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<p>\def\CC{{C\nolinebreak[4]\hspace{-.05em}\raisebox{.4ex}{\tiny\bf ++}}}</p>
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<h1 id="summary">Summary</h1>
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<p>Point cloud registration is a task of aligning two point clouds measured by 3D ranging
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sensors, for example, LiDARs and range cameras. Iterative point cloud registration,
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also known as fine registration or local registration, iteratively refines the transformation
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between point clouds starting from an initial guess.
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Each iteration involves a proximity-based point correspondence search and the minimization
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of the distance between corresponding points, continuing until convergence.
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Iterative closest point (ICP) and its variants,
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such as Generalized ICP, are representative iterative point cloud registration algorithms.
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They are widely used in applications like autonomous vehicle localization [@Kim], place recognition [@Wang],
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and object classification [@Izadinia]. Since these applications often require real-time or near-real-time
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processing, speed is a critical factor in point cloud registration routines.</p>
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<p><strong>small_gicp</strong> provides efficient and parallel algorithms to create an extremely
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fast point cloud registration pipeline. It offers parallel implementations of
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downsampling, nearest neighbor search, local feature extraction, and registration
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to accelerate the entire process.
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small_gicp is implemented as a header-only \CC library with minimal dependencies
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to offer efficiency, portability, and customizability.</p>
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<h1 id="statement-of-need">Statement of need</h1>
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<p>There are several point cloud processing libraries, and PCL [@Rusu], Open3D
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[@Zhou], libpointmatcher [@Pomerleau] are commonly used in real-time applications
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owing to their performant implementations.
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Although they offer numerous functionalities, including those required for point cloud
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registration, they present several challenges for practical applications and scientific
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research.</p>
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<p><strong>Processing speed:</strong>
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A typical point cloud registration pipeline includes processes such as downsampling,
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nearest neighbor search (e.g., KdTree construction), local feature estimation, and
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registration error minimization.
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PCL and Open3D support multi-threading only for parts of these processes (feature
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estimation and registration error minimization), with the remaining single-threaded
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parts often limiting the overall processing speed.
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Additionally, the multi-thread implementations in these libraries can have significant
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overheads, reducing scalability to many-core CPUs.
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These issues make it difficult to meet real-time processing requirements, especially on
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low-specification CPUs. It is also difficult to fully utilize the computational power
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of modern high-end CPUs.</p>
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<p><strong>Customizability:</strong>
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Customizing the internal workings (e.g., replacing the registration cost function or
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changing the correspondence search method) of existing implementations is challenging
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due to hard-coded processes. This poses a significant hurdle for research and development,
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where testing new cost functions and search algorithms is essential.</p>
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<p><strong>small_gicp:</strong>
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To address these issues and accelerate the development of point cloud registration-related systems,
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we designed small_gicp with the following features:</p>
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<ul>
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<li>
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<p>Fully parallelized point cloud preprocessing and registration algorithms with minimal overhead,
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offering up to 2x speed gain in single-threaded scenarios and better scalability in multi-core
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environments.</p>
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</li>
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<li>
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<p>A modular and customizable framework using \CC templates, allowing easy customization of the
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algorithm's internal workings while maintaining efficiency.</p>
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</li>
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<li>
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<p>A header-only \CC library implementation for easy integration into user projects, with Python bindings
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provided for collaborative use with other libraries (e.g., Open3D).</p>
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</li>
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</ul>
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<h1 id="functionalities">Functionalities</h1>
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<p><strong>small_gicp</strong> implements several preprocessing algorithms related to point cloud registration, and
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ICP variant algorithms (point-to-point ICP, point-to-plane ICP, and Generalized ICP based on
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distribution-to-distribution correspondence).</p>
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<ul>
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<li>Downsampling<ul>
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<li>Voxelgrid sampling</li>
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<li>Random sampling</li>
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</ul>
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</li>
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<li>Nearest neighbor search and point accumulation structures<ul>
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<li>KdTree</li>
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<li>Linear iVox (supports incremental points insertion and LRU-cache-based voxel deletion) [@Bai]</li>
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<li>Gaussian voxelmap (supports incremental points insertion and LRU-cache-based voxel deletion) [@Koide]</li>
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</ul>
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</li>
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<li>Registration error functions<ul>
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<li>Point-to-point ICP error [@Zhang]</li>
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<li>Point-to-plane ICP error</li>
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<li>Generalized ICP error [@Segal]</li>
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<li>Robust kernels</li>
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</ul>
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</li>
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<li>Least squares optimizers<ul>
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<li>GaussNewton optimizer</li>
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<li>LevenbergMarquardt optimizer</li>
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</ul>
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</li>
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</ul>
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<h1 id="benchmark-results">Benchmark results</h1>
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<ul>
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<li>Single-threaded and multi-threaded (6 threads) <code>small_gicp::voxelgrid_sampling</code> are approximately 1.3x and 3.2x faster than <code>pcl::VoxelGrid</code>, respectively.</li>
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<li>Multi-threaded construction of <code>small_gicp::KdTree</code> can be up to 6x faster than that of <code>nanoflann</code>.</li>
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<li>Single-threaded <code>small_gicp::GICP</code> is about 2.4x faster than <code>pcl::GICP</code>, with the multi-threaded version showing better scalability.</li>
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</ul>
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<p>More details can be found at \url{https://github.com/koide3/small_gicp/blob/master/BENCHMARK.md}.</p>
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<h1 id="future-work">Future work</h1>
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<p>The efficiency of nearest neighbor search significantly impacts the overall performance of point cloud registration.
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While small_gicp currently offers efficient and parallel implementations of KdTree and voxelmap, which are general and useful in many situations,
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there are other nearest neighbor search methods that can be more efficient under mild assumptions about the point cloud measurement model
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(e.g., projective search [@Serafin]).
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We plan to implement these alternative neighbor search algorithms to further enhance the speed of the point cloud registration process.
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The design of small_gicp, where nearest neighbor search and pose optimization are decoupled, facilitates the easy integration of these new search algorithms.</p>
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<h1 id="acknowledgements">Acknowledgements</h1>
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<p>This work was supported in part by JSPS KAKENHI Grant Number 23K16979.</p>
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<h1 id="references">References</h1>
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