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dcf.py
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dcf.py
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import torch
import math
from pytracking import fourier
from pytracking import complex
import torch.nn.functional as F
def hann1d(sz: int, centered = True) -> torch.Tensor:
"""1D cosine window."""
if centered:
return 0.5 * (1 - torch.cos((2 * math.pi / (sz + 1)) * torch.arange(1, sz + 1).float()))
w = 0.5 * (1 + torch.cos((2 * math.pi / (sz + 2)) * torch.arange(0, sz//2 + 1).float()))
return torch.cat([w, w[1:sz-sz//2].flip((0,))])
def hann2d(sz: torch.Tensor, centered = True) -> torch.Tensor:
"""2D cosine window."""
return hann1d(sz[0].item(), centered).reshape(1, 1, -1, 1) * hann1d(sz[1].item(), centered).reshape(1, 1, 1, -1)
def hann2d_clipped(sz: torch.Tensor, effective_sz: torch.Tensor, centered = True) -> torch.Tensor:
"""1D clipped cosine window."""
# Ensure that the difference is even
effective_sz += (effective_sz - sz) % 2
effective_window = hann1d(effective_sz[0].item(), True).reshape(1, 1, -1, 1) * hann1d(effective_sz[1].item(), True).reshape(1, 1, 1, -1)
pad = (sz - effective_sz) / 2
window = F.pad(effective_window, (pad[1].item(), pad[1].item(), pad[0].item(), pad[0].item()), 'replicate')
if centered:
return window
else:
mid = (sz / 2).int()
window_shift_lr = torch.cat((window[:, :, :, mid[1]:], window[:, :, :, :mid[1]]), 3)
return torch.cat((window_shift_lr[:, :, mid[0]:, :], window_shift_lr[:, :, :mid[0], :]), 2)
def gauss_fourier(sz: int, sigma: float, half: bool = False) -> torch.Tensor:
if half:
k = torch.arange(0, int(sz/2+1))
else:
k = torch.arange(-int((sz-1)/2), int(sz/2+1))
return (math.sqrt(2*math.pi) * sigma / sz) * torch.exp(-2 * (math.pi * sigma * k.float() / sz)**2)
def gauss_spatial(sz, sigma, center=0, end_pad=0):
k = torch.arange(-(sz-1)/2, (sz+1)/2+end_pad)
return torch.exp(-1.0/(2*sigma**2) * (k - center)**2)
def label_function(sz: torch.Tensor, sigma: torch.Tensor):
return gauss_fourier(sz[0].item(), sigma[0].item()).reshape(1, 1, -1, 1) * gauss_fourier(sz[1].item(), sigma[1].item(), True).reshape(1, 1, 1, -1)
def label_function_spatial(sz: torch.Tensor, sigma: torch.Tensor, center: torch.Tensor = torch.zeros(2), end_pad: torch.Tensor = torch.zeros(2)):
"""The origin is in the middle of the image."""
return gauss_spatial(sz[0].item(), sigma[0].item(), center[0], end_pad[0].item()).reshape(1, 1, -1, 1) * \
gauss_spatial(sz[1].item(), sigma[1].item(), center[1], end_pad[1].item()).reshape(1, 1, 1, -1)
def cubic_spline_fourier(f, a):
"""The continuous Fourier transform of a cubic spline kernel."""
bf = (6*(1 - torch.cos(2 * math.pi * f)) + 3*a*(1 - torch.cos(4 * math.pi * f))
- (6 + 8*a)*math.pi*f*torch.sin(2 * math.pi * f) - 2*a*math.pi*f*torch.sin(4 * math.pi * f)) \
/ (4 * math.pi**4 * f**4)
bf[f == 0] = 1
return bf
def get_interp_fourier(sz: torch.Tensor, method='ideal', bicubic_param=0.5, centering=True, windowing=False, device='cpu'):
ky, kx = fourier.get_frequency_coord(sz)
if method=='ideal':
interp_y = torch.ones(ky.shape) / sz[0]
interp_x = torch.ones(kx.shape) / sz[1]
elif method=='bicubic':
interp_y = cubic_spline_fourier(ky / sz[0], bicubic_param) / sz[0]
interp_x = cubic_spline_fourier(kx / sz[1], bicubic_param) / sz[1]
else:
raise ValueError('Unknown method.')
if centering:
interp_y = complex.mult(interp_y, complex.exp_imag((-math.pi/sz[0]) * ky))
interp_x = complex.mult(interp_x, complex.exp_imag((-math.pi/sz[1]) * kx))
if windowing:
raise NotImplementedError
return interp_y.to(device), interp_x.to(device)
def interpolate_dft(a: torch.Tensor, interp_fs) -> torch.Tensor:
if isinstance(interp_fs, torch.Tensor):
return complex.mult(a, interp_fs)
if isinstance(interp_fs, (tuple, list)):
return complex.mult(complex.mult(a, interp_fs[0]), interp_fs[1])
raise ValueError('"interp_fs" must be tensor or tuple of tensors.')
def get_reg_filter(sz: torch.Tensor, target_sz: torch.Tensor, params):
"""Computes regularization filter in CCOT and ECO."""
if not params.use_reg_window:
return params.reg_window_min * torch.ones(1,1,1,1)
if getattr(params, 'reg_window_square', False):
target_sz = target_sz.prod().sqrt() * torch.ones(2)
# Normalization factor
reg_scale = 0.5 * target_sz
# Construct grid
if getattr(params, 'reg_window_centered', True):
wrg = torch.arange(-int((sz[0]-1)/2), int(sz[0]/2+1), dtype=torch.float32).view(1,1,-1,1)
wcg = torch.arange(-int((sz[1]-1)/2), int(sz[1]/2+1), dtype=torch.float32).view(1,1,1,-1)
else:
wrg = torch.cat([torch.arange(0, int(sz[0]/2+1), dtype=torch.float32),
torch.arange(-int((sz[0] - 1) / 2), 0, dtype=torch.float32)]).view(1,1,-1,1)
wcg = torch.cat([torch.arange(0, int(sz[1]/2+1), dtype=torch.float32),
torch.arange(-int((sz[1] - 1) / 2), 0, dtype=torch.float32)]).view(1,1,1,-1)
# Construct regularization window
reg_window = (params.reg_window_edge - params.reg_window_min) * \
(torch.abs(wrg/reg_scale[0])**params.reg_window_power +
torch.abs(wcg/reg_scale[1])**params.reg_window_power) + params.reg_window_min
# Compute DFT and enforce sparsity
reg_window_dft = torch.rfft(reg_window, 2) / sz.prod()
reg_window_dft_abs = complex.abs(reg_window_dft)
reg_window_dft[reg_window_dft_abs < params.reg_sparsity_threshold * reg_window_dft_abs.max(), :] = 0
# Do the inverse transform to correct for the window minimum
reg_window_sparse = torch.irfft(reg_window_dft, 2, signal_sizes=sz.long().tolist())
reg_window_dft[0,0,0,0,0] += params.reg_window_min - sz.prod() * reg_window_sparse.min()
reg_window_dft = complex.real(fourier.rfftshift2(reg_window_dft))
# Remove zeros
max_inds,_ = reg_window_dft.nonzero().max(dim=0)
mid_ind = int((reg_window_dft.shape[2]-1)/2)
top = max_inds[-2].item() + 1
bottom = 2*mid_ind - max_inds[-2].item()
right = max_inds[-1].item() + 1
reg_window_dft = reg_window_dft[..., bottom:top, :right]
if reg_window_dft.shape[-1] > 1:
reg_window_dft = torch.cat([reg_window_dft[..., 1:].flip((2, 3)), reg_window_dft], -1)
return reg_window_dft
def max2d(a: torch.Tensor) -> (torch.Tensor, torch.Tensor):
"""Computes maximum and argmax in the last two dimensions."""
max_val_row, argmax_row = torch.max(a, dim=-2)
max_val, argmax_col = torch.max(max_val_row, dim=-1)
argmax_row = argmax_row.view(argmax_col.numel(),-1)[torch.arange(argmax_col.numel()), argmax_col.view(-1)]
argmax_row = argmax_row.reshape(argmax_col.shape)
argmax = torch.cat((argmax_row.unsqueeze(-1), argmax_col.unsqueeze(-1)), -1)
return max_val, argmax