| import torch |
| import math |
| 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_bias(sz: torch.Tensor, ctr_point: torch.Tensor, centered = True) -> torch.Tensor: |
| """2D cosine window.""" |
| distance = torch.stack([ctr_point, sz-ctr_point], dim=0) |
| max_distance, _ = distance.max(dim=0) |
|
|
| hann1d_x = hann1d(max_distance[0].item() * 2, centered) |
| hann1d_x = hann1d_x[max_distance[0] - distance[0, 0]: max_distance[0] + distance[1, 0]] |
| hann1d_y = hann1d(max_distance[1].item() * 2, centered) |
| hann1d_y = hann1d_y[max_distance[1] - distance[0, 1]: max_distance[1] + distance[1, 1]] |
|
|
| return hann1d_y.reshape(1, 1, -1, 1) * hann1d_x.reshape(1, 1, 1, -1) |
|
|
|
|
|
|
| def hann2d_clipped(sz: torch.Tensor, effective_sz: torch.Tensor, centered = True) -> torch.Tensor: |
| """1D clipped cosine window.""" |
|
|
| |
| 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 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 |
|
|
