File size: 9,656 Bytes
2571f24 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 |
# ported from https://github.com/pvigier/perlin-numpy
import torch
import numpy as np
import matplotlib.pyplot as plt
def center_crop(img, win_size = [220, 220, 220]):
# center crop
if len(img.shape) == 4:
img = torch.permute(img, (3, 0, 1, 2)) # (move last dim to first)
img = img[None]
permuted = True
else:
assert len(img.shape) == 3
img = img[None, None]
permuted = False
orig_shp = img.shape[2:] # (1, d, s, r, c)
if win_size is None:
if permuted:
return torch.permute(img, (0, 2, 3, 4, 1)), [0, 0, 0], orig_shp
return img, [0, 0, 0], orig_shp
elif orig_shp[0] > win_size[0] or orig_shp[1] > win_size[1] or orig_shp[2] > win_size[2]:
crop_start = [ max((orig_shp[i] - win_size[i]), 0) // 2 for i in range(3) ]
crop_img = img[ :, :, crop_start[0] : crop_start[0] + win_size[0],
crop_start[1] : crop_start[1] + win_size[1],
crop_start[2] : crop_start[2] + win_size[2]]
if permuted:
return torch.permute(crop_img, (0, 2, 3, 4, 1)), [0, 0, 0], orig_shp
return crop_img, crop_start, orig_shp
else:
if permuted:
return torch.permute(img, (0, 2, 3, 4, 1)), [0, 0, 0], orig_shp
return img, [0, 0, 0], orig_shp
def V_plot(Vx, Vy, save_path):
# Meshgrid
X,Y = np.meshgrid(np.arange(0, Vx.shape[0], 1), np.arange(0, Vx.shape[1], 1))
# Assign vector directions
Ex = Vx
Ey = Vy
# Depict illustration
plt.figure()
plt.streamplot(X,Y,Ex,Ey, density=1.4, linewidth=None, color='orange')
plt.axis('off')
plt.savefig(save_path)
#plt.show()
def stream_2D(Phi, batched = False, delta_lst = [1., 1.]):
'''
input: Phi as a scalar field in 2D grid: (r, c) or (n_batch, r, c)
output: curl of Phi (divergence-free by definition)
'''
dD = gradient_c(Phi, batched = batched, delta_lst = delta_lst)
Vx = - dD[..., 1]
Vy = dD[..., 0]
return Vx, Vy
def stream_3D(Phi_a, Phi_b, Phi_c, batched = False, delta_lst = [1., 1., 1.]):
'''
input: (batch, s, r, c)
'''
device = Phi_a.device
dDa = gradient_c(Phi_a, batched = batched, delta_lst = delta_lst)
dDb = gradient_c(Phi_b, batched = batched, delta_lst = delta_lst)
dDc = gradient_c(Phi_c, batched = batched, delta_lst = delta_lst)
Va_x, Va_y, Va_z = dDa[..., 0], dDa[..., 1], dDa[..., 2]
Vb_x, Vb_y, Vb_z = dDb[..., 0], dDb[..., 1], dDb[..., 2]
Vc_x, Vc_y, Vc_z = dDc[..., 0], dDc[..., 1], dDc[..., 2]
Vx = Vc_y - Vb_z
Vy = Va_z - Vc_x
Vz = Vb_x - Va_y
return Vx, Vy, Vz
def gradient_f(X, batched = False, delta_lst = [1., 1., 1.]):
'''
Compute gradient of a torch tensor "X" in each direction
Upper-boundaries: Backward Difference
Non-boundaries & Upper-boundaries: Forward Difference
if X is batched: (n_batch, ...);
else: (...)
'''
device = X.device
dim = len(X.size()) - 1 if batched else len(X.size())
#print(batched)
#print(dim)
if dim == 1:
#print('dim = 1')
dX = torch.zeros(X.size(), dtype = torch.float, device = device)
X = X.permute(1, 0) if batched else X
dX = dX.permute(1, 0) if batched else dX
dX[-1] = X[-1] - X[-2] # Backward Difference
dX[:-1] = X[1:] - X[:-1] # Forward Difference
dX = dX.permute(1, 0) if batched else dX
dX /= delta_lst[0]
elif dim == 2:
#print('dim = 2')
dX = torch.zeros(X.size() + tuple([2]), dtype = torch.float, device = device)
X = X.permute(1, 2, 0) if batched else X
dX = dX.permute(1, 2, 3, 0) if batched else dX # put batch to last dim
dX[-1, :, 0] = X[-1, :] - X[-2, :] # Backward Difference
dX[:-1, :, 0] = X[1:] - X[:-1] # Forward Difference
dX[:, -1, 1] = X[:, -1] - X[:, -2] # Backward Difference
dX[:, :-1, 1] = X[:, 1:] - X[:, :-1] # Forward Difference
dX = dX.permute(3, 0, 1, 2) if batched else dX
dX[..., 0] /= delta_lst[0]
dX[..., 1] /= delta_lst[1]
elif dim == 3:
#print('dim = 3')
dX = torch.zeros(X.size() + tuple([3]), dtype = torch.float, device = device)
X = X.permute(1, 2, 3, 0) if batched else X
dX = dX.permute(1, 2, 3, 4, 0) if batched else dX
dX[-1, :, :, 0] = X[-1, :, :] - X[-2, :, :] # Backward Difference
dX[:-1, :, :, 0] = X[1:] - X[:-1] # Forward Difference
dX[:, -1, :, 1] = X[:, -1] - X[:, -2] # Backward Difference
dX[:, :-1, :, 1] = X[:, 1:] - X[:, :-1] # Forward Difference
dX[:, :, -1, 2] = X[:, :, -1] - X[:, :, -2] # Backward Difference
dX[:, :, :-1, 2] = X[:, :, 1:] - X[:, :, :-1] # Forward Difference
dX = dX.permute(4, 0, 1, 2, 3) if batched else dX
dX[..., 0] /= delta_lst[0]
dX[..., 1] /= delta_lst[1]
dX[..., 2] /= delta_lst[2]
return dX
def gradient_b(X, batched = False, delta_lst = [1., 1., 1.]):
'''
Compute gradient of a torch tensor "X" in each direction
Non-boundaries & Upper-boundaries: Backward Difference
Lower-boundaries: Forward Difference
if X is batched: (n_batch, ...);
else: (...)
'''
device = X.device
dim = len(X.size()) - 1 if batched else len(X.size())
#print(batched)
#print(dim)
if dim == 1:
#print('dim = 1')
dX = torch.zeros(X.size(), dtype = torch.float, device = device)
X = X.permute(1, 0) if batched else X
dX = dX.permute(1, 0) if batched else dX
dX[1:] = X[1:] - X[:-1] # Backward Difference
dX[0] = X[1] - X[0] # Forward Difference
dX = dX.permute(1, 0) if batched else dX
dX /= delta_lst[0]
elif dim == 2:
#print('dim = 2')
dX = torch.zeros(X.size() + tuple([2]), dtype = torch.float, device = device)
X = X.permute(1, 2, 0) if batched else X
dX = dX.permute(1, 2, 3, 0) if batched else dX # put batch to last dim
dX[1:, :, 0] = X[1:, :] - X[:-1, :] # Backward Difference
dX[0, :, 0] = X[1] - X[0] # Forward Difference
dX[:, 1:, 1] = X[:, 1:] - X[:, :-1] # Backward Difference
dX[:, 0, 1] = X[:, 1] - X[:, 0] # Forward Difference
dX = dX.permute(3, 0, 1, 2) if batched else dX
dX[..., 0] /= delta_lst[0]
dX[..., 1] /= delta_lst[1]
elif dim == 3:
#print('dim = 3')
dX = torch.zeros(X.size() + tuple([3]), dtype = torch.float, device = device)
X = X.permute(1, 2, 3, 0) if batched else X
dX = dX.permute(1, 2, 3, 4, 0) if batched else dX
dX[1:, :, :, 0] = X[1:, :, :] - X[:-1, :, :] # Backward Difference
dX[0, :, :, 0] = X[1] - X[0] # Forward Difference
dX[:, 1:, :, 1] = X[:, 1:] - X[:, :-1] # Backward Difference
dX[:, 0, :, 1] = X[:, 1] - X[:, 0] # Forward Difference
dX[:, :, 1:, 2] = X[:, :, 1:] - X[:, :, :-1] # Backward Difference
dX[:, :, 0, 2] = X[:, :, 1] - X[:, :, 0] # Forward Difference
dX = dX.permute(4, 0, 1, 2, 3) if batched else dX
dX[..., 0] /= delta_lst[0]
dX[..., 1] /= delta_lst[1]
dX[..., 2] /= delta_lst[2]
return dX
def gradient_c(X, batched = False, delta_lst = [1., 1., 1.]):
'''
Compute gradient of a torch tensor "X" in each direction
Non-boundaries: Central Difference
Upper-boundaries: Backward Difference
Lower-boundaries: Forward Difference
if X is batched: (n_batch, ...);
else: (...)
'''
device = X.device
dim = len(X.size()) - 1 if batched else len(X.size())
#print(X.size())
#print(batched)
#print(dim)
if dim == 1:
#print('dim = 1')
dX = torch.zeros(X.size(), dtype = torch.float, device = device)
X = X.permute(1, 0) if batched else X
dX = dX.permute(1, 0) if batched else dX
dX[1:-1] = (X[2:] - X[:-2]) / 2 # Central Difference
dX[0] = X[1] - X[0] # Forward Difference
dX[-1] = X[-1] - X[-2] # Backward Difference
dX = dX.permute(1, 0) if batched else dX
dX /= delta_lst[0]
elif dim == 2:
#print('dim = 2')
dX = torch.zeros(X.size() + tuple([2]), dtype = torch.float, device = device)
X = X.permute(1, 2, 0) if batched else X
dX = dX.permute(1, 2, 3, 0) if batched else dX # put batch to last dim
dX[1:-1, :, 0] = (X[2:, :] - X[:-2, :]) / 2
dX[0, :, 0] = X[1] - X[0]
dX[-1, :, 0] = X[-1] - X[-2]
dX[:, 1:-1, 1] = (X[:, 2:] - X[:, :-2]) / 2
dX[:, 0, 1] = X[:, 1] - X[:, 0]
dX[:, -1, 1] = X[:, -1] - X[:, -2]
dX = dX.permute(3, 0, 1, 2) if batched else dX
dX[..., 0] /= delta_lst[0]
dX[..., 1] /= delta_lst[1]
elif dim == 3:
#print('dim = 3')
dX = torch.zeros(X.size() + tuple([3]), dtype = torch.float, device = device)
X = X.permute(1, 2, 3, 0) if batched else X
dX = dX.permute(1, 2, 3, 4, 0) if batched else dX
dX[1:-1, :, :, 0] = (X[2:, :, :] - X[:-2, :, :]) / 2
dX[0, :, :, 0] = X[1] - X[0]
dX[-1, :, :, 0] = X[-1] - X[-2]
dX[:, 1:-1, :, 1] = (X[:, 2:, :] - X[:, :-2, :]) / 2
dX[:, 0, :, 1] = X[:, 1] - X[:, 0]
dX[:, -1, :, 1] = X[:, -1] - X[:, -2]
dX[:, :, 1:-1, 2] = (X[:, :, 2:] - X[:, :, :-2]) / 2
dX[:, :, 0, 2] = X[:, :, 1] - X[:, :, 0]
dX[:, :, -1, 2] = X[:, :, -1] - X[:, :, -2]
dX = dX.permute(4, 0, 1, 2, 3) if batched else dX
dX[..., 0] /= delta_lst[0]
dX[..., 1] /= delta_lst[1]
dX[..., 2] /= delta_lst[2]
return dX
|