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import torch
import torch.nn as nn
import torch.nn.functional as F
class TpsWarp(nn.Module):
def __init__(self, s):
super(TpsWarp, self).__init__()
iy, ix = torch.meshgrid(torch.linspace(-1, 1, s),
torch.linspace(-1, 1, s))
self.gs = torch.stack((ix, iy), dim=2).reshape((1, -1, 2))
self.sz = s
def forward(self, src, dst):
# src and dst are B.n.2
B, n, _ = src.size()
# B.n.1.2
delta = src.unsqueeze(2)
delta = delta - delta.permute(0, 2, 1, 3)
# B.n.n
K = delta.norm(dim=3)
# Rsq = torch.sum(delta**2, dim=3)
# Rsq += torch.eye(n)
# Rsq[Rsq == 0] = 1.
# K = 0.5 * Rsq * torch.log(Rsq)
# c = -150
# K = torch.exp(c * Rsq)
# K = torch.abs(Rsq - 0.5) - 0.5
# WARNING: TORCH.SQRT HAS NAN GRAD AT 0
# K = torch.sqrt(Rsq)
# print(K)
# K[torch.isnan(K)] = 0.
P = torch.cat((torch.ones((B, n, 1)), src), 2)
L = torch.cat((K, P), 2)
t = torch.cat(
(P.permute(0, 2, 1), torch.zeros((B, 3, 3))), 2)
L = torch.cat((L, t), 1)
# LInv = L.inverse()
# # wv is B.n+3.2
# wv = torch.matmul(LInv, torch.cat((dst, torch.zeros((B, 3, 2))), 1))
# the above implementation has stability problem near the boundaries
wv = torch.solve(
torch.cat((dst, torch.zeros((B, 3, 2))), 1), L)[0]
# get the grid sampler
s = self.gs.size(1)
gs = self.gs
delta = gs.unsqueeze(2)
delta = delta - src.unsqueeze(1)
K = delta.norm(dim=3)
# Rsq = torch.sum(delta**2, dim=3)
# K = torch.exp(c * Rsq)
# Rsq[Rsq == 0] = 1.
# K = 0.5 * Rsq * torch.log(Rsq)
# K = torch.abs(Rsq - 0.5) - 0.5
# K = torch.sqrt(Rsq)
# K[torch.isnan(K)] = 0.
gs = gs.expand(B, -1, -1)
P = torch.cat((torch.ones((B, s, 1)), gs), 2)
L = torch.cat((K, P), 2)
gs = torch.matmul(L, wv)
return gs.reshape(B, self.sz, self.sz, 2).permute(0, 3, 1, 2)
class PspWarp(nn.Module):
def __init__(self):
super().__init__()
def pspmat(self, src, dst):
# B, 4, 2
B, _, _ = src.size()
s = torch.cat([
torch.cat([src,
torch.ones((B, 4, 1)),
torch.zeros((B, 4, 3)),
-dst[..., 0: 1] * src[..., 0: 1], -dst[..., 0: 1] * src[..., 1: 2]], dim=2),
torch.cat([torch.zeros((B, 4, 3)), src, torch.ones((B, 4, 1)),
-dst[..., 1: 2] * src[..., 0: 1], -dst[..., 1: 2] * src[..., 1: 2]], dim=2)
], dim=1)
t = torch.cat([dst[..., 0: 1], dst[..., 1: 2]], dim=1)
# M = s.inverse() @ t
M = torch.solve(t, s)[0]
# M is B 8 1
return M
def forward(self, xy, M):
# permute M to B 1 8
M = M.permute(0, 2, 1)
t = M[..., 6] * xy[..., 0] + M[..., 7] * xy[..., 1] + 1
u = (M[..., 0] * xy[..., 0] + M[..., 1] * xy[..., 1] + M[..., 2]) / t
v = (M[..., 3] * xy[..., 0] + M[..., 4] * xy[..., 1] + M[..., 5]) / t
return torch.stack((u, v), dim=2)
# for ii in range(4):
# xy = src[:, ii : ii + 1, :]
# uv = dst[:, ii : ii + 1, :]
# t0 = [xy, torch.ones((B, 1, 1)), torch.zeros((B, 1, 3)), -uv[..., 0] * xy[..., 0], -uv[..., 0] * xy[..., 1]]
# t0 = torch.cat(t0, dim=2)
# t1 = [torch.zeros((B, 1, 3)), xy, torch.ones((B, 1, 1)), -uv[..., 1] * xy[..., 0], -uv[..., 1] * xy[..., 1]]
# t1 = torch.cat(t1, dim=2)
class IdwWarp(nn.Module):
# inverse distance weighting
def __init__(self, s):
super().__init__()
iy, ix = torch.meshgrid(torch.linspace(-1, 1, s),
torch.linspace(-1, 1, s))
self.gs = torch.stack((ix, iy), dim=2).reshape((1, -1, 2)).to('cuda')
self.s = s
def forward(self, src, dst):
# B n 2
B, n, _ = src.size()
# B.n.1.2
delta = src.unsqueeze(2)
delta = delta - self.gs.unsqueeze(0)
# B.n.K
p = 1
Rsq = torch.sum(delta**2, dim=3)**p
w = 1 / Rsq
# turn inf to [0...1...0]
t = torch.isinf(w)
idx = t.any(dim=1).nonzero()
w[idx[:, 0], :, idx[:, 1]] = t[idx[:, 0], :, idx[:, 1]].float()
wwx = w * dst[..., 0: 1]
wwx = wwx.sum(dim=1) / w.sum(dim=1)
wwy = w * dst[..., 1: 2]
wwy = wwy.sum(dim=1) / w.sum(dim=1)
# print(wwy.size())
gs = torch.stack((wwx, wwy), dim=2).reshape(
B, self.s, self.s, 2).permute(0, 3, 1, 2)
return gs
if __name__ == "__main__":
import cv2
import numpy as np
from hdf5storage import loadmat
from visdom import Visdom
vis = Visdom(port=10086)
# bm_path = '/nfs/bigdisk/sagnik/swat3d/bm/7/2_471_7-ec_Page_375-5LI0001.mat'
# img_path = '/nfs/bigdisk/sagnik/swat3d/img/7/2_471_7-ec_Page_375-5LI0001.png'
# bm = loadmat(bm_path)['bm']
# bm = (bm - 224) / 224.
# bm = cv2.resize(bm, (64, 64), cv2.INTER_LINEAR).astype(np.float32)
# im = cv2.imread(img_path) / 255.
# im = im[..., ::-1].copy()
# im = cv2.resize(im, (256, 256), cv2.INTER_AREA).astype(np.float32)
# im = torch.from_numpy(im.transpose(2, 0, 1)).unsqueeze(0).to('cuda')
# x = np.random.choice(np.arange(64), 50, False)
# y = np.random.choice(np.arange(64), 50, False)
# src = torch.tensor([[x, y]], dtype=torch.float32).permute(0, 2, 1)
# src = (src - 32) / 32.
# dst = torch.from_numpy(bm[y, x, :]).unsqueeze(0).to('cuda')
# # print(src.size())
# # print(dst.size())
# tpswarp = TpsWarp(64)
# import time
# t = time.time()
# for _ in range(100):
# gs = tpswarp(src, dst)
# print(f'time:{time.time() - t}')
# gs = gs.view(-1, 64, 64, 2)
# print(gs.size())
# bm2x2 = F.interpolate(gs.permute(0, 3, 1, 2), size=256, mode='bilinear', align_corners=True).permute(0, 2, 3, 1)
# rim = F.grid_sample(im, bm2x2, align_corners=True)
# vis.images(rim, win='sk3')
tpswarp = TpsWarp(16)
import matplotlib.pyplot as plt
cn = torch.tensor([[-1, -1], [1, -1], [1, 1], [-1, 1], [-0.5, -1],
[0, -1], [0.5, -1]], dtype=torch.float).unsqueeze(0)
pn = torch.tensor([[-1, -0.5], [1, -1], [1, 1], [-1, 0.5],
[-0.5, -1], [0, -0.5], [0.5, -1]]).unsqueeze(0)
pspwarp = PspWarp()
# # print(cn.dtype)
M = pspwarp.pspmat(cn[..., 0: 4, :], pn[..., 0: 4, :])
invM = pspwarp.pspmat(pn[..., 0: 4, :], cn[..., 0: 4, :])
# iy, ix = torch.meshgrid(torch.linspace(-1, 1, 8), torch.linspace(-1, 1, 8))
# gs = torch.stack((ix, iy), dim=2).reshape((1, -1, 2)).to('cuda')
# t = pspwarp(gs, M).reshape(8, 8, 2).detach().cpu().numpy()
# print(M)
t = tpswarp(cn, pn)
from tsdeform import WarperUtil
wu = WarperUtil(16)
tgs = wu.global_post_warp(t, 16, invM, M)
t = tgs.permute(0, 2, 3, 1)[0].detach().cpu().numpy()
plt.clf()
plt.pcolormesh(t[..., 0], t[..., 1],
np.zeros_like(t[..., 0]), edgecolors='r')
plt.gca().invert_yaxis()
plt.gca().axis('equal')
vis.matplot(plt, env='grid', win='mpl')
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