{"id":1905,"date":"2018-08-12T21:15:54","date_gmt":"2018-08-12T13:15:54","guid":{"rendered":"http:\/\/www.storagelab.org.cn\/zhangdi\/?p=1905"},"modified":"2018-08-12T21:15:54","modified_gmt":"2018-08-12T13:15:54","slug":"chinavis2018%e5%8f%82%e4%bc%9a%e8%ae%b0%e5%bd%951%ef%bc%9a%e4%bf%a1%e6%81%af%e8%ae%ba%e5%9c%a8%e5%8f%af%e8%a7%86%e5%8c%96%e4%b8%ad%e7%9a%84%e5%ba%94%e7%94%a8","status":"publish","type":"post","link":"https:\/\/www.divis.cn\/index.php\/2018\/08\/12\/chinavis2018%e5%8f%82%e4%bc%9a%e8%ae%b0%e5%bd%951%ef%bc%9a%e4%bf%a1%e6%81%af%e8%ae%ba%e5%9c%a8%e5%8f%af%e8%a7%86%e5%8c%96%e4%b8%ad%e7%9a%84%e5%ba%94%e7%94%a8\/","title":{"rendered":"chinavis2018\u53c2\u4f1a\u603b\u7ed31\uff1a\u4fe1\u606f\u8bba\u5728\u53ef\u89c6\u5316\u4e2d\u7684\u5e94\u7528"},"content":{"rendered":"<p>\u4eca\u5e747\u670825\u65e5\uff0c\u4e2d\u56fd\u53ef\u89c6\u5316\u4e0e\u53ef\u89c6\u5206\u6790\u5927\u4f1achinavis 2018\u5728\u4e0a\u6d77\u4e3e\u884c\uff08\u5927\u4f1a\u7f51\u5740http:\/\/www.chinavis.org\/2018\/challenge.html\uff09\u3002\u668c\u8fdd\u4e24\u5e74\u4e4b\u4e45\uff0c\u6211\u4e5f\u4e13\u7a0b\u524d\u5f80\u3002\u53ef\u80fd\u56e0\u4e3a\u662f\u5728\u4e0a\u6d77\u7684\u7f18\u6545\u5427\uff0c\u8fd9\u51e0\u65e5\u5929\u6c14\u76f8\u5f53\u6e7f\u70ed\uff0c\u540c\u65f6\u4f1a\u8bae\u8d39\u4e5f\u4e3a\u5386\u5c4a\u6700\u9ad8\u3002\u867d\u7136\u5982\u6b64\uff0c\u4f9d\u7136\u6321\u4e0d\u4f4f\u6211\u7b49\u4e0e\u4f1a\u8005\u7684\u70ed\u60c5\u30023\u5929\u7684\u4f1a\u8bae\u5185\u5bb9\uff0c\u5305\u62ec\u7279\u9080\u62a5\u544a\u3001\u524d\u5bfc\u8bfe\u7a0b\u3001\u535a\u58eb\u751f\u8bba\u575b\u3001\u4e13\u9898\u3001\u7279\u522bPanel\u3001\u4ea7\u5b66\u7814\u9ad8\u5cf0\u8bba\u575b\u53ca\u4f01\u4e1a\u5c55\u89c8\u62a5\u544a\u3001360\u676f\u6570\u636e\u53ef\u89c6\u5206\u6790\u6311\u6218\u8d5b\uff0c\u4ee5\u53ca\u5305\u62ecVIS\u5206\u4eab\u4e4b\u591c\u3001\u53ef\u89c6\u5316\u4e0e\u53ef\u89c6\u5206\u6790\u4e13\u59d4\u4f1a\u4f1a\u8bae\u3001\u6e38\u8239\u665a\u5bb4\u5728\u5185\u7684\u5176\u4ed6\u8bae\u7a0b\u3002\u4f1a\u8bae\u5185\u5bb9\u5982\u6b64\u4e4b\u4e30\u5bcc\uff0c\u65e0\u6cd5\u5c3d\u8ff0\uff0c\u6545\u800c\u672c\u4eba\u53ea\u4ee5\u4e2a\u4eba\u7814\u7a76\u5174\u8da3\u2014\u2014\u201c\u7f51\u7edc\u5b89\u5168\u53ef\u89c6\u5316\u201d\u4e3a\u4e2d\u5fc3\uff0c\u8bb0\u5f55\u4e00\u4e9b\u76f8\u5173\u5185\u5bb9\u3002<\/p>\n<p>\u9996\u5148\u60f3\u8bb0\u5f55\u7684\u5185\u5bb9\u662f7\u670825\u65e5\u4e0b\u5348\u5728\u534e\u4e1c\u5e08\u8303\u5927\u5b66\u8ba1\u7b97\u673a\u5b66\u9662\u5185\u4e3e\u529e\u7684\u524d\u5bfc\u8bfe\u7a0b\uff0c\u300aInformation Theory for Visualization\u300b(\u4fe1\u606f\u8bba\u5728\u53ef\u89c6\u5316\u4e2d\u7684\u5e94\u7528)\u3002\u6f14\u8bb2\u8005\u4e3a\u6c88\u6c49\u5a01\u6559\u6388\uff0c\u4ed6\u672c\u4eba\u662f\u53f0\u6e7e\u4eba\uff0c\u73b0\u5c31\u804c\u4e8e\u7f8e\u56fd\u4fc4\u4ea5\u4fc4\u5dde\u5927\u5b66\uff0c\u627f\u63a5\u8fc7\u5f88\u591aNASA\u9879\u76ee\uff0c\u4e3b\u8981\u7814\u7a76\u65b9\u5411\u662f\u9762\u5411\u6d41\u4f53\u529b\u5b66\u7684\u79d1\u5b66\u53ef\u89c6\u5316\u3002\u4ed6\u8fd8\u6709\u6c11\u4e50\u65b9\u9762\u7684\u4e2a\u4eba\u7231\u597d\uff0c\u5bf9\u97f3\u4e50\u53ef\u89c6\u5316\u5f88\u6709\u5174\u8da3\u3002\u6b64\u6b21\u524d\u6765\uff0c\u9664\u4e86\u529e\u8bb2\u5ea7\uff0c\u4e5f\u6709\u62db\u6536\u535a\u58eb\u751f\u7684\u76ee\u7684\u3002\u6bd5\u7adf\u7f8e\u56fd\u90a3\u8fb9\u7684\u79d1\u7814\u4e3b\u529b\uff0c\u8fd8\u662f\u6253\u62fcH1B\u7684\u5404\u8def\u535a\u58eb\u751f\u3002\u4ee5\u4e0b\u6587\u5b57\u662f\u6211\u8bfe\u4e0a\u7684\u62cd\u7167\u8bb0\u5f55\uff0c\u518d\u52a0\u4e0a\u6211\u5927\u91cf\u7684\u5185\u5bb9\u8865\u5145\u3002\u5e0c\u671b\u5404\u4f4d\u8bfb\u8005\u770b\u540e\u80fd\u5bf9\u4fe1\u606f\u8bba\u7684\u5e94\u7528\u573a\u666f\u6709\u66f4\u4e30\u5bcc\u7684\u8054\u60f3\u3002\u5982\u6709\u4e0d\u5bf9\u7684\u5730\u65b9\u6b22\u8fce\u5927\u5bb6\u6279\u8bc4\u6307\u6b63\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a1.png\" width=\"607\" height=\"436\" \/><\/p>\n<p>\u4fe1\u606f\u8bba\u5bf9\u6211\u7b49\u800c\u8a00\u5e76\u975e\u751f\u758f\u7684\u6982\u5ff5\u3002\u56e0\u4e3a\u8ba1\u7b97\u673a\u79d1\u5b66\u4e0e\u5e94\u7528\u6570\u5b66\u672c\u6765\u5c31\u662f\u4e00\u5806\u5b6a\u751f\u5144\u5f1f\uff0c\u90fd\u6e90\u81ea\u4e8c\u6218\u671f\u95f4\u5f39\u9053\u8ba1\u7b97\u548c\u5bc6\u7801\u5206\u6790\u5b66\u7814\u7a76\u3002\u5e94\u7528\u6570\u5b66\u4e2d\u5305\u62ec\u4e09\u4e2a\u91cd\u8981\u7406\u8bba\uff1a\u4fe1\u606f\u8bba\u3001\u5bc6\u7801\u5b66\u548c\u8ba1\u7b97\u6570\u8bba\u3002\u4fe1\u606f\u8bba\u662f\u5173\u4e8e\u4fe1\u606f\u7684\u7406\u8bba\uff0c\u800c\u4fe1\u606f\u7684\u4f20\u64ad\u53c8\u79bb\u4e0d\u5f00\u52a0\u5bc6\uff0c\u52a0\u5bc6\u7684\u4e3b\u8981\u65b9\u6cd5\u76ee\u524d\u53c8\u662f\u901a\u8fc7\u6570\u8bba\u3001\u8d28\u6570\u8fd9\u65b9\u9762\u7684\u77e5\u8bc6\u6765\u5b9e\u73b0\u3002\u8fd9\u4e9b\u5e94\u7528\u6570\u5b66\u7406\u8bba\u76f4\u63a5\u6784\u6210\u4e86\u73b0\u4ee3\u8ba1\u7b97\u673a\u6280\u672f\u7684\u57fa\u7840\uff0c\u5728\u6570\u636e\u53ef\u89c6\u5316\u3001\u6570\u636e\u5206\u6790\u9886\u57df\u6709\u7740\u91cd\u8981\u7684\u4f5c\u7528\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a2.png\" width=\"359\" height=\"270\" \/><\/p>\n<h2>\u95ee\u9898\u7684\u63d0\u51fa\uff1a\u5927\u6570\u636e\u53ef\u89c6\u5316\u4e2d\u5e38\u89c1\u7684\u95ee\u9898<\/h2>\n<blockquote><p>\u6570\u636e\u7cbe\u7b80\u548c\u7b5b\u9009<\/p>\n<p style=\"padding-left: 30px\">\u54ea\u91cc\u662f\u663e\u8457\u533a\u57df\uff1f\u5e94\u8be5\u4f7f\u7528\u4ec0\u4e48\u6837\u7684\u5206\u8fa8\u7387\u5448\u73b0\u6570\u636e\uff1f\u5982\u4f55\u627e\u5230\u6570\u636e\u6700\u7cbe\u9ad3\u7684\u4ee3\u8868\u8005?<\/p>\n<p>\u7279\u5f81\u63d0\u53d6\u548c\u8ffd\u8e2a<\/p>\n<p style=\"padding-left: 30px\">\u5982\u4f55\u9009\u62e9\u6700\u597d\u7684\u7b97\u6cd5\u53c2\u6570(\u5982\u6d41\u7ebf\u8d77\u59cb\u70b9\uff0c\u7b49\u503c\u9762\u7b49)\uff1f<\/p>\n<p style=\"padding-left: 30px\">\u6570\u636e\u53ef\u89c6\u5316\u65f6\u80fd\u63ed\u793a\u591a\u5c11\u6709\u7528\u7684\u4fe1\u606f\uff1f<\/p>\n<p>\u53ef\u89c6\u5316\u6620\u5c04\u548c\u56fe\u50cf\u5206\u6790<\/p>\n<p style=\"padding-left: 30px\">\u8fd9\u662f\u4e00\u4e2a\u597d\u7684\u89c2\u5bdf\u70b9\u5417\uff1f\u8fd9\u662f\u4e00\u4e2a\u597d\u7684\u8f6c\u6362\u65b9\u6cd5\u5417\uff1f\u8861\u91cf\u6307\u6807\u662f\u4ec0\u4e48\uff1f<\/p>\n<\/blockquote>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a3.png\" width=\"330\" height=\"239\" \/><\/p>\n<p>\u4f17\u6240\u5468\u77e5\uff0c\u6570\u636e\u53ef\u89c6\u5316\u7684\u4e00\u822c\u8fc7\u7a0b\u5982\u4e0b\uff1a<\/p>\n<blockquote><p>\u6570\u636e&#8211;&gt;filtering(\u8fc7\u6ee4\u6216\u8005\u7cbe\u7b80)&#8211;&gt;feature extraction(\u7279\u5f81\u63d0\u53d6) &#8211;&gt;visual mapping(\u89c6\u89c9\u6620\u5c04)&#8211;&gt;rendering(\u6e32\u67d3)<\/p><\/blockquote>\n<p>\u4ee5\u4e0a\u6bcf\u4e00\u6b65\u5904\u7406\uff0c\u90fd\u4f1a\u4e22\u5931\u4e00\u4e9b\u6570\u636e\u3002\u5982\u4f55\u786e\u5b9a\u54ea\u4e9b\u6570\u636e\u53ef\u4ee5\u4e22\uff0c\u54ea\u4e9b\u4e0d\u80fd\u4e22\uff1f\u4e3a\u4e86\u5fc5\u987b\u8981\u6709\u4e00\u4e2a\u91cf\u5316\u6807\u51c6\u3002<\/p>\n<h2>\u5e38\u89c4\u7edf\u8ba1\u5206\u6790\u65b9\u6cd5<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a4.png\" width=\"441\" height=\"314\" \/><\/p>\n<p>\u5728\u6570\u636e\u5206\u6790\u8fc7\u7a0b\u4e2d\uff0c\u5206\u6790\u4eba\u5458\u5f80\u5f80\u4f1a\u6839\u636e\u6570\u636e\u96c6\u7684\u7279\u70b9\uff0c\u8ba1\u7b97\u5176\u8303\u56f4\u5206\u5e03\u3001\u5411\u91cf\u5206\u5e03\u3001\u7279\u5f81\u5206\u5e03\u7b49\u7684\u6982\u7387\u5bc6\u5ea6\u6a21\u578b\uff0c\u4ee5\u6b64\u4f5c\u4e3a\u6570\u636e\u96c6\u6700\u7cbe\u9ad3\u7684\u4ee3\u8868\u3002\u8ba1\u7b97\u6982\u7387\u5bc6\u5ea6\u6a21\u578b\u6709\u53c2\u6570\u4f30\u8ba1\u548c\u975e\u53c2\u6570\u4f30\u8ba1\u4e24\u5927\u7c7b\u65b9\u6cd5\u3002\u53c2\u6570\u4f30\u8ba1\u5c31\u662f\u5047\u5b9a\u6837\u672c\u96c6\u7b26\u5408\u67d0\u4e00\u6982\u7387\u5206\u5e03\uff0c\u7136\u540e\u6839\u636e\u6837\u672c\u96c6\u62df\u5408\u8be5\u5206\u5e03\u4e2d\u7684\u53c2\u6570\uff0c\u5f97\u5230\u4e00\u4e2a\u89e3\u6790\u89e3\u3002\u5178\u578b\u4f8b\u5b50\u6709<a href=\"https:\/\/www.jianshu.com\/p\/f1d3906e4a3e\">\u4f3c\u7136\u4f30\u8ba1<\/a>\u3001<a href=\"https:\/\/www.cnblogs.com\/lvchaoshun\/p\/7115460.html\">\u9ad8\u65af\u5206\u5e03<\/a>\u3001<a href=\"https:\/\/www.cnblogs.com\/lvchaoshun\/p\/7115460.html\">\u6df7\u5408\u9ad8\u65af<\/a>\u7b49\u7b49\uff0c\u8fd9\u4e9b\u5185\u5bb9\u5728\u5927\u5b66\u6982\u7387\u8bba\u91cc\u90fd\u8bb2\u8fc7\u3002\u975e\u53c2\u6570\u4f30\u8ba1\u5219\u662f\u4e0d\u9884\u5148\u8bbe\u5b9a\u6982\u7387\u5206\u5e03\u6a21\u578b\uff0c\u53ea\u5229\u7528\u6570\u636e\u672c\u8eab\u6765\u5bf9\u6982\u7387\u5bc6\u5ea6\u505a\u62df\u5408\uff0c\u5f97\u5230\u4e00\u4e2a\u8fd1\u4f3c\u89e3\u3002\u5178\u578b\u4f8b\u5b50\u6709<a href=\"https:\/\/en.wikipedia.org\/wiki\/Histogram\">\u76f4\u65b9\u56fe<\/a>\uff0c<a href=\"https:\/\/blog.csdn.net\/unixtch\/article\/details\/78556499\">\u6838\u5bc6\u5ea6\u4f30\u8ba1<\/a>\u7b49\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/wa.jpg\" width=\"291\" height=\"168\" \/><\/p>\n<p>\u6982\u7387\u5bc6\u5ea6\u6a21\u578b\u7ed9\u51fa\u4e86\u6570\u636e\u5206\u5e03\u89c4\u5f8b\uff0c\u65b9\u4fbf\u4eba\u4eec\u8fdb\u884c\u4f30\u503c\u548c\u9884\u6d4b\uff0c\u4e0d\u8fc7\u5e76\u6ca1\u6709\u6307\u660e\u201c\u54ea\u4e9b\u6570\u636e\u53ef\u4ee5\u4e22\uff0c\u54ea\u4e9b\u4e0d\u80fd\u4e22\u201d\u3002\u663e\u7136\u6211\u4eec\u5e0c\u671b\u4e22\u6389\u7684\u6570\u636e\u662f\u90a3\u4e9b\u91cd\u590d\u7684\u3001\u610f\u4e49\u4e0d\u5927\u7684\u6570\u636e\uff0c\u800c\u4fe1\u606f\u8bba\u7ed9\u51fa\u4e86\u4e00\u4e2a\u5224\u65ad\u6807\u51c6\u3002<\/p>\n<h2>\u4fe1\u606f\u71b5\u7684\u6982\u5ff5<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a5.png\" width=\"813\" height=\"470\" \/><\/p>\n<p>\u4fe1\u606f\u8bba\u5c06\u4fe1\u606f\u4f20\u9012\u4f5c\u4e3a\u4e00\u79cd\u7edf\u8ba1\u73b0\u8c61\u6765\u8003\u8651\u3002\u4fe1\u606f\u8bba\u7684\u6838\u5fc3\uff0c\u662f\u4fe1\u606f\u91cf\u548c\u4fe1\u606f\u71b5\uff08Entropy\uff09\u4e24\u4e2a\u6982\u5ff5\uff1a<\/p>\n<p>\u8bbe\u4e00\u4e2a\u79bb\u6563\u578b\u968f\u673a\u53d8\u91cfX\u53ef\u4ee5\u6709n\u79cd\u53d6\u503c{X1, X2, X3, &#8230; , Xn}\uff0c\u6bcf\u79cd\u53d6\u503c\u7684\u6982\u7387\u662f{p1, p2, p3, &#8230;, pn}\u3002p(Xi)=pi\u3002\u90a3\u4e48\u6bcf\u79cd\u53d6\u503cXi\u53d1\u751f\u65f6\u6240\u4ea7\u751f\u7684\u201c\u4fe1\u606f\u91cf\u201d\u88ab\u5b9a\u4e49\u4e3a\uff1a<\/p>\n<p>H(Xi) = \u2212\u00a0<img loading=\"lazy\" decoding=\"async\" title=\"\" src=\"http:\/\/zhangdi.dengxinbo.cn\/c2fdfc039245d688753aac5da6c27d1ed21b240a.jpg\" alt=\"\" width=\"46\" height=\"18\" align=\"absmiddle\" \/><\/p>\n<p>\u800c\u968f\u673a\u53d8\u91cfX\u7684\u201c\u4fe1\u606f\u71b5\u201d\u8bb0\u4e3a\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/7de5d59a442f5305853d4392826b1f51dc43f6d0.svg\" width=\"265\" height=\"62\" \/><\/p>\n<p>\u516c\u5f0f\u4e00\u591a\u5927\u5bb6\u4e0d\u5bb9\u6613\u7406\u89e3\u3002\u90a3\u4e48\u4e3e\u4e2a\u4f8b\u5b50\uff1a\u5728\u65b0\u95fbX\u4e2d\uff0c\u72d7\u54ac\u4eba\u53d1\u751f\u7684\u53ef\u80fd\u6027\u662f0.9\uff08\u8bb0\u4e3a\u4e8b\u4ef6X1\uff09\uff0c\u4eba\u54ac\u72d7\u7684\u53ef\u80fd\u6027\u662f0.1\uff08\u8bb0\u4e3a\u4e8b\u4ef6X2\uff09\u3002\u90a3\u4e48\u65b0\u95fb\u5185\u5bb9\u662fX1\u7684\u4fe1\u606f\u91cf\u662f\u591a\u5c11\uff1f\u662fX2\u7684\u4fe1\u606f\u91cf\u662f\u591a\u5c11\uff1f\u8ba1\u7b97\u5982\u4e0b\uff1a<\/p>\n<p>H(X1)=-\u00a0<img loading=\"lazy\" decoding=\"async\" title=\"\" src=\"http:\/\/zhangdi.dengxinbo.cn\/5bafa40f4bfbfbed6d3228867af0f736aec31fdb.jpg\" alt=\"\" width=\"76\" height=\"19\" align=\"absmiddle\" \/>\u00a0\u22480.152\uff08\u6bd4\u7279\uff09<\/p>\n<p>H(X2)=-\u00a0<img loading=\"lazy\" decoding=\"async\" title=\"\" src=\"http:\/\/zhangdi.dengxinbo.cn\/962bd40735fae6cdcc79b4980db30f2443a70f7d.jpg\" alt=\"\" width=\"76\" height=\"19\" align=\"absmiddle\" \/>\u00a0\u22483.32\uff08\u6bd4\u7279\uff09<\/p>\n<p>\u901a\u8fc7\u8ba1\u7b97\u5f97\u51fa\u7684\u7ed3\u679c\uff0c\u663e\u7136\u662f\u4eba\u54ac\u72d7\u4e8b\u4ef6X2\u5305\u542b\u7684\u4fe1\u606f\u91cf\u66f4\u5927\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6781\u5c11\u89c1\u7684\u4e8b\u4ef6\u6240\u5e26\u6765\u7684\u4fe1\u606f\u91cf\u591a\uff0c\u8fd9\u4e5f\u7b26\u5408\u6211\u4eec\u65e5\u5e38\u751f\u6d3b\u7ecf\u9a8c\u3002\u5982\u679c\u7528\u7edf\u8ba1\u5b66\u7684\u672f\u8bed\u6765\u63cf\u8ff0\uff0c\u5c31\u662f\u51fa\u73b0<a href=\"https:\/\/baike.baidu.com\/item\/%E6%A6%82%E7%8E%87\" target=\"_blank\" rel=\"noopener\">\u6982\u7387<\/a>\u5c0f\u7684\u4e8b\u4ef6\u4fe1\u606f\u91cf\u591a\u3002\u56e0\u6b64\uff0c\u4e8b\u4ef6\u51fa\u73b0\u5f97<a href=\"https:\/\/baike.baidu.com\/item\/%E6%A6%82%E7%8E%87\" target=\"_blank\" rel=\"noopener\">\u6982\u7387<\/a>\u8d8a\u5c0f\uff0c\u4fe1\u606f\u91cf\u6108\u5927\u3002\u5373\u4fe1\u606f\u91cf\u7684\u591a\u5c11\u662f\u4e0e\u4e8b\u4ef6\u53d1\u751f\u9891\u7e41\uff08\u5373<a href=\"https:\/\/baike.baidu.com\/item\/%E6%A6%82%E7%8E%87\" target=\"_blank\" rel=\"noopener\">\u6982\u7387<\/a>\u5927\u5c0f\uff09\u6210\u53cd\u6bd4\u3002\u4fe1\u606f\u91cf\u7684\u6982\u5ff5\u867d\u7136\u7b80\u5355\uff0c\u4e0d\u8fc7\u8fd9\u6837\u6211\u4eec\u5c31\u6709\u4e86\u4e00\u4e2a\u8861\u91cf\u4fe1\u606f\u4ef7\u503c\u9ad8\u4f4e\u7684\u6807\u51c6\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a6.png\" width=\"412\" height=\"276\" \/><\/p>\n<p>\u5bf9\u4e8e\u65b0\u95fbX\uff0c\u5b83\u7684\u201c\u4fe1\u606f\u71b5\u201d\u4e3a\uff1a<\/p>\n<p>H(X) = -0.9*\u00a0<img loading=\"lazy\" decoding=\"async\" title=\"\" src=\"http:\/\/zhangdi.dengxinbo.cn\/5bafa40f4bfbfbed6d3228867af0f736aec31fdb.jpg\" alt=\"\" width=\"76\" height=\"19\" align=\"absmiddle\" \/>\u00a0&#8211; 0.1*\u00a0<img loading=\"lazy\" decoding=\"async\" title=\"\" src=\"http:\/\/zhangdi.dengxinbo.cn\/962bd40735fae6cdcc79b4980db30f2443a70f7d.jpg\" alt=\"\" width=\"76\" height=\"19\" align=\"absmiddle\" \/>\u00a0= 0.468 (\u6bd4\u7279)<\/p>\n<p>\u4fe1\u606f\u71b5\u7684\u8ba1\u7b97\u7ed3\u679c\uff0c\u5176\u5b9e\u5c31\u662f\u65b0\u95fbX\u5305\u542b\u4fe1\u606f\u91cf\u7684\u6570\u5b66\u671f\u671b\u3002\u201c\u4fe1\u606f\u71b5\u201d\u53cd\u6620\u4e86\u4fe1\u606f\u672c\u8eab\u662f\u5426\u96be\u4ee5\u9884\u6d4b\u3002\u5982\u679c\u65b0\u95fbX\u968f\u673a\u6027\u5f88\u5927\uff0c\u6bd4\u5982\u72d7\u54ac\u4eba\u548c\u4eba\u54ac\u72d7\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387\u76f8\u540c\u90fd\u662f0.5\uff0c\u5219\u4fe1\u606f\u71b5\u5c31\u8fbe\u5230\u6700\u5927\u503c1\u3002\u53cd\u4e4b\uff0c\u5982\u679c\u65b0\u95fbX\u7684\u968f\u673a\u6027\u5f88\u5c0f\uff0c\u6bd4\u5982\u72d7\u54ac\u4eba\u7684\u6982\u7387\u662f\u8d8b\u8fd1100%\uff0c\u800c\u4eba\u54ac\u72d7\u7684\u6982\u7387\u8d8b\u7d270%\uff0c\u90a3\u4e48\u65b0\u95fbX\u7684\u4fe1\u606f\u71b5\u5c31\u4f1a\u65e0\u9650\u8d8b\u8fd10\u3002\u4e5f\u53ef\u4ee5\u8bf4\uff0c\u4fe1\u606f\u71b5\u8d8a\u5927\uff0c\u5219\u6bcf\u4e2a\u5176\u4e2d\u4e8b\u4ef6\u7684\u53d1\u751f\u6982\u7387\u5c31\u8d8a\u63a5\u8fd1\uff0c\u8d8a\u96be\u4ee5\u9884\u6d4b\u54ea\u4e2a\u4e8b\u4ef6\u4f1a\u53d1\u751f\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a8.png\" width=\"594\" height=\"418\" \/><\/p>\n<p>\u4ee5\u4e0a\u8ba8\u8bba\u7684\u90fd\u662f\u5355\u4e00\u968f\u673a\u53d8\u91cf\u7684\u60c5\u51b5\u3002\u5982\u679c\u6709\u4e24\u4e2a\u968f\u673a\u53d8\u91cfX\u548cY\uff0c\u5219\u8fd8\u6709\u4ea4\u53c9\u71b5H(X,Y)\uff0c\u6761\u4ef6\u71b5\uff08\u4e5f\u88ab\u7528\u4f5c\u8ba1\u7b97\u4e24\u4e2a\u53d8\u91cf\u5206\u5e03\u4e4b\u95f4\u7684\u8ddd\u79bb\uff09H(X|Y)\uff0c\u5171\u6709\u4fe1\u606f\u91cf\uff08\u5373\u4fe1\u606f\u91cd\u53e0\uff09I(X,Y)\uff0c\u4ed6\u4eec\u7684\u8ba1\u7b97\u516c\u5f0f\u5982\u4e0a\u56fe\u6240\u793a\u3002\u5b83\u4eec\u4e4b\u95f4\u7684\u5173\u7cfb\u5219\u53ef\u4ee5\u7528\u4e0b\u56fe\u8868\u793a\uff1a<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a9.png\" width=\"548\" height=\"296\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><span class=\"mwe-math-element\">\u603b\u800c\u8a00\u4e4b\uff0c<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/5fe8f152e001507cbf5e7db0788de9dd0d5deca8.svg\" width=\"226\" height=\"26\" \/>\u3002\u5173\u952e\u5c31\u5728\u4e8e\u4fe1\u606f\u91cd\u53e0\u7684\u90e8\u5206I(X,Y)\u7684\u5927\u5c0f\u3002<\/span><\/p>\n<p><span class=\"mwe-math-element\">\u5982\u679cX\u548cY\u662f\u72ec\u7acb\u968f\u673a\u53d8\u91cf\uff0c\u90a3\u4e48\u663e\u7136I(X,Y) =0\uff0cH(X,Y)=H(X)+ H(Y)\u3002<\/span><\/p>\n<h2>\u4fe1\u606f\u71b5\u7684\u5e94\u7528<\/h2>\n<p>\u663e\u7136\uff0c\u6570\u636e\u96c6\u4e5f\u662f\u4e00\u79cd\u4fe1\u606f\u3002\u53ea\u8981\u80fd\u88ab\u8ba1\u7b97\u6982\u7387\u5bc6\u5ea6\u6a21\u578b\uff0c\u5c31\u53ef\u4ee5\u4f7f\u7528\u4fe1\u606f\u8bba\u65b9\u6cd5\u8fdb\u884c\u5904\u7406\u3002\u56e0\u800c\u4fe1\u606f\u8bba\u53ef\u4ee5\u5e7f\u6cdb\u5e94\u7528\u4e8e\u6570\u636e\u5904\u7406\u8fc7\u7a0b\u4e2d\uff0c\u5305\u62ec\u89e3\u51b3\u201c\u54ea\u4e9b\u6570\u636e\u53ef\u4ee5\u4e22\uff0c\u54ea\u4e9b\u4e0d\u80fd\u4e22\u201d\u7684\u8bc4\u4ef7\u6807\u51c6\u95ee\u9898\u3002\u4e0b\u9762\u662f\u4e00\u4e9b\u5e94\u7528\u4e3e\u4f8b\u3002<\/p>\n<p><!--more--><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a10.png\" width=\"642\" height=\"444\" \/><\/p>\n<h2>\u5e94\u7528\u6848\u4f8b1\uff1a\u6700\u4f18\u6295\u5f71\u89c6\u56fe\u7684\u9009\u53d6\u6807\u51c6<\/h2>\n<p>\u5982\u4f55\u7ed9\u5b9a\u4e00\u4e2a\u8bc4\u4ef7\u6807\u51c6\uff0c\u786e\u5b9a\u54ea\u4e2a\u53ef\u89c6\u5316\u56fe\u5f62\u6548\u679c\u6700\u597d\uff1f<\/p>\n<p>\u5bf9\u4e8e3D\u6a21\u578b\uff0c\u6839\u636e\u6444\u50cf\u673a\u7684\u4f4d\u7f6e\u4e0d\u540c\uff0c\u770b\u5230\u7684\u56fe\u7247\u7ed3\u679c\u4e5f\u4e0d\u540c\u3002\u6bd4\u5982\u4e00\u9897\u7259\u9f7f\uff0c\u6839\u636e\u89c6\u89d2\u4e0d\u540c\uff0c\u6295\u5f71\u51fa\u6765\u76842D\u56fe\u50cf\u4e5f\u5404\u6709\u4e0d\u540c\uff0c\u4f8b\u5982\u4e0a\u9762\u8fd9\u56db\u4e2a\u7167\u7247\u3002\u90a3\u4e48\u5176\u4e2d\u54ea\u4e2a\u7259\u9f7f\u7167\u7247\u7b97\u662f\u6700\u4f18\u76842D\u89c6\u56fe\u5462\uff1f\u6709\u4ec0\u4e48\u53ef\u4ee5\u91cf\u5316\u7684\u5ba2\u89c2\u8bc4\u4ef7\u6807\u51c6\u5417\uff1f<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a11.png\" width=\"418\" height=\"294\" \/><\/p>\n<p>\u4e00\u4e2a\u6709\u6548\u8bc4\u4ef7\u6807\u51c6\u662f\u8ba1\u7b97\u6bcf\u4e00\u4e2a2D\u89c6\u56fe\u7684\u4fe1\u606f\u71b5\u3002\u6211\u4eec\u6839\u636e3D\u56fe\u5f62\u4e2d\u6bcf\u4e00\u4e2a\u4f53\u7d20\u6295\u5f71\u52302D\u7a7a\u95f4\u4e0a\u65f6\u6240\u8d21\u732e\u7684\u4fe1\u606f\u91cf\uff0c\u6765\u8ba1\u7b97\u6bcf\u4e2a2D\u89c6\u56fe\u7684\u4fe1\u606f\u71b5\u3002\u6240\u8c13\u4f53\u7d20\uff08voxel\uff09\uff0c\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u6700\u5c0f\u7acb\u4f53\u5355\u4f4d\uff0c\u7c7b\u4f3c\u4e8c\u7ef4\u7a7a\u95f4\u4e2d\u7684\u6700\u5c0f\u5355\u4f4d\u50cf\u7d20pixel\u3002\u7ecf\u6b64\u8ba1\u7b97\u540e\uff0c\u5982\u679c\u4e00\u4e2a2D\u89c6\u56fe\u7684\u4fe1\u606f\u71b5\u9ad8\uff0c\u90a3\u4e48\u5c31\u610f\u5473\u7740\u5404\u4e2a\u4f53\u7d20\u51fa\u73b0\u7684\u6982\u7387\u63a5\u8fd1\uff0c\u4e5f\u5c31\u662f\u8bf4\u8fd9\u4e2a2D\u89c6\u56fe\u80fd\u53cd\u6620\u66f4\u591a\u7684\u4f53\u7d20\u3002\u53ef\u4ee5\u8bf4\u8fd9\u662f\u4e00\u4e2a\u8f83\u5bb9\u6613\u8ba1\u7b97\u5e76\u4e14\u6709\u4e00\u5b9a\u53c2\u8003\u4ef7\u503c\u7684\u6700\u4f18\u89c6\u56fe\u8bc4\u9009\u6807\u51c6\u4e86\u3002<\/p>\n<p><img decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/p12.png\" width=\"70%\" height=\"70%\" \/><br \/>\n<img decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/p13.png\" width=\"70%\" height=\"70%\" \/><\/p>\n<p>\u5177\u4f53\u7684\u8ba1\u7b97\u8fc7\u7a0b\u5982\u4ee5\u4e0a\u4e24\u5f20\u56fe\u6240\u793a\uff1a\u9996\u5148\u8ba1\u7b97\u6bcf\u4e2a\u4f53\u7d20Vi\u7684\u8d21\u732e\u7387Pi\u3002Pi\u7684\u503c\u57fa\u4e8e\u80fd\u89c1\u5ea6V\u548c\u6743\u91cdW\u6765\u8ba1\u7b97\u3002\u8fd9\u6837\u6211\u4eec\u5c31\u53ef\u4ee5\u6839\u636ePi\u8ba1\u7b97\u51fa\u6bcf\u4e2a\u4f53\u7d20Vi\u7684\u4fe1\u606f\u91cf\uff0c\u6700\u540e\u518d\u8ba1\u7b97\u6574\u4e2a2D\u89c6\u56fe\u7684\u5e73\u5747\u4fe1\u606f\u71b5\u3002<\/p>\n<p>\u53ef\u4ee5\u60f3\u89c1\uff0c\u7528\u8fd9\u79cd\u65b9\u5f0f\u8ba1\u7b97\u51fa\u6765\u7684\u6700\u4f182D\u89c6\u56fe\uff0c\u5e94\u8be5\u662f\u6bcf\u4e2a\u4f53\u7d20\u90fd\u6709\u76f8\u540c\u8d21\u732e\u7387\u7684\u89c6\u89d2\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u4fe1\u606f\u71b5\u6700\u5927\u3002<\/p>\n<p><!--more--><\/p>\n<h2>\u5e94\u7528\u6848\u4f8b2\uff1a\u56fe\u50cf\u538b\u7f29<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/p14.png\" width=\"591\" height=\"433\" \/><\/p>\n<p>\u5bf9\u5927\u56fe\u7684\u538b\u7f29\uff0c\u901a\u5e38\u662f\u5c06\u5176\u5206\u5272\u6210\u5f88\u591a\u5c0f\u56fe\uff08chunks\uff09\uff0c\u6bcf\u4e2a\u5c0f\u56fe\u4f9d\u636e\u4e0d\u540c\u7684\u538b\u7f29\u7387\u8fdb\u884c\u538b\u7f29\uff0c\u6548\u679c\u6bd4\u4ee5\u540c\u79cd\u538b\u7f29\u7387\u8fdb\u884c\u538b\u7f29\u8981\u597d\u3002\u95ee\u9898\u662f\uff0c\u6211\u4eec\u5e94\u4ee5\u4f55\u79cd\u6807\u51c6\uff0c\u786e\u5b9a\u54ea\u4e2a\u5c0f\u56fe\u538b\u7f29\u7387\u9ad8\uff0c\u54ea\u4e2a\u5c0f\u56fe\u538b\u7f29\u7387\u4f4e\uff1f<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/p15.png\" width=\"605\" height=\"397\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/p16.png\" width=\"585\" height=\"421\" \/><\/p>\n<p>\u5982\u540c\u4e0a\u4e00\u4e2a\u95ee\u9898\uff0c\u56fe\u50cf\u4e2d\u4e3b\u8981\u8d1f\u8d23\u8d21\u732e\u89c6\u89c9\u6548\u679c\u7684\u5143\u7d20\uff0c\u88ab\u79f0\u4e3a\u6570\u636e\u5757\uff08data block\uff09\u3002\u663e\u7136\uff0c\u6709\u66f4\u591a\u6570\u636e\u5757\u8d77\u4f5c\u7528\u7684\u5c0f\u56fe\uff0c\u538b\u7f29\u7387\u5e94\u964d\u4f4e\uff0c\u8fd9\u6837\u6709\u52a9\u4e8e\u4fdd\u6301\u6570\u636e\u7cbe\u5ea6\u3002\u5982\u4f55\u8861\u91cf\u5c0f\u56fe\u4e2d\u6709\u591a\u5c11\u6570\u636e\u5757\u8d77\u4f5c\u7528\u5462\uff1f\u6211\u4eec\u7684\u4f9d\u636e\u5c31\u662f\u5c0f\u56fe\u5728\u7279\u5b9a\u7684\u7ec6\u8282\u7b49\u7ea7\uff08Level of Detail, LOD\uff09\u4e0b\u7684\u4fe1\u606f\u71b5\u3002<\/p>\n<p>\u5177\u4f53\u800c\u8a00\uff0c\u8ba1\u7b97\u8fc7\u7a0b\u5982\u4e0a\u9762\u4e24\u5f20\u56fe\u6240\u793a\uff1a\u9996\u5148\u8ba1\u7b97\u6bcf\u4e2a\u6570\u636e\u5757\u7684\u8d21\u732e\u7387Pi\uff0cPi\u7684\u503c\u57fa\u4e8e\u56fe\u50cf\u6e32\u67d3\u65f6\u6570\u636e\u5355\u5143\u7684\u8d21\u732eCi\uff08\u57fa\u4e8e\u6570\u636e\u5355\u5143\u7684\u989c\u8272\u3001\u6295\u5f71\u9762\u79ef\u3001\u6d53\u5ea6\u3001\u53ef\u89c1\u5ea6\uff09\u548c\u5f62\u53d8\u7a0b\u5ea6Di\uff08\u57fa\u4e8e\u6570\u636e\u5355\u5143\u5728\u5f53\u524d\u548c\u539f\u59cb\u5206\u8fa8\u7387\u4e0b\u7684\u5dee\u5f02\uff09\u6765\u8ba1\u7b97\u3002\u6839\u636ePi\uff0c\u5c31\u53ef\u4ee5\u8ba1\u7b97\u6bcf\u4e2a\u6570\u636e\u5757\u7684\u4fe1\u606f\u91cf\uff0c\u8fdb\u800c\u8ba1\u7b97\u6bcf\u4e2a\u5c0f\u56fe\u4fe1\u606f\u71b5\u3002<\/p>\n<p><!--more--><\/p>\n<h2>\u5e94\u75283\uff0c\u5411\u91cf\u573a\u7684\u7ed8\u5236<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a17.png\" width=\"614\" height=\"407\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a18.png\" width=\"558\" height=\"464\" \/><\/p>\n<p>\u5411\u91cf\u573a\u7684\u6982\u7387\u5bc6\u5ea6\u5206\u5e03\uff0c\u53ef\u4ee5\u901a\u8fc7polar histogram\uff08\u5f84\u5411\u76f4\u65b9\u56fe\uff09\u6765\u8868\u793a\uff0c\u8fdb\u800c\u53ef\u4ee5\u8ba1\u7b97\u5411\u91cf\u573a\u7684\u71b5\u3002\u4e0d\u8fc7\u5f84\u5411\u76f4\u65b9\u56fe\u5bf9\u4e8e\u4eba\u4eec\u7406\u89e3\u5411\u91cf\u573a\u4e0d\u591f\u76f4\u89c2\uff0c\u66f4\u76f4\u89c2\u7684\u65b9\u5f0f\u662f\u7ed8\u5236\u6d41\u7ebf\u56fe\u3002\u5728\u7ed8\u5236\u6d41\u7ebf\u65f6\uff0c\u6211\u4eec\u9700\u8981\u5148\u653e\u7f6e\u4e00\u4e9b\u79cd\u5b50\u70b9\uff0c\u4f5c\u4e3a\u7ed8\u5236\u6d41\u7ebf\u7684\u57fa\u7840\u3002\u95ee\u9898\u662f\uff0c\u79cd\u5b50\u70b9\u5e94\u8be5\u653e\u591a\u5c11\uff1f\u653e\u5230\u54ea\u91cc\u6bd4\u8f83\u597d\uff1f<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a19.png\" width=\"562\" height=\"406\" \/><\/p>\n<p>\u9996\u5148\u5173\u4e8e\u79cd\u5b50\u70b9\u653e\u591a\u5c11\u7684\u95ee\u9898\uff0c\u53ef\u4ee5\u901a\u8fc7\u6761\u4ef6\u71b5\u6765\u51b3\u5b9a\u3002\u8bbe\u539f\u59cb\u5411\u91cf\u573a\u7684\u71b5\u4e3aH(X). \u6d41\u7ebf\u56fe\u4e2d\u7684\u71b5\u4e3aH(Y)\u3002\u90a3\u4e48\u5b83\u7684\u6761\u4ef6\u71b5H(X|Y)\u7684\u503c\u5c31\u662f\u6307\uff0c\u5728\u539f\u59cb\u5411\u91cf\u573aX\u4e2d\u5b58\u5728\u800c\u5728\u6d41\u7ebf\u56feY\u4e2d\u4e0d\u5b58\u5728\u7684\u4fe1\u606f\u91cf\u3002\u663e\u7136\uff0c\u6211\u4eec\u5e0c\u671bH(X|Y)\u8d8a\u5c0f\u8d8a\u597d\uff0c\u8fd9\u6837\u6d41\u7ebf\u56fe\u624d\u66f4\u52a0\u63a5\u8fd1\u771f\u5b9e\u60c5\u51b5\u3002\u6709\u4e86\u8fd9\u4e2a\u6807\u51c6\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u901a\u8fc7\u53cd\u590d\u8fed\u4ee3\u7684\u65b9\u6cd5\uff0c\u4e0d\u65ad\u8ba1\u7b97H(X|Y)\uff0c\u4ee5\u6c42\u5f97\u79cd\u5b50\u70b9\u653e\u7f6e\u6570\u91cf\u7684\u6700\u4f73\u6c34\u5e73\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a20.png\" width=\"606\" height=\"440\" \/><\/p>\n<p>\u79cd\u5b50\u70b9\u7684\u4f4d\u7f6e\uff0c\u53ef\u4ee5\u901a\u8fc7\u8ba1\u7b97\u5c40\u90e8\u71b5\u5f97\u5230\u3002\u5177\u4f53\u7684\u8bf4\uff0c\u5c31\u662f\u8ba1\u7b97\u6bcf\u4e2a\u9884\u8bbe\u70b9\u4f4d\u4e34\u8fd1\u533a\u57df\u7684\u71b5\uff0c\u7136\u540e\u505a\u6bd4\u8f83\u3002\u71b5\u8d8a\u5927\uff0c\u8bf4\u660e\u8be5\u70b9\u4f4d\u5177\u6709\u66f4\u591a\u4fe1\u606f\u91cf\uff0c\u79cd\u5b50\u70b9\u653e\u5728\u8fd9\u91cc\uff0c\u5176\u4ee3\u8868\u610f\u4e49\u6bd4\u5176\u4ed6\u4f4d\u7f6e\u8981\u5927\u3002<\/p>\n<p><!--more--><\/p>\n<h2>\u5e94\u75284\uff1a\u591a\u5143\u6570\u636e\u5206\u6790<\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a21.png\" width=\"582\" height=\"371\" \/><\/p>\n<p>\u5206\u6790\u9ad8\u7ef4\u6570\u636e\u96c6\u7684\u4e00\u822c\u65b9\u6cd5\u662f\uff1a\u56fa\u5b9a\u67d0\u4e2a\u6570\u636e\u7ef4\u5ea6X\uff0c\u7136\u540e\u89c2\u5bdf\u5176\u4ed6\u7ef4\u5ea6\uff08Y\uff0cZ &#8230;\uff09\u6570\u503c\u7684\u53d8\u5316\uff0c\u4ece\u800c\u4e00\u6b65\u4e00\u6b65\u63a2\u7d22\u6570\u636e\u7ef4\u5ea6\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u95ee\u9898\u7684\u5173\u952e\u5728\u4e8e\uff0c\u9009\u62e9\u5206\u6790\u8def\u5f84X\u7684\u6807\u51c6\u662f\u4ec0\u4e48\uff1f\u5c24\u5176\u662f\u5728\u7f3a\u4e4f\u5148\u9a8c\u77e5\u8bc6\u7684\u60c5\u51b5\u4e0b\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a24.png\" width=\"652\" height=\"447\" \/><\/p>\n<p>\u4fe1\u606f\u8bba\u7ed9\u51fa\u4e86\u4e00\u4e2a\u901a\u7528\u7684\u8bc4\u5224\u6807\u51c6\u3002\u6bd4\u65b9\u8bf4\u6709\u4e24\u4e2a\u6570\u636e\u7ef4\u5ea6X\u548cY\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97X\u548cY\u7684\u5171\u6709\u4fe1\u606f\u91cf\uff08\u5373\u4fe1\u606f\u91cd\u53e0\uff09I(X,Y)\u3002I(X,Y)\u7684\u503c\u8d8a\u9ad8\u8bf4\u660eX\u548cY\u5173\u7cfb\u8d8a\u7d27\u5bc6\uff0c\u53cd\u4e4b\u5173\u7cfb\u8d8a\u6de1\u8584\u3002\u518d\u901a\u8fc7\u6761\u4ef6\u71b5H(X|Y)\u548cH(Y |X)\u7684\u6bd4\u8f83\uff0c\u6211\u4eec\u53ef\u4ee5\u77e5\u9053\u54ea\u4e2a\u6570\u636e\u7ef4\u5ea6\u5177\u6709\u66f4\u591a\u7684\u72ec\u7acb\u4fe1\u606f\u91cf\u3002\u6211\u4eec\u53ef\u4ee5\u9009\u62e9\u6761\u4ef6\u71b5\u66f4\u9ad8\u7684\u6570\u636e\u7ef4\u5ea6\u4f5c\u4e3a\u5206\u6790\u8def\u5f84\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a22.png\" width=\"600\" height=\"419\" \/><\/p>\n<p>\u56de\u987e\u4e00\u4e0b\u4ea4\u53c9\u71b5\u3001\u6761\u4ef6\u71b5\u3001\u5171\u6709\u4fe1\u606f\u91cf\u7684\u8ba1\u7b97\u516c\u5f0f\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a25.png\" width=\"611\" height=\"410\" \/><\/p>\n<p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u6570\u636e\u96c6\u5f80\u5f80\u4f1a\u6709\u6570\u5341\u4e2a\u6570\u636e\u7ef4\u5ea6\u3002\u90a3\u4e48\u600e\u4e48\u8fdb\u884c\u6311\u9009\u5462\uff1f\u53ef\u4ee5\u6784\u9020\u5206\u5c42\u805a\u7c7b\u6811\uff0c\u628a\u5927\u91cf\u6570\u636e\u7ef4\u5ea6\u6700\u7ec8\u5206\u4e3a2\u7ec4\uff0c\u9009\u62e9\u4fe1\u606f\u71b5\u6700\u5927\u7684\u90a3\u4e00\u7ec4\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a26.png\" width=\"605\" height=\"420\" \/><\/p>\n<p>\u7136\u540e\u518d\u5206\u6790\u7ec4\u5185\u6570\u636e\u7ef4\u5ea6\u3002\u53ef\u4ee5\u5148\u8ba1\u7b97\u672c\u7ec4\u5185\u6570\u636e\u7ef4\u5ea6\u7684\u4ea4\u53c9\u71b5\uff0c\u7136\u540e\u53bb\u6389\u4e00\u4e2a\u6570\u636e\u7ef4\u5ea6\uff0c\u518d\u8ba1\u7b97\u4e00\u4e0b\u4ea4\u53c9\u71b5\u3002\u5982\u679c\u4ea4\u53c9\u71b5\u964d\u4f4e\u7684\u591a\uff0c\u8bf4\u660e\u53bb\u6389\u7684\u6570\u636e\u7ef4\u5ea6\u5177\u6709\u66f4\u591a\u7684\u72ec\u7acb\u4fe1\u606f\uff0c\u8fd9\u4e2a\u6570\u636e\u7ef4\u5ea6\u66f4\u91cd\u8981\uff0c\u53ef\u7528\u4f5c\u5206\u6790\u8def\u5f84\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large\" src=\"http:\/\/zhangdi.dengxinbo.cn\/a27.png\" width=\"620\" height=\"409\" 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