PointNet++论文解读和代码解析

目录 

一、论文动机

二、论文方法

三、网络结构

Set Abstraction

非均匀采样密度下的鲁棒性学习

上采样

四、代码阅读


论文地址:https://arxiv.org/pdf/1706.02413.pdf

代码地址:https://github.com/yanx27/Pointnet_Pointnet2_pytorch

一、论文动机

1.PointNet只使用了MLP和最大池化,没有能力捕获局部特征,然而局部结构已被证明是卷积结构成功的重要因素(就是感受野越来越大,由局部逐渐到整体)

2.PointNet里全局特征直接由max pooling获得,这会有巨大的信息损失

3.分割任务的全局特征是直接与点特征拼接,生成的特征辨别能力有限

二、论文方法

1.使用多个set abstraction层叠加,逐步提取局部特征

2.分割任务使用encoder-decoder结构,先降采样再上采样,通过多个set abstraction结构实现多层次的降采样,得到不同规模的point-wise feature,最后一个输出可以看作global feature,decoder通过反向插值和skip connection将对应层的特征进行拼接,实现上采样的同时还可以获得local+global的point-wise feature,使得最终的特征更具辨识力。

三、网络结构

PointNet++论文解读和代码解析_第1张图片

 pointnet++先使用集合抽象层提取局部特征,从小的邻域获得精细的几何结构,通过叠加集合抽象层,这些局部特征被进一步划分为更大的单元,并处理产生更高层次的特征,这个过程不断重复,直到获取整个点集的特征。

Set Abstraction

1.采样层

在输入点集中使用最远点采样(FPS)来选取中心点,该算法选取的中心点可以更好的覆盖点集

该层的输入为N*(d+c),d为坐标,c为额外特征,输出为 N1*(d),N1为采样后的中心点。(具体看代码)

FPS流程:先随机选一个点加入集合,计算其他点离它的距离,选择最远的点,加入集合,再计算其他点离集合的位置(后面集合里面有好多点,算这个点到集合里面所有点的距离,选最小的作为它离集合的距离),重复上面的,直到选择了我们提前设定的N1个中心点。

2.分组层

以每个选取的中心点为中心,找到其规模内的K个邻点,共同组成一个局部区域

该层的输入N*(d+c)和N1*(d),分组完输出N1*K*(d+c),其中K为我们选定的邻域规模

邻域的选取有两种方法:KNN选择离中心点最近的K个点

                                        球半径查询,选定半径球体,如果球体里面的点大于K,直接取前K个,不足的话就重采样,凑够K。

3.Pointnet层

输入N1*K*(d+c),输出N1*(d+c1),c1是指卷积完的局部特征。

首先将局部区域中的点坐标转换为相对于质心的坐标,然后通过相对坐标和点特征,我们可以捕获到局部区域内点与点的关系。

非均匀采样密度下的鲁棒性学习

 因为pointnet++主要是对局部特征的一个提取,但这样面临一个问题,就是稀疏点云的局部邻域训练可能不能很好的挖掘点云的局部信息。这里pointnet++提出两种方案:

1.Multi-scale grouping(MSG)

对当前层的每个中心点,取不同的radius,得到多个不同大小的同心圆,也就是得到了多个相同中心但规模不同的局部区域,分别对这些局部区域进行pointnet提取,然后再将所有表征拼接。

2.Multi-resolution grouping(MRG)

MSG的计算量特别大,而MRG的某一层特征是由两部分组成的,左边是对上一层的各个局部邻域特征进行聚合,右边是用一个单一的pointnet在当前局部区域处理原始点云。具体看代码部分。

上采样

Pointnet++会随着网络逐层降采样点,这样可以保证网络获取足够的全局信息,但这样就无法用于分割,因为分割必须输入输出点一样,所以常见的方法就是插值上采样,上采样使用的反向插值,根据上一层距离当前层要推理点最近的K个点的特征进行加权,离得远权重就小,离得近就大,插值出推理点特征。具体见代码的Feature Propagation(FP)模块

分类和分割网络结构

分类网络:

先使用多层PointNetSetAbstractionMSG类,最后使用一个PointNetSetAbstraction类,将所有点分为一组,得到全局特征,三个全连接层,前两个有bn,relu,dropout

分割网络

先使用多层PointNetSetAbstractionMSG类,然后使用相同个数的PointNetFeaturePropagation上采样类最终得到 [B,N,D1],然后使用conv1d对点特征降维到K,conv1d后bn,relu,dropout。

四、代码阅读

import torch
import torch.nn as nn
import torch.nn.functional as F
from time import time
import numpy as np

#打印时间
def timeit(tag, t):
    print("{}: {}s".format(tag, time() - t))
    return time()

#对点云数据进行归一化处理,以centor为中心,球半径为1
def pc_normalize(pc):
    #pc维度[n,3]
    l = pc.shape[0]
    #求中心,对pc数组的每一列求平均值,得到[x_mean,y_mean,z_mean]
    centroid = np.mean(pc, axis=0)
    #求这个点集里面的点到中心点的相对坐标
    pc = pc - centroid
    #将同一行的元素求平方再相加,再开方求最大。x^2+y^2+z^2,得到最大标准差
    m = np.max(np.sqrt(np.sum(pc**2, axis=1)))
    #进行归一化,这里使用的是Z-score标准化方法
    pc = pc / m
    return pc

#主要用来在ball query过程中确定每一个点距离采样点的距离,返回的是两组点之间的欧氏距离,N*M矩阵
def square_distance(src, dst):
    """
    Calculate Euclid distance between each two points.
    src^T * dst = xn * xm + yn * ym + zn * zm;
    sum(src^2, dim=-1) = xn*xn + yn*yn + zn*zn;
    sum(dst^2, dim=-1) = xm*xm + ym*ym + zm*zm;
    dist = (xn - xm)^2 + (yn - ym)^2 + (zn - zm)^2
         = sum(src**2,dim=-1)+sum(dst**2,dim=-1)-2*src^T*dst
    Input:
        src: source points, [B, N, C]
        dst: target points, [B, M, C]
    Output:
        dist: per-point square distance, [B, N, M]
    """
    B, N, _ = src.shape
    _, M, _ = dst.shape
    #torch.matmul也是一种矩阵相乘操作,但是它具有广播机制,可以进行维度不同的张量相乘
    dist = -2 * torch.matmul(src, dst.permute(0, 2, 1)) #[B,N,M]
    dist += torch.sum(src ** 2, -1).view(B, N, 1)  #[B,N,M]+[B,N,1]dist每一列都加上后面的列值
    dist += torch.sum(dst ** 2, -1).view(B, 1, M)  #[B,N,M]+[B,1,N]dist每一行都加上后面的行值
    return dist

#按照输入的点云数据和索引返回索引的点云数据
def index_points(points, idx):
    """
    Input:
        points: input points data, [B, N, C]
        idx: sample index data, [B, S]
    Return:
        new_points:, indexed points data, [B, S, C]
    """
    device = points.device
    B = points.shape[0]
    view_shape = list(idx.shape) #view_shape=[B,S]
    view_shape[1:] = [1] * (len(view_shape) - 1) #去掉第零个数,其余变为1,[B,1]

    repeat_shape = list(idx.shape)
    repeat_shape[0] = 1  #[1,S]
    #arrange生成[0,...,B-1],view后变为列向量[B,1],repeat后[B,S]
    batch_indices = torch.arange(B, dtype=torch.long).to(device).view(view_shape).repeat(repeat_shape)
    #下面这个感觉理解不了,后面自己敲一下验证一波
    new_points = points[batch_indices, idx, :]#从points中取出每个batch_indices对应索引的数据点
    return new_points

#最远点采样算法,返回的是npoint个采样点在原始点云中的索引
def farthest_point_sample(xyz, npoint):
    """
    Input:
        xyz: pointcloud data, [B, N, 3]
        npoint: number of samples
    Return:
        centroids: sampled pointcloud index, [B, npoint]
    """
    device = xyz.device
    B, N, C = xyz.shape
    #初始化一个中心点矩阵,用于存储采样点的索引位置
    centroids = torch.zeros(B, npoint, dtype=torch.long).to(device)
    #distance矩阵用于记录某个batch中所有点到某个采样点的距离,初始值很大,后面会迭代
    distance = torch.ones(B, N).to(device) * 1e10
    #farthest表示当前最远的点,也是随机初始化,范围0-N,初始化B个
    farthest = torch.randint(0, N, (B,), dtype=torch.long).to(device)
    #初始化0-B-1的数组
    batch_indices = torch.arange(B, dtype=torch.long).to(device)
    for i in range(npoint):
        centroids[:, i] = farthest#先把第一个随机采样点下标放入
        centroid = xyz[batch_indices, farthest, :].view(B, 1, 3)#取出初始化的B个点的坐标
        dist = torch.sum((xyz - centroid) ** 2, -1) #求每个batch里面每个点到中心点的距离 [B,N]
        #建立一个mask,如果dist中记录的距离小于distance里的,则更新distance的值,这样distance里保留的就是每个点距离所有已采样的点的最小距离
        mask = dist < distance
        distance[mask] = dist[mask]
        farthest = torch.max(distance, -1)[1] #得到最大距离的下标作为下一次的选择点
    return centroids

#用于寻找球形领域中的点,S为FPS得到的中心点个数
def query_ball_point(radius, nsample, xyz, new_xyz):
    """
    Input:
        radius: local region radius
        nsample: max sample number in local region
        xyz: all points, [B, N, 3]
        new_xyz: query points, [B, S, 3]
    Return:
        group_idx: grouped points index, [B, S, nsample]
    """
    device = xyz.device
    B, N, C = xyz.shape
    _, S, _ = new_xyz.shape
    group_idx = torch.arange(N, dtype=torch.long).to(device).view(1, 1, N).repeat([B, S, 1])
    sqrdists = square_distance(new_xyz, xyz) #计算中心点坐标与全部点坐标的距离  [B,S,N]
    group_idx[sqrdists > radius ** 2] = N #找到所有大于半径的,其group_idx直接置N,其余不变
    group_idx = group_idx.sort(dim=-1)[0][:, :, :nsample]#将所有点到中心点的距离从小到大排序,取前nsample个
    #有可能前nsample里有距离大于半径的,我们要去除掉,当半径内的点不够nsample时,我们对距离最小的点进行重复采样
    #group_idx[:, :, 0]获得距离最小的点,他的shape是[B,S],所以view一下,再repeat
    group_first = group_idx[:, :, 0].view(B, S, 1).repeat([1, 1, nsample])
    #看哪些点是球体外的,得到一个mask,用mask进行赋值,把最近的点赋值给刚采样在球体外的点
    mask = group_idx == N
    group_idx[mask] = group_first[mask]
    return group_idx

#采样与分组,xyz与points的区别,一个特征只有xyz,一个是其他特征
def sample_and_group(npoint, radius, nsample, xyz, points, returnfps=False):
    """
    Input:
        npoint:
        radius:
        nsample:
        xyz: input points position data, [B, N, 3]
        points: input points data, [B, N, D]
    Return:
        new_xyz: sampled points position data, [B, npoint, nsample, 3]
        new_points: sampled points data, [B, npoint, nsample, 3+D]
    """
    B, N, C = xyz.shape
    #S个中心点
    S = npoint
    #从原点云通过FPS采样得到采样点的索引,
    fps_idx = farthest_point_sample(xyz, npoint) # [B, npoint]
    new_xyz = index_points(xyz, fps_idx)  #[B,npoint,C]
    idx = query_ball_point(radius, nsample, xyz, new_xyz) #每个中心点采样nsample个点的下标[B,npoint,nsample]
    grouped_xyz = index_points(xyz, idx) # [B, npoint, nsample, C]
    #每个点减去质心的坐标
    grouped_xyz_norm = grouped_xyz - new_xyz.view(B, S, 1, C)

    if points is not None:
        grouped_points = index_points(points, idx)
        new_points = torch.cat([grouped_xyz_norm, grouped_points], dim=-1) # [B, npoint, nsample, C+D]
    else:
        new_points = grouped_xyz_norm
    if returnfps:
        return new_xyz, new_points, grouped_xyz, fps_idx
    else:
        return new_xyz, new_points

#直接将所有点作为一个group
def sample_and_group_all(xyz, points):
    """
    Input:
        xyz: input points position data, [B, N, 3]
        points: input points data, [B, N, D]
    Return:
        new_xyz: sampled points position data, [B, 1, 3]
        new_points: sampled points data, [B, 1, N, 3+D]
    """
    device = xyz.device
    B, N, C = xyz.shape
    new_xyz = torch.zeros(B, 1, C).to(device) #原点为采样点
    grouped_xyz = xyz.view(B, 1, N, C)
    if points is not None:
        new_points = torch.cat([grouped_xyz, points.view(B, 1, N, -1)], dim=-1)
    else:
        new_points = grouped_xyz
    return new_xyz, new_points


#该类实现普通的SetAbstraction,然后通过sample_and_group的操作形成局部的group,然后对局部group的每一个点进行MLP操作,最后进行最大池化,得到局部的全局特征
class PointNetSetAbstraction(nn.Module):
    def __init__(self, npoint, radius, nsample, in_channel, mlp, group_all):
        super(PointNetSetAbstraction, self).__init__()
        self.npoint = npoint
        self.radius = radius
        self.nsample = nsample
        #nn.ModuleList是一个存储器,自动将每个module的参数添加到网络之中,可以把任意nn.module的子类(nn.Conv2d,nn.Linear)加到里面
        self.mlp_convs = nn.ModuleList()
        self.mlp_bns = nn.ModuleList()
        last_channel = in_channel
        for out_channel in mlp:
            self.mlp_convs.append(nn.Conv2d(last_channel, out_channel, 1))
            self.mlp_bns.append(nn.BatchNorm2d(out_channel))
            last_channel = out_channel
        self.group_all = group_all

    def forward(self, xyz, points):
        """
        Input:
            xyz: input points position data, [B, C, N]
            points: input points data, [B, D, N]
        Return:
            new_xyz: sampled points position data, [B, C, S]
            new_points_concat: sample points feature data, [B, D', S]
        """
        xyz = xyz.permute(0, 2, 1)
        if points is not None:
            points = points.permute(0, 2, 1)
        if self.group_all:
            new_xyz, new_points = sample_and_group_all(xyz, points)
        else:
            new_xyz, new_points = sample_and_group(self.npoint, self.radius, self.nsample, xyz, points)
        # new_xyz: sampled points position data, [B, npoint, C]
        # new_points: sampled points data, [B, npoint, nsample, C+D]
        new_points = new_points.permute(0, 3, 2, 1) # [B, C+D, nsample,npoint]
        #下面是pointnet操作,对局部进行MLP操作,利用1*12d卷积相当于把C+D当作特征通道
        #对[nsample,npoint]的维度上进行逐像素卷积
        for i, conv in enumerate(self.mlp_convs):
            bn = self.mlp_bns[i]
            new_points =  F.relu(bn(conv(new_points)))
        #对每一个group做maxpooling得到局部的全局特征,[B,3+D,npoint]
        new_points = torch.max(new_points, 2)[0]
        new_xyz = new_xyz.permute(0, 2, 1)
        return new_xyz, new_points

#MSG方法的set abstraction,radius_list是一个列表
class PointNetSetAbstractionMsg(nn.Module):
    #例如128,[0.2,0.4,0.8],[32,64,128],320,[[64,64,128],[128,128,256],[128,128,256]]
    def __init__(self, npoint, radius_list, nsample_list, in_channel, mlp_list):
        super(PointNetSetAbstractionMsg, self).__init__()
        self.npoint = npoint
        self.radius_list = radius_list
        self.nsample_list = nsample_list
        self.conv_blocks = nn.ModuleList()
        self.bn_blocks = nn.ModuleList()
        for i in range(len(mlp_list)):
            convs = nn.ModuleList()
            bns = nn.ModuleList()
            last_channel = in_channel + 3
            for out_channel in mlp_list[i]:
                convs.append(nn.Conv2d(last_channel, out_channel, 1))
                bns.append(nn.BatchNorm2d(out_channel))
                last_channel = out_channel
            self.conv_blocks.append(convs)
            self.bn_blocks.append(bns)

    def forward(self, xyz, points):
        """
        Input:
            xyz: input points position data, [B, C, N]
            points: input points data, [B, D, N]
        Return:
            new_xyz: sampled points position data, [B, C, S]
            new_points_concat: sample points feature data, [B, D', S]
        """
        xyz = xyz.permute(0, 2, 1)
        if points is not None:
            points = points.permute(0, 2, 1)

        B, N, C = xyz.shape
        S = self.npoint
        #找到S个中心点
        new_xyz = index_points(xyz, farthest_point_sample(xyz, S))
        #对不同的半径做ball query,将不同半径下的点云特征保存在new_points_list中,最后再拼接到一起
        new_points_list = []
        for i, radius in enumerate(self.radius_list):
            K = self.nsample_list[i]
            #按照球形分组
            group_idx = query_ball_point(radius, K, xyz, new_xyz)
            grouped_xyz = index_points(xyz, group_idx)
            #进行归一化处理
            grouped_xyz -= new_xyz.view(B, S, 1, C)
            if points is not None:
                grouped_points = index_points(points, group_idx)
                grouped_points = torch.cat([grouped_points, grouped_xyz], dim=-1)
            else:
                grouped_points = grouped_xyz
            #进行维度交换,准备卷积,D维特征,每组K个点
            grouped_points = grouped_points.permute(0, 3, 2, 1)  # [B, D, K, S]
            for j in range(len(self.conv_blocks[i])):
                conv = self.conv_blocks[i][j]
                bn = self.bn_blocks[i][j]
                grouped_points =  F.relu(bn(conv(grouped_points)))
            #卷积完在组内的点进行最大池化
            new_points = torch.max(grouped_points, 2)[0]  # [B, D', S]
            new_points_list.append(new_points)

        new_xyz = new_xyz.permute(0, 2, 1)
        new_points_concat = torch.cat(new_points_list, dim=1)#在特征维度进行合并
        return new_xyz, new_points_concat

#特征上采样模块,当点的个数只有一个时,采用repeat直接复制成N个点,当点数大于1个时,采用线性插值的方法进行上采样,拼接上下采样对应点的SA的特征,再对拼接后的每个点做一次MLP
class PointNetFeaturePropagation(nn.Module):
    def __init__(self, in_channel, mlp):
        super(PointNetFeaturePropagation, self).__init__()
        self.mlp_convs = nn.ModuleList()
        self.mlp_bns = nn.ModuleList()
        last_channel = in_channel
        for out_channel in mlp:
            self.mlp_convs.append(nn.Conv1d(last_channel, out_channel, 1))
            self.mlp_bns.append(nn.BatchNorm1d(out_channel))
            last_channel = out_channel

    def forward(self, xyz1, xyz2, points1, points2):
        """
        Input:
            xyz1: input points position data, [B, C, N]
            xyz2: sampled input points position data, [B, C, S]
            points1: input points data, [B, D, N]
            points2: input points data, [B, D, S]
        Return:
            new_points: upsampled points data, [B, D', N]
        """
        xyz1 = xyz1.permute(0, 2, 1) #[B,N,C]
        xyz2 = xyz2.permute(0, 2, 1) #[B,S,C]
        
        points2 = points2.permute(0, 2, 1) #[B,S,D]
        B, N, C = xyz1.shape
        _, S, _ = xyz2.shape
        #如果该层只有一个点,那么上采样直接复制成N个点即可
        if S == 1:
            interpolated_points = points2.repeat(1, N, 1)
        else:
            dists = square_distance(xyz1, xyz2) #计算上一层与该层点之间的距离[B,N,S]
            dists, idx = dists.sort(dim=-1)#默认升序排列,取距离N个点最小的三个S里面的点
            dists, idx = dists[:, :, :3], idx[:, :, :3]  # [B, N, 3]

            dist_recip = 1.0 / (dists + 1e-8)#求距离的倒数,距离越远,权重越小
            norm = torch.sum(dist_recip, dim=2, keepdim=True) #对离的最近的三个点权重相加
            weight = dist_recip / norm #weight是指计算权重,他们三个权重和为1
            #index_points之后维度是[B,N,3,C],在第二维度求和,等于三个点特征加权之后的和。[B,N,C]
            interpolated_points = torch.sum(index_points(points2, idx) * weight.view(B, N, 3, 1), dim=2)

        if points1 is not None:
            points1 = points1.permute(0, 2, 1)
            new_points = torch.cat([points1, interpolated_points], dim=-1)
        else:
            new_points = interpolated_points

        new_points = new_points.permute(0, 2, 1)
        for i, conv in enumerate(self.mlp_convs):
            bn = self.mlp_bns[i]
            new_points = F.relu(bn(conv(new_points)))
        return new_points

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