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utils.py
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utils.py
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import numpy as np
import torch
from matplotlib import pyplot as plt
from liegroups import SE3
from reproj import depth_tc, depth_tc_, depth_tc2
from mpl_toolkits.mplot3d import Axes3D
from PIL import Image, ImageDraw
from matplotlib import cm
def homSE3tose3(R, t):
''' R is 3 x 3, t is 3 x 1
se3 is 6 (t_3|r_3)
'''
p = np.zeros((4, 4))
p[:3, :3] = R
p[:3, 3:] = t
p[3, 3] = 1.0
p = SE3.from_matrix(p, normalize=True)
p = p.inv().log() # .inv()
return p
def norm_t(T, norm):
T[:3, 3] /= np.linalg.norm(T[:3, 3]) + 1e-8
T[:3, 3] *= norm
return T
def T2traj(poses):
p = np.eye(4)
pts = [p[:, -1]]
for T in poses:
p = p @ T
pts.append(p[:, -1])
pts = np.array(pts)
return pts
def save_poses(p, outfn):
''' p is in homogeneous format
'''
with open(outfn, 'w') as f:
T0 = np.eye(4).reshape(-1)[:12]
T0 = T0.tolist()
T0 = [str(t) for t in T0]
T0 = ' '.join(T0) + '\n'
f.write(T0)
for T in p:
T_ = T.reshape(-1)[:12]
T_ = T_.tolist()
T_ = [str(t) for t in T_]
T_ = ' '.join(T_) + '\n'
f.write(T_)
def pt_cloud(p, p_, T, foe, scale, c, T_):
''' p is 2,N
p_ is 2,N
T is 4,4
foe is 2,1
scale is a scalar
c is 3,3
'''
p = p.permute(1, 0)
p_ = p_.permute(1, 0)
z = torch.ones(1, p.size(-1)).double()
z_ = torch.ones(1, 1).double()
p = torch.cat([p, z], dim=0)
p_ = torch.cat([p_, z], dim=0)
foe = torch.cat([foe, z_], dim=0)
c_ = torch.inverse(c)
p = c_ @ p
p_ = c_ @ p_
foe = c_ @ foe
T_ = torch.from_numpy(T_)
#d = depth_tc(p[:2], (p_ - p)[:2], foe[:2])
d = depth_tc2(p, (p_ - p), torch.inverse(T_), foe)
#d = depth_tc_(c@p, c@(p_ - p), torch.inverse(T_), c@foe)
d = d * scale
#print(d[:20])
#print(torch.min(d), torch.max(d))
#d = d * (torch.abs(d) < 50.0).double()
#p = c_ @ p
x = p * d
x = T[:3, :3] @ x + T[:3, 3:]
# thresh_d = 5*torch.min(d)
# close = (d < thresh_d).nonzero()
# close = close.reshape(-1)
_, close = torch.topk(-d, k=100)
x = x[:, close]
x = x.detach().numpy()
return x
def plot_pt_cloud(x, outfn):
fig = plt.figure()
plt.axis('equal')
ax = fig.add_subplot(111, projection='3d')
ax.set_xlabel('Z Label')
ax.set_ylabel('X Label')
ax.set_zlabel('Y Label')
ax.view_init(azim=177, elev=65)
ax.scatter(x[2, :], -x[0, :], x[1, :], marker='.')
ax_data = ax.plot([0], [0], [0], marker='.')[0]
plt.show()
# plt.savefig(outfn)
# plt.close(fig)
def plot_traj(poses, poses_, outfn):
pts = T2traj(poses)
pts_ = T2traj(poses_)
fig = plt.figure()
plt.axis('equal')
ax = fig.add_subplot(111)
ax.plot(pts[:, 0], pts[:, 2], 'g-')
ax.plot(pts_[:, 0], pts_[:, 2], 'b-')
plt.savefig(outfn)
plt.close(fig)
def plot_trajs(P, outfn, colors='gbr', glb=False):
''' P is k,n,6
'''
pts = []
if not glb:
for p in P:
pts.append(T2traj(p))
else:
for p in P:
pts.append(p)
pts = np.array(pts)
# fig = plt.figure()
fig, axs = plt.subplots(1) # 3
plt.axis('equal')
# ax = fig.add_subplot(111)
# ax2 = fig.add_subplot(111)
for i, p in enumerate(pts):
axs.plot(p[:, 0], p[:, 2], f'{colors[i]}-')
# axs[1].plot(p[:,0],p[:,1],f'{colors[i]}-')
# axs[2].plot(p[:,1],p[:,2],f'{colors[i]}-')
plt.savefig(outfn)
plt.close(fig)
def ba_graph(i, j):
assert i != j, f'Check indexes {i} {j}'
if i > j:
i, j = min(i, j), max(i, j)
g = []
for start in range(i, j):
g.append((start, start + 1))
g.append((start + 1, start))
if start < j - 1:
g.append((start, start + 2))
g.append((start + 2, start))
#if start < j - 2:
# g.append((start, start + 3))
# g.append((start + 3, start))
return g
def compose(i, j, T, ep, c):
'''
T is n,4,4
ep is n,2,1
'''
assert i != j, f'Check indexes {i} {j}'
i_ = min(i, j)
j_ = max(i, j)
z = torch.ones(ep.size(0), 1, 1).double()
ep = 1e3 * ep
ep = torch.cat([ep, z], dim=1) # n,3,1
c_ = torch.inverse(c)
Tji = T[j] @ torch.inverse(T[i])
Tji[:3, 3:] = Tji[:3, 3:].clone()\
/ (torch.norm(Tji[:3, 3:].clone()) + 1e-10) # kinda weird
#t = Tji[:3, 3:]
#ep_ = (c @ (t/(t[-1]+1e-10))) / 1e3
#print(ep_.detach().numpy())
#ep_ = ep_[:2]
ac = torch.zeros(3, 1).double()
for k in range(i_+1, j_+1):
ac += T[k, :3, :3].T @ c_ @ ep[k]
epji = c @ T[j_, :3, :3] @ ac
if i > j:
epji = c @ Tji[:3, :3] @ c_ @ epji
epji = epji / (epji[-1] + 1e-10)
reg = torch.norm(c_ @ epji)
epji = epji / 1e3
epji = epji[:2]
#print(epji)
return Tji, epji, reg
def compose_local(i, j, T, ep, scale, c, base=0):
'''
T is n,4,4
ep is n,2,1
'''
assert i != j, f'Check indexes {i} {j}'
i_ = min(i, j)
j_ = max(i, j)
j_ -= base
i_ -= base
#print('i j', i_, j_)
z = torch.ones(ep.size(0), 1, 1).double()
ep = 1e3 * ep
ep = torch.cat([ep, z], dim=1) # n,3,1
#scale = 1e1 * scale
c_ = torch.inverse(c)
#Tji = T[j] @ torch.inverse(T[i])
Tji = torch.eye(4).double()
for k in range(i_, j_):
Tk = T[k].clone()
#Tk[:3, 3:] *= scale[k]
Tji = Tk @ Tji
Tji[:3, 3:] = Tji[:3, 3:].clone()\
/ (torch.norm(Tji[:3, 3:].clone()) + 1e-10) # kinda weird
#print(i_, j_)
#print(Tji[2, 3].clone())
#Tji[:3, 3:] = Tji[:3, 3:].clone()\
# / (torch.abs(Tji[2, 3].clone()) + 1e-10)
#ep_ = ep_[:2]
T_jt = torch.eye(4).double()
ac = torch.zeros(3, 1).double()
for k in range(j_, i_, -1):
ac = ac.clone() + c @ T_jt[:3, :3] @ c_ @ (ep[k - 1] * scale[k - 1])
Tk_ = T[k - 1].clone()
#Tk_[:3, 3:] *= scale[k - 1]
T_jt = T_jt.clone() @ Tk_
epji = ac.clone()
if i > j:
Tji = torch.inverse(Tji)
epji = c @ Tji[:3, :3] @ c_ @ epji
t = Tji[:3, 3:]
ep_ = (c @ (t / (t[-1] + 1e-10))) / 1e3
ep_ = ep_[:2]
#print(ep_.detach().numpy())
epji = epji / (epji[-1] + 1e-10)
#reg = torch.norm(c_ @ epji)
epji = epji / 1e3
epji = epji[:2]
#print(epji)
return Tji, epji, ep_
def compose_slocal(i, j, T, ep, scale, c, base=0):
'''
T is n,4,4
ep is n,2,1
'''
assert i != j, f'Check indexes {i} {j}'
i_ = min(i, j)
j_ = max(i, j)
j_ -= base
i_ -= base
z = torch.ones(ep.size(0), 1, 1).double()
#ep = 1e3 * ep
c_ = torch.inverse(c)
Tji = torch.eye(4).double()
for k in range(i_, j_):
Tk = T[k].clone()
Tji = Tk @ Tji
#Tji[:3, 3:] = Tji[:3, 3:].clone()\
# / (torch.norm(Tji[:3, 3:].clone()) + 1e-10) # kinda weird
T_jt = torch.eye(4).double()
ac = torch.zeros(3, 1).double()
for k in range(j_, i_, -1):
ac = ac.clone() + c @ T_jt[:3, :3] @ c_ @ ep[k - 1]
Tk_ = T[k - 1].clone()
T_jt = T_jt.clone() @ Tk_
epji = ac.clone()
if i > j:
Tji = torch.inverse(Tji)
epji = c @ Tji[:3, :3] @ c_ @ epji
t = Tji[:3, 3:]
ep_ = (c @ t) # / 1e3
#epji = epji / 1e3
return Tji, epji, ep_
def cmap(n):
assert 0 <= n <= 255
if n < 64:
return (255, 4 * n, 0)
elif n < 128:
return (4 * (128 - n), 255, 0)
elif n < 192:
return (0, 255, 4 * (n - 128))
else:
return (0, 4 * (255 - n), 255)
def draw_heat(im, vd, velo, ep=None, fn=None):
'''
velo is N x 2
'''
im0_ = Image.fromarray(np.uint8(cm.gray(im) * 255))
img_draw = ImageDraw.Draw(im0_)
for xz, x in zip(vd, velo):
py, px = x
img_draw.rectangle([py - 1, px - 1, py + 1, px + 1],
fill=cmap(xz),
width=2)
if ep is not None:
py, px = ep
img_draw.ellipse([py - 5, px - 5, py + 5, px + 5],
fill=(0, 0, 0),
outline=(255, 255, 255),
width=2)
if fn is not None:
im0_.save(fn)
else:
im0_.show()