def reconstruct(self, coeff):
if self.nbands != len(coeff[1]):
raise Exception("Unmatched number of orientations")
height, width = coeff[0].shape[2], coeff[0].shape[1]
log_rad, angle = math_utils.prepare_grid(height, width)
Xrcos, Yrcos = math_utils.rcosFn(1, -0.5)
Yrcos = np.sqrt(Yrcos)
YIrcos = np.sqrt(np.abs(1 - Yrcos**2))
lo0mask = pointOp(log_rad, YIrcos, Xrcos)
hi0mask = pointOp(log_rad, Yrcos, Xrcos)
# Note that we expand dims to support broadcasting later
lo0mask = torch.from_numpy(lo0mask).float()[None,:,:,None].to(self.device)
hi0mask = torch.from_numpy(hi0mask).float()[None,:,:,None].to(self.device)
# Start recursive reconstruction
tempdft = self._reconstruct_levels(coeff[1:], log_rad, Xrcos, Yrcos, angle)
hidft = torch.rfft(coeff[0], signal_ndim=2, onesided=False)
hidft = math_utils.batch_fftshift2d(hidft)
outdft = tempdft * lo0mask + hidft * hi0mask
reconstruction = math_utils.batch_ifftshift2d(outdft)
reconstruction = torch.ifft(reconstruction, signal_ndim=2)
reconstruction = torch.unbind(reconstruction, -1)[0] # real
return reconstruction
def build(self, im_batch):
''' Decomposes a batch of images into a complex steerable pyramid.
The pyramid typically has ~4 levels and 4-8 orientations.
Args:
im_batch (torch.Tensor): Batch of images of shape [N,C,H,W]
Returns:
pyramid: list containing torch.Tensor objects storing the pyramid
'''
assert im_batch.device == self.device, 'Devices invalid (pyr = {}, batch = {})'.format(self.device, im_batch.device)
assert im_batch.dtype == torch.float32, 'Image batch must be torch.float32'
assert im_batch.dim() == 4, 'Image batch must be of shape [N,C,H,W]'
assert im_batch.shape[1] == 1, 'Second dimension must be 1 encoding grayscale image'
im_batch = im_batch.squeeze(1) # flatten channels dim
height, width = im_batch.shape[2], im_batch.shape[1]
# Check whether image size is sufficient for number of levels
if self.height > int(np.floor(np.log2(min(width, height))) - 2):
raise RuntimeError('Cannot build {} levels, image too small.'.format(self.height))
# Prepare a grid
log_rad, angle = math_utils.prepare_grid(height, width)
# Radial transition function (a raised cosine in log-frequency):
Xrcos, Yrcos = math_utils.rcosFn(1, -0.5)
Yrcos = np.sqrt(Yrcos)
YIrcos = np.sqrt(1 - Yrcos**2)
lo0mask = pointOp(log_rad, YIrcos, Xrcos)
hi0mask = pointOp(log_rad, Yrcos, Xrcos)
# Note that we expand dims to support broadcasting later
lo0mask = torch.from_numpy(lo0mask).float()[None,:,:,None].to(self.device)
hi0mask = torch.from_numpy(hi0mask).float()[None,:,:,None].to(self.device)
# Fourier transform (2D) and shifting
batch_dft = torch.rfft(im_batch, signal_ndim=2, onesided=False)
batch_dft = math_utils.batch_fftshift2d(batch_dft)
# Low-pass
lo0dft = batch_dft * lo0mask
# Start recursively building the pyramids
coeff = self._build_levels(lo0dft, log_rad, angle, Xrcos, Yrcos, self.height-1)
# High-pass
hi0dft = batch_dft * hi0mask
hi0 = math_utils.batch_ifftshift2d(hi0dft)
hi0 = torch.ifft(hi0, signal_ndim=2)
hi0_real = torch.unbind(hi0, -1)[0]
coeff.insert(0, hi0_real)
return coeff
def _build_levels(self, lodft, log_rad, angle, Xrcos, Yrcos, height):
if height <= 1:
# Low-pass
lo0 = math_utils.batch_ifftshift2d(lodft)
lo0 = torch.ifft(lo0, signal_ndim=2)
lo0_real = torch.unbind(lo0, -1)[0]
coeff = [lo0_real]
else:
Xrcos = Xrcos - np.log2(self.scale_factor)
####################################################################
####################### Orientation bandpass #######################
####################################################################
himask = pointOp(log_rad, Yrcos, Xrcos)
himask = torch.from_numpy(himask[None,:,:,None]).float().to(self.device)
order = self.nbands - 1
const = np.power(2, 2*order) * np.square(factorial(order)) / (self.nbands * factorial(2*order))
#SF ADAPTATION: Modified from the below:
#Ycosn = 2*np.sqrt(const) * np.power(np.cos(self.Xcosn), order) * (np.abs(self.alpha) < np.pi/2) # [n,]
Ycosn = np.sqrt(const) * np.power(np.cos(self.Xcosn), order)
# Loop through all orientation bands
orientations = []
for b in range(self.nbands):
anglemask = pointOp(angle, Ycosn, self.Xcosn + np.pi*b/self.nbands)
anglemask = anglemask[None,:,:,None] # for broadcasting
anglemask = torch.from_numpy(anglemask).float().to(self.device)
# Bandpass filtering
banddft = lodft * anglemask * himask
# Now multiply with complex number
# (x+yi)(u+vi) = (xu-yv) + (xv+yu)i
banddft = torch.unbind(banddft, -1)
banddft_real = self.complex_fact_construct.real*banddft[0] - self.complex_fact_construct.imag*banddft[1]
banddft_imag = self.complex_fact_construct.real*banddft[1] + self.complex_fact_construct.imag*banddft[0]
banddft = torch.stack((banddft_real, banddft_imag), -1)
band = math_utils.batch_ifftshift2d(banddft)
band = torch.ifft(band, signal_ndim=2)
#SF ADAPTATION: For SF pyramid, just take real part of band.
band = band[..., 0] #Real part is first entry in last dimension
orientations.append(band)
####################################################################
######################## Subsample lowpass #########################
####################################################################
# Don't consider batch_size and imag/real dim
dims = np.array(lodft.shape[1:3])
# Both are tuples of size 2
low_ind_start = (np.ceil((dims+0.5)/2) - np.ceil((np.ceil((dims-0.5)/2)+0.5)/2)).astype(int)
low_ind_end = (low_ind_start + np.ceil((dims-0.5)/2)).astype(int)
# Subsampling indices
log_rad = log_rad[low_ind_start[0]:low_ind_end[0],low_ind_start[1]:low_ind_end[1]]
angle = angle[low_ind_start[0]:low_ind_end[0],low_ind_start[1]:low_ind_end[1]]
# Actual subsampling
lodft = lodft[:,low_ind_start[0]:low_ind_end[0],low_ind_start[1]:low_ind_end[1],:]
# Filtering
YIrcos = np.abs(np.sqrt(1 - Yrcos**2))
lomask = pointOp(log_rad, YIrcos, Xrcos)
lomask = torch.from_numpy(lomask[None,:,:,None]).float()
lomask = lomask.to(self.device)
# Convolution in spatial domain
lodft = lomask * lodft
####################################################################
####################### Recursion next level #######################
####################################################################
coeff = self._build_levels(lodft, log_rad, angle, Xrcos, Yrcos, height-1)
coeff.insert(0, orientations)
return coeff
ifft_numpy1 = np.fft.ifftshift(fft_numpy)
ifft_numpy = np.fft.ifft2(ifft_numpy1)
################################################################################
# Torch
device = torch.device('cpu')
im_torch = torch.from_numpy(im[None, :, :]) # add batch dim
im_torch = im_torch.to(device)
# fft = complex-to-complex, rfft = real-to-complex
fft_torch = torch.rfft(im_torch, signal_ndim=2, onesided=False)
fft_torch = fft_utils.batch_fftshift2d(fft_torch)
ifft_torch = fft_utils.batch_ifftshift2d(fft_torch)
ifft_torch = torch.ifft(ifft_torch, signal_ndim=2, normalized=False)
ifft_torch_to_numpy = ifft_torch.numpy()
ifft_torch_to_numpy = np.split(ifft_torch_to_numpy, 2,
-1) # complex => real/imag
ifft_torch_to_numpy = np.squeeze(ifft_torch_to_numpy, -1)
ifft_torch_to_numpy = ifft_torch_to_numpy[0] + 1j * ifft_torch_to_numpy[1]
all_close_ifft = np.allclose(ifft_numpy, ifft_torch_to_numpy, atol=tolerance)
print('ifft all close: ', all_close_ifft)
fft_torch = fft_torch.cpu().numpy().squeeze()
fft_torch = np.split(fft_torch, 2, -1) # complex => real/imag
fft_torch = np.squeeze(fft_torch, -1)
fft_torch = fft_torch[0] + 1j * fft_torch[1]