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. 2021 Nov 10;4(1):e210211. doi: 10.1148/ryai.2021210211

Figure 2:

Flow diagram of loss functions incorporated into the training of the lung deformable image registration algorithm (LungReg). Inspiratory (I) and affine-registered expiratory (E) images are propagated through a three-dimensional (3D) U-Net convolutional neural network (CNN), gw(I,E), to predict a displacement field (u). The spatial transformation is then applied to affine-registered expiratory images using a spatial transformer to deformably register expiratory images to inspiratory images. Four loss function components point to the U-Net because they are used to optimize U-Net weights: cross-correlation for image similarity (ℒCC), displacement regularization for smooth deformations (ℒφ), Dice overlap score for alignment of anatomic structures (ℒseg), and percentage of voxels with nonpositive Jacobian determinants (ℒjac) to encourage transformation invertibility. Note the segmentations are only used during LungReg training and are not required during inference time. Black lines = forward propagation, blue lines = spatial transformations, orange lines = loss functions, ϕ = spatial transformation function.

Flow diagram of loss functions incorporated into the training of the lung deformable image registration algorithm (LungReg). Inspiratory (I) and affine-registered expiratory (E) images are propagated through a three-dimensional (3D) U-Net convolutional neural network (CNN), gw(I,E), to predict a displacement field (u). The spatial transformation is then applied to affine-registered expiratory images using a spatial transformer to deformably register expiratory images to inspiratory images. Four loss function components point to the U-Net because they are used to optimize U-Net weights: cross-correlation for image similarity (ℒCC), displacement regularization for smooth deformations (ℒφ), Dice overlap score for alignment of anatomic structures (ℒseg), and percentage of voxels with nonpositive Jacobian determinants (ℒjac) to encourage transformation invertibility. Note the segmentations are only used during LungReg training and are not required during inference time. Black lines = forward propagation, blue lines = spatial transformations, orange lines = loss functions, ϕ = spatial transformation function.