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cross_correlation.py
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from math import ceil
import numpy as np
from skimage.transform.integral import integral_image as integral
import torch
import torch.nn.functional as F
def xcorr(img_1, img_2, half_width):
"""
Cross-Correlation Field computation.
Parameters
----------
img_1 : Numpy Array
First image on which calculate the cross-correlation. Dimensions: H, W
img_2 : Numpy Array
Second image on which calculate the cross-correlation. Dimensions: H, W
half_width : int
The semi-size of the window on which calculate the cross-correlation
Return
------
L : Numpy array
The cross-correlation map between img_1 and img_2
"""
w = ceil(half_width)
ep = 1e-20
if (len(img_1.shape)) != 3:
img_1 = np.expand_dims(img_1, axis=-1)
if (len(img_2.shape)) != 3:
img_2 = np.expand_dims(img_2, axis=-1)
img_1 = np.pad(img_1.astype(np.float64), ((w, w), (w, w), (0, 0)))
img_2 = np.pad(img_2.astype(np.float64), ((w, w), (w, w), (0, 0)))
img_1_cum = np.zeros(img_1.shape)
img_2_cum = np.zeros(img_2.shape)
for i in range(img_1.shape[-1]):
img_1_cum[:, :, i] = integral(img_1[:, :, i]).astype(np.float64)
for i in range(img_2.shape[-1]):
img_2_cum[:, :, i] = integral(img_2[:, :, i]).astype(np.float64)
img_1_mu = (img_1_cum[2*w:, 2*w:, :] - img_1_cum[:-2*w, 2*w:, :] - img_1_cum[2*w:, :-2*w, :] + img_1_cum[:-2*w, :-2*w, :]) / (4*w**2)
img_2_mu = (img_2_cum[2*w:, 2*w:, :] - img_2_cum[:-2*w, 2*w:, :] - img_2_cum[2*w:, :-2*w, :] + img_2_cum[:-2*w, :-2*w, :]) / (4*w**2)
img_1 = img_1[w:-w, w:-w, :] - img_1_mu
img_2 = img_2[w:-w, w:-w, :] - img_2_mu
img_1 = np.pad(img_1.astype(np.float64), ((w, w), (w, w), (0, 0)))
img_2 = np.pad(img_2.astype(np.float64), ((w, w), (w, w), (0, 0)))
i2 = img_1**2
j2 = img_2**2
ij = img_1*img_2
i2_cum = np.zeros(i2.shape)
j2_cum = np.zeros(j2.shape)
ij_cum = np.zeros(ij.shape)
for i in range(i2_cum.shape[-1]):
i2_cum[:, :, i] = integral(i2[:, :, i]).astype(np.float64)
for i in range(j2_cum.shape[-1]):
j2_cum[:, :, i] = integral(j2[:, :, i]).astype(np.float64)
for i in range(ij_cum.shape[-1]):
ij_cum[:, :, i] = integral(ij[:, :, i]).astype(np.float64)
sig2_ij_tot = (ij_cum[2*w:, 2*w:, :] - ij_cum[:-2*w, 2*w:, :] - ij_cum[2*w:, :-2*w, :] + ij_cum[:-2*w, :-2*w, :])
sig2_ii_tot = (i2_cum[2*w:, 2*w:, :] - i2_cum[:-2*w, 2*w:, :] - i2_cum[2*w:, :-2*w, :] + i2_cum[:-2*w, :-2*w, :])
sig2_jj_tot = (j2_cum[2*w:, 2*w:, :] - j2_cum[:-2*w, 2*w:, :] - j2_cum[2*w:, :-2*w, :] + j2_cum[:-2*w, :-2*w, :])
sig2_ij_tot = np.clip(sig2_ij_tot, ep, sig2_ij_tot.max())
sig2_ii_tot = np.clip(sig2_ii_tot, ep, sig2_ii_tot.max())
sig2_jj_tot = np.clip(sig2_jj_tot, ep, sig2_jj_tot.max())
L = sig2_ij_tot / ((sig2_ii_tot*sig2_jj_tot)**0.5 + ep)
return L
def xcorr_torch(img_1, img_2, half_width, device):
"""
A PyTorch implementation of Cross-Correlation Field computation.
Parameters
----------
img_1 : Torch Tensor
First image on which calculate the cross-correlation. Dimensions: 1, 1, H, W
img_2 : Torch Tensor
Second image on which calculate the cross-correlation. Dimensions: 1, 1, H, W
half_width : int
The semi-size of the window on which calculate the cross-correlation
device : Torch Device
The device on which perform the operation.
Return
------
L : Torch Tensor
The cross-correlation map between img_1 and img_2
"""
w = ceil(half_width)
ep = 1e-20
img_1 = img_1.type(torch.DoubleTensor)
img_2 = img_2.type(torch.DoubleTensor)
img_1 = img_1.to(device)
img_2 = img_2.to(device)
img_1 = F.pad(img_1, (w, w, w, w))
img_2 = F.pad(img_2, (w, w, w, w))
img_1_cum = torch.cumsum(torch.cumsum(img_1, dim=-1), dim=-2)
img_2_cum = torch.cumsum(torch.cumsum(img_2, dim=-1), dim=-2)
img_1_mu = (img_1_cum[:, :, 2*w:, 2*w:] - img_1_cum[:, :, :-2*w, 2*w:] - img_1_cum[:, :, 2*w:, :-2*w] + img_1_cum[:, :, :-2*w, :-2*w]) / (4*w**2)
img_2_mu = (img_2_cum[:, :, 2*w:, 2*w:] - img_2_cum[:, :, :-2*w, 2*w:] - img_2_cum[:, :, 2*w:, :-2*w] + img_2_cum[:, :, :-2*w, :-2*w]) / (4*w**2)
img_1 = img_1[:, :, w:-w, w:-w] - img_1_mu
img_2 = img_2[:, :, w:-w, w:-w] - img_2_mu
img_1 = F.pad(img_1, (w, w, w, w))
img_2 = F.pad(img_2, (w, w, w, w))
i2_cum = torch.cumsum(torch.cumsum(img_1**2, dim=-1), dim=-2)
j2_cum = torch.cumsum(torch.cumsum(img_2**2, dim=-1), dim=-2)
ij_cum = torch.cumsum(torch.cumsum(img_1*img_2, dim=-1), dim=-2)
sig2_ij_tot = (ij_cum[:, :, 2*w:, 2*w:] - ij_cum[:, :, :-2*w, 2*w:] - ij_cum[:, :, 2*w:, :-2*w] + ij_cum[:, :, :-2*w, :-2*w])
sig2_ii_tot = (i2_cum[:, :, 2*w:, 2*w:] - i2_cum[:, :, :-2*w, 2*w:] - i2_cum[:, :, 2*w:, :-2*w] + i2_cum[:, :, :-2*w, :-2*w])
sig2_jj_tot = (j2_cum[:, :, 2*w:, 2*w:] - j2_cum[:, :, :-2*w, 2*w:] - j2_cum[:, :, 2*w:, :-2*w] + j2_cum[:, :, :-2*w, :-2*w])
sig2_ij_tot = torch.clip(sig2_ij_tot, ep, sig2_ij_tot.max().item())
sig2_ii_tot = torch.clip(sig2_ii_tot, ep, sig2_ii_tot.max().item())
sig2_jj_tot = torch.clip(sig2_jj_tot, ep, sig2_jj_tot.max().item())
L = sig2_ij_tot / ((sig2_ii_tot * sig2_jj_tot) ** 0.5 + ep)
return L