Midas_loss scale and shift invariant loss

import torch import torch.nn as nn def compute_scale_and_shift(prediction, target, mask): # system matrix: A = [[a_00, a_01], [a_10, a_11]] a_00 = torch.sum(mask * prediction * prediction, (1, 2)) a_01 = torch.sum(mask * prediction, (1, 2)) a_11 = torch.sum(mask, (1, 2)) # right hand side: b = [b_0, b_1] b_0 = torch.sum(mask * prediction * target, (1, 2)) b_1 = torch.sum(mask * target, (1, 2)) # solution: x = A^-1 . b = [[a_11, -a_01], [-a_10, a_00]] / (a_00 * a_11 - a_01 * a_10) . b x_0 = torch.zeros_like(b_0) x_1 = torch.zeros_like(b_1) det = a_00 * a_11 - a_01 * a_01 valid = det.nonzero() x_0[valid] = (a_11[valid] * b_0[valid] - a_01[valid] * b_1[valid]) / det[valid] x_1[valid] = (-a_01[valid] * b_0[valid] + a_00[valid] * b_1[valid]) / det[valid] return x_0, x_1 def reduction_batch_based(image_loss, M): # average of all valid pixels of the batch # avoid division by 0 (if sum(M) = sum(sum(mask)) = 0: sum(image_loss) = 0) divisor = torch.sum(M) if divisor == 0: return 0 else: return torch.sum(image_loss) / divisor def reduction_image_based(image_loss, M): # mean of average of valid pixels of an image # avoid division by 0 (if M = sum(mask) = 0: image_loss = 0) valid = M.nonzero() image_loss[valid] = image_loss[valid] / M[valid] return torch.mean(image_loss) def mse_loss(prediction, target, mask, reduction=reduction_batch_based): M = torch.sum(mask, (1, 2)) res = prediction - target image_loss = torch.sum(mask * res * res, (1, 2)) return reduction(image_loss, 2 * M) def gradient_loss(prediction, target, mask, reduction=reduction_batch_based): M = torch.sum(mask, (1, 2)) diff = prediction - target diff = torch.mul(mask, diff) grad_x = torch.abs(diff[:, :, 1:] - diff[:, :, :-1]) mask_x = torch.mul(mask[:, :, 1:], mask[:, :, :-1]) grad_x = torch.mul(mask_x, grad_x) grad_y = torch.abs(diff[:, 1:, :] - diff[:, :-1, :]) mask_y = torch.mul(mask[:, 1:, :], mask[:, :-1, :]) grad_y = torch.mul(mask_y, grad_y) image_loss = torch.sum(grad_x, (1, 2)) + torch.sum(grad_y, (1, 2)) return reduction(image_loss, M) class MSELoss(nn.Module): def __init__(self, reduction='batch-based'): super().__init__() if reduction == 'batch-based': self.__reduction = reduction_batch_based else: self.__reduction = reduction_image_based def forward(self, prediction, target, mask): return mse_loss(prediction, target, mask, reduction=self.__reduction) class GradientLoss(nn.Module): def __init__(self, scales=4, reduction='batch-based'): super().__init__() if reduction == 'batch-based': self.__reduction = reduction_batch_based else: self.__reduction = reduction_image_based self.__scales = scales def forward(self, prediction, target, mask): total = 0 for scale in range(self.__scales): step = pow(2, scale) total += gradient_loss(prediction[:, ::step, ::step], target[:, ::step, ::step], mask[:, ::step, ::step], reduction=self.__reduction) return total class ScaleAndShiftInvariantLoss(nn.Module): def __init__(self, alpha=0.5, scales=4, reduction='batch-based'): super().__init__() self.__data_loss = MSELoss(reduction=reduction) self.__regularization_loss = GradientLoss(scales=scales, reduction=reduction) self.__alpha = alpha self.__prediction_ssi = None def forward(self, prediction, target, mask): scale, shift = compute_scale_and_shift(prediction, target, mask) self.__prediction_ssi = scale.view(-1, 1, 1) * prediction + shift.view(-1, 1, 1) total = self.__data_loss(self.__prediction_ssi, target, mask) if self.__alpha > 0: total += self.__alpha * self.__regularization_loss(self.__prediction_ssi, target, mask) return total def __get_prediction_ssi(self): return self.__prediction_ssi prediction_ssi = property(__get_prediction_ssi)