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import math
import numpy as np
import torch
def cubic(x):
"""cubic function used for calculate_weights_indices."""
absx = torch.abs(x)
absx2 = absx**2
absx3 = absx**3
return (1.5 * absx3 - 2.5 * absx2 + 1) * (
(absx <= 1).type_as(absx)) + (-0.5 * absx3 + 2.5 * absx2 - 4 * absx + 2) * (((absx > 1) *
(absx <= 2)).type_as(absx))
def calculate_weights_indices(in_length, out_length, scale, kernel, kernel_width, antialiasing):
"""Calculate weights and indices, used for imresize function.
Args:
in_length (int): Input length.
out_length (int): Output length.
scale (float): Scale factor.
kernel_width (int): Kernel width.
antialisaing (bool): Whether to apply anti-aliasing when downsampling.
"""
if (scale < 1) and antialiasing:
# Use a modified kernel (larger kernel width) to simultaneously
# interpolate and antialias
kernel_width = kernel_width / scale
# Output-space coordinates
x = torch.linspace(1, out_length, out_length)
# Input-space coordinates. Calculate the inverse mapping such that 0.5
# in output space maps to 0.5 in input space, and 0.5 + scale in output
# space maps to 1.5 in input space.
u = x / scale + 0.5 * (1 - 1 / scale)
# What is the left-most pixel that can be involved in the computation?
left = torch.floor(u - kernel_width / 2)
# What is the maximum number of pixels that can be involved in the
# computation? Note: it's OK to use an extra pixel here; if the
# corresponding weights are all zero, it will be eliminated at the end
# of this function.
p = math.ceil(kernel_width) + 2
# The indices of the input pixels involved in computing the k-th output
# pixel are in row k of the indices matrix.
indices = left.view(out_length, 1).expand(out_length, p) + torch.linspace(0, p - 1, p).view(1, p).expand(
out_length, p)
# The weights used to compute the k-th output pixel are in row k of the
# weights matrix.
distance_to_center = u.view(out_length, 1).expand(out_length, p) - indices
# apply cubic kernel
if (scale < 1) and antialiasing:
weights = scale * cubic(distance_to_center * scale)
else:
weights = cubic(distance_to_center)
# Normalize the weights matrix so that each row sums to 1.
weights_sum = torch.sum(weights, 1).view(out_length, 1)
weights = weights / weights_sum.expand(out_length, p)
# If a column in weights is all zero, get rid of it. only consider the
# first and last column.
weights_zero_tmp = torch.sum((weights == 0), 0)
if not math.isclose(weights_zero_tmp[0], 0, rel_tol=1e-6):
indices = indices.narrow(1, 1, p - 2)
weights = weights.narrow(1, 1, p - 2)
if not math.isclose(weights_zero_tmp[-1], 0, rel_tol=1e-6):
indices = indices.narrow(1, 0, p - 2)
weights = weights.narrow(1, 0, p - 2)
weights = weights.contiguous()
indices = indices.contiguous()
sym_len_s = -indices.min() + 1
sym_len_e = indices.max() - in_length
indices = indices + sym_len_s - 1
return weights, indices, int(sym_len_s), int(sym_len_e)
@torch.no_grad()
def imresize(img, scale, antialiasing=True):
"""imresize function same as MATLAB.
It now only supports bicubic.
The same scale applies for both height and width.
Args:
img (Tensor | Numpy array):
Tensor: Input image with shape (c, h, w), [0, 1] range.
Numpy: Input image with shape (h, w, c), [0, 1] range.
scale (float): Scale factor. The same scale applies for both height
and width.
antialisaing (bool): Whether to apply anti-aliasing when downsampling.
Default: True.
Returns:
Tensor: Output image with shape (c, h, w), [0, 1] range, w/o round.
"""
squeeze_flag = False
if type(img).__module__ == np.__name__: # numpy type
numpy_type = True
if img.ndim == 2:
img = img[:, :, None]
squeeze_flag = True
img = torch.from_numpy(img.transpose(2, 0, 1)).float()
else:
numpy_type = False
if img.ndim == 2:
img = img.unsqueeze(0)
squeeze_flag = True
in_c, in_h, in_w = img.size()
out_h, out_w = math.ceil(in_h * scale), math.ceil(in_w * scale)
kernel_width = 4
kernel = 'cubic'
# get weights and indices
weights_h, indices_h, sym_len_hs, sym_len_he = calculate_weights_indices(in_h, out_h, scale, kernel, kernel_width,
antialiasing)
weights_w, indices_w, sym_len_ws, sym_len_we = calculate_weights_indices(in_w, out_w, scale, kernel, kernel_width,
antialiasing)
# process H dimension
# symmetric copying
img_aug = torch.FloatTensor(in_c, in_h + sym_len_hs + sym_len_he, in_w)
img_aug.narrow(1, sym_len_hs, in_h).copy_(img)
sym_patch = img[:, :sym_len_hs, :]
inv_idx = torch.arange(sym_patch.size(1) - 1, -1, -1).long()
sym_patch_inv = sym_patch.index_select(1, inv_idx)
img_aug.narrow(1, 0, sym_len_hs).copy_(sym_patch_inv)
sym_patch = img[:, -sym_len_he:, :]
inv_idx = torch.arange(sym_patch.size(1) - 1, -1, -1).long()
sym_patch_inv = sym_patch.index_select(1, inv_idx)
img_aug.narrow(1, sym_len_hs + in_h, sym_len_he).copy_(sym_patch_inv)
out_1 = torch.FloatTensor(in_c, out_h, in_w)
kernel_width = weights_h.size(1)
for i in range(out_h):
idx = int(indices_h[i][0])
for j in range(in_c):
out_1[j, i, :] = img_aug[j, idx:idx + kernel_width, :].transpose(0, 1).mv(weights_h[i])
# process W dimension
# symmetric copying
out_1_aug = torch.FloatTensor(in_c, out_h, in_w + sym_len_ws + sym_len_we)
out_1_aug.narrow(2, sym_len_ws, in_w).copy_(out_1)
sym_patch = out_1[:, :, :sym_len_ws]
inv_idx = torch.arange(sym_patch.size(2) - 1, -1, -1).long()
sym_patch_inv = sym_patch.index_select(2, inv_idx)
out_1_aug.narrow(2, 0, sym_len_ws).copy_(sym_patch_inv)
sym_patch = out_1[:, :, -sym_len_we:]
inv_idx = torch.arange(sym_patch.size(2) - 1, -1, -1).long()
sym_patch_inv = sym_patch.index_select(2, inv_idx)
out_1_aug.narrow(2, sym_len_ws + in_w, sym_len_we).copy_(sym_patch_inv)
out_2 = torch.FloatTensor(in_c, out_h, out_w)
kernel_width = weights_w.size(1)
for i in range(out_w):
idx = int(indices_w[i][0])
for j in range(in_c):
out_2[j, :, i] = out_1_aug[j, :, idx:idx + kernel_width].mv(weights_w[i])
if squeeze_flag:
out_2 = out_2.squeeze(0)
if numpy_type:
out_2 = out_2.numpy()
if not squeeze_flag:
out_2 = out_2.transpose(1, 2, 0)
return out_2
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