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"""
This file implements the homographic transforms for data augmentation.
Code adapted from https://github.com/rpautrat/SuperPoint
"""
import numpy as np
from math import pi
from ..synthetic_util import get_line_map, get_line_heatmap
import cv2
import copy
import shapely.geometry
def sample_homography(
shape,
perspective=True,
scaling=True,
rotation=True,
translation=True,
n_scales=5,
n_angles=25,
scaling_amplitude=0.1,
perspective_amplitude_x=0.1,
perspective_amplitude_y=0.1,
patch_ratio=0.5,
max_angle=pi / 2,
allow_artifacts=False,
translation_overflow=0.0,
):
"""
Computes the homography transformation between a random patch in the
original image and a warped projection with the same image size.
As in `tf.contrib.image.transform`, it maps the output point
(warped patch) to a transformed input point (original patch).
The original patch, initialized with a simple half-size centered crop,
is iteratively projected, scaled, rotated and translated.
Arguments:
shape: A rank-2 `Tensor` specifying the height and width of the original image.
perspective: A boolean that enables the perspective and affine transformations.
scaling: A boolean that enables the random scaling of the patch.
rotation: A boolean that enables the random rotation of the patch.
translation: A boolean that enables the random translation of the patch.
n_scales: The number of tentative scales that are sampled when scaling.
n_angles: The number of tentatives angles that are sampled when rotating.
scaling_amplitude: Controls the amount of scale.
perspective_amplitude_x: Controls the perspective effect in x direction.
perspective_amplitude_y: Controls the perspective effect in y direction.
patch_ratio: Controls the size of the patches used to create the homography.
max_angle: Maximum angle used in rotations.
allow_artifacts: A boolean that enables artifacts when applying the homography.
translation_overflow: Amount of border artifacts caused by translation.
Returns:
homo_mat: A numpy array of shape `[1, 3, 3]` corresponding to the
homography transform.
selected_scale: The selected scaling factor.
"""
# Convert shape to ndarry
if not isinstance(shape, np.ndarray):
shape = np.array(shape)
# Corners of the output image
pts1 = np.array([[0.0, 0.0], [0.0, 1.0], [1.0, 1.0], [1.0, 0.0]])
# Corners of the input patch
margin = (1 - patch_ratio) / 2
pts2 = margin + np.array(
[[0, 0], [0, patch_ratio], [patch_ratio, patch_ratio], [patch_ratio, 0]]
)
# Random perspective and affine perturbations
if perspective:
if not allow_artifacts:
perspective_amplitude_x = min(perspective_amplitude_x, margin)
perspective_amplitude_y = min(perspective_amplitude_y, margin)
# normal distribution with mean=0, std=perspective_amplitude_y/2
perspective_displacement = np.random.normal(
0.0, perspective_amplitude_y / 2, [1]
)
h_displacement_left = np.random.normal(0.0, perspective_amplitude_x / 2, [1])
h_displacement_right = np.random.normal(0.0, perspective_amplitude_x / 2, [1])
pts2 += np.stack(
[
np.concatenate([h_displacement_left, perspective_displacement], 0),
np.concatenate([h_displacement_left, -perspective_displacement], 0),
np.concatenate([h_displacement_right, perspective_displacement], 0),
np.concatenate([h_displacement_right, -perspective_displacement], 0),
]
)
# Random scaling: sample several scales, check collision with borders,
# randomly pick a valid one
if scaling:
scales = np.concatenate(
[[1.0], np.random.normal(1, scaling_amplitude / 2, [n_scales])], 0
)
center = np.mean(pts2, axis=0, keepdims=True)
scaled = (pts2 - center)[None, ...] * scales[..., None, None] + center
# all scales are valid except scale=1
if allow_artifacts:
valid = np.array(range(n_scales))
# Chech the valid scale
else:
valid = np.where(np.all((scaled >= 0.0) & (scaled < 1.0), (1, 2)))[0]
# No valid scale found => recursively call
if valid.shape[0] == 0:
return sample_homography(
shape,
perspective,
scaling,
rotation,
translation,
n_scales,
n_angles,
scaling_amplitude,
perspective_amplitude_x,
perspective_amplitude_y,
patch_ratio,
max_angle,
allow_artifacts,
translation_overflow,
)
idx = valid[np.random.uniform(0.0, valid.shape[0], ()).astype(np.int32)]
pts2 = scaled[idx]
# Additionally save and return the selected scale.
selected_scale = scales[idx]
# Random translation
if translation:
t_min, t_max = np.min(pts2, axis=0), np.min(1 - pts2, axis=0)
if allow_artifacts:
t_min += translation_overflow
t_max += translation_overflow
pts2 += (
np.stack(
[
np.random.uniform(-t_min[0], t_max[0], ()),
np.random.uniform(-t_min[1], t_max[1], ()),
]
)
)[None, ...]
# Random rotation: sample several rotations, check collision with borders,
# randomly pick a valid one
if rotation:
angles = np.linspace(-max_angle, max_angle, n_angles)
# in case no rotation is valid
angles = np.concatenate([[0.0], angles], axis=0)
center = np.mean(pts2, axis=0, keepdims=True)
rot_mat = np.reshape(
np.stack(
[np.cos(angles), -np.sin(angles), np.sin(angles), np.cos(angles)],
axis=1,
),
[-1, 2, 2],
)
rotated = (
np.matmul(
np.tile((pts2 - center)[None, ...], [n_angles + 1, 1, 1]), rot_mat
)
+ center
)
if allow_artifacts:
# All angles are valid, except angle=0
valid = np.array(range(n_angles))
else:
valid = np.where(np.all((rotated >= 0.0) & (rotated < 1.0), axis=(1, 2)))[0]
if valid.shape[0] == 0:
return sample_homography(
shape,
perspective,
scaling,
rotation,
translation,
n_scales,
n_angles,
scaling_amplitude,
perspective_amplitude_x,
perspective_amplitude_y,
patch_ratio,
max_angle,
allow_artifacts,
translation_overflow,
)
idx = valid[np.random.uniform(0.0, valid.shape[0], ()).astype(np.int32)]
pts2 = rotated[idx]
# Rescale to actual size
shape = shape[::-1].astype(np.float32) # different convention [y, x]
pts1 *= shape[None, ...]
pts2 *= shape[None, ...]
def ax(p, q):
return [p[0], p[1], 1, 0, 0, 0, -p[0] * q[0], -p[1] * q[0]]
def ay(p, q):
return [0, 0, 0, p[0], p[1], 1, -p[0] * q[1], -p[1] * q[1]]
a_mat = np.stack([f(pts1[i], pts2[i]) for i in range(4) for f in (ax, ay)], axis=0)
p_mat = np.transpose(
np.stack([[pts2[i][j] for i in range(4) for j in range(2)]], axis=0)
)
homo_vec, _, _, _ = np.linalg.lstsq(a_mat, p_mat, rcond=None)
# Compose the homography vector back to matrix
homo_mat = np.concatenate(
[
homo_vec[0:3, 0][None, ...],
homo_vec[3:6, 0][None, ...],
np.concatenate((homo_vec[6], homo_vec[7], [1]), axis=0)[None, ...],
],
axis=0,
)
return homo_mat, selected_scale
def convert_to_line_segments(junctions, line_map):
"""Convert junctions and line map to line segments."""
# Copy the line map
line_map_tmp = copy.copy(line_map)
line_segments = np.zeros([0, 4])
for idx in range(junctions.shape[0]):
# If no connectivity, just skip it
if line_map_tmp[idx, :].sum() == 0:
continue
# Record the line segment
else:
for idx2 in np.where(line_map_tmp[idx, :] == 1)[0]:
p1 = junctions[idx, :]
p2 = junctions[idx2, :]
line_segments = np.concatenate(
(line_segments, np.array([p1[0], p1[1], p2[0], p2[1]])[None, ...]),
axis=0,
)
# Update line_map
line_map_tmp[idx, idx2] = 0
line_map_tmp[idx2, idx] = 0
return line_segments
def compute_valid_mask(image_size, homography, border_margin, valid_mask=None):
# Warp the mask
if valid_mask is None:
initial_mask = np.ones(image_size)
else:
initial_mask = valid_mask
mask = cv2.warpPerspective(
initial_mask,
homography,
(image_size[1], image_size[0]),
flags=cv2.INTER_NEAREST,
)
# Optionally perform erosion
if border_margin > 0:
kernel = cv2.getStructuringElement(cv2.MORPH_ELLIPSE, (border_margin * 2,) * 2)
mask = cv2.erode(mask, kernel)
# Perform dilation if border_margin is negative
if border_margin < 0:
kernel = cv2.getStructuringElement(
cv2.MORPH_ELLIPSE, (abs(int(border_margin)) * 2,) * 2
)
mask = cv2.dilate(mask, kernel)
return mask
def warp_line_segment(line_segments, homography, image_size):
"""Warp the line segments using a homography."""
# Separate the line segements into 2N points to apply matrix operation
num_segments = line_segments.shape[0]
junctions = np.concatenate(
(
line_segments[:, :2], # The first junction of each segment.
line_segments[:, 2:],
), # The second junction of each segment.
axis=0,
)
# Convert to homogeneous coordinates
# Flip the junctions before converting to homogeneous (xy format)
junctions = np.flip(junctions, axis=1)
junctions = np.concatenate((junctions, np.ones([2 * num_segments, 1])), axis=1)
warped_junctions = np.matmul(homography, junctions.T).T
# Convert back to segments
warped_junctions = warped_junctions[:, :2] / warped_junctions[:, 2:]
# (Convert back to hw format)
warped_junctions = np.flip(warped_junctions, axis=1)
warped_segments = np.concatenate(
(warped_junctions[:num_segments, :], warped_junctions[num_segments:, :]), axis=1
)
# Check the intersections with the boundary
warped_segments_new = np.zeros([0, 4])
image_poly = shapely.geometry.Polygon(
[
[0, 0],
[image_size[1] - 1, 0],
[image_size[1] - 1, image_size[0] - 1],
[0, image_size[0] - 1],
]
)
for idx in range(warped_segments.shape[0]):
# Get the line segment
seg_raw = warped_segments[idx, :] # in HW format.
# Convert to shapely line (flip to xy format)
seg = shapely.geometry.LineString([np.flip(seg_raw[:2]), np.flip(seg_raw[2:])])
# The line segment is just inside the image.
if seg.intersection(image_poly) == seg:
warped_segments_new = np.concatenate(
(warped_segments_new, seg_raw[None, ...]), axis=0
)
# Intersect with the image.
elif seg.intersects(image_poly):
# Check intersection
try:
p = np.array(seg.intersection(image_poly).coords).reshape([-1, 4])
# If intersect at exact one point, just continue.
except:
continue
segment = np.concatenate([np.flip(p[0, :2]), np.flip(p[0, 2:], axis=0)])[
None, ...
]
warped_segments_new = np.concatenate((warped_segments_new, segment), axis=0)
else:
continue
warped_segments = (np.round(warped_segments_new)).astype(np.int)
return warped_segments
class homography_transform(object):
"""# Homography transformations."""
def __init__(self, image_size, homograpy_config, border_margin=0, min_label_len=20):
self.homo_config = homograpy_config
self.image_size = image_size
self.target_size = (self.image_size[1], self.image_size[0])
self.border_margin = border_margin
if (min_label_len < 1) and isinstance(min_label_len, float):
raise ValueError("[Error] min_label_len should be in pixels.")
self.min_label_len = min_label_len
def __call__(
self, input_image, junctions, line_map, valid_mask=None, homo=None, scale=None
):
# Sample one random homography or use the given one
if homo is None or scale is None:
homo, scale = sample_homography(self.image_size, **self.homo_config)
# Warp the image
warped_image = cv2.warpPerspective(
input_image, homo, self.target_size, flags=cv2.INTER_LINEAR
)
valid_mask = compute_valid_mask(
self.image_size, homo, self.border_margin, valid_mask
)
# Convert junctions and line_map back to line segments
line_segments = convert_to_line_segments(junctions, line_map)
# Warp the segments and check the length.
# Adjust the min_label_length
warped_segments = warp_line_segment(line_segments, homo, self.image_size)
# Convert back to junctions and line_map
junctions_new = np.concatenate(
(warped_segments[:, :2], warped_segments[:, 2:]), axis=0
)
if junctions_new.shape[0] == 0:
junctions_new = np.zeros([0, 2])
line_map = np.zeros([0, 0])
warped_heatmap = np.zeros(self.image_size)
else:
junctions_new = np.unique(junctions_new, axis=0)
# Generate line map from points and segments
line_map = get_line_map(junctions_new, warped_segments).astype(np.int)
# Compute the heatmap
warped_heatmap = get_line_heatmap(
np.flip(junctions_new, axis=1), line_map, self.image_size
)
return {
"junctions": junctions_new,
"warped_image": warped_image,
"valid_mask": valid_mask,
"line_map": line_map,
"warped_heatmap": warped_heatmap,
"homo": homo,
"scale": scale,
}
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