{"id":30,"date":"2025-08-13T17:06:06","date_gmt":"2025-08-13T09:06:06","guid":{"rendered":"https:\/\/alyname.top\/index.php\/2025\/08\/13\/nerf-representing-scenes-as-neural-radiance-fields-for-view-synthesis\/"},"modified":"2025-08-15T16:35:56","modified_gmt":"2025-08-15T08:35:56","slug":"nerf-representing-scenes-as-neural-radiance-fields-for-view-synthesis","status":"publish","type":"post","link":"https:\/\/alyname.top\/index.php\/2025\/08\/13\/nerf-representing-scenes-as-neural-radiance-fields-for-view-synthesis\/","title":{"rendered":"\u7b14\u8bb0 – NeRF – Representing Scenes as Neural Radiance Fields for View Synthesis"},"content":{"rendered":"

\u57fa\u4e8e\u6df1\u5ea6\u5b66\u4e60\u7684 3D \u573a\u666f\u8868\u793a\u4e0e\u4e09\u7ef4\u91cd\u5efa\u3002\u8f83\u65e9\u671f\u800c\u6700\u77e5\u540d\u7684\u9690\u5f0f 3D \u8868\u793a\u3002<\/p>\n

2003.08934<\/a>\uff082020 \u5e74 8 \u6708\uff09<\/p>\n

\n
\u8fd9\u662f\u5565\uff1f<\/h5>\n

NeRF \u901a\u8fc7\u7279\u6b8a\u7684 3D \u573a\u666f\u8868\u793a\u65b9\u5f0f\uff0c\u5b9e\u73b0\uff1a\u7ed9\u5b9a\u5bf9\u540c\u4e00\u573a\u666f\u7684\u5927\u91cf\u4e0d\u540c\u89c6\u89d2\u89c2\u6d4b\u56fe\u7247\uff0c\u795e\u7ecf\u7f51\u7edc\u7ecf\u5b66\u4e60\u540e\u53ef\u4ee5\uff08\u5728\u67d0\u79cd\u610f\u4e49\u4e0b\uff09\u7406\u89e3\u8fd9\u4e2a\u573a\u666f\u7684\u5185\u5bb9\uff0c\u5e76\u6e32\u67d3\u51fa\u8be5\u573a\u666f\u5728\u4efb\u610f\u89c6\u89d2\u4e0b\u7684\u89c2\u6d4b\u7ed3\u679c\u3002<\/p>\n

\u795e\u7ecf\u7f51\u7edc\u5e76\u4e0d\u5b66\u5230\u5173\u4e8e\u8fd9\u4e2a\u573a\u666f\u7684 mesh \u7b49\u4fe1\u606f\uff1b\u5b83\u5b66\u4e60\u7684\u5185\u5bb9\u662f\u89c2\u6d4b\u7ed3\u679c\u3002\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48\u5b83\u88ab\u79f0\u4e3a\u201c\u9690\u5f0f\u8868\u793a\u201d\u3002<\/p>\n

\u4e3a\u5565\uff1f<\/h5>\n

\u5c06\u4e00\u4e2a 3D \u573a\u666f\u89c6\u4f5c\u4e00\u4e2a <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>R<\/mi><\/mrow>5<\/mn><\/msup>\u2192<\/mo>R<\/mi><\/mrow>4<\/mn><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684\u51fd\u6570 <\/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>f<\/mi>:<\/mo>(<\/mo>(<\/mo>x<\/mi>,<\/mo>y<\/mi>,<\/mo>z<\/mi>)<\/mo>,<\/mo>(<\/mo>\u03b8<\/mi>,<\/mo>\u03d5<\/mi>)<\/mo>)<\/mo>\u2192<\/mo>(<\/mo>(<\/mo>r<\/mi>,<\/mo>g<\/mi>,<\/mo>b<\/mi>)<\/mo>,<\/mo>\u03c3<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002\u5176\u4e2d <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>=<\/mo>(<\/mo>x<\/mi>,<\/mo>y<\/mi>,<\/mo>z<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u8868\u793a\u573a\u666f\u4e2d\u4e00\u4e2a\u70b9\uff1b<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>d<\/mi>=<\/mo>(<\/mo>\u03b8<\/mi>,<\/mo>\u03d5<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u8868\u793a\u662f\u4ece\u54ea\u4e2a\u65b9\u5411\u89c2\u6d4b\u5b83\u7684\uff1b<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>c<\/mi>=<\/mo>(<\/mo>r<\/mi>,<\/mo>g<\/mi>,<\/mo>b<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u8868\u793a\u8fd9\u65f6\u89c2\u6d4b\u8fd9\u4e2a\u70b9\u770b\u5230\u7684\u989c\u8272\uff1b<\/g><\/g><\/g><\/svg>\u03c3<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u8868\u793a\u4f53\u5bc6\u5ea6\u3002<\/p>\n

\u4e00\u822c\u6765\u8bf4\u8fd9\u4e2a\u51fd\u6570\u662f\u8fde\u7eed\u7684\u3002<\/p>\n

\n

\u4f53\u5bc6\u5ea6 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03c3<\/mi>(<\/mo>p<\/mi>,<\/mo>d<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u662f\u4e00\u4e2a\u4f53\u6e32\u67d3\u4e2d\u7684\u6982\u5ff5\u3002\u5b9a\u4e49\uff1a\u4e00\u6761\u5149\u7ebf\u4ece\u65b9\u5411 <\/g><\/g><\/g><\/svg>d<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u5c04\u8fc7\u6765\uff0c\u5728 <\/g><\/g><\/g><\/svg>p<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u88ab\u4e00\u4e2a\u65e0\u7a77\u5c0f\u7c92\u5b50\u6321\u4f4f\u7684\u6982\u7387\u3002<\/p>\n

\u7406\u60f3\u4e0d\u900f\u660e\u7269\u4f53\u5728\u4efb\u610f\u70b9\u4ece\u4efb\u610f\u65b9\u5411\u89c2\u6d4b\u7684\u4f53\u5bc6\u5ea6\u4e3a <\/g><\/g><\/g><\/svg>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002\u4f53\u5bc6\u5ea6\u53ef\u4ee5\u88ab\u7406\u89e3\u4e3a\u67d0\u79cd\u201c\u4e0d\u900f\u660e\u5ea6\u201d\uff0c\u4e0d\u540c\u6d53\u5ea6\u7684\u96fe\u662f\u4e00\u79cd\u76f4\u89c2\u4f53\u73b0\u4f53\u5bc6\u5ea6\u5dee\u5f02\u5e26\u6765\u89c6\u89c9\u6548\u679c\u5dee\u5f02\u7684\u4f8b\u5b50\u3002<\/p>\n<\/blockquote>\n

\u5982\u679c\u6211\u4eec\u5f97\u5230\u4e86\u8fd9\u4e2a\u51fd\u6570 <\/g><\/g><\/g><\/svg>f<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u90a3\u901a\u8fc7\u4f53\u6e32\u67d3\u7684\u65b9\u6cd5\uff0c\u53ef\u4ee5\u5f97\u5230\u8be5\u573a\u666f\u4efb\u610f\u89c6\u89d2\u7684\u6e32\u67d3\u7ed3\u679c\u3002<\/p>\n

\n

\u5565\u662f\u4f53\u6e32\u67d3\uff1f<\/p>\n

\u4f53\u6e32\u67d3\u4ec5\u6839\u636e\u573a\u666f\u4e2d\u6bcf\u4e2a\u70b9\u7684\u989c\u8272 <\/g><\/g><\/g><\/svg>c<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c\u4f53\u5bc6\u5ea6 <\/g><\/g><\/g><\/svg>\u03c3<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u6e32\u67d3\u573a\u666f\uff0c\u800c\u4e0d\u501f\u52a9\u4efb\u4f55 mesh \u6216\u5149\u7ebf\u4fe1\u606f\u3002<\/p>\n

\u76f8\u6bd4\u4e8e\u57fa\u4e8e Mesh \u7684\u6e32\u67d3\uff08\u9762\u6e32\u67d3\uff1f\uff09\u4e2d\u91c7\u7528\u7684\u5149\u7ebf\u8ffd\u8e2a\uff08Ray Tracing\uff09\u65b9\u6cd5\uff0c\u4f53\u6e32\u67d3\u4e2d\u7684\u5bf9\u5e94\u7cfb\u5217\u65b9\u6cd5\u88ab\u79f0\u4e3a\u5149\u7ebf\u884c\u8fdb\uff08Ray Marching\uff09\u3002\u5176\u7279\u5f81\u662f\u4e00\u6761\u5149\u7ebf\u4e00\u76f4\u5c04\u5230\u5e95\uff0c\u628a\u6cbf\u8def\u5404\u79cd\u5404\u6837\u7684\u4e1c\u897f\u79ef\u5206\u8d77\u6765\u3002<\/p>\n

\u8003\u8651\u5728\u6446\u653e\u597d\u76f8\u673a\u4f4d\u7f6e\u540e\uff0c\u4ece\u76f8\u673a\u89c6\u89d2\u53d1\u5c04\u4e00\u6761\u5c04\u7ebf <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>r<\/mi>(<\/mo>t<\/mi>)<\/mo>=<\/mo>o<\/mi>+<\/mo>t<\/mi>d<\/mi>,<\/mo>t<\/mi>\u2208<\/mo>[<\/mo>t<\/mi>n<\/mi><\/msub>,<\/mo>t<\/mi>f<\/mi><\/msub>]<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8fd9\u6761\u5c04\u7ebf\u7684\u989c\u8272\u8ba1\u7b97\u4e3a<\/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><\/g><\/g><\/g><\/g><\/svg>C<\/mi>(<\/mo>r<\/mi>)<\/mo>=<\/mo>\u222b<\/mo>t<\/mi>n<\/mi><\/msub><\/mrow>t<\/mi>r<\/mi><\/msub><\/mrow><\/msubsup>T<\/mi>(<\/mo>t<\/mi>)<\/mo>\u22c5<\/mo>\u03c3<\/mi>(<\/mo>r<\/mi>(<\/mo>t<\/mi>)<\/mo>)<\/mo>\u22c5<\/mo>c<\/mi>(<\/mo>r<\/mi>(<\/mo>t<\/mi>)<\/mo>,<\/mo>d<\/mi>)<\/mo>d<\/mi>t<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/p><\/blockquote>\n

\n

\u8fd9\u4e2a\u5f0f\u5b50\u5f88\u597d\u7406\u89e3\uff1a\u5c04\u7ebf\u7b2c\u4e00\u6b21\u649e\u5230\u7c92\u5b50\u7684\u989c\u8272\u671f\u671b\u3002<\/g><\/g><\/g><\/g><\/g><\/g><\/svg>T<\/mi>(<\/mo>t<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u8868\u793a <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>[<\/mo>t<\/mi>n<\/mi><\/msub>,<\/mo>t<\/mi>]<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u8fd9\u4e00\u6bb5\u4e00\u76f4\u6ca1\u6709\u88ab\u7c92\u5b50\u6321\u4f4f\u7684\u6982\u7387\uff0c\u5176\u8ba1\u7b97\u5f0f\u4e3a<\/p>\n<\/blockquote>\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><\/svg>T<\/mi>(<\/mo>t<\/mi>)<\/mo>=<\/mo>exp<\/mi>\u2061<\/mo>(<\/mo>\u2212<\/mo>\u222b<\/mo>t<\/mi>n<\/mi><\/msub><\/mrow>t<\/mi><\/msubsup>\u03c3<\/mi>(<\/mo>r<\/mi>(<\/mo>s<\/mi>)<\/mo>)<\/mo>d<\/mi>s<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\n

\u5934\u4e00\u6b21\u89c1\u5230\u8fd9\u4e48\u5bb9\u6613\u7406\u89e3\u7684\u5f0f\u5b50\uff0c\u611f\u52a8<\/p>\n<\/blockquote>\n

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\u5728 NeRF \u7684\u5de5\u4f5c\u91cc\uff0c\u795e\u7ecf\u7f51\u7edc\u76f4\u63a5\u9009\u7528 MLP\u3002<\/p>\n

\u4e00\u4e9b\u5b9e\u73b0\u7ec6\u8282<\/h5>\n

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<\/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>T<\/mi>i<\/mi><\/msub>=<\/mo>exp<\/mi>\u2061<\/mo>(<\/mo>\u2212<\/mo>\u2211<\/mo>j<\/mi>=<\/mo>1<\/mn><\/mrow>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/munderover>\u03c3<\/mi>j<\/mi><\/msub>\u03b4<\/mi>j<\/mi><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u5176\u4e2d <\/g><\/g><\/g><\/g><\/g><\/svg>\u03b4<\/mi>j<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u4e3a\u91c7\u6837\u70b9 <\/g><\/g><\/g><\/g><\/g><\/svg>t<\/mi>j<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u4e0e <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>t<\/mi>j<\/mi>+<\/mo>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684\u8ddd\u79bb\u3002\u7136\u540e<\/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><\/g><\/svg>C<\/mi>^<\/mo><\/mover><\/mrow>(<\/mo>r<\/mi>)<\/mo>=<\/mo>\u2211<\/mo>i<\/mi>=<\/mo>1<\/mn><\/mrow>N<\/mi><\/munderover>T<\/mi>i<\/mi><\/msub>c<\/mi>i<\/mi><\/msub>(<\/mo>1<\/mn>\u2212<\/mo>exp<\/mi>\u2061<\/mo>(<\/mo>\u2212<\/mo>\u03c3<\/mi>i<\/mi><\/msub>\u03b4<\/mi>i<\/mi><\/msub>)<\/mo>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\n

\u4e3a\u5565\u4e0d\u76f4\u63a5\u4e58 <\/g><\/g><\/g><\/g><\/g><\/svg>\u03c3<\/mi>i<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff1f\u56e0\u4e3a\u8fd9\u91cc\u7684\u542b\u4e49\u662f\u5728 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>[<\/mo>t<\/mi>i<\/mi><\/msub>,<\/mo>t<\/mi>i<\/mi>+<\/mo>1<\/mn><\/mrow><\/msub>]<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u5185\u88ab\u81f3\u5c11\u4e00\u4e2a\u7c92\u5b50\u6321\u4f4f\u7684\u6982\u7387\uff0c\u800c\u4e0d\u80fd\u5047\u8bbe\u8fd9\u4e2a\u533a\u95f4\u53ea\u6709\u4e00\u4e2a\u7c92\u5b50\u3002<\/p>\n

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\u53ef\u80fd\u4f1a\u6709\u5f88\u5927\u5dee\u522b\uff0c\u4f46\u6ca1\u8bd5\u8fc7\u4e0d\u77e5\u9053<\/p>\n<\/blockquote>\n

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\u5176\u6b21\u662f\u7f51\u7edc\u8f93\u5165\u3002\u5b9e\u9a8c\u8868\u660e\u76f4\u63a5\u628a\u4e94\u7ef4\u4fe1\u606f\u8f93\u5165\u6548\u679c\u4e0d\u597d\uff0c\u5e0c\u671b\u5148\u628a\u8f93\u5165\u4fe1\u606f\u6620\u5c04\u5230\u9ad8\u7ef4\uff0c\u7c7b\u4f3c Transformer encoder \u7684\u60f3\u6cd5\u3002<\/p>\n

\u867d\u7136\u770b\u4e0d\u592a\u61c2\u4f46\u6620\u5c04\u51fd\u6570\u662f <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03b3<\/mi>:<\/mo>R<\/mi><\/mrow>\u2192<\/mo>[<\/mo>\u2212<\/mo>1<\/mn>,<\/mo>1<\/mn>]<\/mo>2<\/mn>L<\/mi><\/mrow><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/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>\uff0c<\/text><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03b3<\/mi>(<\/mo>p<\/mi>)<\/mo>=<\/mo>(<\/mo>sin<\/mi>\u2061<\/mo>(<\/mo>2<\/mn>0<\/mn><\/msup>\u03c0<\/mi>p<\/mi>)<\/mo>,<\/mo>cos<\/mi>\u2061<\/mo>(<\/mo>2<\/mn>0<\/mn><\/msup>\u03c0<\/mi>p<\/mi>)<\/mo>,<\/mo>\u22ef<\/mo>\uff0c<\/mi>sin<\/mi>\u2061<\/mo>(<\/mo>2<\/mn>L<\/mi><\/msup>\u03c0<\/mi>p<\/mi>)<\/mo>,<\/mo>cos<\/mi>\u2061<\/mo>(<\/mo>2<\/mn>L<\/mi><\/msup>\u03c0<\/mi>p<\/mi>)<\/mo>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

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\u7f51\u7edc\u7ed3\u6784\u4e0a\uff0c\u7531\u4e8e\u4f53\u5bc6\u5ea6\u4e0e\u89c2\u6d4b\u65b9\u5411\u65e0\u5173\uff0c\u6240\u4ee5\u8f93\u5165\u7684\u4f4d\u7f6e\u5750\u6807\u5148\u8fc7\u4e00\u5806\u5c42\u5f97\u5230\u4e00\u4e2a <\/g><\/g><\/g><\/svg>\u03c3<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c\u4e00\u7ec4\u7279\u5f81\u5411\u91cf\uff1b\u7279\u5f81\u5411\u91cf\u8fde\u5e26\u7740\u65b9\u5411\u8fc7\u53e6\u4e00\u5806\u5c42\u5f97\u5230\u989c\u8272\u3002<\/p>\n

\u8bad\u7ec3\u7ec6\u8282\u597d\u6742\u4e0d\u60f3\u770b\uff0c\u7565\u3002<\/p>\n

\u5176\u5b83<\/h5>\n

\u4e3a\u5565\u53eb\u201c\u8f90\u5c04\u573a\u201d\uff08RF\uff09\uff1f\u8f90\u5c04\u573a\uff0c\u5373\u5149\u573a\uff0c\u662f\u7528\u4e8e\u8868\u8fbe\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u5149\u7684\u5206\u5e03\u548c\u5149\u5f3a\u7684\u4e00\u4e2a\u6a21\u578b\u3002\u56de\u987e NeRF \u5bf9\u573a\u666f\u7684\u63cf\u8ff0\uff08\u6bcf\u4e2a\u70b9\u5728\u6bcf\u4e2a\u65b9\u5411\u89c2\u6d4b\u770b\u5230\u7684\u989c\u8272\u7b49\u4fe1\u606f\uff09\uff0c\u5bb9\u6613\u53d1\u73b0\u8fd9\u5176\u5b9e\u662f\u5728\u63cf\u8ff0\u6574\u4e2a\u7a7a\u95f4\u6240\u6709\u70b9\u7684\u5149\u7684\u4fe1\u606f\u3002\u56e0\u6b64\u5c31\u53eb\u5149\u573a\u4e86\u3002\u611f\u89c9\u50cf\u968f\u4fbf\u8d77\u7684\u540d\u5b57<\/s><\/p>\n

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