{"id":1143,"date":"2019-09-12T16:50:00","date_gmt":"2019-09-12T07:50:00","guid":{"rendered":"https:\/\/arithmer.blog\/?p=1143"},"modified":"2022-03-08T15:43:16","modified_gmt":"2022-03-08T06:43:16","slug":"survey-of-3d-deep-learning","status":"publish","type":"post","link":"https:\/\/arithmer.blog\/blog\/survey-of-3d-deep-learning","title":{"rendered":"3D\u6df1\u5c64\u5b66\u7fd2"},"content":{"rendered":"\n<p class=\"has-small-font-size\">\u672c\u8cc7\u6599\u306f2019\u5e749\u670812\u65e5\u306b\u793e\u5185\u5171\u6709\u8cc7\u6599\u3068\u3057\u3066\u5c55\u958b\u3057\u3066\u3044\u305f\u3082\u306e\u3092WEB\u30da\u30fc\u30b8\u5411\u3051\u306b\u30ea\u30cb\u30e5\u30fc\u30a2\u30eb\u3057\u305f\u5185\u5bb9\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"purpose\"><strong>\u25a0Purpose<\/strong><\/h3>\n\n\n\n<p style=\"font-size:18px\"><strong>Purpose of this material<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Overview of 3D deep learning<\/li><li>Comparison b\/w each method of 3D deep learning<\/li><li>Main papers (In this material, I have summarized the material based on following materials and cited papers therein.)<ul><li><a href=\"https:\/\/arxiv.org\/abs\/1808.01462\" target=\"_blank\" rel=\"noreferrer noopener\">E. Ahmed et al, \u201cA survey on Deep Learning Advances on Different 3D Data Representations\u201d, 2018<\/a><\/li><li><a href=\"https:\/\/arxiv.org\/abs\/1611.08097\" target=\"_blank\" rel=\"noreferrer noopener\">M. M. Bronstein et al., \u201cGeometric deep learning: going beyond Euclidean data\u201d, 2016<\/a><\/li><\/ul><\/li><\/ul>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"application\"><strong>\u25a0Application<\/strong><\/h3>\n\n\n\n<p style=\"font-size:18px\"><strong>Application of 3D Deep Learning<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"426\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_01.jpg\" alt=\"\" class=\"wp-image-1198\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_01.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_01-300x125.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_01-768x320.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_01-304x126.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"agenda\"><strong>\u25a0Agenda<\/strong><\/h3>\n\n\n\n<p style=\"font-size:18px\"><strong>Methods of 3D Deep Learning<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li><strong>Euclidean vs Non-Euclidean<\/strong><\/li><li><strong>Euclidean Method<\/strong><ul><li>Projections \/ Multi-View<\/li><li>Voxel<\/li><\/ul><\/li><li><strong>Non-Euclidean Method<\/strong><ul><li>Point Cloud \/ Mesh \/ Graph<\/li><\/ul><\/li><li><strong>Accuracy<\/strong><\/li><li><strong>Dataset \/ Material<\/strong><\/li><li><strong>Appendix<\/strong><ul><li>Mesh Generation<\/li><\/ul><ul><li>Laplacian on Graph<\/li><\/ul><ul><li>Correspondence<\/li><\/ul><\/li><\/ul>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"3d-data\"><strong>\u25a03D Data<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"383\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_02.jpg\" alt=\"\" class=\"wp-image-1199\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_02.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_02-300x112.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_02-768x287.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_02-304x114.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"representation\"><strong>\u25a0Representation<\/strong><\/h3>\n\n\n\n<p style=\"font-size:18px\"><strong>Representation of 3D data<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"441\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_03.jpg\" alt=\"\" class=\"wp-image-1200\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_03.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_03-300x129.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_03-768x331.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_03-304x131.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"436\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_04.jpg\" alt=\"\" class=\"wp-image-1201\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_04.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_04-300x128.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_04-768x327.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_04-304x129.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"euclidean-vs-non-euclidean\"><strong>\u25a0Euclidean vs Non-Euclidean<\/strong><\/h3>\n\n\n\n<p style=\"font-size:18px\"><strong>Euclidean<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"452\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_05.jpg\" alt=\"\" class=\"wp-image-1202\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_05.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_05-300x132.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_05-768x339.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_05-304x134.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Euclidean (detail of feature)<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"427\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_06.jpg\" alt=\"\" class=\"wp-image-1203\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_06.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_06-300x125.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_06-768x320.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_06-304x127.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Non-Euclidean<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"413\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_07.jpg\" alt=\"\" class=\"wp-image-1204\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_07.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_07-300x121.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_07-768x310.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_07-304x123.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Non-Euclidean (detail of feature)<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"440\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_08.jpg\" alt=\"\" class=\"wp-image-1205\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_08.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_08-300x129.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_08-768x330.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_08-304x131.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"euclidean\"><strong>\u25a0Euclidean<\/strong><\/h3>\n\n\n\n<p style=\"font-size:18px\"><strong>Representation of 3D data<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"448\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_09.jpg\" alt=\"\" class=\"wp-image-1206\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_09.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_09-300x131.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_09-768x336.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_09-304x133.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Each Euclidean Method (Projections \/ RGB-D \/ Volumetric \/ Multi-View)<\/strong><\/p>\n\n\n<div id=\"\">\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">Method<\/th><th class=\"has-text-align-left\" data-align=\"left\">Application<\/th><th class=\"has-text-align-left\" data-align=\"left\">Link<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">Deep Pano<\/td><td class=\"has-text-align-left\" data-align=\"left\">Classification<\/td><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/ieeexplore.ieee.org\/document\/7273863\" target=\"_blank\">Link\u2460<\/a><\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">Two-stream CNNs on RGB-D<\/td><td class=\"has-text-align-left\" data-align=\"left\">Classification<\/td><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1507.06821\" target=\"_blank\">Link\u2461<\/a><\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">VoxNet<\/td><td class=\"has-text-align-left\" data-align=\"left\">Classification<\/td><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/www.ri.cmu.edu\/pub_files\/2015\/9\/voxnet_maturana_scherer_iros15.pdf\" target=\"_blank\">Link\u2462<\/a>\u3000<a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/tacky0612\/classification3dmodel\" target=\"_blank\">GitHub(Keras)\u2460<\/a><\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">MVCNN<\/td><td class=\"has-text-align-left\" data-align=\"left\">Classification Retrieval<\/td><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1505.00880\" target=\"_blank\">Link\u2463<\/a>\u3000<a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/suhangpro\/mvcnn\" target=\"_blank\">GitHub(PyTorch\/TensorFlow etc.)\u2461<\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Deep Pano [1]<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Projection to Panoramic image<\/li><li>Row-wise max-pooling for rotational invariant<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"323\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_10.jpg\" alt=\"\" class=\"wp-image-1207\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_10.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_10-300x95.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_10-768x242.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_10-304x96.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Two-stream CNNs on RGB-D [1]<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Concatenate CNN of RGB and CNN of depth map<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"333\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_11.jpg\" alt=\"\" class=\"wp-image-1156\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_11.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_11-300x98.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_11-768x250.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_11-304x99.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>VoxNet [1]<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Voxelization of 3D point cloud to voxel<\/li><li>Not robust for data loss<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"351\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_12.jpg\" alt=\"\" class=\"wp-image-1157\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_12.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_12-300x103.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_12-768x263.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_12-304x104.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>MVCNN [1]<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Merge CNN of each images<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"348\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_13.jpg\" alt=\"\" class=\"wp-image-1158\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_13.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_13-300x102.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_13-768x261.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_13-304x103.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"non-euclidean-point-clouds\"><strong>\u25a0Non-Euclidean (Point Clouds)<\/strong><\/h3>\n\n\n\n<p style=\"font-size:18px\"><strong>Representation of 3D data<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"449\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_14.jpg\" alt=\"\" class=\"wp-image-1159\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_14.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_14-300x132.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_14-768x337.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_14-304x133.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Each Non-Euclidean Method (Point Cloud)<\/strong><\/p>\n\n\n<div id=\"\">\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">Method<\/th><th class=\"has-text-align-left\" data-align=\"left\">Application<\/th><th class=\"has-text-align-left\" data-align=\"left\">Link<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">PointNet<\/td><td class=\"has-text-align-left\" data-align=\"left\">Classification<br>Segmentation<br>Retrieval<br>Correspondence<\/td><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1612.00593\" target=\"_blank\">Paper<\/a><br><a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/charlesq34\/pointnet\" target=\"_blank\">GitHub<\/a> (TensorFlow)<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">PointNet++<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bClassification<br>Segmentation<br>Retrieval<br>Correspondence<\/td><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/proceedings.neurips.cc\/paper\/2017\/file\/d8bf84be3800d12f74d8b05e9b89836f-Paper.pdf\" target=\"_blank\">Paper<\/a><br><a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/charlesq34\/pointnet2\" target=\"_blank\">GitHub<\/a> (TensorFlow)<br>PyTorch-geometric (PointConv)<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">Dynamic Graph CNN(DGCNN)<\/td><td class=\"has-text-align-left\" data-align=\"left\">Classification<br>Segmentation<\/td><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1801.07829\" target=\"_blank\">Paper<\/a><br><a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/WangYueFt\/dgcnn\" target=\"_blank\">GitHub<\/a> (PyTorch\/TensorFlow)<br>PyTorch-geometric (DynamicEdgeConv)<br><\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200bPointCNN<\/td><td class=\"has-text-align-left\" data-align=\"left\">Classification<br>Segmentation<\/td><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1801.07791\" target=\"_blank\">Paper<\/a><br><a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/yangyanli\/PointCNN\" target=\"_blank\">GitHub<\/a> (TensorFlow)<br>PyTorch-geometric (XConv)<br><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>PointNet [1]<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1023\" height=\"489\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_15.jpg\" alt=\"\" class=\"wp-image-1160\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_15.jpg 1023w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_15-300x143.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_15-768x367.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_15-304x145.jpg 304w\" sizes=\"(max-width: 1023px) 100vw, 1023px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>PointNet<\/strong><\/p>\n\n\n\n<p style=\"font-size:16px\"><strong>T-Net [1]<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Similar to Spatial Transformer Networks in 2D<\/li><li>Spatial Transformer Networks<ul><li>Alignment of image (transformation, rotation, distortion etc.) by spatial transformation<\/li><li>Learn affine transformation from input data (not necessarily special data)<\/li><li>Can insert this networks at each point b\/w networks<\/li><\/ul><\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"227\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_16.jpg\" alt=\"\" class=\"wp-image-1161\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_16.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_16-300x67.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_16-768x170.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_16-304x67.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n<div id=\"\">\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">Reference<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u200bContents<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200b<a rel=\"noreferrer noopener\" href=\"https:\/\/proceedings.neurips.cc\/paper\/2015\/file\/33ceb07bf4eeb3da587e268d663aba1a-Paper.pdf\" target=\"_blank\">Paper<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bOriginal Paper<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200b<a rel=\"noreferrer noopener\" href=\"https:\/\/pytorch.org\/tutorials\/intermediate\/spatial_transformer_tutorial.html\" target=\"_blank\">Sample(PyTorch)<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bDataset : MNIST<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"441\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_17.jpg\" alt=\"\" class=\"wp-image-1162\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_17.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_17-300x129.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_17-768x331.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_17-304x131.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>T-Net<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>3D ver. of Spatial Transformer Networks in 2D<\/li><li>Not need sampling grid (There are no gird structure in 3D)<ul><li>Directly apply transformation to each point cloud<\/li><\/ul><\/li><li>Output parameter<ul><li>3 \u00d7 3 in first T-Net<\/li><li>64 \u00d7 64 in second T-Net<\/li><\/ul><\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"306\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_18.jpg\" alt=\"\" class=\"wp-image-1163\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_18.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_18-300x90.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_18-768x230.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_18-304x91.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>PointNet++ [1]<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Comparison b\/w PointNet<\/li><li>Detailed information is kept<\/li><li>Can treat different density of point cloud<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"348\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_19.jpg\" alt=\"\" class=\"wp-image-1164\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_19.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_19-300x102.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_19-768x261.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_19-304x103.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Set abstraction<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Grouping in one scale + feature extraction<ul><li>Sampling Layer : Extraction of sampling points by farthest point sampling (FPS)<\/li><\/ul><ul><li>Grouping Layer : Grouping points around sampling points<\/li><\/ul><ul><li>PointNet Layer : Applying PointNe<\/li><\/ul><\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"263\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_20.jpg\" alt=\"\" class=\"wp-image-1165\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_20.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_20-300x77.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_20-768x197.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_20-304x78.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<ul style=\"font-size:16px\"><li>Point Feature Propagation for segmentation<ul><li>Interpolation : interpolation from k neighbor points<\/li><li>Concatenation<\/li><\/ul><\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"318\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_21.jpg\" alt=\"\" class=\"wp-image-1166\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_21.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_21-300x93.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_21-768x239.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_21-304x94.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<ul style=\"font-size:16px\"><li><strong>Single scale grouping<\/strong><\/li><li><strong>Multi scale\/resolution grouping<\/strong><ul><li>Combination of features from different scales<\/li><li>Combination of features from different scales<\/li><li>Modifying architecture in set abstraction level<\/li><\/ul><\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"262\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_22.jpg\" alt=\"\" class=\"wp-image-1167\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_22.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_22-300x77.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_22-768x197.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_22-304x78.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<ul style=\"font-size:16px\"><li><strong>Detail of architecture<\/strong><\/li><li><strong>Note: <\/strong><a href=\"https:\/\/manage.wix.com\/dashboard\/81eabb3b-1ef3-4ded-81d6-982866704a5e\/blog\/overview\/search\/.hash.vertex?referralInfo=sidebar\"><strong>#vertex<\/strong><\/a><strong> is fixed<\/strong><\/li><\/ul>\n\n\n\n<p class=\"has-text-align-center\" style=\"font-size:16px\">Architecture for classification and part segmentation of ModelNet using single scale grouping<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"460\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_23.jpg\" alt=\"\" class=\"wp-image-1168\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_23.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_23-300x135.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_23-768x345.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_23-304x137.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<ul style=\"font-size:16px\"><li><strong>Detail of architecture<\/strong><\/li><li><strong>Note: <\/strong><a href=\"https:\/\/manage.wix.com\/dashboard\/81eabb3b-1ef3-4ded-81d6-982866704a5e\/blog\/overview\/search\/.hash.vertex?referralInfo=sidebar\"><strong>#vertex<\/strong><\/a><strong> is fixed<\/strong><\/li><\/ul>\n\n\n\n<p style=\"font-size:16px\">Architecture classification of ModelNet using multi-resolution grouping (MRG)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"296\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_24.jpg\" alt=\"\" class=\"wp-image-1169\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_24.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_24-300x87.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_24-768x222.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_24-304x88.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Dynamic Graph CNN (DGCNN) [1]<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>PointNet + w\/ Edge Conv.<\/li><li>Edge Conv.<ul><li>Create local edge structure dynamically (not fixed in each layer)<\/li><\/ul><\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"333\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_25.jpg\" alt=\"\" class=\"wp-image-1170\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_25.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_25-300x98.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_25-768x250.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_25-304x99.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>PointCNN [1]<\/strong><\/p>\n\n\n\n<p style=\"font-size:16px\"><strong>Downsampling information from neighborhoods into fewer representative points<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"347\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_26.jpg\" alt=\"\" class=\"wp-image-1171\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_26.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_26-300x102.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_26-768x260.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_26-304x103.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"non-euclidean-mesh\"><strong>\u25a0Non-Euclidean (Mesh)<\/strong><\/h3>\n\n\n\n<p style=\"font-size:18px\"><strong>Representation of 3D data<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"449\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_27.jpg\" alt=\"\" class=\"wp-image-1172\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_27.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_27-300x132.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_27-768x337.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_27-304x133.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Each Non-Euclidean Method (Mesh)<\/strong><\/p>\n\n\n<div id=\"\">\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">Method<\/th><th class=\"has-text-align-left\" data-align=\"left\">Application<\/th><th class=\"has-text-align-left\" data-align=\"left\">Link<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">MeshCNN<\/td><td class=\"has-text-align-left\" data-align=\"left\">Classification<br>Segmentation<\/td><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1809.05910\" target=\"_blank\">Paper<\/a><br><a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/ranahanocka\/MeshCNN\" target=\"_blank\">GitHub<\/a> (PyTorch)<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">MeshNet<\/td><td class=\"has-text-align-left\" data-align=\"left\">Classification<\/td><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1811.11424\" target=\"_blank\">Paper<\/a><br><a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/iMoonLab\/MeshNet\" target=\"_blank\">GitHub <\/a>(PyTorch)<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>MeshCNN [1]<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li><strong>Edge collapse by pooling<\/strong><\/li><li><strong>Can apply only the manifold mesh<\/strong><\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"285\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_28.jpg\" alt=\"\" class=\"wp-image-1173\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_28.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_28-300x83.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_28-768x214.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_28-304x85.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p id=\"meshnet\" style=\"font-size:18px\"><strong>MeshNet<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li><strong>Input feature<\/strong><ul><li>Center, corner, normal, neighbor inde<\/li><\/ul><\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"416\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_29.jpg\" alt=\"\" class=\"wp-image-1174\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_29.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_29-300x122.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_29-768x312.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_29-304x124.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"non-euclidean-graph\"><strong>\u25a0Non-Euclidean (Graph)<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"449\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_30.jpg\" alt=\"\" class=\"wp-image-1175\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_30.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_30-300x132.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_30-768x337.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_30-304x133.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Each Non-Euclidean Method (Graph)<\/strong><\/p>\n\n\n\n<p style=\"font-size:16px\">Spectral \/ Spatial Method<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"384\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_31.jpg\" alt=\"\" class=\"wp-image-1176\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_31.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_31-300x113.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_31-768x288.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_31-304x114.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Each Non-Euclidean Method (Graph)<\/strong><\/p>\n\n\n\n<p style=\"font-size:16px\">Spatial method is more useful than spectral method.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"198\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_32.jpg\" alt=\"\" class=\"wp-image-1177\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_32.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_32-300x58.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_32-768x149.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_32-304x59.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<p style=\"font-size:16px\">\u203bSome equations from following pages are referred to the documents in PyTorch-geometric. <br>(<a rel=\"noreferrer noopener\" href=\"https:\/\/pytorch-geometric.readthedocs.io\/en\/latest\/modules\/nn.html\" target=\"_blank\">https:\/\/pytorch-geometric.readthedocs.io\/en\/latest\/modules\/nn.html<\/a>) <br>I will explain PyTorch-geometric in later page.<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Each Non-Euclidean Method (Graph)<\/strong><\/p>\n\n\n\n<p style=\"font-size:16px\">Spectral, Spectral free<\/p>\n\n\n<div id=\"\">\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">Method<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u200bMethod<\/th><th class=\"has-text-align-left\" data-align=\"left\">Application<\/th><th class=\"has-text-align-left\" data-align=\"left\">Link<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">Spectral CNN<\/td><td class=\"has-text-align-left\" data-align=\"left\">Spectral<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bGraph<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200b<a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1312.6203\" target=\"_blank\">Paper<\/a><\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">Chebyshev Spectral CNN (ChebNet)<\/td><td class=\"has-text-align-left\" data-align=\"left\">Spectral free<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bGraph<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200b<a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1606.09375\" target=\"_blank\">Paper<\/a><br><a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/mdeff\/cnn_graph\" target=\"_blank\">GitHub<\/a> (TensorFlow)<br>PyTorch-geometric (ChebConv)<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">Graph Convolutional Network<br>(GCN)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bSpectral free<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bGraph<\/td><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1609.02907\" target=\"_blank\">Paper<\/a><br>PyTorch-geometric (GCNConv)<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">Graph Neural Network<br>(GNN)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bSpectral free<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bGraph<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200b<a rel=\"noreferrer noopener\" href=\"https:\/\/persagen.com\/files\/misc\/scarselli2009graph.pdf\" target=\"_blank\">Paper<\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Spectral CNN [2]<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li><strong>cannot use different shape<\/strong><ul><li>Spectral filter coefficients is base dependent<\/li><\/ul><\/li><li><strong>High computational cost<\/strong><\/li><li><strong>No locality<\/strong><\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"374\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_33.jpg\" alt=\"\" class=\"wp-image-1178\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_33.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_33-300x110.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_33-768x281.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_33-304x111.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p id=\"chebyshev-spectral-cnn-chebnet-1\" style=\"font-size:18px\"><strong>Chebyshev Spectral CNN (ChebNet) [1]<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Not calculate Laplacian eigenvectors directly<\/li><li>Locality (K hops)<\/li><li>Approximate filter as polynomial<\/li><\/ul>\n\n\n\n<p style=\"font-size:18px\"><strong>Graph Convolutional Network (GCN) [2]<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Special ver. of ChebNet (\ud835\udc3e = 2)<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"206\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_34.jpg\" alt=\"\" class=\"wp-image-1179\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_34.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_34-300x60.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_34-768x155.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_34-304x61.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Each Non-Euclidean Method (Graph)<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Charting<\/li><\/ul>\n\n\n<div id=\"\">\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><\/th><th class=\"has-text-align-left\" data-align=\"left\">\u200bApplication<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u200bLink<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200bGeodesic CNN<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bMesh<br>Shape retrieval \/correspondence<\/td><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1501.06297\" target=\"_blank\">Paper<\/a><\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200bAnisotropic CNN<\/td><td class=\"has-text-align-left\" data-align=\"left\">Mesh \/ point cloud<br>Shape correspondence<\/td><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1605.06437\" target=\"_blank\">Paper<\/a><\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200bMoNet<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bGraph \/ mesh \/ point cloud<br>Shape correspondence<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200b<a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1611.08402\" target=\"_blank\">Paper<\/a><br>PyTorch-geometric (GMMConv)<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200bSplineCNN<\/td><td class=\"has-text-align-left\" data-align=\"left\">Graph \/ Mesh<br>Classification<br>Shape correspondence<\/td><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1711.08920\" target=\"_blank\">Paper<\/a><br><a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/rusty1s\/pytorch_spline_conv\" target=\"_blank\">GitHub<\/a> (PyTorch)<br>PyTorch-geometric (SplineConv)<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">FeaStNet<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bGraph \/ Mesh<br>Shape correspondence<br>Segmentation<\/td><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1706.05206\" target=\"_blank\">Paper<\/a><br>PyTorch-geometric (FeaStConv)<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"477\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_35.jpg\" alt=\"\" class=\"wp-image-1180\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_35.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_35-300x140.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_35-768x358.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_35-304x142.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Geodesic CNN (GCNN)<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Create local coordinate<\/li><li>Do not verify the meaningful chart (need to create small radius chart)<\/li><\/ul>\n\n\n\n<p style=\"font-size:18px\"><strong>Anisotropic CNN (ACNN)<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Fourier basis is based on anisotropic heat diffusion eq.<\/li><\/ul>\n\n\n\n<p style=\"font-size:18px\"><strong>MoNet<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Learn filter as parametric kernel<\/li><li>Generalization of geodesic CNN and anisotropic CNN<\/li><\/ul>\n\n\n\n<p style=\"font-size:18px\"><strong>SplineCNN [1]<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Filter based on B-spline fun<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"371\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_36.jpg\" alt=\"\" class=\"wp-image-1181\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_36.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_36-300x109.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_36-768x278.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_36-304x110.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>FeaStNet [1]<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Dynamically determine relation b\/w filter weight and local graph of a node<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"387\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_37.jpg\" alt=\"\" class=\"wp-image-1182\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_37.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_37-300x113.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_37-768x290.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_37-304x115.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>PyTorch-geometric<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"95\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_38.jpg\" alt=\"\" class=\"wp-image-1183\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_38.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_38-300x28.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_38-768x71.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_38-304x28.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<ul style=\"font-size:16px\"><li><a href=\"https:\/\/github.com\/rusty1s\/pytorch_geometric\">https:\/\/github.com\/rusty1s\/pytorch_geometric<\/a><\/li><li><strong>Library based on PyTorchLibrary based on PyTorch<\/strong><\/li><li><strong>For point cloud, mesh (not only graph)<\/strong><\/li><li><strong>Include Point cloud, graph-type approach code<\/strong><ul><li>PointNet++, DGCNN, PointCNN<\/li><li>ChebNet, GCN, MoNet, SplineCNN, FeaStNet<\/li><\/ul><\/li><li><strong>Easy to get the famous sample data and transform same data format<\/strong><ul><li>ModelNet, ShapeNet, etc.<\/li><\/ul><\/li><li><strong>Many example and benchmark<\/strong><\/li><\/ul>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"accuracy\"><strong>\u25a0Accuracy<\/strong><\/h3>\n\n\n\n<p style=\"font-size:18px\"><strong>Accuracy (Classification)<\/strong><\/p>\n\n\n\n<ul><li>around 90% in any method (except VoxNet)<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"373\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_39.jpg\" alt=\"\" class=\"wp-image-1184\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_39.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_39-300x109.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_39-768x280.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_39-304x111.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Accuracy (Segmentation)<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"379\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_40.jpg\" alt=\"\" class=\"wp-image-1185\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_40.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_40-300x111.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_40-768x284.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_40-304x113.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"dataset\"><strong>\u25a0Dataset<\/strong><\/h3>\n\n\n\n<p style=\"font-size:18px\"><strong>3D Dataset<\/strong><\/p>\n\n\n<div id=\"\">\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><\/th><th class=\"has-text-align-left\" data-align=\"left\">\u200bContents<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u200bData Format<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u200bPurpose<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u200bPyTorch-geometric<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"http:\/\/modelnet.cs.princeton.edu\/\" target=\"_blank\">ModelNet10\/40<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200b3D CAD Model (10 or 40 classes)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bMesh (.OFF)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bClassification<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bModelNet<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200b<a rel=\"noreferrer noopener\" href=\"https:\/\/shapenet.cs.stanford.edu\/iccv17\/\" target=\"_blank\">ShapeNet<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200b3D Shape<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bPoint Cloud (.pts)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bSegmentation<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bShapeNet<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"http:\/\/www.scan-net.org\/#code-and-data\" target=\"_blank\">ScanNet<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bIndoor Scan Data<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bMesh (.ply)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bSegmentation<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u2013<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200bS3DIS(<a rel=\"noreferrer noopener\" href=\"http:\/\/buildingparser.stanford.edu\/dataset.html#Download\" target=\"_blank\">original<\/a> ,<a rel=\"noreferrer noopener\" href=\"https:\/\/shapenet.cs.stanford.edu\/media\/indoor3d_sem_seg_hdf5_data.zip\" target=\"_blank\">h5<\/a>)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200b\u200bIndoor Scan Data<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bPoint Cloud<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bSegmentation<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bS3DIS<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200b<a rel=\"noreferrer noopener\" href=\"https:\/\/www.shrec.net\/\" target=\"_blank\">SHREC<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bmany type for each contest<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u2013<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bRetrieval<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u2013<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/www.dais.unive.it\/~shrec2016\/dataset.php\" target=\"_blank\">SHREC2016<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bAnimal, Human (Part Data)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bMesh (.OFF)<\/td><td class=\"has-text-align-left\" data-align=\"left\">Correspondence<\/td><td class=\"has-text-align-left\" data-align=\"left\">SHREC2016<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"http:\/\/tosca.cs.technion.ac.il\/book\/resources_data.html\" target=\"_blank\">TOSCA<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">Animal, Human<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bMesh (same #vertices at each category, separate file of vertices and triangles)<\/td><td class=\"has-text-align-left\" data-align=\"left\">Correspondence<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bTOSCA<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"http:\/\/geometry.cs.ucl.ac.uk\/projects\/2018\/pcpnet\/\" target=\"_blank\">PCPNet<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200b3D Shape<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bPoint Cloud (.xyz) (Including normal, curvature files.)<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bEstimation of local shape (Normal, curvature)<\/td><td class=\"has-text-align-left\" data-align=\"left\">PCPNet<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"http:\/\/faust.is.tue.mpg.de\/\" target=\"_blank\">FAUST<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bHuman body<\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bMesh<\/td><td class=\"has-text-align-left\" data-align=\"left\">Correspondence<\/td><td class=\"has-text-align-left\" data-align=\"left\">FAUST<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<p style=\"font-size:16px\">ScanNet\uff1aregistration required <br>S3DIS : registration required (for original)<br>FAUST(Note) : registration required<\/p>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"material\"><strong>\u25a0Material<\/strong><\/h3>\n\n\n\n<p style=\"font-size:18px\"><strong>Material of 3D deep learning (3D \/ point cloud)<\/strong><\/p>\n\n\n<div id=\"\">\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">\u200bPaper<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u200bComment<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200b<a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1808.01462\" target=\"_blank\">A survey on Deep Learning Advances on Different 3D Data Representations<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200b\u30fbReview of 3D Deep Learning<br>\u30fbEasier to read it<br>\u30fbWritten from point of view about Euclidean and Non-Euclidean method<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/paperswithcode.com\/task\/3d\" target=\"_blank\">\u200bPaperswithcode<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u30fb\u200bPaper w\/ code about 3D<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/speakerdeck.com\/nnchiba\/point-cloud-deep-learning-survey-ver-2\" target=\"_blank\">\u200bPoint Cloud Deep Learning Survey Ver. 2<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u30fb\u200bDeep learning for point cloud<br>\u30fbSurvey of many papers<br><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Material of 3D deep learning (graph)<\/strong><\/p>\n\n\n<div id=\"\">\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">\u200bPaper<\/th><th class=\"has-text-align-left\" data-align=\"left\">Comment<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200b<a rel=\"noreferrer noopener\" href=\"https:\/\/arxiv.org\/abs\/1611.08097\" target=\"_blank\">Geometric deep learning: going beyond Euclidean data<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bReview of geometric deep learning<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"https:\/\/geometricdeeplearning.com\/\" target=\"_blank\">Geometric deep learning<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bsummary of paper and code about geometric deep learning<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200b<a rel=\"noreferrer noopener\" href=\"https:\/\/www.youtube.com\/watch?v=LvmjbXZyoP0\" target=\"_blank\">Geometric deep learning on Graphs and Manifolds(NIPS2017)<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bPresentation (youtube) about geometric deep learning<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"summary\"><strong>\u25a0Summary<\/strong><\/h3>\n\n\n\n<p style=\"font-size:18px\"><strong>There are many methods of 3D deep learning.<\/strong><\/p>\n\n\n\n<p style=\"font-size:16px\"><strong>Two main method<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li><strong>Euclidean vs Non-Euclidean<\/strong><\/li><li><strong>Euclidean Method<\/strong><ul><li>Projections \/ Multi-View \/ Voxel<\/li><\/ul><\/li><li><strong>Non-Euclidean Method<\/strong><ul><li>Point Cloud \/ Mesh \/ Graph<\/li><\/ul><\/li><\/ul>\n\n\n\n<p style=\"font-size:16px\"><strong>Each method have merit and demerit.<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>We need to choose the better method for each data type and application.<\/li><\/ul>\n\n\n\n<p style=\"font-size:16px\"><strong>The research about 3D deep learning is growing.<\/strong><\/p>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"appendix\"><strong>\u25a0Appendix<\/strong><\/h3>\n\n\n\n<p style=\"font-size:18px\"><strong>Appendix<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li><strong>Mesh Generation <\/strong><\/li><li><strong>Laplacian on Graph <\/strong><\/li><li><strong>Correspondence<\/strong><\/li><\/ul>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"appendix-mesh-generation\"><strong>\u25a0Appendix : Mesh Generation<\/strong><\/h3>\n\n\n\n<p style=\"font-size:18px\"><strong>Mesh Generation<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>In this material, I have summarized these materials.<\/li><\/ul>\n\n\n<div id=\"\">\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">Link<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u200bContents<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200b<a rel=\"noreferrer noopener\" href=\"http:\/\/precipedia.jspe.or.jp\/wiki\/index.php?title=%E7%82%B9%E7%BE%A4%E9%9D%A2%E5%BC%B5%E3%82%8A\" target=\"_blank\">\u70b9\u7fa4\u9762\u5f35\u308a(\u7cbe\u5bc6\u5de5\u5b66\u4f1a)<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bSurface reconstruction<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"http:\/\/precipedia.jspe.or.jp\/wiki\/index.php?title=%E3%83%A1%E3%83%83%E3%82%B7%E3%83%A5%E5%87%A6%E7%90%86\" target=\"_blank\">\u30e1\u30c3\u30b7\u30e5\u51e6\u7406(\u7cbe\u5bc6\u5de5\u5b66\u4f1a)<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bMesh processing<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200b<a rel=\"noreferrer noopener\" href=\"https:\/\/www.slideshare.net\/FujimotoKeisuke\/20190414-point-cloud-reconstruction-survey-140757963\" target=\"_blank\">CV\u52c9\u5f37\u4f1a@\u95a2\u6771\u767a\u8868\u8cc7\u6599\u3000\u70b9\u7fa4\u518d\u69cb\u6210\u306b\u95a2\u3059\u308b\u30b5\u30fc\u30d9\u30a4<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bSurvey of point cloud reconstruction<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Difficulty of Mesh Generation<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"370\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_41.jpg\" alt=\"\" class=\"wp-image-1186\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_41.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_41-300x108.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_41-768x278.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_41-304x110.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Kinds of Mesh Generation<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"375\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_42.jpg\" alt=\"\" class=\"wp-image-1187\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_42.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_42-300x110.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_42-768x281.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_42-304x111.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Classification of the method<\/strong><\/p>\n\n\n\n<p style=\"font-size:16px\">In general, it is easier to use the implicit method, since there are noise of point cloud.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"179\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_43.jpg\" alt=\"\" class=\"wp-image-1188\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_43.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_43-300x52.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_43-768x134.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_43-304x53.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Kinds of Mesh Generation (Detail)<\/strong><\/p>\n\n\n\n<p style=\"font-size:16px\">Direct Triangulation (example of built-in function in MeshLab)<\/p>\n\n\n<div id=\"\">\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">\u200bMethod<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u200bFeature<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\"><a rel=\"noreferrer noopener\" href=\"http:\/\/compbio.mit.edu\/publications\/C01_Amenta_Siggraph_98.pdf\" target=\"_blank\">Voronoi-Based Surface Reconstruction<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bCreation of Delaunay diagram adding the vertices using Voronoi diagram<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200b<a rel=\"noreferrer noopener\" href=\"https:\/\/lidarwidgets.com\/samples\/bpa_tvcg.pdf\" target=\"_blank\">Ball-Pivoting Algorithm<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bRoll the ball over the point cloud and generate mesh from the point cloud located within a certain distance<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Voronoi-Based Surface Reconstruction<\/strong><\/p>\n\n\n\n<p style=\"font-size:16px\"><strong>Voronoi diagram<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>Region divided by the bisector of each vertices (in 2D)<\/li><\/ul>\n\n\n\n<p style=\"font-size:16px\"><strong>Delaunay triangulation<\/strong><\/p>\n\n\n\n<ul style=\"font-size:16px\"><li>riangulation by connection of vertices<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"271\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_44.jpg\" alt=\"\" class=\"wp-image-1189\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_44.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_44-300x79.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_44-768x203.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_44-304x80.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Ball-Pivoting Algorithm<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"343\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_45.jpg\" alt=\"\" class=\"wp-image-1190\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_45.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_45-300x100.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_45-768x257.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_45-304x102.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Kinds of Mesh Generation (Detail)<\/strong><\/p>\n\n\n\n<p style=\"font-size:16px\">Surface Smoothness (example of built-in function in MeshLab)<\/p>\n\n\n<div id=\"\">\n<figure class=\"wp-block-table is-style-stripes has-small-font-size\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\">\u200bMethod<\/th><th class=\"has-text-align-left\" data-align=\"left\">\u200bFeature<\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200b<a rel=\"noreferrer noopener\" href=\"https:\/\/hhoppe.com\/recon.pdf\" target=\"_blank\">Signed distance function + Marching Cubes<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bCreation of Signed distance function by using the distance b\/w vertices and surface + Mesh generation by using Marching Cubes<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">\u200b<a rel=\"noreferrer noopener\" href=\"https:\/\/www.cs.jhu.edu\/~misha\/MyPapers\/ToG13.pdf\" target=\"_blank\">Screened Poisson surface reconstruction<\/a><br><a rel=\"noreferrer noopener\" href=\"https:\/\/hhoppe.com\/poissonrecon.pdf\" target=\"_blank\">(Poisson surface reconstruction)<\/a><\/td><td class=\"has-text-align-left\" data-align=\"left\">\u200bDistinguish b\/w inside and outside of surface by using Poisson eq.<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div>\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Signed distance function + Marching Cubes<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"430\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_46.jpg\" alt=\"\" class=\"wp-image-1191\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_46.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_46-300x126.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_46-768x323.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_46-304x128.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p style=\"font-size:18px\"><strong>Screened Poisson surface reconstruction<\/strong><\/p>\n\n\n\n<p style=\"font-size:16px\">get Indicator Function by solving the Poisson eq.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"345\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_47.jpg\" alt=\"\" class=\"wp-image-1192\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_47.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_47-300x101.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_47-768x259.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_47-304x102.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"appendix-laplacian-on-graph\"><strong>\u25a0Appendix : Laplacian on Graph<\/strong><\/h3>\n\n\n\n<p style=\"font-size:18px\"><strong>Laplacian on Graph [1]<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"489\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_48.jpg\" alt=\"\" class=\"wp-image-1193\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_48.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_48-300x143.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_48-768x367.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_48-304x145.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"290\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_49.jpg\" alt=\"\" class=\"wp-image-1194\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_49.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_49-300x85.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_49-768x218.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_49-304x86.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<p style=\"font-size:18px\"><strong>Convolution<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"370\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_50.jpg\" alt=\"\" class=\"wp-image-1195\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_50.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_50-300x108.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_50-768x278.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_50-304x110.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"appendix-correspondence\"><strong>\u25a0Appendix :Correspondence<\/strong><\/h3>\n\n\n\n<p style=\"font-size:18px\"><strong>Correspondence [1]<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"1024\" height=\"434\" src=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_51.jpg\" alt=\"\" class=\"wp-image-1196\" srcset=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_51.jpg 1024w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_51-300x127.jpg 300w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_51-768x326.jpg 768w, https:\/\/arithmer.blog\/wp-content\/uploads\/2022\/02\/NS20190912_51-304x129.jpg 304w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h3 class=\"has-medium-font-size wp-block-heading\" id=\"\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\"><strong>\u25a0\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9<\/strong><\/h3>\n\n\n\n<p><a href=\"https:\/\/arithmer.blog\/wp-content\/uploads\/2019\/09\/04_3D\u6df1\u5c64\u5b66\u7fd2.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">3D\u6df1\u5c64\u5b66\u7fd2.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u672c\u8cc7\u6599\u306f2019\u5e749\u670812\u65e5\u306b\u793e\u5185\u5171\u6709\u8cc7\u6599\u3068\u3057\u3066\u5c55\u958b\u3057\u3066\u3044\u305f\u3082\u306e\u3092WEB\u30da\u30fc\u30b8\u5411\u3051\u306b\u30ea\u30cb\u30e5\u30fc\u30a2\u30eb\u3057\u305f\u5185\u5bb9\u306b\u306a\u308a\u307e\u3059\u3002 \u25a0Purpose Purpose of this material Overview of 3D de &#8230; <\/p>\n","protected":false},"author":3,"featured_media":1197,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[57,20,96,95,35,24],"_links":{"self":[{"href":"https:\/\/arithmer.blog\/index.php?rest_route=\/wp\/v2\/posts\/1143"}],"collection":[{"href":"https:\/\/arithmer.blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/arithmer.blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/arithmer.blog\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/arithmer.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1143"}],"version-history":[{"count":16,"href":"https:\/\/arithmer.blog\/index.php?rest_route=\/wp\/v2\/posts\/1143\/revisions"}],"predecessor-version":[{"id":1229,"href":"https:\/\/arithmer.blog\/index.php?rest_route=\/wp\/v2\/posts\/1143\/revisions\/1229"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/arithmer.blog\/index.php?rest_route=\/wp\/v2\/media\/1197"}],"wp:attachment":[{"href":"https:\/\/arithmer.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1143"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/arithmer.blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1143"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/arithmer.blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1143"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}