3002<br \/>\n\u6211\u4eec\u5c06\u5305\u542b\u5355\u4e2a1\u800c\u5176\u4f59\u90fd\u662f0\u7684\u51fd\u6570\u79f0\u4e3a\u79bb\u6563\u5355\u4f4d\u51b2\u6fc0\u3002<br \/>\n\u5377\u79ef\u7684\u6982\u5ff5\u662f\u7ebf\u6027\u7cfb\u7edf\u7406\u8bba\u7684\u57fa\u77f3\u3002<br \/>\n\u4e00\u4e2a\u5927\u5c0f\u4e3amxn\u7684\u6ee4\u6ce2\u5668<span class=\"katex math inline\">w(x,y)<\/span>\u4e0e\u4e00\u5e45\u56fe\u50cf<span class=\"katex math inline\">f(x,y)<\/span>\u505a\u76f8\u5173\u64cd\u4f5c\uff0c\u53ef\u8868\u793a\u4e3a<span class=\"katex math inline\">w(x,y)\u2606f(x,y)<\/span>,<\/p>\n<div class=\"katex math multi-line no-emojify\">w(x,y)\u2606f(x,y)=\\sum_{s=-a}^{a}\\sum_{s=-b}^{b}w(s,t)f(x+s,y+t)\n<\/div>\n<div class=\"katex math multi-line no-emojify\">a=(m-1)\/2,b=(n-1)\/2\n<\/div>\n<p>\u7c7b\u4f3c\u7684\uff0c<span class=\"katex math inline\">w(x,y)\u548cf(x,y)<\/span>\u7684\u5377\u79ef\u8868\u793a\u4e3a<span class=\"katex math inline\">w(x,y)\u2605f(x,y)<\/span><\/p>\n<div class=\"katex math multi-line no-emojify\">w(x,y)\u2605f(x,y)=\\sum_{s=-a}^{a}\\sum_{s=-b}^{b}w(s,t)f(x-s,y-t) \\tag{3.4-2}\n<\/div>\n<h2><span id=\"343\">3.4.3 \u7ebf\u6027\u6ee4\u6ce2\u7684\u5411\u91cf\u8868\u793a<\/span><\/h2>\n<p>\u5f53\u6211\u4eec\u7684\u5174\u8da3\u5728\u4e8e\u76f8\u5173\u6216\u5377\u79ef\u7684\u6a21\u677f\u7684\u54cd\u5e94\u7279\u6027R\u65f6\uff0c\u6709\u65f6\u5199\u6210\u4e58\u79ef\u7684\u6c42\u548c\u5f62\u5f0f\u662f\u65b9\u4fbf\u7684\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">R=w_1z_1+w_2z_2+&#8230;+w_{mn}z_{mn}=\\sum_{k=1}^{mn}w_kz_k=w^Tz \\tag{3.4-3}\n<\/div>\n<p>\u5176\u4e2dw\u9879\u662f\u4e00\u4e2a\u5927\u5c0f\u4e3amxn\u7684\u6ee4\u6ce2\u5668\u7684\u7cfb\u6570\uff0cz\u4e3a\u7531\u6ee4\u6ce2\u5668\u8986\u76d6\u7684\u76f8\u5e94\u56fe\u50cf\u7684\u7070\u5ea6\u503c\u3002\u5982\u679c\u6765\u505a\u76f8\u5173\uff0c\u53ef\u4ee5\u7528\u7ed9\u5b9a\u7684\u6a21\u677f\uff0c\u4e3a\u4e86\u4f7f\u7528\u76f8\u540c\u7684\u516c\u5f0f\u8fdb\u884c\u5377\u79ef\u64cd\u4f5c\uff0c\u9700\u8981\u628a\u6a21\u677f\u65cb\u8f6c180\u00b0<\/p>\n<h2><span id=\"344\">3.4.4 \u7a7a\u95f4\u6ee4\u6ce2\u5668\u6a21\u677f\u7684\u4ea7\u751f<\/span><\/h2>\n<p>\u751f\u6210\u4e00\u4e2a\u5927\u5c0f\u4e3amxn\u7684\u7ebf\u6027\u7a7a\u95f4\u6ee4\u6ce2\u5668\u8981\u6307\u5b9amn\u4e2a\u6a21\u677f\u7cfb\u6570\uff0c\u6211\u4eec\u4f7f\u7528\u7ebf\u6027\u6ee4\u6ce2\u5668\u6240\u80fd\u505a\u7684\u6240\u6709\u4e8b\u60c5\u662f\u5b9e\u73b0\u4e58\u79ef\u6c42\u548c\u64cd\u4f5c<\/p>\n<h1><span id=\"35\">3.5 \u5e73\u6ed1\u7a7a\u95f4\u6ee4\u6ce2\u5668<\/span><\/h1>\n<p>\u5e73\u6ed1\u6ee4\u6ce2\u5668\u7528\u4e8e\u6a21\u7cca\u5904\u7406\u548c\u964d\u4f4e\u566a\u58f0\uff0c\u6a21\u7cca\u5904\u7406\u7ecf\u5e38\u5e94\u7528\u9884\u5904\u7406\u4efb\u52a1\u4e2d\uff0c\u4f8b\u5982\u5728\u76ee\u6807\u63d0\u53d6\u4e4b\u524d\u53d6\u51fa\u56fe\u50cf\u4e2d\u7684\u4e00\u4e9b\u7410\u788e\u7ec6\u8282\uff0c\u4ee5\u53ca\u6865\u63a5\u76f4\u7ebf\u6216\u66f2\u7ebf\u7684\u7f1d\u9699\u3002<\/p>\n<h2><span id=\"351\">3.5.1 \u5e73\u6ed1\u7ebf\u6027\u6ee4\u6ce2\u5668<\/span><\/h2>\n<p>\u5e73\u6ed1\u7ebf\u6027\u7a7a\u95f4\u6ee4\u6ce2\u5668\u7684\u8f93\u51fa\u662f\u5305\u542b\u5728\u6ee4\u6ce2\u5668\u6a21\u677f\u90bb\u57df\u5185\u7684\u50cf\u7d20\u7684\u7b80\u5355\u5e73\u5747\u503c\uff0c\u4e5f\u6210\u4e3a\u5747\u503c\u6ee4\u6ce2\u5668\uff0c\u53ef\u4ee5\u628a\u4ed6\u4eec\u5f52\u5165\u5230\u4f4e\u901a\u6ee4\u6ce2\u5668<\/p>\n<p>&#8220;`math<br \/>\n R=\\frac{1}{9}\\sum_{i=1}^9z_i<br \/>\n &#8220;`<br \/>\n R\u662f\u7531\u6a21\u677f\u5b9a\u4e49\u76843&#215;3\u90bb\u57df\u5185\u50cf\u7d20\u7070\u5ea6\u7684\u5e73\u5747\u503c\u3002<br \/>\n \u4e00\u4e2amxn\u6a21\u677f\u5e94\u6709\u7b49\u4e8e<span class=\"katex math inline\">1\/mn<\/span>\u7684\u5f52\u4e00\u5316\u5e38\u6570\u3002\u6240\u6709\u7cfb\u6570\u90fd\u76f8\u7b49\u7684\u7a7a\u95f4\u5747\u503c\u6ee4\u6ce2\u5668\u6709\u65f6\u6210\u4e3a\u76d2\u88c5\u6ee4\u6ce2\u5668<\/p>\n<p>\u4e00\u4e2aMXN\u7684\u56fe\u50cf\u7ecf\u8fc7\u4e00\u4e2a\u5927\u5c0f\u4e3amxn\uff08m\u548cn\u90fd\u662f\u5947\u6570\uff09\u7684\u52a0\u6743\u5747\u503c\u6ee4\u6ce2\u5668\u7684\u65b9\u7a0b\uff1a<\/p>\n<p>&#8220;`math<br \/>\n g(x,y)=\\frac{ \\sum_{s=-a}^{a}\\sum_{t=-b}^bw(s,t)f(x+s,y+t)}{\\sum_{s=-a}^a\\sum_{t=-b}^bw(s,t)}<br \/>\n &#8220;`<\/p>\n<p>## 3.5.2 \u7edf\u8ba1\u6392\u5e8f\uff08\u975e\u7ebf\u6027\uff09\u6ee4\u6ce2\u5668<br \/>\n \u4ee5\u6ee4\u6ce2\u5668\u5305\u56f4\u7684\u56fe\u50cf\u533a\u57df\u4e2d\u6240\u542b\u7684\u50cf\u7d20\u6392\u5e8f\u4e3a\u57fa\u7840\uff0c\u7136\u540e\u4f7f\u7528\u7edf\u8ba1\u6392\u5e8f\u7ed3\u679c\u51b3\u5b9a\u7684\u503c\u4ee3\u66ff\u4e2d\u5fc3\u50cf\u7d20\u7684\u503c\uff0c\u6700\u6709\u540d\u7684\u662f\u4e2d\u503c\u6ee4\u6ce2\u5668\u3002<br \/>\n \u4e00\u4e2a3&#215;3\u7684\u6700\u5927\u503c\u6ee4\u6ce2\u5668\u7684\u54cd\u5e94\u53ef\u4ee5\u7531\u516c\u5f0f<span class=\"katex math inline\">R=max &#92;{ z_k|k=1,2,&#8230;,9&#92;}<\/span>\u7ed9\u51fa<\/p>\n<p># 3.6 \u9510\u5316\u7a7a\u95f4\u6ee4\u6ce2\u5668<br \/>\n \u9510\u5316\u5904\u7406\u7684\u4e3b\u8981\u76ee\u7684\u662f\u7a81\u51fa\u7070\u5ea6\u7684\u8fc7\u6e21\u90e8\u5206\u3002\u9510\u5316\u5904\u7406\u53ef\u4ee5\u7531\u7a7a\u95f4\u5fae\u5206\u6765\u5b9e\u73b0\u3002\u5fae\u5206\u7b97\u5b50\u7684\u54cd\u5e94\u5f3a\u5ea6\u4e0e\u56fe\u50cf\u5728\u7528\u7b97\u5b50\u64cd\u4f5c\u7684\u8fd9\u4e00\u70b9\u7684\u7a81\u53d8\u7a0b\u5ea6\u6210\u6b63\u6bd4\uff0c\u8fd9\u6837\uff0c\u56fe\u50cf\u5fae\u5206\u589e\u5f3a\u8fb9\u7f18\u548c\u5176\u4ed6\u51f8\u51fa\uff0c\u800c\u524a\u5f31\u7070\u5ea6\u53d8\u5316\u7f13\u6162\u7684\u533a\u57df<\/p>\n<p>\u5bf9\u4e8e\u4e00\u9636\u5fae\u5206\u7684\u4efb\u4f55\u5b9a\u4e49\u90fd\u5fc5\u987b\u4fdd\u8bc1\u4ee5\u4e0b\u51e0\u70b9\uff1a<br \/>\n 1. \u5728\u6052\u5b9a\u7070\u5ea6\u533a\u57df\u7684\u5fae\u5206\u503c\u4e3a\u96f6<br \/>\n 2. \u5728\u7070\u5ea6\u53f0\u9636\u6216\u659c\u5761\u5904\u5fae\u5206\u503c\u975e\u96f6<br \/>\n 3. \u6cbf\u7740\u659c\u5761\u7684\u5fae\u5206\u503c\u975e\u96f6<\/p>\n<p>\u4efb\u4f55\u4e8c\u9636\u5fae\u5206\u7684\u5b9a\u4e49\u5fc5\u987b\u4fdd\u8bc1\u4ee5\u4e0b\u51e0\u70b9\uff1a<br \/>\n 1. \u5728\u6052\u5b9a\u7070\u5ea6\u533a\u57df\u7684\u5fae\u5206\u503c\u4e3a\u96f6<br \/>\n 2. \u5728\u7070\u5ea6\u53f0\u9636\u6216\u659c\u5761\u5904\u5fae\u5206\u503c\u975e\u96f6<br \/>\n 3. \u6cbf\u7740\u659c\u5761\u7684\u5fae\u5206\u503c\u975e\u96f6<\/p>\n<p>\u5bf9\u4e8e\u4e00\u7ef4\u51fd\u6570<span class=\"katex math inline\">f(x)<\/span>,\u5176\u4e00\u9636\u5fae\u5206\u7684\u5b9a\u4e49\u662f\u63d2\u503c<\/p>\n<p>&#8220;`math<br \/>\n \\frac{\\partial f}{\\partial x}=f(x+1)-f(x) \\tag{3.6-1}<br \/>\n &#8220;`<\/p>\n<p>\u5c06\u4e8c\u9636\u5fae\u5206\u5b9a\u4e49\u4e3a\u5982\u4e0b\u5dee\u5206\uff1a<\/p>\n<p>&#8220;`math<br \/>\n \\frac{\\partial ^2 f}{\\partial x^2}=f(x+1)+f(x-1)-2f(x) \\tag{3.6-2}<br \/>\n &#8220;`<br \/>\n \u4e8c\u9636\u5fae\u5206\u5728\u589e\u5f3a\u7ec6\u8282\u65b9\u9762\u8981\u6bd4\u4e00\u9636\u5fae\u5206\u597d\u5f88\u591a\uff0c\u8fd9\u662f\u4e00\u4e2a\u9002\u5408\u9510\u5316\u56fe\u50cf\u7684\u7406\u60f3\u7279\u5f81<\/p>\n<p>## 3.6.2 \u4f7f\u7528\u4e8c\u9636\u5fae\u5206\u8fdb\u884c\u56fe\u50cf\u9510\u5316\u2014\u2014\u62c9\u666e\u62c9\u65af\u7b97\u5b50<br \/>\n \u8fd9\u79cd\u65b9\u6cd5\u57fa\u672c\u4e0a\u662f\u4e00\u79cd\u5404\u5411\u540c\u6027\u7684\u6ee4\u6ce2\u5668\uff0c\u8fd9\u79cd\u6ee4\u6ce2\u5668\u7684\u54cd\u5e94\u4e0e\u6ee4\u6ce2\u5668\u4f5c\u7528\u7684\u56fe\u50cf\u7684\u7a81\u53d8\u65b9\u5411\u65e0\u5173\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5404\u5411\u540c\u6027\u6ee4\u6ce2\u5668\u662f\u65cb\u8f6c\u4e0d\u53d8\u7684\uff0c\u5373\u5c06\u539f\u56fe\u50cf\u65cb\u8f6c\u540e\u8fdb\u884c\u6ee4\u6ce2\u7ed9\u51fa\u7684\u7ed3\u679c\u4e0e\u5148\u5bf9\u56fe\u50cf\u6ee4\u6ce2\u7136\u540e\u5728\u65cb\u8f6c\u5f97\u51fa\u7684\u7ed3\u679c\u76f8\u540c\u3002<\/p>\n<p>\u6700\u7b80\u5355\u7684\u5404\u5411\u540c\u6027\u5fae\u5206\u7b97\u5b50\u662f\u62c9\u666e\u62c9\u65af\u7b97\u5b50\uff0c\u4e00\u4e2a\u4e8c\u7ef4\u56fe\u50cf\u51fd\u6570<span class=\"katex math inline\">f(x,y)<\/span>\u7684\u62c9\u666e\u62c9\u65af\u7b97\u5b50\u5b9a\u4e49\u4e3a\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">\\bigtriangledown  ^2f=\\frac{\\partial ^2 f}{\\partial x^2}+\\frac{\\partial ^2 f}{\\partial y^2}\n<\/div>\n<p>\u56e0\u4e3a\u4efb\u610f\u9636\u5fae\u5206\u90fd\u662f\u7ebf\u6027\u64cd\u4f5c\uff0c\u6240\u4ee5\u62c9\u666e\u62c9\u65af\u53d8\u6362\u4e5f\u662f\u4e00\u4e2a\u7ebf\u6027\u7b97\u5b50\u3002\u8bb0\u4f4f\uff0c\u6211\u4eec\u5fc5\u987b\u652f\u6301\u7b2c\u4e8c\u4e2a\u53d8\u91cf\uff0c\u5728x\u65b9\u5411\u4e0a\uff0c\u6211\u4eec\u6709<\/p>\n<div class=\"katex math multi-line no-emojify\">\\frac{\\partial ^2 f}{\\partial x^2}=f(x+1,y)+f(x-1,y)-2f(x,y) \\tag{3.6-4}\n<\/div>\n<p>\u7c7b\u4f3c\u7684\uff0c\u5728y\u65b9\u5411\uff0c\u6211\u4eec\u6709<\/p>\n<div class=\"katex math multi-line no-emojify\">\\frac{\\partial ^2 f}{\\partial ^2}=f(x,y+1)+f(x,y-1)-2f(x,y) \\tag{3.6-5}\n<\/div>\n<p>\u4e24\u4e2a\u53d8\u91cf\u7684\u79bb\u6563\u62c9\u666e\u62c9\u65af\u7b97\u5b50\u662f<\/p>\n<div class=\"katex math multi-line no-emojify\">\\bigtriangledown  ^2f=f(x,y+1)+f(x,y-1)+f(x,y+1)+f(x,y-1)-4f(x,y)\n<\/div>\n<p>\u6211\u4eec\u4f7f\u7528\u62c9\u666e\u62c9\u65af\u5bf9\u56fe\u50cf\u589e\u5f3a\u7684\u57fa\u672c\u65b9\u6cd5\u53ef\u8868\u793a\u4e3a\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">g(x,y)=f(x,y)+c[\\bigtriangledown^2f(x,y)] \\tag{3.6-7}\n<\/div>\n<p>\u5176\u4e2d\uff0cf(x,y)\u548cg(x,y)\u5206\u522b\u662f\u8f93\u5165\u56fe\u50cf\u548c\u9510\u5316\u540e\u7684\u56fe\u50cf\u3002<br \/>\n\u4e00\u4e2a\u5178\u578b\u7684\u6807\u5b9a\u62c9\u666e\u62c9\u65af\u56fe\u50cf\u7684\u65b9\u6cd5\u662f\u5bf9\u5b83\u7684\u6700\u5c0f\u503c\u52a0\u4e00\u4e2a\u65b0\u7684\u4ee3\u66ff0\u7684\u6700\u5c0f\u503c\uff0c\u7136\u540e\u5c06\u7ed3\u679c\u6807\u5b9a\u5230\u6574\u4e2a\u7070\u5ea6\u8303\u56f4<span class=\"katex math inline\">[ 0,L-1]<\/span>\u5185\u3002<\/p>\n<h2><span id=\"363\">3.6.3 \u975e\u9510\u5316\u63a9\u853d\u548c\u9ad8\u63d0\u5347\u6ee4\u6ce2<\/span><\/h2>\n<p>\u56fe\u50cf\u9510\u5316\u8fc7\u7a0b\uff0c\u4ece\u539f\u56fe\u50cf\u4e2d\u51cf\u53bb\u4e00\u5e45\u975e\u9510\u5316\uff08\u5e73\u6ed1\u8fc7\u7684\uff09\u7248\u672c\uff0c\u8fd9\u4e2a\u6210\u4e3a\u975e\u9510\u5316\u63a9\u853d\u7684\u5904\u7406\u7531\u4e0b\u5217\u6b65\u9aa4\u7ec4\u6210\uff1a<br \/>\n1. \u6a21\u7cca\u539f\u56fe\u50cf<br \/>\n2. \u4ece\u539f\u56fe\u50cf\u4e2d\u51cf\u53bb\u6a21\u7cca\u56fe\u50cf\uff08\u4ea7\u751f\u7684\u63d2\u503c\u56fe\u50cf\u6210\u4e3a\u6a21\u677f\uff09<br \/>\n3. \u5c06\u6a21\u677f\u52a0\u5230\u539f\u56fe\u50cf\u4e0a<\/p>\n<p>\u4ee4<span class=\"katex math inline\">\\bar{f}(x,y)<\/span>\u8868\u793a\u6a21\u7cca\u56fe\u50cf\uff0c\u975e\u9510\u5316\u63a9\u853d\u4ee5\u516c\u5f0f\u5f62\u5f0f\u63cf\u8ff0\u5982\u4e0b\uff0c\u9996\u5148\uff0c\u6211\u4eec\u5f97\u5230\u6a21\u677f\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">g_{mask}(x,y)=f(x,y)-\\bar{f}(x,y) \\tag{3.6-8}\n<\/div>\n<p>\u7136\u540e\uff0c\u5728\u539f\u56fe\u50cf\u4e0a\u52a0\u4e0a\u8be5\u6a21\u677f\u7684\u4e00\u4e2a\u6743\u91cd<\/p>\n<div class=\"katex math multi-line no-emojify\">g(x,y)=f(x,y)+k*g_{mask}(x,y) \\tag{3.6-9}\n<\/div>\n<p>\u901a\u5e38\uff0c\u6211\u4eec\u4f1a\u5728\u4e0a\u5e02\u5305\u542b\u4e00\u4e2a\u6743\u91cd\u7cfb\u6570<span class=\"katex math inline\">k(k\\geq0)<\/span>\u3002\u5f53k=1\u65f6\uff0c\u6211\u4eec\u5f97\u5230\u4e0a\u9762\u5b9a\u4e49\u7684\u975e\u9510\u5316\u63a9\u853d\uff0c\u5f53<span class=\"katex math inline\">k > 1<\/span>\u65f6\uff0c\u8be5\u5904\u7406\u6210\u4e3a\u9ad8\u63d0\u5347\u6ee4\u6ce2\uff0c\u9009\u62e9<span class=\"katex math inline\">k&lt;1<\/span>\u5219\u4e0d\u5f3a\u8c03\u975e\u9510\u5316\u6a21\u677f\u7684\u8d21\u732e\u3002<\/p>\n<h2><span id=\"364\">3.6.4 \u4f7f\u7528\u4e00\u9636\u5fae\u5206\u5bf9\uff08\u975e\u7ebf\u6027\uff09\u56fe\u50cf\u9510\u5316\u2014\u2014\u68af\u5ea6<\/span><\/h2>\n<p>\u56fe\u50cf\u5904\u7406\u4e2d\u7684\u4e00\u9636\u5fae\u5206\u662f\u7528\u68af\u5ea6\u5e45\u503c\u6765\u5b9e\u73b0\u7684\u3002\u5bf9\u4e8e\u51fd\u6570f(x,y),f\u5728\u5750\u6807(x,y)\u5904\u7684\u68af\u5ea6\u5b9a\u4e49\u4e3a\u4e8c\u7ef4\u5217\u5411\u91cf<\/p>\n<div class=\"katex math multi-line no-emojify\">\\bigtriangledown \\equiv grad(f) \\equiv<br \/>\n\\begin{bmatrix}<br \/>\n g_x\\\\g_y<br \/>\n\\end{bmatrix} =<br \/>\n\\begin{bmatrix}<br \/>\n\\frac{\\partial f}{\\partial x} \\\\<br \/>\n\\frac{\\partial f}{\\partial y}<br \/>\n\\end{bmatrix}<br \/>\n \\tag{3.6-10}\n<\/div>\n<p>\u5411\u91cf<span class=\"katex math inline\">\\bigtriangledown f<\/span>\u7684\u5e45\u5ea6\u503c\uff08\u957f\u5ea6\uff09\u8868\u793a\u4e3a<span class=\"katex math inline\">M\uff08x,y\uff09<\/span>:<\/p>\n<div class=\"katex math multi-line no-emojify\">M(x,y)=mag(\\bigtriangledown f) = \\sqrt{g_x^2+g_y^2} \\tag{3.6-11}\n<\/div>\n<p>\u8be5\u56fe\u50cf\u901a\u5e38\u79f0\u4e3a\u68af\u5ea6\u56fe\u50cf<br \/>\n\u5728\u67d0\u4e9b\u5b9e\u73b0\u4e2d\uff0c\u7528\u7edd\u5bf9\u503c\u6765\u8fd1\u4f3c\u5e73\u65b9\u548c\u5e73\u65b9\u6839\u64cd\u4f5c\u66f4\u9002\u5408\u8ba1\u7b97\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">M(x,y) \\approx|g_x|+|g_y|  \\tag{3.6-12}\n<\/div>\n<p>\u7f57\u4f2f\u7279\u4ea4\u53c9\u68af\u5ea6\u7b97\u5b50<br \/>\nSoble\u7b97\u5b50<\/p>\n<h1><span id=\"37\">3.7 \u6df7\u5408\u7a7a\u95f4\u589e\u5f3a\u6cd5<\/span><\/h1>\n<h1><span id=\"38\">3.8 \u4f7f\u7528\u6a21\u7cca\u6280\u672f\u8fdb\u884c\u7070\u5ea6\u53d8\u6362\u548c\u7a7a\u95f4\u6ee4\u6ce2<\/span><\/h1>\n<h1><span id=\"382\">3.8.2 \u6a21\u7cca\u5ea6\u96c6\u5408\u8bba\u539f\u7406<\/span><\/h1>\n<p>\u5b9a\u4e49\uff1a\u4ee4Z\u4e3a\u5143\u7d20\uff08\u5bf9\u8c61\uff09\u96c6\uff0cz\u8868\u793aZ\u7684\u4e00\u7c7b\u5143\u7d20\uff0c\u5373Z={z}\u3002\u8be5\u96c6\u5408\u79f0\u4e3a\u8bba\u57df\u3002Z\u4e2d\u7684\u6a21\u7cca\u96c6\u5408A\u7531\u96b6\u5c5e\u5ea6\u51fd\u6570<span class=\"katex math inline\">\\mu_A(z)<\/span>\u8868\u5f81\uff0c\u5b83\u662f\u4e0eZ\u7684\u5143\u7d20\u76f8\u5173\u7684\u5728\u533a\u95f4<span class=\"katex math inline\">[0,1]<\/span>\u5185\u7684\u4e00\u4e2a\u5b9e\u6570.<span class=\"katex math inline\">\\mu_A(z)<\/span>\u5728z\u5904\u7684\u503c\u8868\u793aA\u4e2dz\u7684\u96b6\u5c5e\u5ea6\u7b49\u7ea7\u3002<br \/>\n\u5bf9\u4e8e\u6a21\u7cca\u96c6\u5408\uff0c\u6211\u4eec\u8bf4<span class=\"katex math inline\">\\mu_A(z)=1<\/span>\u7684\u6240\u6709z\u90fd\u662f\u96c6\u5408\u7684\u5b8c\u5168\u6210\u5458\uff0c\u5bf9\u4e8e<span class=\"katex math inline\">\\mu_A(z)=0<\/span>\u7684\u6240\u6709z\u90fd\u4e0d\u662f\u96c6\u5408\u7684\u6210\u5458\uff0c\u800c<span class=\"katex math inline\">\\mu_A(z)<\/span>\u7684\u503c\u4ecb\u4e8e0\u548c1\u4e4b\u95f4\u7684\u6240\u6709z\u662f\u96c6\u5408\u7684\u90e8\u5206\u6210\u5458\u3002\u56e0\u6b64\uff0c\u6a21\u7cca\u96c6\u5408\u662f\u4e00\u4e2a\u7531z\u503c\u548c\uff08\u8d4b\u4e88z\u6210\u5458\u7b49\u7ea7\u7684\uff09\u76f8\u5e94\u96b6\u5c5e\u5ea6\u51fd\u6570\u7ec4\u6210\u7684\u5e8f\u5bf9\uff0c\u5373\uff1a<\/p>\n<div class=\"katex math multi-line no-emojify\">A=\\{z,\\mu_A(z)|z \\in Z\\} \\tag{3.8 -1}\n<\/div>\n<div class=\"katex math multi-line no-emojify\">A={(1,1),(2,1),(3,1),&#8230;,(20,1),(21,0.9),(22,0.8),&#8230;,(25,0.5),(24,0.4),&#8230;,(29,0.1)}\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Contents1 3.1 \u80cc\u666f\u77e5\u8bc61.1 3.1.1 \u7070\u5ea6\u53d8\u6362\u548c\u7a7a\u95f4\u6ee4\u6ce2\u57fa\u78402 3.2 \u4e00\u4e9b\u57fa\u672c\u7684\u7070\u5ea6\u53d8\u6362\u51fd [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[43,17],"tags":[],"class_list":["post-964","post","type-post","status-publish","format-standard","hentry","category-43","category-17"],"_links":{"self":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/964","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=964"}],"version-history":[{"count":12,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/964\/revisions"}],"predecessor-version":[{"id":966,"href":"https:\/\/www.wayln.com\/index.php?rest_route=\/wp\/v2\/posts\/964\/revisions\/966"}],"wp:attachment":[{"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=964"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=964"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wayln.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=964"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}