Add Normal Distributions Transform (NDT) registration (#7517)

NDT is a common LiDAR / point-cloud registration
method that optimizes a source-to-target rigid transform against voxelized
Gaussian target distributions instead of nearest-neighbor point
correspondences.

This PR adds a legacy CPU registration API:

    NormalDistributionsTransformOption
    RegistrationNDT
    Python binding: open3d.pipelines.registration.registration_ndt

The implementation builds a target voxel Gaussian map once per registration
call, accepts either center-voxel or six-neighbor voxel residuals, regularizes
small covariance eigenvalues, rejects residuals by squared Mahalanobis distance,
and solves the rigid update using Open3D's existing Eigen SE(3) utilities.

The returned RegistrationResult includes fitness, Euclidean RMSE over the returned representative target-point correspondences, the estimated transform, and representative target-point
indices for accepted voxel residuals.

This implementation is based on the Normal Distributions Transform (NDT) registration algorithm originally proposed by Biber and Straßer [1]. The concrete implementation follows the open‑source reference code by Gao [2], while being adapted to Open3D's registration API and coding style.

[1] P. Biber and W. Straßer, "The Normal Distributions Transform: A New Approach to Laser Scan Matching," Proceedings of the 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003), vol. 3, pp. 2743–2748, IEEE, 2003.
[2] Xiang Gao, SLAM Technology in Autonomous Driving and Robotics: From Theory to Practice (in Chinese), Publishing House of Electronics Industry, 2023. Code available at: https://github.com/gaoxiang12/slam_in_autonomous_driving/blob/master/src/ch7/ndt_3d.cc

Eigen based implementation, parallelized with TBB.

Fix main CI failures: SYCL Python version & Windows RPC port

---------
Co-authored-by: Sameer Sheorey <sameer.sheorey@intel.com>

Author: Xiang-Zeng

.github/workflows/ubuntu-sycl.yml

@@ -171,6 +171,13 @@ jobs:
           # We execute docker buildscript with python version argument.
           docker/docker_build.sh sycl-shared py${{ matrix.python_version }}
 
+          # Wheel produced by the Docker build matches the matrix Python version
+          # via -DPython3_EXECUTABLE in Dockerfile.ci. Keep only that wheel.
+          PYTHON_ABI="cp${PYTHON_VERSION/./}"
+          find . -maxdepth 1 -name 'open3d*.whl' \
+            ! -name "*${PYTHON_ABI}-${PYTHON_ABI}-*.whl" -delete
+          compgen -G "open3d*${PYTHON_ABI}-${PYTHON_ABI}-*.whl" > /dev/null
+
       - name: Docker test (Python)
         run: docker/docker_test.sh sycl-shared python
 

CHANGELOG.md

@@ -57,6 +57,7 @@
 -   Fix macOS arm64 builds, add CI runner for macOS arm64 (PR #6695)
 -   Fix KDTreeFlann possibly using a dangling pointer instead of internal storage and simplified its members (PR #6734)
 -   Fix RANSAC early stop if no inliers in a specific iteration (PR #6789)
+-   Add 3D Normal Distributions Transform registration with C++ and Python APIs (PR #7517).
 -   Fix segmentation fault (infinite recursion) of DetectPlanarPatches if multiple points have same coordinates (PR #6794)
 -   `TriangleMesh`'s `+=` operator appends UVs regardless of the presence of existing features (PR #6728)
 -   Fix build with fmt v10.2.0 (#6783)

cpp/open3d/Open3D.h.in

@@ -63,6 +63,7 @@
 #include "open3d/pipelines/registration/Feature.h"
 #include "open3d/pipelines/registration/GeneralizedICP.h"
 #include "open3d/pipelines/registration/GlobalOptimization.h"
+#include "open3d/pipelines/registration/NormalDistributionsTransform.h"
 #include "open3d/pipelines/registration/Registration.h"
 #include "open3d/pipelines/registration/SymmetricICP.h"
 #include "open3d/pipelines/registration/TransformationEstimation.h"

cpp/open3d/io/rpc/DummyReceiver.h

@@ -19,6 +19,7 @@ namespace rpc {
 class DummyReceiver : public ZMQReceiver {
 public:
     DummyReceiver(const std::string& address, int timeout);
+    using ZMQReceiver::GetLastEndpoint;
 };
 
 }  // namespace rpc

cpp/open3d/io/rpc/ZMQReceiver.cpp

@@ -92,6 +92,11 @@ std::runtime_error ZMQReceiver::GetLastError() {
     return result;
 }
 
+std::string ZMQReceiver::GetLastEndpoint() const {
+    if (!socket_) return "";
+    return socket_->get(zmq::sockopt::last_endpoint);
+}
+
 void ZMQReceiver::Mainloop() {
     context_ = GetZMQContext();
     socket_ = std::unique_ptr<zmq::socket_t>(

cpp/open3d/io/rpc/ZMQReceiver.h

@@ -60,6 +60,10 @@ class ZMQReceiver {
     /// Returns the last error from the mainloop thread.
     std::runtime_error GetLastError();
 
+    /// Returns the endpoint the OS actually bound to (e.g. when address_ is
+    /// tcp://localhost:0). Must be called after Start() succeeds.
+    std::string GetLastEndpoint() const;
+
     /// Sets the message processor object which will process incoming messages.
     void SetMessageProcessor(std::shared_ptr<MessageProcessorBase> processor);
 

cpp/open3d/pipelines/CMakeLists.txt

@@ -25,6 +25,7 @@ target_sources(pipelines PRIVATE
     registration/GeneralizedICP.cpp
     registration/SymmetricICP.cpp
     registration/GlobalOptimization.cpp
+    registration/NormalDistributionsTransform.cpp
     registration/PoseGraph.cpp
     registration/Registration.cpp
     registration/RobustKernel.cpp