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import math | |
import numpy as np | |
from numpy.linalg import norm,inv,pinv | |
import cv2 | |
from PIL import Image | |
depth = Image.load('depth.png') | |
# cam2world: intrinsic parameters | |
w = int(640) | |
h = int(480) | |
u_0 = w/2 | |
v_0 = h/2 | |
vfovd = 55 | |
f = v_0/math.tan((vfovd/2)*3.1415926/180.0) | |
cx = u_0 | |
cy = v_0 | |
K = np.array([[f,0,cx],[0,f,cy],[0,0,1]]) | |
iK = inv(K) | |
# Meshgrid of starting image pixel coordinates | |
u = np.linspace(0, w-1, w) | |
v = np.linspace(0, h-1, h) | |
uv, vv = np.meshgrid(u, v) | |
img_coords = np.transpose(np.dstack((uv,vv,np.ones((h,w)))),(2,0,1)) | |
img_coords_flat = img_coords.reshape((3,-1)) | |
# Back-projection | |
x_hat_flat = np.dot(iK,img_coords_flat) | |
x_hat = x_hat_flat | |
norms = norm(x_hat,axis=0) | |
Xt = np.vstack((x_hat * 1/norms * depth.reshape(1,h*w), np.ones((1,h*w)))) | |
import torch | |
from torch.autograd import Variable | |
x_ = Xt[:3,:] | |
p_ = np.zeros((6,1)) | |
p = Variable(torch.Tensor(p_), requires_grad=True) | |
x = Variable(torch.Tensor(x_)) | |
K = Variable(torch.Tensor(np.array([[f,0,cx],[0,f,cy],[0,0,1]]))) | |
theta = torch.norm(p[0:3]) | |
r = p[0:3] / theta.expand_as(p[0:3]) | |
cosTheta = torch.cos(theta).expand_as(torch.eye(3)) | |
oneMinuscosTheta = (1-torch.cos(theta)).expand_as(torch.eye(3)) | |
sinTheta = torch.sin(theta).expand_as(torch.eye(3)) | |
rx = r[0].expand_as(torch.eye(3)) | |
ry = r[1].expand_as(torch.eye(3)) | |
rz = r[2].expand_as(torch.eye(3)) | |
Rx = Variable(torch.Tensor([[0,0,0],[0,0,-1],[0,1,0]]))*rx | |
Ry = Variable(torch.Tensor([[0,0,1],[0,0,0],[-1,0,0]]))*ry | |
Rz = Variable(torch.Tensor([[0,-1,0],[1,0,0],[0,0,0]]))*rz | |
R1 = cosTheta * Variable(torch.eye(3)) | |
R2 = oneMinuscosTheta*torch.ger(r.squeeze(),r.squeeze()) | |
R3 = (Rx+Ry+Rz)*sinTheta | |
R = R1+R2+R3 | |
x2 = torch.mm(R,x) + p[3:6].expand_as(x) | |
x3 = torch.mm(K,x2) | |
piv = x3[1]/x3[2] | |
piu = x3[0]/x3[2] | |
P = np.vstack((piu,piv)) | |
img = Image.load('img.png') | |
# define accumulator | |
accum = np.zeros((h,w)) | |
# cv2 remap | |
P_reshape = P.reshape(2,h,w) | |
Py = P_reshape[1].astype(np.float32) | |
Px = P_reshape[0].astype(np.float32) | |
accum = cv2.remap(img,Px,Py,cv2.INTER_LINEAR) | |
pgrad = [] | |
for pi in [piu,piv]: | |
m = x_.shape[1] | |
Jacobian = torch.Tensor(m,6).zero_() | |
for n in range(m): | |
grad_mask = torch.zeros(m) | |
grad_mask[n] = 1 | |
pi.backward(grad_mask, retain_variables=True) | |
Jacobian[n,:] = p.grad.data | |
p.grad.data.zero_() | |
pgrad.append(Jacobian) | |
# Calculate image gradient | |
graduimg = cv2.Sobel(img,cv2.CV_32F,1,0,ksize=int(31)) | |
gradvimg = cv2.Sobel(img,cv2.CV_32F,0,1,ksize=int(31)) | |
wGradu_flat = gradximg.reshape((1,-1)) | |
wGradv_flat = gradyimg.reshape((1,-1)) | |
# Prepare vectorizing operations | |
pgrad_u = pgrad[0] | |
pgrad_v = pgrad[1] | |
Wp = np.vstack([pgrad_u.numpy(),pgrad_v.numpy()]) | |
delI = np.hstack([np.diag(wGradu_flat),np.diag(wGradv_flat)]) | |
# get Jacobian | |
Jac = delI.dot(Wp) | |
# solve for parameter update | |
# residual error | |
r = (accum - img).reshape(-1,1) | |
delP = pinv(Jac).dot(r) | |
p_ = p_ - 1*delP |
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