Normal Distributions Transform

Normal Distributions Transform (NDT) registration aligns a source point cloud to a target point cloud represented as a voxel grid of local Gaussian distributions. The method can be useful when a smooth target distribution is preferred over point-to-point nearest-neighbor correspondences.

This implementation is a Gauss-Newton point-to-distribution variant of the Normal Distributions Transform. It is based on the voxel model and practical 3D formulation described by Gao [Gao2023], while the original NDT method was introduced by Biber and Straßer [BiberAndStrasser2003]. Unlike the original Newton optimization of a Gaussian score, this variant minimizes squared Mahalanobis residuals.

Open3D exposes NDT through open3d.pipelines.registration.registration_ndt. The main parameters are collected in NormalDistributionsTransformOption, including both voxel Gaussian model parameters and convergence criteria. Optimization stops when the pose update is small or the relative change in mean Mahalanobis objective falls below the configured threshold. In the returned RegistrationResult, each accepted voxel is represented by the target point closest to its mean, and inlier_rmse is the Euclidean RMSE over those representative point correspondences:

        voxel_size=0.5,
        min_points_per_voxel=6,
        covariance_regularization=1e-6,
        transformation_epsilon=1e-6,
        relative_objective=1e-6,
        max_iteration=200,
        outlier_threshold=9.0,
        neighbor_search_type=1)

The full runnable script is available at examples/python/pipelines/ndt_registration.py.