Algorithm 1. Deformation-preserving classifier-guided ICP

Input: reference cloud $\mathcal{P}$; current cloud $\mathcal{Q}$; initial transform ${\mathrm{T}}^{\left(0\right)}$; trained classifier $g_{\theta }$; maximum iterations $K$.  Output: rigid transform $\widehat{\mathrm{T}}$; class scores; signed-residual and deformation-score maps. Remove invalid points and apply identical optional filtering/downsampling. Estimate normals, neighbourhood covariance eigenvalues, and local densities. Obtain a transparent coarse alignment or apply the controlled initial pose. For $k=0,\dots ,K-1$: Transform $\mathcal{P}$ by ${\mathrm{T}}^{\left(k\right)}$. Construct candidate correspondences using a physical distance threshold. Compute interpretable feature vectors ${\mathrm{f}}_{ij}$. Predict ${\pi }_{ij}^S$, ${\pi }_{ij}^D$, and ${\pi }_{ij}^O$. Compute stable reliability and robust IRLS weights. Assemble and solve the weighted point-to-plane normal equations. Update the pose on $SE\left(3\right)$ and evaluate conditioning. Stop when pose and objective convergence criteria are satisfied. 5. Recompute final correspondences and class scores. 6. Calculate signed normal residuals and deformation scores. Apply spatial filtering only to the deformation map, not to the pose estimate. Return $\widehat{\mathrm{T}}$ and monitoring outputs.