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utils_3d.py
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utils_3d.py
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import numpy as np
import contextlib
import sys
import math
from menpo.transform import UniformScale, Translation, Homogeneous, scale_about_centre, Rotation, Scale
from menpo.shape import PointCloud, TriMesh
from functools import reduce
class DummyFile(object):
def write(self, x): pass
@contextlib.contextmanager
def nostdout():
f = open('/dev/null', 'w')
save_stdout = sys.stdout
sys.stdout = f
yield
sys.stdout = save_stdout
def clip_texture(image):
image.pixels = image.pixels.clip(0, 1)
return image
def rescale_values(arr, minimum, maximum):
min_, max_ = arr.min(), arr.max()
sf = ((maximum - minimum) * 1.0) / (max_ - min_)
return ((arr - min_) * sf) + minimum
def clip_to_image(height, width):
# 2. invert the y direction (up becomes down)
invert_y = Scale([1, -1])
# 3. [-1, 1] [-1, 1] -> [0, 2] [0, 2]
t = Translation([1, 1])
# 4. [0, 2] [0, 2] -> [0, 1] [0, 1]
unit_scale = Scale(0.5, n_dims=2)
# 5. [0, 1] [0, 1] -> [0, w] [0, h]
im_scale = Scale([width, height])
# 6. [0, w] [0, h] -> [0, h] [0, w]
xy_yx = Homogeneous(np.array([[0, 1, 0],
[1, 0, 0],
[0, 0, 1]], dtype=np.float))
# reduce the full transform chain to a single affine matrix
transforms = [invert_y, t, unit_scale, im_scale, xy_yx]
return reduce(lambda a, b: a.compose_before(b), transforms)
def get_vertices(mesh):
old_to_new = mesh.trilist.ravel()
new_trilist = np.arange(old_to_new.shape[0]).reshape([-1, 3])
new_points = mesh.points[old_to_new]
return mesh.points
def calculate_weights(x):
return model.project(AlignmentSimilarity(x, model.mean()).apply(x))
def model_to_clip_space(im, mesh):
view_t, c_t, proj_t = retrieve_camera_matrix(im, mesh, initialize=True)
proj_t = weak_projection_matrix(im.shape[1], im.shape[0], view_t.apply(mesh))
view_t = view_t.compose_before(axes_flip_t)
transform = Homogeneous(proj_t.dot(view_t.h_matrix))
return transform
def duplicate_vertices(mesh):
# generate a new mesh with unique vertices per triangle
# (i.e. duplicate verts so that each triangle is unique) old_to_new = mesh.trilist.ravel()
old_to_new = mesh.trilist.ravel()
new_trilist = np.arange(old_to_new.shape[0]).reshape([-1, 3])
new_points = mesh.points[old_to_new]
return TriMesh(new_points, trilist=new_trilist), old_to_new
def quaternion_from_matrix(matrix, isprecise=False):
"""Return quaternion from rotation matrix."""
M = np.array(matrix, dtype=np.float64, copy=False)[:4, :4]
if isprecise:
q = np.empty((4, ))
t = np.trace(M)
if t > M[3, 3]:
q[0] = t
q[3] = M[1, 0] - M[0, 1]
q[2] = M[0, 2] - M[2, 0]
q[1] = M[2, 1] - M[1, 2]
else:
i, j, k = 1, 2, 3
if M[1, 1] > M[0, 0]:
i, j, k = 2, 3, 1
if M[2, 2] > M[i, i]:
i, j, k = 3, 1, 2
t = M[i, i] - (M[j, j] + M[k, k]) + M[3, 3]
q[i] = t
q[j] = M[i, j] + M[j, i]
q[k] = M[k, i] + M[i, k]
q[3] = M[k, j] - M[j, k]
q *= 0.5 / np.sqrt(t * M[3, 3])
else:
m00 = M[0, 0]
m01 = M[0, 1]
m02 = M[0, 2]
m10 = M[1, 0]
m11 = M[1, 1]
m12 = M[1, 2]
m20 = M[2, 0]
m21 = M[2, 1]
m22 = M[2, 2]
# symmetric matrix K
K = np.array([[m00-m11-m22, 0.0, 0.0, 0.0],
[m01+m10, m11-m00-m22, 0.0, 0.0],
[m02+m20, m12+m21, m22-m00-m11, 0.0],
[m21-m12, m02-m20, m10-m01, m00+m11+m22]])
K /= 3.0
# quaternion is eigenvector of K that corresponds to largest eigenvalue
try:
w, V = np.linalg.eigh(K)
except:
return quaternion_from_matrix(matrix, isprecise=True)
q = V[[3, 0, 1, 2], np.argmax(w)]
if q[0] < 0.0:
np.negative(q, q)
return q
def quaternion_matrix(quaternion, eps=.00000001):
"""Return homogeneous rotation matrix from quaternion."""
q = np.array(quaternion, dtype=np.float64, copy=True)
n = np.dot(q, q)
if n < eps:
return np.identity(4)
q *= np.sqrt(2.0 / n)
q = np.outer(q, q)
return np.array([
[1.0-q[2, 2]-q[3, 3], q[1, 2]-q[3, 0], q[1, 3]+q[2, 0], 0.0],
[ q[1, 2]+q[3, 0], 1.0-q[1, 1]-q[3, 3], q[2, 3]-q[1, 0], 0.0],
[ q[1, 3]-q[2, 0], q[2, 3]+q[1, 0], 1.0-q[1, 1]-q[2, 2], 0.0],
[ 0.0, 0.0, 0.0, 1.0]])
def euler_from_matrix(matrix, axes='sxyz'):
"""Return Euler angles from rotation matrix for specified axis sequence.
"""
try:
firstaxis, parity, repetition, frame = _AXES2TUPLE[axes.lower()]
except (AttributeError, KeyError):
_TUPLE2AXES[axes] # validation
firstaxis, parity, repetition, frame = axes
i = firstaxis
j = _NEXT_AXIS[i+parity]
k = _NEXT_AXIS[i-parity+1]
M = np.array(matrix, dtype=np.float64, copy=False)[:3, :3]
if repetition:
sy = np.sqrt(M[i, j]*M[i, j] + M[i, k]*M[i, k])
if sy > _EPS:
ax = math.atan2( M[i, j], M[i, k])
ay = math.atan2( sy, M[i, i])
az = math.atan2( M[j, i], -M[k, i])
else:
ax = math.atan2(-M[j, k], M[j, j])
ay = math.atan2( sy, M[i, i])
az = 0.0
else:
cy = np.sqrt(M[i, i]*M[i, i] + M[j, i]*M[j, i])
if cy > _EPS:
ax = math.atan2( M[k, j], M[k, k])
ay = math.atan2(-M[k, i], cy)
az = math.atan2( M[j, i], M[i, i])
else:
ax = math.atan2(-M[j, k], M[j, j])
ay = math.atan2(-M[k, i], cy)
az = 0.0
if parity:
ax, ay, az = -ax, -ay, -az
if frame:
ax, az = az, ax
return ax, ay, az
def retrieve_camera_matrix(image, mesh, group=None, initialize=True):
import cv2
drop_h = Homogeneous(np.eye(4)[:3])
flip_xy_yx = Homogeneous(np.array([[0, 1, 0],
[1, 0, 0],
[0, 0, 1]]))
rows = image.shape[0]
cols = image.shape[1]
max_d = max(rows, cols)
camera_matrix = np.array([[max_d, 0, cols / 2.0],
[0, max_d, rows / 2.0],
[0, 0, 1.0]])
distortion_coeffs = np.zeros(4)
# Initial guess for rotation/translation.
if initialize:
r_vec = np.array([[-2.7193267 ], [-0.14545351], [-0.34661788]])
t_vec = np.array([[0.], [ 0. ], [280.]])
converged, r_vec, t_vec = cv2.solvePnP(mesh.landmarks[group].lms.points,
image.landmarks[group].lms.points[:, ::-1],
camera_matrix,
distortion_coeffs, r_vec, t_vec, 1)
else:
converged, r_vec, t_vec = cv2.solvePnP(mesh.landmarks[group].lms.points,
image.landmarks[group].lms.points[:, ::-1],
camera_matrix,
distortion_coeffs)
rotation_matrix = cv2.Rodrigues(r_vec)[0]
h_camera_matrix = np.eye(4)
h_camera_matrix[:3, :3] = camera_matrix
t_vec = t_vec.ravel()
if t_vec[2] < 0:
print('Position has a negative value in z-axis')
c = Homogeneous(h_camera_matrix)
t = Translation(t_vec)
r = Rotation(rotation_matrix)
view_t = r.compose_before(t)
proj_t = c.compose_before(drop_h).compose_before(flip_xy_yx)
return view_t, c, proj_t
def weak_projection_matrix(width, height, mesh_camera_space):
# Identify how far and near the mesh is in camera space.
# we want to ensure that the near and far planes are
# set so that all the mesh is displayed.
near_bounds, far_bounds = mesh_camera_space.bounds()
# Rather than just use the bounds, we add 10% in each direction
# just to avoid any numerical errors.
average_plane = (near_bounds[-1] + far_bounds[-1]) * 0.5
padded_range = mesh_camera_space.range()[-1] * 1.1
near_plane = average_plane - padded_range
far_plane = average_plane + padded_range
plane_sum = far_plane + near_plane
plane_prod = far_plane * near_plane
denom = far_plane - near_plane
max_d = max(width, height)
return np.array([[2.0 * max_d / width, 0, 0, 0],
[0, 2.0 * max_d / height, 0, 0],
[0, 0, (-plane_sum) / denom, (-2.0 * plane_prod) / denom],
[0, 0, -1, 0]])
def duplicate_vertices(mesh):
# generate a new mesh with unique vertices per triangle
# (i.e. duplicate verts so that each triangle is unique) old_to_new = mesh.trilist.ravel()
old_to_new = mesh.trilist.ravel()
new_trilist = np.arange(old_to_new.shape[0]).reshape([-1, 3])
new_points = mesh.points[old_to_new]
return TriMesh(new_points, trilist=new_trilist), old_to_new
def crop_face(img, boundary=50, group=None, shape=(256, 256), order=1):
pc = img.landmarks[group].lms
nan_points = np.any(np.isnan(pc.points).reshape(-1, 2), 1)
pc = PointCloud(pc.points[~nan_points, :])
min_indices, max_indices = pc.bounds(boundary=boundary)
h = max_indices[0] - min_indices[0]
w = max_indices[1] - min_indices[1]
pad = abs(w - h)
try:
index = 1 - int(w > h)
min_indices[index] -= int(pad / 2.)
max_indices[index] += int(pad / 2.) + int(pad) % 2
img = img.crop(min_indices, max_indices, constrain_to_boundary=True)
except Exception as e:
print("Exception in crop_face", e)
img = img.resize(shape, order=order)
return img