{"id":9337,"date":"2022-10-21T21:01:07","date_gmt":"2022-10-21T13:01:07","guid":{"rendered":"http:\/\/139.9.1.231\/?p=9337"},"modified":"2022-10-21T21:01:44","modified_gmt":"2022-10-21T13:01:44","slug":"pointnetplus","status":"publish","type":"post","link":"http:\/\/139.9.1.231\/index.php\/2022\/10\/21\/pointnetplus\/","title":{"rendered":"PointNet++"},"content":{"rendered":"\n

\u8bba\u6587\uff1ahttps:\/\/arxiv.org\/abs\/1706.02413<\/a>\uff08NIPS 2017\uff09<\/p>\n\n\n\n

code\uff1a https:\/\/github.com\/charlesq34\/pointnet2<\/a><\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n\n\n

1\u3001\u6539\u8fdb<\/h2>\n\n\n\n

PointNet\u56e0\u4e3a\u662f\u53ea\u4f7f\u7528\u4e86MLP\u548cmax pooling\uff0c\u6ca1\u6709\u80fd\u529b\u6355\u83b7\u5c40\u90e8\u7ed3\u6784\uff0c\u56e0\u6b64\u5728\u7ec6\u8282\u5904\u7406\u548c\u6cdb\u5316\u5230\u590d\u6742\u573a\u666f\u4e0a\u80fd\u529b\u5f88\u6709\u9650\u3002<\/p>\n\n\n\n

  1. point-wise MLP\uff0c\u4ec5\u4ec5\u662f\u5bf9\u6bcf\u4e2a\u70b9\u8868\u5f81\uff0c\u5bf9\u5c40\u90e8\u7ed3\u6784\u4fe1\u606f\u6574\u5408\u80fd\u529b\u592a\u5f31 –> PointNet++\u7684\u6539\u8fdb\uff1asampling\u548cgrouping\u6574\u5408\u5c40\u90e8\u90bb\u57df<\/strong><\/li>
  2. global feature\u76f4\u63a5\u7531max pooling\u83b7\u5f97\uff0c\u65e0\u8bba\u662f\u5bf9\u5206\u7c7b\u8fd8\u662f\u5bf9\u5206\u5272\u4efb\u52a1\uff0c\u90fd\u4f1a\u9020\u6210\u5de8\u5927\u7684\u4fe1\u606f\u635f\u5931 <\/strong>–> PointNet++\u7684\u6539\u8fdb\uff1ahierarchical feature learning framework\uff0c\u901a\u8fc7\u591a\u4e2aset abstraction\u9010\u7ea7\u964d\u91c7\u6837\uff0c\u83b7\u5f97\u4e0d\u540c\u89c4\u6a21\u4e0d\u540c\u5c42\u6b21\u7684local-global feature<\/strong><\/li>
  3. \u5206\u5272\u4efb\u52a1\u7684\u5168\u5c40\u7279\u5f81global feature\u662f\u76f4\u63a5\u590d\u5236\u4e0elocal feature\u62fc\u63a5\uff0c\u751f\u6210discriminative feature\u80fd\u529b\u6709\u9650 –> PointNet++\u7684\u6539\u8fdb\uff1a\u5206\u5272\u4efb\u52a1\u8bbe\u8ba1\u4e86encoder-decoder\u7ed3\u6784\uff0c\u5148\u964d\u91c7\u6837\u518d\u4e0a\u91c7\u6837\uff0c\u4f7f\u7528skip connection\u5c06\u5bf9\u5e94\u5c42\u7684local-global feature\u62fc\u63a5<\/strong><\/li><\/ol>\n\n\n\n

    2\u3001\u65b9\u6cd5<\/h2>\n\n\n\n
    \"\"<\/figure>\n\n\n\n

    PointNet++\u7684\u7f51\u7edc\u5927\u4f53\u662fencoder-decoder\u7ed3\u6784<\/p>\n\n\n\n

    encoder\u4e3a\u964d\u91c7\u6837\u8fc7\u7a0b\uff0c\u901a\u8fc7\u591a\u4e2aset abstraction\u7ed3\u6784\u5b9e\u73b0\u591a\u5c42\u6b21\u7684\u964d\u91c7\u6837\uff0c\u5f97\u5230\u4e0d\u540c\u89c4\u6a21\u7684point-wise feature\uff0c\u6700\u540e\u4e00\u4e2aset abstraction\u8f93\u51fa\u53ef\u4ee5\u8ba4\u4e3a\u662fglobal feature\u3002\u5176\u4e2dset abstraction\u7531sampling\uff0cgrouping\uff0cpointnet\u4e09\u4e2a\u6a21\u5757\u6784\u6210\u3002<\/p>\n\n\n\n

    decoder\u6839\u636e\u5206\u7c7b\u548c\u5206\u5272\u5e94\u7528\uff0c\u53c8\u6709\u6240\u4e0d\u540c\u3002\u5206\u7c7b\u4efb\u52a1decoder\u6bd4\u8f83\u7b80\u5355\uff0c\u4e0d\u4ecb\u7ecd\u4e86\u3002\u5206\u5272\u4efb\u52a1decoder\u4e3a\u4e0a\u91c7\u6837\u8fc7\u7a0b\uff0c\u901a\u8fc7\u53cd\u5411\u63d2\u503c\u548cskip connection\u5b9e\u73b0\u5728\u4e0a\u91c7\u6837\u7684\u540c\u65f6\uff0c\u8fd8\u80fd\u591f\u83b7\u5f97local+global\u7684point-wise feature\uff0c\u4f7f\u5f97\u6700\u7ec8\u7684\u8868\u5f81\u80fd\u591fdiscriminative\uff08\u5206\u8fa9\u80fd\u529b\uff09\u3002<\/p>\n\n\n\n

    \u601d\u8003\uff1a<\/strong><\/p>\n\n\n\n

    1. PointNet++\u964d\u91c7\u6837\u8fc7\u7a0b\u662f\u600e\u4e48\u5b9e\u73b0\u7684\uff1f\/PointNet++\u662f\u5982\u4f55\u8868\u5f81global feature\u7684\uff1f\uff08\u5173\u6ce8set abstraction, sampling layer, grouping layer, pointnet layer\uff09<\/li>
    2. PointNet++\u7528\u4e8e\u5206\u5272\u4efb\u52a1\u7684\u4e0a\u91c7\u6837\u8fc7\u7a0b\u662f\u600e\u4e48\u5b9e\u73b0\u7684\uff1f\/PointNet++\u662f\u5982\u4f55\u8868\u5f81\u7528\u4e8e\u5206\u5272\u4efb\u52a1\u7684point-wise feature\u7684\uff1f\uff08\u5173\u6ce8\u53cd\u5411\u63d2\u503c\uff0cskip connection\uff09<\/li><\/ol>\n\n\n\n

       \ud83d\udc16\uff1a\u4e0a\u56fe\u4e2d\u7684 d \u8868\u793a\u5750\u6807\u7a7a\u95f4\u7ef4\u5ea6\uff0c C \u8868\u793a\u7279\u5f81\u7a7a\u95f4\u7ef4\u5ea6<\/strong><\/p>\n\n\n\n

      2.1 encoder<\/strong><\/h3>\n\n\n\n

      \u5728PointNet\u7684\u57fa\u7840\u4e0a\u589e\u52a0\u4e86hierarchical \uff08\u5c42\u7ea7\uff09feature learning framework\u7684\u7ed3\u6784\u3002\u8fd9\u79cd\u591a\u5c42\u6b21\u7684\u7ed3\u6784\u7531set abstraction\u5c42\u7ec4\u6210\u3002<\/p>\n\n\n\n

      \u5728\u6bcf\u4e00\u4e2a\u5c42\u6b21\u7684set abstraction\uff0c\u70b9\u96c6\u90fd\u4f1a\u88ab\u5904\u7406\u548c\u62bd\u8c61\uff0c\u800c\u4ea7\u751f\u4e00\u4e2a\u89c4\u6a21\u66f4\u5c0f\u7684\u70b9\u96c6\uff0c\u53ef\u4ee5\u7406\u89e3\u6210\u662f\u4e00\u4e2a\u964d\u91c7\u6837\u8868\u5f81\u8fc7\u7a0b\uff0c\u53ef\u53c2\u8003\u4e0a\u56fe\u5de6\u534a\u90e8\u5206\u3002<\/p>\n\n\n\n

      set abstraction\u7531\u4e09\u4e2a\u90e8\u5206\u6784\u6210\uff08\u4ee3\u7801\u8d34\u5728\u4e0b\u9762\uff09\uff1a<\/p>\n\n\n\n

      def pointnet_sa_module(xyz, points, npoint, radius, nsample, mlp, mlp2, group_all, is_training, bn_decay, scope, bn=True, pooling='max', knn=False, use_xyz=True, use_nchw=False):\n    ''' PointNet Set Abstraction (SA) Module\n        Input:\n            xyz: (batch_size, ndataset, 3) TF tensor\n            points: (batch_size, ndataset, channel) TF tensor\n            npoint: int32 -- #points sampled in farthest point sampling\n            radius: float32 -- search radius in local region\n            nsample: int32 -- how many points in each local region\n            mlp: list of int32 -- output size for MLP on each point\n            mlp2: list of int32 -- output size for MLP on each region\n            group_all: bool -- group all points into one PC if set true, OVERRIDE\n                npoint, radius and nsample settings\n            use_xyz: bool, if True concat XYZ with local point features, otherwise just use point features\n            use_nchw: bool, if True, use NCHW data format for conv2d, which is usually faster than NHWC format\n        Return:\n            new_xyz: (batch_size, npoint, 3) TF tensor\n            new_points: (batch_size, npoint, mlp[-1] or mlp2[-1]) TF tensor\n            idx: (batch_size, npoint, nsample) int32 -- indices for local regions\n    '''\n    data_format = 'NCHW' if use_nchw else 'NHWC'\n    with tf.variable_scope(scope) as sc:\n        # Sample and Grouping<\/em>\n        if group_all:\n            nsample = xyz.get_shape()[1].value\n            new_xyz, new_points, idx, grouped_xyz = sample_and_group_all(xyz, points, use_xyz)\n        else:\n            new_xyz, new_points, idx, grouped_xyz = sample_and_group(npoint, radius, nsample, xyz, points, knn, use_xyz)\n        # Point Feature Embedding<\/em>\n        if use_nchw: new_points = tf.transpose(new_points, [0,3,1,2])\n        for i, num_out_channel in enumerate(mlp):\n            new_points = tf_util.conv2d(new_points, num_out_channel, [1,1],\n                                        padding='VALID', stride=[1,1],\n                                        bn=bn, is_training=is_training,\n                                        scope='conv%d'%(i), bn_decay=bn_decay,\n                                        data_format=data_format) \n        if use_nchw: new_points = tf.transpose(new_points, [0,2,3,1])\n        # Pooling in Local Regions<\/em>\n        if pooling=='max':\n            new_points = tf.reduce_max(new_points, axis=[2], keep_dims=True, name='maxpool')\n        elif pooling=='avg':\n            new_points = tf.reduce_mean(new_points, axis=[2], keep_dims=True, name='avgpool')\n        elif pooling=='weighted_avg':\n            with tf.variable_scope('weighted_avg'):\n                dists = tf.norm(grouped_xyz,axis=-1,ord=2,keep_dims=True)\n                exp_dists = tf.exp(-dists * 5)\n                weights = exp_dists\/tf.reduce_sum(exp_dists,axis=2,keep_dims=True) # (batch_size, npoint, nsample, 1)<\/em>\n                new_points *= weights # (batch_size, npoint, nsample, mlp[-1])<\/em>\n                new_points = tf.reduce_sum(new_points, axis=2, keep_dims=True)\n        elif pooling=='max_and_avg':\n            max_points = tf.reduce_max(new_points, axis=[2], keep_dims=True, name='maxpool')\n            avg_points = tf.reduce_mean(new_points, axis=[2], keep_dims=True, name='avgpool')\n            new_points = tf.concat([avg_points, max_points], axis=-1)\n        # [Optional] Further Processing <\/em>\n        if mlp2 is not None:\n            if use_nchw: new_points = tf.transpose(new_points, [0,3,1,2])\n            for i, num_out_channel in enumerate(mlp2):\n                new_points = tf_util.conv2d(new_points, num_out_channel, [1,1],\n                                            padding='VALID', stride=[1,1],\n                                            bn=bn, is_training=is_training,\n                                            scope='conv_post_%d'%(i), bn_decay=bn_decay,\n                                            data_format=data_format) \n            if use_nchw: new_points = tf.transpose(new_points, [0,2,3,1])\n        new_points = tf.squeeze(new_points, [2]) # (batch_size, npoints, mlp2[-1])<\/em>\n        return new_xyz, new_points, idx<\/code><\/pre>\n\n\n\n
      2.1.1 sampling layer<\/h4>\n\n\n\n
             \u4f7f\u7528FPS\uff08\u6700\u8fdc\u70b9\u91c7\u6837\uff09\u5bf9\u70b9\u96c6\u8fdb\u884c\u964d\u91c7\u6837\uff0c\u5c06\u8f93\u5165\u70b9\u96c6\u4ece\u89c4\u6a21 N1 \u964d\u5230\u66f4\u5c0f\u7684\u89c4\u6a21 N2 \u3002FPS\u53ef\u4ee5\u7406\u89e3\u6210\u662f\u4f7f\u5f97\u91c7\u6837\u7684\u5404\u4e2a\u70b9\u4e4b\u95f4\u5c3d\u53ef\u80fd\u8fdc\uff0c\u8fd9\u79cd\u91c7\u6837\u7684\u597d\u5904\u662f\u53ef\u4ee5\u964d\u91c7\u6837\u7ed3\u679c\u4f1a\u6bd4\u8f83\u5747\u5300\u3002<\/p>\n\n\n\n
      FPS\u5b9e\u73b0\u65b9\u5f0f\u5982\u4e0b<\/strong>\uff1a\u968f\u673a\u9009\u62e9\u4e00\u4e2a\u70b9\u4f5c\u4e3a\u521d\u59cb\u70b9\u4f5c\u4e3a\u5df2\u9009\u62e9\u91c7\u6837\u70b9\uff0c\u8ba1\u7b97\u672a\u9009\u62e9\u91c7\u6837\u70b9\u96c6\u4e2d\u6bcf\u4e2a\u70b9\u4e0e\u5df2\u9009\u62e9\u91c7\u6837\u70b9\u96c6\u4e4b\u95f4\u7684\u8ddd\u79bbdistance\uff0c\u5c06\u8ddd\u79bb\u6700\u5927\u7684\u90a3\u4e2a\u70b9\u52a0\u5165\u5df2\u9009\u62e9\u91c7\u6837\u70b9\u96c6\uff0c\u7136\u540e\u66f4\u65b0distance\uff0c\u4e00\u76f4\u5faa\u73af\u8fed\u4ee3\u4e0b\u53bb\uff0c\u76f4\u81f3\u83b7\u5f97\u4e86\u76ee\u6807\u6570\u91cf\u7684\u91c7\u6837\u70b9\u3002<\/p>\n\n\n\n
      class FarthestSampler:\n    def __init__(self):\n        pass\n    def _calc_distances(self, p0, points):\n        return ((p0 - points) ** 2).sum(axis=1)\n    def __call__(self, pts, k):\n        farthest_pts = np.zeros((k, 3), dtype=np.float32)\n        farthest_pts[0] = pts[np.random.randint(len(pts))]\n        distances = self._calc_distances(farthest_pts[0], pts)\n        for i in range(1, k):\n            farthest_pts[i] = pts[np.argmax(distances)]\n            distances = np.minimum(\n                distances, self._calc_distances(farthest_pts[i], pts))\n        return farthest_pts<\/code><\/pre>\n\n\n\n
      \u8f93\u5165\u89c4\u6a21\u4e3a B\u2217N\u2217(d+C) \uff0c\u5176\u4e2d B \u8868\u793abatch size\uff0c N \u8868\u793a\u70b9\u96c6\u4e2d\u70b9\u7684\u6570\u91cf\uff0c d \u8868\u793a\u70b9\u7684\u5750\u6807\u7ef4\u5ea6\uff0c C \u8868\u793a\u70b9\u7684\u5176\u4ed6\u7279\u5f81\uff08\u6bd4\u5982\u6cd5\u5411\u91cf\u7b49\uff09\u7ef4\u5ea6\u3002\u4e00\u822c d=3 \uff0c c=0<\/p>\n\n\n\n
      \u8f93\u51fa\u89c4\u6a21\u4e3a B\u2217N1\u2217(d+C) \uff0c N1<N \uff0c\u56e0\u4e3a\u8fd9\u662f\u4e00\u4e2a\u964d\u91c7\u6837\u8fc7\u7a0b\u3002<\/p>\n\n\n\n
      sampling\u548cgrouping\u5177\u4f53\u5b9e\u73b0\u662f\u5199\u5728\u4e00\u4e2a\u51fd\u6570\u91cc\u7684\uff1a<\/strong><\/p>\n\n\n\n
      def sample_and_group(npoint, radius, nsample, xyz, points, knn=False, use_xyz=True):\n    '''\n    Input:\n        npoint: int32\n        radius: float32\n        nsample: int32\n        xyz: (batch_size, ndataset, 3) TF tensor\n        points: (batch_size, ndataset, channel) TF tensor, if None will just use xyz as points\n        knn: bool, if True use kNN instead of radius search\n        use_xyz: bool, if True concat XYZ with local point features, otherwise just use point features\n    Output:\n        new_xyz: (batch_size, npoint, 3) TF tensor\n        new_points: (batch_size, npoint, nsample, 3+channel) TF tensor\n        idx: (batch_size, npoint, nsample) TF tensor, indices of local points as in ndataset points\n        grouped_xyz: (batch_size, npoint, nsample, 3) TF tensor, normalized point XYZs\n            (subtracted by seed point XYZ) in local regions\n    '''\n    new_xyz = gather_point(xyz, farthest_point_sample(npoint, xyz)) # (batch_size, npoint, 3)<\/em>\n    if knn:\n        _,idx = knn_point(nsample, xyz, new_xyz)\n    else:\n        idx, pts_cnt = query_ball_point(radius, nsample, xyz, new_xyz)\n    grouped_xyz = group_point(xyz, idx) # (batch_size, npoint, nsample, 3)<\/em>\n    grouped_xyz -= tf.tile(tf.expand_dims(new_xyz, 2), [1,1,nsample,1]) # translation normalization<\/em>\n    if points is not None:\n        grouped_points = group_point(points, idx) # (batch_size, npoint, nsample, channel)<\/em>\n        if use_xyz:\n            new_points = tf.concat([grouped_xyz, grouped_points], axis=-1) # (batch_size, npoint, nample, 3+channel)<\/em>\n        else:\n            new_points = grouped_points\n    else:\n        new_points = grouped_xyz\n    return new_xyz, new_points, idx, grouped_xyz<\/code><\/pre>\n\n\n\n
      \u5176\u4e2dsampling\u5bf9\u5e94\u7684\u90e8\u5206\u662f\uff1a<\/p>\n\n\n\n
      new_xyz = gather_point(xyz, farthest_point_sample(npoint, xyz)) # (batch_size, npoint, 3)<\/em><\/code><\/pre>\n\n\n\n
            xyz\u65e2\u662f B\u2217N\u22173 \u7684\u70b9\u4e91\uff0cnpoint\u662f\u964d\u91c7\u6837\u70b9\u7684\u89c4\u6a21\u3002\u6ce8\u610f\uff1aPointNet++\u7684FPS\u5747\u662f\u5728\u5750\u6807\u7a7a\u95f4\u505a\u7684\uff0c\u800c\u4e0d\u662f\u5728\u7279\u5f81\u7a7a\u95f4\u505a\u7684\u3002\u8fd9\u4e00\u70b9\u5f88\u5173\u952e\uff0c\u56e0\u4e3aFPS\u672c\u8eab\u662f\u4e0d\u53ef\u5fae\u7684\uff0c\u65e0\u6cd5\u8ba1\u7b97\u68af\u5ea6\u53cd\u5411\u4f20\u64ad\u3002<\/p>\n\n\n\n
      \u672c\u7740\u5228\u6839\u95ee\u9898\u7684\u5fc3\u6001\uff0c\u6211\u4eec\u6765\u770b\u770bfarthest_point_sample\u548cgather_point\u7a76\u7adf\u5728\u505a\u4ec0\u4e48<\/p>\n\n\n\n
      farthest_point_sample\u8f93\u5165\u8f93\u51fa\u975e\u5e38\u660e\u6670\uff0c\u8f93\u51fa\u7684\u662f\u964d\u91c7\u6837\u70b9\u5728inp\u4e2d\u7684\u7d22\u5f15\uff0c\u56e0\u6b64\u662f B\u2217N1 int32\u7c7b\u578b\u7684\u5f20\u91cf<\/p>\n\n\n\n
      def farthest_point_sample(npoint,inp):\n    '''\ninput:\n    int32\n    batch_size * ndataset * 3   float32\nreturns:\n    batch_size * npoint         int32\n    '''\n    return sampling_module.farthest_point_sample(inp, npoint)<\/code><\/pre>\n\n\n\n
      gather_point\u7684\u4f5c\u7528\u5c31\u662f\u5c06\u4e0a\u9762\u8f93\u51fa\u7684\u7d22\u5f15\uff0c\u8f6c\u5316\u6210\u771f\u6b63\u7684\u70b9\u4e91<\/p>\n\n\n\n
      def gather_point(inp,idx):\n    '''\ninput:\n    batch_size * ndataset * 3   float32\n    batch_size * npoints        int32\nreturns:\n    batch_size * npoints * 3    float32\n    '''\n    return sampling_module.gather_point(inp,idx)<\/code><\/pre>\n\n\n\n
      2.1.2 grouping layer<\/strong><\/h4>\n\n\n\n
              \u4e0a\u4e00\u6b65sampling\u7684\u8fc7\u7a0b\u662f\u5c06 N\u2217(d+C) \u964d\u5230 N1\u2217(d+C) \uff08\u8fd9\u91cc\u8bba\u8ff0\u65b9\u4fbf\u5148\u4e0d\u8003\u8651batch\uff0c\u5c31\u8003\u8651\u5355\u4e2a\u70b9\u4e91\uff09\uff0c\u5b9e\u9645\u4e0a\u53ef\u4ee5\u7406\u89e3\u6210\u662f\u5728 N \u4e2a\u70b9\u4e2d\u9009\u53d6 N1 \u4e2a\u4e2d\u5fc3\u70b9(key point)\u3002<\/p>\n\n\n\n
              \u90a3\u4e48\u8fd9\u4e00\u6b65grouping\u7684\u76ee\u7684\u5c31\u662f\u4ee5\u8fd9\u6bcf\u4e2akey point\u4e3a\u4e2d\u5fc3\uff0c\u627e\u5176\u56fa\u5b9a\u89c4\u6a21\uff08\u4ee4\u89c4\u6a21\u4e3a K\uff09\u7684\u90bb\u70b9\uff0c\u5171\u540c\u7ec4\u6210\u4e00\u4e2a\u5c40\u90e8\u90bb\u57df(patch)\u3002\u4e5f\u5c31\u662f\u4f1a\u751f\u6210 N1 \u4e2a\u5c40\u90e8\u90bb\u57df\uff0c\u8f93\u51fa\u89c4\u6a21\u4e3a N1\u2217K\u2217(d+C)<\/p>\n\n\n\n
      if knn:\n    _,idx = knn_point(nsample, xyz, new_xyz)\nelse:\n    idx, pts_cnt = query_ball_point(radius, nsample, xyz, new_xyz)\n    grouped_xyz = group_point(xyz, idx) # (batch_size, npoint, nsample, 3)<\/em><\/code><\/pre>\n\n\n\n
      1)\u627e\u90bb\u57df\u7684\u8fc7\u7a0b\u4e5f\u662f\u5728\u5750\u6807\u7a7a\u95f4\u8fdb\u884c\uff08\u4e5f\u5c31\u662f\u4ee5\u4e0a\u4ee3\u7801\u8f93\u5165\u8f93\u51fa\u7ef4\u5ea6\u90fd\u662f<\/strong> d \uff0c\u6ca1\u6709<\/strong> C \uff0c<\/strong> C \u662f\u5728\u540e\u9762\u7684\u4ee3\u7801\u62fc\u63a5\u4e0a\u7684\uff09\uff0c\u800c\u4e0d\u662f\u7279\u5f81\u7a7a\u95f4\u3002<\/strong><\/p>\n\n\n\n
      2)\u627e\u90bb\u57df\u8fd9\u91cc\u6709\u4e24\u79cd\u65b9\u5f0f\uff1aKNN\u548cquery ball point.<\/p>\n\n\n\n
      \u5176\u4e2d\u524d\u8005KNN\u5c31\u662f\u5927\u5bb6\u8033\u719f\u80fd\u8be6\u7684K\u8fd1\u90bb\uff0c\u627eK\u4e2a\u5750\u6807\u7a7a\u95f4\u6700\u8fd1\u7684\u70b9\u3002
      \u540e\u8005query ball point\u5c31\u662f\u5212\u5b9a\u67d0\u4e00\u534a\u5f84\uff0c\u627e\u5728\u8be5\u534a\u5f84\u7403\u5185\u7684\u70b9\u4f5c\u4e3a\u90bb\u70b9\u3002<\/p>\n\n\n\n
      \u8fd8\u6709\u4e2a\u95ee\u9898\uff1aquery ball point\u5982\u4f55\u4fdd\u8bc1\u5bf9\u4e8e\u6bcf\u4e2a\u5c40\u90e8\u90bb\u57df\uff0c\u91c7\u6837\u70b9\u7684\u6570\u91cf\u90fd\u662f\u4e00\u6837\u7684\u5462\uff1f
      \u4e8b\u5b9e\u4e0a\uff0c\u5982\u679cquery ball\u7684\u70b9\u6570\u91cf\u5927\u4e8e\u89c4\u6a21 K \uff0c\u90a3\u4e48\u76f4\u63a5\u53d6\u524d K \u4e2a\u4f5c\u4e3a\u5c40\u90e8\u90bb\u57df\uff1b\u5982\u679c\u5c0f\u4e8e\uff0c\u90a3\u4e48\u76f4\u63a5\u5bf9\u67d0\u4e2a\u70b9\u91cd\u91c7\u6837\uff0c\u51d1\u591f\u89c4\u6a21 K<\/p>\n\n\n\n
      KNN\u548cquery ball\u7684\u533a\u522b\uff1a\uff08\u6458\u81ea\u539f\u6587\uff09Compared with kNN, ball query’s local neighborhood guarantees a fixed region scale thus making local region feature more generalizable across space, which is preferred for tasks requiring local pattern recognition (e.g. semantic point labeling).\u4e5f\u5c31\u662fquery ball\u66f4\u52a0\u9002\u5408\u4e8e\u5e94\u7528\u5728\u5c40\u90e8\/\u7ec6\u8282\u8bc6\u522b\u7684\u5e94\u7528\u4e0a\uff0c\u6bd4\u5982\u5c40\u90e8\u5206\u5272\u3002<\/p>\n\n\n\n
      \u8865\u5145\u6750\u6599\u4e2d\u4e5f\u6709\u5b9e\u9a8c\u6765\u5bf9\u6bd4KNN\u548cquery ball:<\/p>\n\n\n\n
      \"\"<\/figure>\n\n\n\n
      sample_and_group\u4ee3\u7801\u7684\u5269\u4f59\u90e8\u5206\uff1a<\/p>\n\n\n\n
      sample\u548cgroup\u64cd\u4f5c\u90fd\u662f\u5728\u5750\u6807\u7a7a\u95f4\u8fdb\u884c\u7684\uff0c\u56e0\u6b64\u5982\u679c\u8fd8\u6709\u7279\u5f81\u7a7a\u95f4\u4fe1\u606f\uff08\u5373point-wise feature\uff09\uff0c\u53ef\u4ee5\u5728\u8fd9\u91cc\u5c06\u5176\u4e0e\u5750\u6807\u7a7a\u95f4\u62fc\u63a5\uff0c\u7ec4\u6210\u65b0\u7684point-wise feature\uff0c\u51c6\u5907\u9001\u5165\u540e\u9762\u7684unit point\u8fdb\u884c\u7279\u5f81\u5b66\u4e60\u3002<\/p>\n\n\n\n
      if points is not None:\n    grouped_points = group_point(points, idx) # (batch_size, npoint, nsample, channel)<\/em>\n    if use_xyz:\n        new_points = tf.concat([grouped_xyz, grouped_points], axis=-1) # (batch_size, npoint, nample, 3+channel)<\/em>\n    else:\n        new_points = grouped_points\nelse:\n    new_points = grouped_xyz<\/code><\/pre>\n\n\n\n
      2.1.3 PointNet layer<\/strong><\/h4>\n\n\n\n
      \u4f7f\u7528PointNet\u5bf9\u4ee5\u4e0a\u7ed3\u679c\u8868\u5f81<\/p>\n\n\n\n
      \u8f93\u5165 B\u2217N\u2217K\u2217(d+C) \uff0c\u8f93\u51fa B\u2217N\u2217(d+C1)<\/p>\n\n\n\n
      \u4ee5\u4e0b\u4ee3\u7801\u4e3b\u8981\u5206\u62103\u4e2a\u90e8\u5206\uff1a<\/p>\n\n\n\n
      1)point feature embedding<\/p>\n\n\n\n
      \u8fd9\u91cc\u8f93\u5165\u662f B\u2217N\u2217K\u2217(d+C) \uff0c\u53ef\u4ee5\u7c7b\u6bd4\u6210\u662fbatch size\u4e3a B \uff0c\u5bbd\u9ad8\u4e3a N\u2217K \uff0c\u901a\u9053\u6570\u4e3a d+C \u7684\u56fe\u50cf\uff0c\u8fd9\u6837\u4e00\u7c7b\u6bd4\uff0c\u8fd9\u91cc\u7684\u5377\u79ef\u5c31\u597d\u7406\u89e3\u591a\u4e86\u5b9e\u9645\u4e0a\u5c31\u662f 1\u22171 \u5377\u79ef\uff0c\u4e0d\u6539\u53d8feature map\u5927\u5c0f\uff0c\u53ea\u6539\u53d8\u901a\u9053\u6570\uff0c\u5c06\u901a\u9053\u6570\u5347\u9ad8\uff0c\u5b9e\u73b0\u6240\u8c13\u201cembedding\u201d<\/p>\n\n\n\n
      \u8fd9\u90e8\u5206\u8f93\u51fa\u662f B\u2217N\u2217K\u2217C1<\/p>\n\n\n\n
      2)pooling in local regions<\/p>\n\n\n\n
      pooling\uff0c\u53ea\u662f\u662f\u5bf9\u6bcf\u4e2a\u5c40\u90e8\u90bb\u57dfpooling,\u8f93\u51fa\u662f B\u2217N\u22171\u2217C1<\/p>\n\n\n\n
      3)further processing<\/p>\n\n\n\n
           \u518d\u5bf9\u6c60\u5316\u540e\u7684\u7ed3\u679c\u505aMLP\uff0c\u4e5f\u662f\u7b80\u5355\u7684 1\u22171 \u5377\u79ef\u3002\u8fd9\u4e00\u90e8\u5206\u5728\u5b9e\u9645\u5b9e\u9a8c\u4e2dPointNet++\u5e76\u6ca1\u6709\u8bbe\u7f6e\u53bb\u505a<\/p>\n\n\n\n
      # Point Feature Embedding<\/em>\nif use_nchw: new_points = tf.transpose(new_points, [0,3,1,2])\nfor i, num_out_channel in enumerate(mlp):\n    new_points = tf_util.conv2d(new_points, num_out_channel, [1,1],\n                                padding='VALID', stride=[1,1],\n                                bn=bn, is_training=is_training,\n                                scope='conv%d'%(i), bn_decay=bn_decay,\n                                data_format=data_format) \nif use_nchw: new_points = tf.transpose(new_points, [0,2,3,1])\n\n# Pooling in Local Regions<\/em>\nif pooling=='max':\n    new_points = tf.reduce_max(new_points, axis=[2], keep_dims=True, name='maxpool')\nelif pooling=='avg':\n    new_points = tf.reduce_mean(new_points, axis=[2], keep_dims=True, name='avgpool')\nelif pooling=='weighted_avg':\n    with tf.variable_scope('weighted_avg'):\n        dists = tf.norm(grouped_xyz,axis=-1,ord=2,keep_dims=True)\n        exp_dists = tf.exp(-dists * 5)\n        weights = exp_dists\/tf.reduce_sum(exp_dists,axis=2,keep_dims=True) # (batch_size, npoint, nsample, 1)<\/em>\n        new_points *= weights # (batch_size, npoint, nsample, mlp[-1])<\/em>\n        new_points = tf.reduce_sum(new_points, axis=2, keep_dims=True)\nelif pooling=='max_and_avg':\n    max_points = tf.reduce_max(new_points, axis=[2], keep_dims=True, name='maxpool')\n    avg_points = tf.reduce_mean(new_points, axis=[2], keep_dims=True, name='avgpool')\n    new_points = tf.concat([avg_points, max_points], axis=-1)\n\n# [Optional] Further Processing <\/em>\nif mlp2 is not None:\n    if use_nchw: new_points = tf.transpose(new_points, [0,3,1,2])\n    for i, num_out_channel in enumerate(mlp2):\n        new_points = tf_util.conv2d(new_points, num_out_channel, [1,1],\n                                    padding='VALID', stride=[1,1],\n                                    bn=bn, is_training=is_training,\n                                    scope='conv_post_%d'%(i), bn_decay=bn_decay,\n                                    data_format=data_format) \n    if use_nchw: new_points = tf.transpose(new_points, [0,2,3,1])<\/code><\/pre>\n\n\n\n
      2.1.4 Encoder\u8fd8\u6709\u4e00\u4e2a\u95ee\u9898<\/strong><\/h4>\n\n\n\n
      pointnet++\u5b9e\u9645\u4e0a\u5c31\u662f\u5bf9\u5c40\u90e8\u90bb\u57df\u8868\u5f81\u3002<\/p>\n\n\n\n
             \u90a3\u5c31\u4e0d\u5f97\u4e0d\u9762\u5bf9\u4e00\u4e2a\u6311\u6218\uff1anon-uniform sampling density(\u70b9\u4e91\u7684\u5bc6\u5ea6\u4e0d\u5747\u5300)\uff0c\u4e5f\u5c31\u662f\u5728\u7a00\u758f\u70b9\u4e91\u5c40\u90e8\u90bb\u57df\u8bad\u7ec3\u53ef\u80fd\u4e0d\u80fd\u5f88\u597d\u6316\u6398\u70b9\u4e91\u7684\u5c40\u90e8\u7ed3\u6784<\/p>\n\n\n\n
      PointNet++\u505a\u6cd5\uff1alearn to combine features from regions of different scales when the input sampling density changes.<\/p>\n\n\n\n
      \u56e0\u6b64\u6587\u7ae0\u63d0\u51fa\u4e86\u4e24\u4e2a\u65b9\u6848\uff1a<\/p>\n\n\n\n
      \u4e00\u3001Multi-scale grouping\uff08MSG\uff09<\/p>\n\n\n\n
      \"\"<\/figure><\/div>\n\n\n\n
      \u5bf9\u5f53\u524d\u5c42\u7684\u6bcf\u4e2a\u4e2d\u5fc3\u70b9\uff0c\u53d6\u4e0d\u540cradius\u7684query ball\uff0c\u53ef\u4ee5\u5f97\u5230\u591a\u4e2a\u4e0d\u540c\u5927\u5c0f\u7684\u540c\u5fc3\u7403\uff0c\u4e5f\u5c31\u662f\u5f97\u5230\u4e86\u591a\u4e2a\u76f8\u540c\u4e2d\u5fc3\u4f46\u89c4\u6a21\u4e0d\u540c\u7684\u5c40\u90e8\u90bb\u57df\uff0c\u5206\u522b\u5bf9\u8fd9\u4e9b\u5c40\u90e8\u90bb\u57df\u8868\u5f81\uff0c\u5e76\u5c06\u6240\u6709\u8868\u5f81\u62fc\u63a5\u3002\u5982\u4e0a\u56fe\u6240\u793a\u3002<\/p>\n\n\n\n
      \u8be5\u65b9\u6cd5\u6bd4\u8f83\u9ebb\u70e6\uff0c\u8fd0\u7b97\u8f83\u591a\u3002<\/p>\n\n\n\n
      \u4ee3\u7801\u5c42\u9762\u5176\u5b9e\u5c31\u662f\u52a0\u4e86\u4e2a\u904d\u5386radius_list\u7684\u5faa\u73af\uff0c\u5206\u522b\u5904\u7406\uff0c\u5e76\u6700\u540econcat<\/p>\n\n\n\n
      new_xyz = gather_point(xyz, farthest_point_sample(npoint, xyz))\nnew_points_list = []\nfor i in range(len(radius_list)):\n    radius = radius_list[i]\n    nsample = nsample_list[i]\n    idx, pts_cnt = query_ball_point(radius, nsample, xyz, new_xyz)\n    grouped_xyz = group_point(xyz, idx)\n    grouped_xyz -= tf.tile(tf.expand_dims(new_xyz, 2), [1,1,nsample,1])\n    if points is not None:\n        grouped_points = group_point(points, idx)\n        if use_xyz:\n            grouped_points = tf.concat([grouped_points, grouped_xyz], axis=-1)\n    else:\n        grouped_points = grouped_xyz\n    if use_nchw: grouped_points = tf.transpose(grouped_points, [0,3,1,2])\n    for j,num_out_channel in enumerate(mlp_list[i]):\n        grouped_points = tf_util.conv2d(grouped_points, num_out_channel, [1,1],\n                                        padding='VALID', stride=[1,1], bn=bn, is_training=is_training,\n                                        scope='conv%d_%d'%(i,j), bn_decay=bn_decay)\n    if use_nchw: grouped_points = tf.transpose(grouped_points, [0,2,3,1])\n    new_points = tf.reduce_max(grouped_points, axis=[2])\n    new_points_list.append(new_points)\nnew_points_concat = tf.concat(new_points_list, axis=-1)<\/code><\/pre>\n\n\n\n
      \u4e8c\u3001Multi-resolution grouping\uff08MRG\uff09<\/p>\n\n\n\n
      \"\"\/<\/figure><\/div>\n\n\n\n
      \uff08\u6458\u81ea\u539f\u6587\uff09features of a region at some level Li is a concatenation of two vectors.<\/p>\n\n\n\n
      One vector (left in figure) is obtained by summarizing the features at each subregion from the lower level <\/strong>Li\u22121 using the set abstraction level.<\/p>\n\n\n\n
      The other vector (right) is the feature that is obtained by directly processing all raw points in the local region using a single PointNet<\/strong>.<\/p>\n\n\n\n
      \u7b80\u5355\u6765\u8bf4\uff0c\u5c31\u662f\u5f53\u524dset abstraction\u7684\u5c40\u90e8\u90bb\u57df\u8868\u5f81\u7531\u4e24\u90e8\u5206\u6784\u6210\uff1a<\/p>\n\n\n\n
      \u5de6\u8fb9\u8868\u5f81\uff1a\u5bf9\u4e0a\u4e00\u5c42set abstraction\uff08\u8fd8\u8bb0\u5f97\u4e0a\u4e00\u5c42\u7684\u70b9\u89c4\u6a21\u662f\u66f4\u5927\u7684\u5417\uff1f\uff09\u5404\u4e2a\u5c40\u90e8\u90bb\u57df\uff08\u6216\u8005\u8bf4\u4e2d\u5fc3\u70b9\uff09\u7684\u7279\u5f81\u8fdb\u884c\u805a\u5408\u3002  \u53f3\u8fb9\u8868\u5f81\uff1a\u4f7f\u7528\u4e00\u4e2a\u5355\u4e00\u7684PointNet\u76f4\u63a5\u5728\u5c40\u90e8\u90bb\u57df\u5904\u7406\u539f\u59cb\u70b9\u4e91<\/p>\n\n\n\n
      2.2 decoder\uff1a<\/strong><\/h3>\n\n\n\n
      2.2.1 \u5206\u7c7b\u4efb\u52a1\u7684decoder<\/strong><\/h4>\n\n\n\n
      \"\"<\/figure><\/div>\n\n\n\n
      \u6bd4\u8f83\u7b80\u5355\uff0c\u5c06encoder\u964d\u91c7\u6837\u5f97\u5230\u7684global feature\u9001\u5165\u51e0\u5c42\u5168\u8fde\u63a5\u7f51\u7edc\uff0c\u6700\u540e\u901a\u8fc7\u4e00\u4e2asoftmax\u5206\u7c7b\u3002<\/p>\n\n\n\n
      2.2.2 \u5206\u5272\u4efb\u52a1\u7684decoder<\/strong><\/h4>\n\n\n\n
      \"\"<\/figure>\n\n\n\n
      \u7ecf\u8fc7\u524d\u534a\u90e8\u5206\u7684encoder\uff0c\u6211\u4eec\u5f97\u5230\u7684\u662fglobal feature\uff0c\u6216\u8005\u662f\u6781\u5c11\u6570\u70b9\u7684\u8868\u5f81\uff08\u5176\u5b9e\u4e5f\u5c31\u662fglobal feature\uff09<\/p>\n\n\n\n
      \u800c\u5982\u679c\u505a\u5206\u5272\uff0c\u6211\u4eec\u9700\u8981\u7684\u662fpoint-wise feature\uff0c\u8fd9\u53ef\u600e\u4e48\u529e\u5462\uff1f<\/p>\n\n\n\n
      PointNet\u5904\u7406\u601d\u8def\u5f88\u7b80\u5355\uff0c\u76f4\u63a5\u628aglobal feature\u590d\u5236\u5e76\u4e0e\u4e4b\u524d\u7684local feature\u62fc\u63a5\uff0c\u4f7f\u5f97\u8fd9\u4e2a\u65b0point-wise feature\u80fd\u591f\u83b7\u5f97\u4e00\u5b9a\u7a0b\u5ea6\u7684\u201c\u90bb\u57df\u201d\u4fe1\u606f\u3002\u8fd9\u79cd\u7b80\u5355\u7c97\u66b4\u7684\u65b9\u6cd5\u663e\u7136\u5e76\u4e0d\u80fd\u5f97\u5230\u5f88discriminative\u7684\u8868\u5f81<\/p>\n\n\n\n
      \u522b\u6025\uff0cPointNet++\u6765\u4e86\u3002<\/p>\n\n\n\n
      PointNet++\u8bbe\u8ba1\u4e86\u4e00\u79cd\u53cd\u5411\u63d2\u503c\u7684\u65b9\u6cd5\u6765\u5b9e\u73b0\u4e0a\u91c7\u6837\u7684decoder\u7ed3\u6784\uff0c\u901a\u8fc7\u53cd\u5411\u63d2\u503c\u548cskip connection\u6765\u83b7\u5f97discriminative point-wise feature\uff1a<\/p>\n\n\n\n
      \"\"<\/figure>\n\n\n\n
      \u8bbe\u7ea2\u8272\u77e9\u5f62\u70b9\u96c6 P1 : N1\u2217C \uff0c\u84dd\u8272\u77e9\u5f62\u70b9\u96c6 P2 : N2\u2217C2 \uff0c\u56e0\u4e3adecoder\u662f\u4e0a\u91c7\u6837\u8fc7\u7a0b\uff0c\u56e0\u6b64 N2>N1<\/p>\n\n\n\n
      \u4e00\u3001\u53cd\u5411\u63d2\u503c<\/strong>\u5177\u4f53\u505a\u6cd5\uff1a<\/p>\n\n\n\n
      \"\"<\/figure>\n\n\n\n
      \u5bf9\u4e8e P2 \u4e2d\u7684\u6bcf\u4e2a\u70b9 x \uff0c\u627e\u5728\u539f\u59cb\u70b9\u4e91\u5750\u6807\u7a7a\u95f4\u4e0b\uff0c P1 \u4e2d\u4e0e\u5176\u6700\u63a5\u8fd1\u7684 k \u4e2a\u70b9 x1,\u2026,xk<\/p>\n\n\n\n
      \u5f53\u524d\u6211\u4eec\u60f3\u901a\u8fc7\u53cd\u5411\u63d2\u503c\u7684\u65b9\u5f0f\u7528\u8f83\u5c11\u7684\u70b9\u628a\u66f4\u591a\u7684\u70b9\u7684\u7279\u5f81\u63d2\u51fa\u6765\uff0c\u5b9e\u73b0\u4e0a\u91c7\u6837<\/p>\n\n\n\n
      \u6b64\u65f6 x1,\u2026,xk \u7684\u7279\u5f81\u6211\u4eec\u662f\u77e5\u9053\u7684\uff0c\u6211\u4eec\u60f3\u5f97\u5230 x \u7684\u7279\u5f81\u3002\u5982\u4e0a\u516c\u5f0f\uff0c\u5b9e\u9645\u4e0a\u5c31\u662f\u5c06 x1,\u2026,xk \u7684\u7279\u5f81\u52a0\u6743\u6c42\u548c\uff0c\u5f97\u5230x\u7684\u7279\u5f81\u3002\u5176\u4e2d\u8fd9\u4e2a\u6743\u91cd\u662f\u4e0ex\u548c x1,\u2026,xk \u7684\u8ddd\u79bb\u6210\u53cd\u5411\u76f8\u5173\u7684\uff0c\u610f\u601d\u5c31\u662f\u8ddd\u79bb\u8d8a\u8fdc\u7684\u70b9\uff0c\u5bf9x\u7279\u5f81\u7684\u8d21\u732e\u7a0b\u5ea6\u8d8a\u5c0f\u3002P2 \u4e2d\u5176\u4ed6\u70b9\u4ee5\u6b64\u7c7b\u63a8\uff0c\u4ece\u800c\u5b9e\u73b0\u4e86\u7279\u5f81\u7684\u4e0a\u91c7\u6837\u56de\u4f20<\/p>\n\n\n\n
      \u4e8c<\/strong>\u3001skip connection<\/strong>\u5177\u4f53\u505a\u6cd5\uff1a<\/p>\n\n\n\n
            \u56de\u4f20\u5f97\u5230\u7684point-wise feature\u662f\u4ecedecoder\u7684\u4e0a\u4e00\u5c42\u5f97\u5230\u7684\uff0c\u56e0\u6b64\u7b97\u662fglobal\u7ea7\u522b\u7684\u4fe1\u606f\uff0c\u8fd9\u5bf9\u4e8e\u60f3\u5f97\u5230discriminative\u8fd8\u662f\u4e0d\u591f\uff0c\u56e0\u4e3a\u6211\u4eec\u8fd8\u7f3a\u5c11local\u7ea7\u522b\u7684\u4fe1\u606f\uff01\uff01\uff01<\/p>\n\n\n\n
      \u5982\u4e0a\u56fe\u5c31\u662f\u6211\u4eec\u53cd\u5411\u63d2\u503c\u53ea\u5f97\u5230\u4e86 C2 \uff0c\u4f46\u662f\u6211\u4eec\u8fd8\u9700\u8981\u63d0\u4f9blocal\u7ea7\u522b\u4fe1\u606f\u7684 C1 \u7279\u5f81\uff01\uff01\uff01<\/p>\n\n\n\n
      \u8fd9\u65f6skip connection\u6765\u4e86\uff01\uff01\uff01<\/p>\n\n\n\n
      skip connection\u5176\u5b9e\u5c31\u662f\u5c06\u4e4b\u524dencoder\u5bf9\u5e94\u5c42\u7684\u8868\u5f81\u76f4\u63a5\u62fc\u63a5\u4e86\u8fc7\u6765<\/p>\n\n\n\n
      \u56e0\u4e3a\u4e0a\u56fe\u4e2dencoder\u84dd\u8272\u77e9\u5f62\u70b9\u96c6\u7684 C1 \u8868\u5f81\u662f\u6765\u81ea\u4e8e\u89c4\u6a21\u66f4\u5927\u7684\u7eff\u8272\u77e9\u5f62\u70b9\u96c6\u7684\u8868\u5f81\uff0c\u8fd9\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u5176\u5b9e\u662f\u5b9e\u73b0\u4e86local\u7ea7\u522b\u7684\u4fe1\u606f<\/p>\n\n\n\n
      \u6211\u4eec\u901a\u8fc7\u53cd\u5411\u63d2\u503c\u548cskip connection\u5728decoder\u4e2d\u9010\u7ea7\u4e0a\u91c7\u6837\u5f97\u5230local + global point-wise feature\uff0c\u5f97\u5230\u4e86discriminative feature\uff0c\u5e94\u7528\u4e8e\u5206\u5272\u4efb\u52a1\u3002<\/p>\n\n\n\n
      2.3 loss<\/strong><\/h3>\n\n\n\n
      \u65e0\u8bba\u662f\u5206\u7c7b\u8fd8\u662f\u5206\u5272\u5e94\u7528\uff0c\u672c\u8d28\u4e0a\u90fd\u662f\u5206\u7c7b\u95ee\u9898\uff0c\u56e0\u6b64loss\u5c31\u662f\u5206\u7c7b\u4efb\u52a1\u4e2d\u5e38\u7528\u7684\u4ea4\u53c9\u71b5loss<\/p>\n\n\n\n
      2.4 \u5176\u4ed6\u7684\u95ee\u9898<\/strong><\/h3>\n\n\n\n
      Q\uff1aPointNet++\u68af\u5ea6\u662f\u5982\u4f55\u56de\u4f20\u7684\uff1f\uff1f\uff1f<\/p>\n\n\n\n
      A\uff1aPointNet++ fps\u5b9e\u9645\u4e0a\u5e76\u6ca1\u6709\u53c2\u4e0e\u68af\u5ea6\u8ba1\u7b97\u548c\u53cd\u5411\u4f20\u64ad\u3002<\/p>\n\n\n\n
      \u53ef\u4ee5\u7406\u89e3\u6210\u662fPointNet++\u5c06\u70b9\u4e91\u8fdb\u884c\u4e0d\u540c\u89c4\u6a21\u7684fps\u964d\u91c7\u6837\uff0c\u4e8b\u5148\u5c06\u8fd9\u4e9b\u6570\u636e\u51c6\u5907\u597d\uff0c\u518d\u9001\u5230\u7f51\u7edc\u4e2d\u53bb\u8bad\u7ec3\u7684<\/p>\n\n\n\n
      3 dataset and experiments<\/strong><\/h2>\n\n\n\n
      3.1 dataset<\/strong><\/h3>\n\n\n\n