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import torch
from torch import nn
def knn(x, k):
inner = -2*torch.matmul(x.transpose(2, 1), x)
xx = torch.sum(x**2, dim=1, keepdim=True)
pairwise_distance = -xx - inner - xx.transpose(2, 1)
idx = pairwise_distance.topk(k=k, dim=-1)[1] # (batch_size, num_points, k)
return idx, pairwise_distance
def local_operator(x, k):
batch_size = x.size(0)
num_points = x.size(2)
x = x.view(batch_size, -1, num_points)
idx, _ = knn(x, k=k)
device = torch.device('cpu')
idx_base = torch.arange(0, batch_size, device=device).view(-1, 1, 1) * num_points
idx = idx + idx_base
idx = idx.view(-1)
_, num_dims, _ = x.size()
x = x.transpose(2, 1).contiguous()
neighbor = x.view(batch_size * num_points, -1)[idx, :]
neighbor = neighbor.view(batch_size, num_points, k, num_dims)
x = x.view(batch_size, num_points, 1, num_dims).repeat(1, 1, k, 1)
feature = torch.cat((neighbor-x, neighbor), dim=3).permute(0, 3, 1, 2) # local and global all in
return feature
def local_operator_withnorm(x, norm_plt, k):
batch_size = x.size(0)
num_points = x.size(2)
x = x.view(batch_size, -1, num_points)
norm_plt = norm_plt.view(batch_size, -1, num_points)
idx, _ = knn(x, k=k) # (batch_size, num_points, k)
device = torch.device('cpu')
idx_base = torch.arange(0, batch_size, device=device).view(-1, 1, 1) * num_points
idx = idx + idx_base
idx = idx.view(-1)
_, num_dims, _ = x.size()
x = x.transpose(2, 1).contiguous()
norm_plt = norm_plt.transpose(2, 1).contiguous()
neighbor = x.view(batch_size * num_points, -1)[idx, :]
neighbor_norm = norm_plt.view(batch_size * num_points, -1)[idx, :]
neighbor = neighbor.view(batch_size, num_points, k, num_dims)
neighbor_norm = neighbor_norm.view(batch_size, num_points, k, num_dims)
x = x.view(batch_size, num_points, 1, num_dims).repeat(1, 1, k, 1)
feature = torch.cat((neighbor-x, neighbor, neighbor_norm), dim=3).permute(0, 3, 1, 2) # 3c
return feature
def GDM(x, M):
"""
Geometry-Disentangle Module
M: number of disentangled points in both sharp and gentle variation components
"""
k = 64 # number of neighbors to decide the range of j in Eq.(5)
tau = 0.2 # threshold in Eq.(2)
sigma = 2 # parameters of f (Gaussian function in Eq.(2))
###############
"""Graph Construction:"""
device = torch.device('cpu')
batch_size = x.size(0)
num_points = x.size(2)
x = x.view(batch_size, -1, num_points)
idx, p = knn(x, k=k) # p: -[(x1-x2)^2+...]
# here we add a tau
p1 = torch.abs(p)
p1 = torch.sqrt(p1)
mask = p1 < tau
# here we add a sigma
p = p / (sigma * sigma)
w = torch.exp(p) # b,n,n
w = torch.mul(mask.float(), w)
b = 1/torch.sum(w, dim=1)
b = b.reshape(batch_size, num_points, 1).repeat(1, 1, num_points)
c = torch.eye(num_points, num_points, device=device)
c = c.expand(batch_size, num_points, num_points)
D = b * c # b,n,n
A = torch.matmul(D, w) # normalized adjacency matrix A_hat
# Get Aij in a local area:
idx2 = idx.view(batch_size * num_points, -1)
idx_base2 = torch.arange(0, batch_size * num_points, device=device).view(-1, 1) * num_points
idx2 = idx2 + idx_base2
idx2 = idx2.reshape(batch_size * num_points, k)[:, 1:k]
idx2 = idx2.reshape(batch_size * num_points * (k - 1))
idx2 = idx2.view(-1)
A = A.view(-1)
A = A[idx2].reshape(batch_size, num_points, k - 1) # Aij: b,n,k
###############
"""Disentangling Point Clouds into Sharp(xs) and Gentle(xg) Variation Components:"""
idx_base = torch.arange(0, batch_size, device=device).view(-1, 1, 1) * num_points
idx = idx + idx_base
idx = idx.reshape(batch_size * num_points, k)[:, 1:k]
idx = idx.reshape(batch_size * num_points * (k - 1))
_, num_dims, _ = x.size()
x = x.transpose(2, 1).contiguous() # b,n,c
neighbor = x.view(batch_size * num_points, -1)[idx, :]
neighbor = neighbor.view(batch_size, num_points, k - 1, num_dims) # b,n,k,c
A = A.reshape(batch_size, num_points, k - 1, 1) # b,n,k,1
n = A.mul(neighbor) # b,n,k,c
n = torch.sum(n, dim=2) # b,n,c
pai = torch.norm(x - n, dim=-1).pow(2) # Eq.(5)
pais = pai.topk(k=M, dim=-1)[1] # first M points as the sharp variation component
paig = (-pai).topk(k=M, dim=-1)[1] # last M points as the gentle variation component
pai_base = torch.arange(0, batch_size, device=device).view(-1, 1) * num_points
indices = (pais + pai_base).view(-1)
indiceg = (paig + pai_base).view(-1)
xs = x.view(batch_size * num_points, -1)[indices, :]
xg = x.view(batch_size * num_points, -1)[indiceg, :]
xs = xs.view(batch_size, M, -1) # b,M,c
xg = xg.view(batch_size, M, -1) # b,M,c
return xs, xg
class SGCAM(nn.Module):
"""Sharp-Gentle Complementary Attention Module:"""
def __init__(self, in_channels, inter_channels=None, bn_layer=True):
super(SGCAM, self).__init__()
self.in_channels = in_channels
self.inter_channels = inter_channels
if self.inter_channels is None:
self.inter_channels = in_channels // 2
if self.inter_channels == 0:
self.inter_channels = 1
conv_nd = nn.Conv1d
bn = nn.BatchNorm1d
self.g = conv_nd(in_channels=self.in_channels, out_channels=self.inter_channels,
kernel_size=1, stride=1, padding=0)
if bn_layer:
self.W = nn.Sequential(
conv_nd(in_channels=self.inter_channels, out_channels=self.in_channels,
kernel_size=1, stride=1, padding=0),
bn(self.in_channels)
)
nn.init.constant(self.W[1].weight, 0)
nn.init.constant(self.W[1].bias, 0)
else:
self.W = conv_nd(in_channels=self.inter_channels, out_channels=self.in_channels,
kernel_size=1, stride=1, padding=0)
nn.init.constant(self.W.weight, 0)
nn.init.constant(self.W.bias, 0)
self.theta = conv_nd(in_channels=self.in_channels, out_channels=self.inter_channels,
kernel_size=1, stride=1, padding=0)
self.phi = conv_nd(in_channels=self.in_channels, out_channels=self.inter_channels,
kernel_size=1, stride=1, padding=0)
def forward(self, x, x_2):
batch_size = x.size(0)
g_x = self.g(x_2).view(batch_size, self.inter_channels, -1)
g_x = g_x.permute(0, 2, 1)
theta_x = self.theta(x).view(batch_size, self.inter_channels, -1)
theta_x = theta_x.permute(0, 2, 1)
phi_x = self.phi(x_2).view(batch_size, self.inter_channels, -1)
W = torch.matmul(theta_x, phi_x) # Attention Matrix
N = W.size(-1)
W_div_C = W / N
y = torch.matmul(W_div_C, g_x)
y = y.permute(0, 2, 1).contiguous()
y = y.view(batch_size, self.inter_channels, *x.size()[2:])
W_y = self.W(y)
y = W_y + x
return y
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