{"id":116,"date":"2025-08-15T16:37:24","date_gmt":"2025-08-15T08:37:24","guid":{"rendered":"https:\/\/alyname.top\/index.php\/2025\/08\/15\/%e7%ac%94%e8%ae%b0-3d-gaussian-splatting-for-real-time-radiance-field-rendering\/"},"modified":"2025-08-16T00:11:31","modified_gmt":"2025-08-15T16:11:31","slug":"3d-gaussian-splatting-for-real-time-radiance-field-rendering","status":"publish","type":"post","link":"https:\/\/alyname.top\/index.php\/2025\/08\/15\/3d-gaussian-splatting-for-real-time-radiance-field-rendering\/","title":{"rendered":"\u7b14\u8bb0 – 3D Gaussian Splatting for Real-Time Radiance Field Rendering"},"content":{"rendered":"

\u975e\u5e38\u73b0\u4ee3\u7684\u6280\u672f\u3002\u867d\u7136\u73b0\u5728\u4e5f\u6709\u70b9\u5165\u571f\u4e86\u3002<\/p>\n

3DGS \u8fd9\u4e2a\u540d\u5b57\u51e0\u4e4e\u628a\u6574\u7247\u8bba\u6587\u6982\u62ec\u5176\u4e2d\uff1a\u4efb\u52a1\u7c7b\u578b\u662f\u4e09\u7ef4\u91cd\u5efa\uff1b\u8868\u793a\u573a\u666f\u7684\u65b9\u6cd5\u662f\u4e00\u7ec4 Gaussian \u5206\u5e03\uff0c\u53ef\u4ee5\u7406\u89e3\u6210\u8fb9\u7f18\u7cca\u7cca\u7684\u692d\u7403\uff1bSplatting \u662f\u6e32\u67d3\u65b9\u6cd5\uff0c\u901a\u8fc7\u628a\u8fd9\u4e00\u5806 Gaussian \u5206\u5e03\u201c\u6cfc\u201d\u5230\u4e00\u4e2a\u4e8c\u7ef4\u5e73\u9762\u4e0a\u5b8c\u6210\u6e32\u67d3\uff0c\u5f88\u6709\u5149\u6805\u5316\u7684\u5473\u9053\u3002<\/p>\n

3DGS \u7684\u6548\u679c\u662f\u76f8\u5f53\u5f3a\u5927\u7684\uff0c\u5728\u7ed9\u5b9a\u591a\u5f20\u4e0d\u540c\u89c6\u89d2\u7684\u56fe\u7247\u4e0b\uff0c\u5176\u540c\u65f6\u5b9e\u73b0\u4e86\uff1a\u5bf9\u573a\u666f\u7684\u6e32\u67d3\uff08\u800c\u975e\u5355\u4e2a\u7269\u4f53\uff09\u30011080p\u3001\u5b9e\u65f6\u6e32\u67d3\uff08<\/g><\/g><\/g><\/svg>\u2265<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> 30fps\uff09\u3002<\/p>\n

arxiv.org\/pdf\/2308.04079<\/a>\uff082023 \u5e74 8 \u6708\uff09<\/p>\n

\u5199\u7684\u5f88\u597d\u7684\u535a\u5ba2\uff1a\u4e00\u6587\u5e26\u4f60\u5165\u95e8 3D Gaussian Splatting – \u77e5\u4e4e<\/a><\/p>\n

\n
3D Gaussian<\/h5>\n

3D Gaussian \u957f\u8fd9\u6837\uff1a<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>G<\/mi>(<\/mo>x<\/mi>)<\/mo>=<\/mo>\u03b1<\/mi>exp<\/mi>\u2061<\/mo>(<\/mo>\u2212<\/mo>1<\/mn>2<\/mn><\/mfrac>x<\/mi>T<\/mi><\/msup>\u03a3<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup>x<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u5bb9\u6613\u53d1\u73b0\u8fd9\u662f\u4e00\u4e2a\uff08\u4e0d\u8003\u8651\u4f4d\u7f6e <\/g><\/g><\/g><\/svg>\u03bc<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684\uff09\u4e09\u7ef4\u6b63\u6001\u5206\u5e03\uff0c\u524d\u9762\u4e00\u5768\u7cfb\u6570\u88ab\u7528\u4e00\u4e2a\u989d\u5916\u53c2\u6570 <\/g><\/g><\/g><\/svg>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u4ee3\u66ff\uff0c\u8fd9\u4e2a <\/g><\/g><\/g><\/svg>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u88ab\u8ba4\u4e3a\u63cf\u8ff0\u4e86\u4e0d\u900f\u660e\u5ea6\u3002\u6b64\u5916\u8fd8\u5e94\u8be5\u6709\u4e00\u4e2a\u7403\u8c10\u51fd\u6570 <\/g><\/g><\/g><\/svg>c<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u8868\u793a\u5404\u4e2a\u65b9\u5411\u89c2\u5bdf\u5230\u7684\u989c\u8272\uff0c\u6682\u4e0d\u8003\u8651\u3002<\/p>\n

\u5728\u70b9\u4e91\u8868\u793a\u4e2d\uff0c\u4e00\u4e2a\u573a\u666f\u88ab\u7406\u89e3\u4e3a\u4e00\u4e2a\u758f\u5bc6\u4e0d\u5747\u7684\u70b9\u96c6\uff1bGaussian \u8868\u793a\u53ea\u662f\u628a\u70b9\u4e91\u4e2d\u7684\u70b9\u90fd\u6362\u6210\u4e86 3D Gaussian\uff0c\u5c31\u50cf\u5728\u6bcf\u4e2a\u70b9\u7684\u9644\u8fd1\u7b3c\u4e0a\u4e00\u4e2a\u7535\u5b50\u4e91\u3002<\/p>\n

\u7406\u8bba\u4e0a\u534f\u65b9\u5dee <\/g><\/g><\/g><\/svg>\u03a3<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u53ef\u4ee5\u957f\u6210\u4efb\u4f55\u4e00\u4e2a\u534a\u6b63\u5b9a\u77e9\u9635\uff0c\u4f46\u8fd9\u91cc\u6211\u4eec\u5047\u8bbe\u5176\u53ef\u4ee5\u88ab\u4e00\u4e2a\u4eff\u5c04\u53d8\u6362\u63cf\u8ff0<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03a3<\/mi>=<\/mo>R<\/mi>S<\/mi>S<\/mi>T<\/mi><\/msup>R<\/mi>T<\/mi><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u5176\u4e2d <\/g><\/g><\/g><\/svg>R<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u662f\u4e00\u4e2a\u65cb\u8f6c\uff0c<\/g><\/g><\/g><\/svg>S<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u662f\u4e00\u4e2a\u7f29\u653e\uff0c\u5b83\u4eec\u53ef\u4ee5\u5206\u522b\u7528\u4e00\u4e2a\u56db\u5143\u6570 <\/g><\/g><\/g><\/svg>q<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c\u4e00\u7ec4\u7f29\u653e\u7cfb\u6570 <\/g><\/g><\/g><\/svg>s<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u63cf\u8ff0\u3002<\/p>\n

\n

\u4e3a\u5565\u8fd9\u4e48\u5047\u8bbe\uff1f\u5230\u65f6\u5019\u7f51\u7edc\u8981\u5b66\u7684\u4e1c\u897f\u5c31\u662f\u8fd9\u4e2a <\/g><\/g><\/g><\/svg>\u03a3<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5982\u679c\u76f4\u63a5\u4f18\u5316 <\/g><\/g><\/g><\/svg>\u03a3<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684\u8bdd\u96be\u4ee5\u4fdd\u8bc1\u534a\u6b63\u5b9a\uff0c\u62c6\u6210\u8fd9\u6837\u7684\u8bdd\u6bcf\u4e00\u6b65\u90fd\u662f\u53ef\u5fae\u7684\uff0c\u4f18\u5316\u76ee\u6807\u53ef\u4ee5\u4f20\u5230 <\/g><\/g><\/g><\/svg>q<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c <\/g><\/g><\/g><\/svg>s<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u4e0a\uff0c\u53c8\u80fd\u4fdd\u8bc1\u6b63\u5b9a\u6027\u3002<\/p>\n<\/blockquote>\n

\u5982\u679c <\/g><\/g><\/g><\/svg>\u03a3<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u662f\u5355\u4f4d\u9635\u7684\u8bdd\u53ef\u4ee5\u60f3\u8c61\u8fd9\u4e2a 3D Gaussian \u4f1a\u957f\u5f97\u50cf\u4e00\u4e2a\u8fb9\u7f18\u6a21\u7cca\u7684\u7403\uff1b\u5728\u4e0a\u8ff0 <\/g><\/g><\/g><\/svg>\u03a3<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684\u7b80\u5316\u4e0b\u81ea\u7136\u5c31\u50cf\u4e00\u4e2a\u692d\u7403\u4e86\u3002<\/p>\n

\n

\u7efc\u4e0a\u4e00\u4e2a\u4e0d\u8003\u8651\u989c\u8272\u7684 3D Gaussian \u9700\u8981 11 \u7ef4\u53c2\u6570\u63cf\u8ff0\uff1a<\/g><\/g><\/g><\/svg>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4f4d\u7f6e <\/g><\/g><\/g><\/svg>\u03bc<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4e24\u4e2a\u534f\u65b9\u5dee\u77e9\u9635\u53c2\u6570 <\/g><\/g><\/g><\/svg>q<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c <\/g><\/g><\/g><\/svg>s<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002\u6d41\u7a0b\u4e2d\u7684\u6bcf\u4e2a\u53c2\u6570\u90fd\u662f\u53ef\u5fae\u7684\u3002\u8bba\u6587\u91cc\u9762\u751a\u81f3\u7ec6\u81f4\u5730\u63a8\u4e86\u5b83\u4eec\u7684\u5fae\u5206\u5f0f\u5b50<\/s><\/p>\n<\/blockquote>\n

3DGS \u7684\u8f93\u5165\u662f SfM \u7ed3\u6784\u5316\u5904\u7406\uff08Structure from Motion\uff09\u540e\u7684\u4e00\u7ec4\u591a\u89c6\u89d2\u56fe\u7247\u5e26\u76f8\u673a\u4f4d\u59ff\u3002SfM \u7684\u526f\u4ea7\u7269\u662f\u4e00\u4e2a\u63cf\u8ff0\u573a\u666f\u7684\u7a00\u758f\u70b9\u4e91\uff0c3DGS \u5c31\u5728\u8fd9\u4e2a\u70b9\u4e91\u7684\u70b9\u4e0a\u8ba1\u7b97\u5e76\u4f18\u5316 Gaussian\u3002<\/p>\n

\n

\u5565\u662f SfM\uff1f<\/p>\n

\u7528\u6444\u50cf\u673a\u7ed9\u573a\u666f\u5f55\u4e00\u6bb5\u89c6\u9891\uff0c\u9010\u5e27\u62bd\u51fa\u56fe\u50cf\uff0cSfM \u53ef\u4ee5\u8fd8\u539f\u51fa\u6bcf\u5e27\u5bf9\u5e94\u7684\u76f8\u673a\u4f4d\u59ff\uff0c\u987a\u4fbf\u5f97\u5230\u4e00\u4e2a\u7a00\u758f\u70b9\u4e91\u3002SfM \u4e00\u822c\u57fa\u4e8e\u7ecf\u5178\u7684\u7279\u5f81\u70b9\u5339\u914d\u6280\u672f\u5b9e\u73b0\uff0c\u5bf9\u6bcf\u5e27\u627e\u7279\u5f81\u7136\u540e\u8ffd\u8e2a\u8fd9\u4e9b\u7279\u5f81\u70b9\u7684\u79fb\u52a8\u60c5\u51b5\u3002<\/p>\n<\/blockquote>\n

\u5230\u65f6\u5019\u4f1a\u5229\u7528\u68af\u5ea6\u4e0b\u964d\u7b49\u65b9\u6cd5\u5b66\u4e60 \u6bcf\u4e2a Gaussian \u7684\u5404\u4e2a\u53c2\u6570\u3002<\/p>\n

\n

\u4f5c\u4e3a Gaussian \u57fa\u7840\u7684\u70b9\u4e91\u5e76\u4e0d\u662f\u4e00\u6210\u4e0d\u53d8\u7684\u3002\u53ef\u4ee5\u901a\u8fc7\u81ea\u9002\u5e94\u5bc6\u5ea6\u63a7\u5236\u7b49\u65b9\u5f0f\u52a0\u70b9\u5220\u70b9\u7b49\u3002<\/p>\n<\/blockquote>\n

Splatting<\/h5>\n

\u9996\u5148\u662f\u628a\u6240\u6709\u4e16\u754c\u7a7a\u95f4\u7684 Gaussian \u53d8\u5230\u76f8\u673a\u7a7a\u95f4\u91cc\u9762\uff0c\u7ed9\u4e00\u4e2a\u89c6\u56fe\u53d8\u6362 <\/g><\/g><\/g><\/svg>W<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c\u4e00\u4e2a\u6295\u5f71\u7684\u60c5\u51b5\u4e0b\uff1a<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03a3<\/mi>\u2032<\/mo><\/msup>=<\/mo>J<\/mi>W<\/mi>\u03a3<\/mi>W<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup>J<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

<\/g><\/g><\/g><\/svg>J<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u662f\u6295\u5f71\u53d8\u6362\u7684 Local affine approximation \u8fd1\u4f3c\uff08\u5565\u73a9\u610f\u770b\u4e0d\u61c2\uff0c\u5148\u8fd9\u4e48\u5199\u7740\u5427\u611f\u89c9\u662f\u7ecf\u5178\u6280\u672f\uff09\u7684 Jacobian \u77e9\u9635\u3002\u8fd9\u6837\u5904\u7406\u7684\u597d\u5904\u662f\uff0c3D Gaussian \u53d8\u6362\u5b8c\u4e4b\u540e\u53d8\u6210\u7684\u8fd8\u662f 3D Gaussian\u3002
\n\"Pasted
\n\u5176\u5b83\u7684\u7167\u5e38\u8ba1\u7b97\u3002\u7279\u522b\u5730\uff0c\u6295\u5f71\u5f97\u5230\u7684 Gaussian \u7684\u4e0d\u900f\u660e\u5ea6 <\/g><\/g><\/g><\/svg>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u4e0d\u518d\u662f\u539f\u6765\u7684 <\/g><\/g><\/g><\/svg>\u03b1<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u9700\u8981\u624b\u63a8\u4e00\u904d\u3002<\/p>\n

\u53ef\u4ee5\u60f3\u89c1\u4e4b\u540e\u4f1a\u6709\u4e00\u4e2a\u7c7b\u4f3c Alpha Blending \u7684\u8fc7\u7a0b\uff0c\u91cc\u9762\u4f1a\u5bf9\u6240\u6709 3D Gaussian \u5728\u6574\u4e2a\u5149\u7a0b\u79ef\u5206\u7136\u540e\u6c42\u548c\u3002\u4e00\u4e2a\u5c0f Trick \u5728\u4e8e\u8fd9\u91cc\u5b9e\u9645\u4e0a\u4e0d\u7528\u771f\u7684\u53bb\u6570\u503c\u79ef\u5206\uff1a3D Gaussian \u7684\u79ef\u5206\u5c31\u662f 2D Gaussian\uff0c\u5176\u534f\u65b9\u5dee\u77e9\u9635\u4e5f\u53ef\u4ee5\u76f4\u63a5\u7b97\u51fa\u6765\u3002<\/p>\n

\n

\u5e76\u4e14\u5982\u679c\u6cbf\u6b63\u786e\u7684\u65b9\u5411\u79ef\u5206\u7684\u8bdd\uff0c\u65b0\u7684\u534f\u65b9\u5dee\u77e9\u9635\u53ea\u9700\u8981\u628a\u539f\u6765\u7684\u4e22\u6389\u4e00\u884c\u4e00\u5217\u5c31\u884c\u4e86\u3002<\/p>\n<\/blockquote>\n

\n

\u7f51\u4e0a\u6709\u4eba\u8bf4\u8fd9\u4e00\u6b65\u5f88\u5999\u3002\u5999\u5728\u54ea\u4e86\u2026\u2026\u6982\u7387\u8bba\u6ca1\u5b66\u597d\u5427\u2026\u2026<\/s><\/p>\n

\u4e4b\u6240\u4ee5\u9009\u62e9 Gaussian \u51fd\u6570\u4f5c\u8868\u793a\u4f1a\u4e0d\u4f1a\u5c31\u662f\u56e0\u4e3a\u5b83\u79ef\u8d77\u6765\u5f88\u65b9\u4fbf\uff08\u5e76\u4e14\u6709\u76f4\u89c2\u610f\u4e49\uff09\uff1f<\/p>\n<\/blockquote>\n

\u7136\u540e\u6309\u6df1\u5ea6\u6392\u5e8f\uff0cAlpha Blending \u6e32\u67d3\u4e00\u4e0b<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>C<\/mi>=<\/mo>\u2211<\/mo>i<\/mi>=<\/mo>1<\/mn><\/mrow>n<\/mi><\/mrow><\/munderover>c<\/mi>i<\/mi><\/msub>\u03b1<\/mi>i<\/mi>\u2032<\/mo><\/msubsup>\u220f<\/mo>j<\/mi>=<\/mo>1<\/mn><\/mrow>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/munderover>(<\/mo>1<\/mn>\u2212<\/mo>\u03b1<\/mi>j<\/mi>\u2032<\/mo><\/msubsup>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u5176\u4e2d <\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03b1<\/mi>i<\/mi>\u2032<\/mo><\/msubsup><\/math><\/mjx-assistive-mml><\/mjx-container> \u88ab\u5982\u4e0b\u8ba1\u7b97\uff1a<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03b1<\/mi>i<\/mi>\u2032<\/mo><\/msubsup>=<\/mo>\u03b1<\/mi>i<\/mi><\/msub>G<\/mi>(<\/mo>x<\/mi>,<\/mo>\u03bc<\/mi>i<\/mi><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u5176\u4e2d <\/g><\/g><\/g><\/g><\/g><\/svg>\u03bc<\/mi>i<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u662f\u7b2c <\/g><\/g><\/g><\/svg>i<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u4e2a Gaussian \u7684\u4f4d\u7f6e\uff0c<\/g><\/g><\/g><\/svg>G<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u662f 2D Gaussian\u3002<\/p>\n

\n

\u6ce8\u610f\u5230\u6bcf\u4e2a Gaussian \u957f\u5f97\u50cf\u4e2a\u7403\u4f46\u5b9e\u9645\u5f25\u6563\u5230\u4e86\u6574\u4e2a\u7a7a\u95f4\uff0c\u5bf9\u6bcf\u4e2a\u50cf\u7d20\u70b9\u628a\u5168\u4f53 Gaussian \u8fc7\u4e00\u904d\u7684\u8bdd\u5f00\u9500\u592a\u5927\u3002\u4e00\u4e2a\u57fa\u672c\u60f3\u6cd5\u662f\uff0c\u628a\u5c4f\u5e55\u7a7a\u95f4\u5212\u5206\u4e3a\u4e00\u5806 Tile\uff0c\u5bf9\u6bcf\u4e2a Tile \u4ec5\u8003\u8651\u91cc\u9762\u7684 Gaussian\u3002<\/p>\n<\/blockquote>\n

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