Medical Image Registration and Alignment

Module: Healthcare AI | Difficulty: Advanced

Deformation Energy

Similarity Metric (MI)

B-Spline Deformation

Registration Accuracy Metrics

| Metric | Rigid | Affine | Deformable | DL-based | |--------|-------|--------|------------|----------| | TRE (mm) | 5.2 | 3.8 | 1.5 | 1.2 | | Dice | 0.78 | 0.82 | 0.90 | 0.92 | | Runtime | 10s | 15s | 300s | 2s |

import torch
import torch.nn as nn
import torch.nn.functional as F

class SpatialTransformer(nn.Module):
    def __init__(self, size):
        super().__init__()
        vectors = [torch.arange(0, s) for s in size]
        grids = torch.meshgrid(vectors, indexing='ij')
        grid = torch.stack(grids, dim=-1).float()
        self.register_buffer('grid', grid.unsqueeze(0))

    def forward(self, src, flow):
        new_grid = self.grid + flow.permute(0, 2, 3, 4, 1)
        return F.grid_sample(src, new_grid, mode='bilinear',
                            padding_mode='border', align_corners=True)

class RegistrationNet(nn.Module):
    def __init__(self, input_channels=2):
        super().__init__()
        self.encoder = nn.Sequential(
            nn.Conv3d(input_channels, 32, 3, padding=1), nn.ReLU(),
            nn.Conv3d(32, 64, 3, padding=1), nn.ReLU())
        self.flow_head = nn.Conv3d(64, 3, 3, padding=1)
        self.transformer = SpatialTransformer((64, 64, 64))

    def forward(self, fixed, moving):
        concat = torch.cat([fixed, moving], dim=1)
        features = self.encoder(concat)
        flow = self.flow_head(features) * 0.1
        warped = self.transformer(moving, flow)
        return warped, flow

def compute_dice(pred, target, num_classes=2):
    dice_scores = []
    for c in range(1, num_classes):
        pred_mask = (pred == c).float()
        target_mask = (target == c).float()
        intersection = (pred_mask * target_mask).sum()
        union = pred_mask.sum() + target_mask.sum()
        dice = (2 * intersection + 1e-6) / (union + 1e-6)
        dice_scores.append(dice.item())
    return np.mean(dice_scores)

model = RegistrationNet()
fixed = torch.randn(1, 1, 64, 64, 64)
moving = torch.randn(1, 1, 64, 64, 64)
warped, flow = model(fixed, moving)
print(f'Warped shape: {warped.shape}, Flow shape: {flow.shape}')

Research Insight: Learning-based registration methods achieve comparable accuracy to classical iterative methods but are orders of magnitude faster. They learn anatomically plausible deformation fields from training data, preventing folding and tearing artifacts. Contrast-agnostic training improves generalization across different MRI sequences and CT protocols.