Anchor point based image registration for absolute scale topographic structure detection in microscopy

Microscopy images obtained through remote sensing often suffer from misalignment and deformation, complicating accurate data analysis. As experimental instruments improve and scientific discoveries deepen, the volume of data requiring processing continues to grow. Image registration can contribute to microscopy automation, which enables more efficient data analysis and experimental workflows. For this implementation, image processing techniques that can handle both image registration and localized object analysis are required. This research introduces a computer interface designed to calibrate and analyze specific structures with prior knowledge of the observed target. Our method achieves image registration by aligning anchor points, which correspond to the coordinates of a structural model within the image. It employs homography transform to correct images, restoring them to their original, undistorted form, thus enabling consistent quantitative comparisons across different images on an absolute scale. Additionally, the method provides valuable information from the registered anchor points, allowing for the precise localization of local objects in the structure. We demonstrate this technique across various microscopy scenarios at different scales and evaluate its precision against a keypoint detection AI approach from our previous research, which promises its enhancement in microscopy data analysis and automation.

Depth-based registration of 3D preoperative models to intraoperative patient anatomy using the HoloLens 2

PURPOSE

In augmented reality (AR) surgical navigation, a registration step is required to align the preoperative data with the patient. This work investigates the use of the depth sensor of HoloLens 2 for registration in surgical navigation.

METHODS

An AR depth-based registration framework was developed. The framework aligns preoperative and intraoperative point clouds and overlays the preoperative model on the patient. For evaluation, three experiments were conducted. First, the accuracy of the HoloLens's depth sensor was evaluated for both Long-Throw (LT) and Articulated Hand Tracking (AHAT) modes. Second, the overall registration accuracy was assessed with different alignment approaches. The accuracy and success rate of each approach were evaluated. Finally, a qualitative assessment of the framework was performed on various objects.

RESULTS

The depth accuracy experiment showed mean overestimation errors of 5.7 mm for AHAT and 9.0 mm for LT. For the overall alignment, the mean translation errors of the different methods ranged from 12.5 to 17.0 mm, while rotation errors ranged from 0.9 to 1.1 degrees.

CONCLUSION

The results show that the depth sensor on the HoloLens 2 can be used for image-to-patient alignment with 1-2 cm accuracy and within 4 s, indicating that with further improvement in the accuracy, this approach can offer a convenient alternative to other time-consuming marker-based approaches. This work provides a generic marker-less registration framework using the depth sensor of the HoloLens 2, with extensive analysis of the sensor's reconstruction and registration accuracy. It supports advancing the research of marker-less registration in surgical navigation.

A structure-based framework for selective inhibitor design and optimization

Structure-based drug design aims to create active compounds with favorable properties by analyzing target structures. Recently, deep generative models have facilitated structure-specific molecular generation. However, many methods are limited by inadequate pharmaceutical data, resulting in suboptimal molecular properties and unstable conformations. Additionally, these approaches often overlook binding pocket interactions and struggle with selective inhibitor design. To address these challenges, we developed a framework called Coarse-grained and Multi-dimensional Data-driven molecular generation (CMD-GEN). CMD-GEN bridges ligand-protein complexes with drug-like molecules by utilizing coarse-grained pharmacophore points sampled from diffusion model, enriching training data. Through a hierarchical architecture, it decomposes three-dimensional molecule generation within the pocket into pharmacophore point sampling, chemical structure generation, and conformation alignment, mitigating instability issues. CMD-GEN outperforms other methods in benchmark tests and controls drug-likeness effectively. Furthermore, CMD-GEN excels in cases across three synthetic lethal targets, and wet-lab validation with PARP1/2 inhibitors confirms its potential in selective inhibitor design.

Certifiably optimal rotation and pose estimation based on the Cayley map

We present novel, convex relaxations for rotation and pose estimation problems that can a posteriori guarantee global optimality for practical measurement noise levels. Some such relaxations exist in the literature for specific problem setups that assume the matrix von Mises-Fisher distribution (a.k.a., matrix Langevin distribution or chordal distance) for isotropic rotational uncertainty. However, another common way to represent uncertainty for rotations and poses is to define anisotropic noise in the associated Lie algebra. Starting from a noise model based on the Cayley map, we define our estimation problems, convert them to Quadratically Constrained Quadratic Programs (QCQPs), then relax them to Semidefinite Programs (SDPs), which can be solved using standard interior-point optimization methods; global optimality follows from Lagrangian strong duality. We first show how to carry out basic rotation and pose averaging. We then turn to the more complex problem of trajectory estimation, which involves many pose variables with both individual and inter-pose measurements (or motion priors). Our contribution is to formulate SDP relaxations for all these problems based on the Cayley map (including the identification of redundant constraints) and to show them working in practical settings. We hope our results can add to the catalogue of useful estimation problems whose solutions can be a posteriori guaranteed to be globally optimal.

Automated dental registration and TMJ segmentation for virtual surgical planning of orthognathic surgery via three-step computer-based method

OBJECTIVE

This study developed and evaluated a computer-based method for automating the registration of scanned dental models with 3D reconstructed skulls and segmentation of the temporomandibular joint (TMJ).

METHODS

A dataset comprising 1274 skull models and corresponding scanned dental models was collected. In total, 1066 cases were used for the development of the computer-based method, while 208 cases were used for validation. Performance was evaluated by comparing the automated results with manual registration and segmentation performed by clinicians, using accuracy and completeness metrics (e.g. intersection of union [IoU] and Dice similarity coefficient [DSC]).

RESULTS

The automated registration achieved a mean absolute error of 0.35 mm for the maxilla and 0.38 mm for the mandible, and a root mean squared error of 0.46 mm and 0.39 mm, respectively. The automatic TMJ segmentation exhibited an accuracy of 97.48 %, a precision of 97.06 %, a IoU of 95.72 %, DSC of 97.3 %, and a Hausdorff value of 1.87 mm, which were sufficient for clinical application.

CONCLUSION

The proposed method significantly improved the efficiency of orthognathic surgical planning by automating the registration and segmentation processes. The accuracy and precision of the automated results were sufficient for clinical use, reducing the workload on clinicians and facilitating faster and more reliable surgical planning.

CLINICAL SIGNIFICANCE

The computer-based method streamlines orthognathic surgical planning, enhancing precision and efficiency without compromising clinical accuracy, ultimately improving patient outcomes and reducing the workload of surgeons.

A Review of Simultaneous Localization and Mapping for the Robotic-Based Nondestructive Evaluation of Infrastructures

The maturity of simultaneous localization and mapping (SLAM) methods has now reached a significant level that motivates in-depth and problem-specific reviews. The focus of this study is to investigate the evolution of vision-based, LiDAR-based, and a combination of these methods and evaluate their performance in enclosed and GPS-denied (EGD) conditions for infrastructure inspection. This paper categorizes and analyzes the SLAM methods in detail, considering the sensor fusion type and chronological order. The paper analyzes the performance of eleven open-source SLAM solutions, containing two visual (VINS-Mono, ORB-SLAM 2), eight LiDAR-based (LIO-SAM, Fast-LIO 2, SC-Fast-LIO 2, LeGO-LOAM, SC-LeGO-LOAM A-LOAM, LINS, F-LOAM) and one combination of the LiDAR and vision-based method (LVI-SAM). The benchmarking section analyzes accuracy and computational resource consumption using our collected dataset and a test dataset. According to the results, LiDAR-based methods performed well under EGD conditions. Contrary to common presumptions, some vision-based methods demonstrate acceptable performance in EGD environments. Additionally, combining vision-based techniques with LiDAR-based methods demonstrates superior performance compared to either vision-based or LiDAR-based methods individually.

A 6D Object Pose Estimation Algorithm for Autonomous Docking with Improved Maximal Cliques

Accurate 6D object pose estimation is critical for autonomous docking. To address the inefficiencies and inaccuracies associated with maximal cliques-based pose estimation methods, we propose a fast 6D pose estimation algorithm that integrates feature space and space compatibility constraints. The algorithm reduces the graph size by employing Laplacian filtering to resample high-frequency signal nodes. Then, the truncated Chamfer distance derived from fusion features and spatial compatibility constraints is used to evaluate the accuracy of candidate pose alignment between source and reference point clouds, and the optimal pose transformation matrix is selected for 6D pose estimation. Finally, a point-to-plane ICP algorithm is applied to refine the 6D pose estimation for autonomous docking. Experimental results demonstrate that the proposed algorithm achieves recall rates of 94.5%, 62.2%, and 99.1% on the 3DMatch, 3DLoMatch, and KITTI datasets, respectively. On the autonomous docking dataset, the algorithm yields rotation and localization errors of 0.96° and 5.82 cm, respectively, outperforming existing methods and validating the effectiveness of our approach.

Global registration of kidneys in 3D ultrasound and CT images

PURPOSE

Automatic registration between abdominal ultrasound (US) and computed tomography (CT) images is needed to enhance interventional guidance of renal procedures, but it remains an open research challenge. We propose a novel method that doesn't require an initial registration estimate (a global method) and also handles registration ambiguity caused by the organ's natural symmetry. Combined with a registration refinement algorithm, this method achieves robust and accurate kidney registration while avoiding manual initialization.

METHODS

We propose solving global registration in a three-step approach: (1) Automatic anatomical landmark localization, where 2 deep neural networks (DNNs) localize a set of landmarks in each modality. (2) Registration hypothesis generation, where potential registrations are computed from the landmarks with a deterministic variant of RANSAC. Due to the Kidney's strong bilateral symmetry, there are usually 2 compatible solutions. Finally, in Step (3), the correct solution is determined automatically, using a DNN classifier that resolves the geometric ambiguity. The registration may then be iteratively improved with a registration refinement method. Results are presented with state-of-the-art surface-based refinement-Bayesian coherent point drift (BCPD).

RESULTS

This automatic global registration approach gives better results than various competitive state-of-the-art methods, which, additionally, require organ segmentation. The results obtained on 59 pairs of 3D US/CT kidney images show that the proposed method, combined with BCPD refinement, achieves a target registration error (TRE) of an internal kidney landmark (the renal pelvis) of 5.78 mm and an average nearest neighbor surface distance (nndist) of 2.42 mm.

CONCLUSION

This work presents the first approach for automatic kidney registration in US and CT images, which doesn't require an initial manual registration estimate to be known a priori. The results show a fully automatic registration approach with performances comparable to manual methods is feasible.

Predictive method for poultry carcass visceral dimensions using 3D point cloud and Genetic Algorithm-based wavelet neural network

In order to avoid damaging viscera during poultry evisceration and enhance the economic value of poultry products, this paper proposes a predictive method for poultry carcass visceral dimensions based on 3D point cloud and a Genetic Algorithm-based Wavelet Neural Network (GA-WNN). In this study, a data set of poultry carcasses was obtained through the use of 3D point cloud scanning equipment combined with reverse engineering software. The inputs and predicted targets of the model were determined through correlation analysis of various carcass dimensions. Then, a prediction model of poultry visceral size (GA-WNN) was built by K-fold cross validation method, Genetic Algorithm and Wavelet Neural Network (WNN). By comparing the prediction results and analyzing Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) of the six models, it was determined that the GA-WNN model had the best prediction results. Finally, in order to verify the generalizability of the method, generalizability experiments were conducted on different breeds of poultry, which proved that the method of this study had superior generalizability ability. In the comparative analysis of the six models, the MAPE and RMSE of the GA-WNN model for the prediction of the three visceral dimensions were the lowest except for the RMSE for the prediction of visceral length. Compared with the largest of the two kinds of errors, the MAPE and RMSE for the prediction of the position of the upper end of the left liver by the method of this study were lower by 5.56% and 0.915 cm, respectively, and the prediction effect had a significant advantage. The experimental results showed that the model built in this paper based on 3D point cloud and GA-WNN network can accurately predict the size of the viscera of poultry carcasses, thus providing theoretical references for the automated evisceration technology without damaging the viscera.

Deep Loss Convexification for Learning Iterative Models

Iterative methods such as iterative closest point (ICP) for point cloud registration often suffer from bad local optimality (e.g. saddle points), due to the nature of nonconvex optimization. To address this fundamental challenge, in this paper we propose learning to form the loss landscape of a deep iterative method w.r.t. predictions at test time into a convex- like shape locally around each ground truth given data, namely Deep Loss Convexification (DLC), thanks to the overparametrization in neural networks. To this end, we formulate our learning objective based on adversarial training by manipulating the ground-truth predictions, rather than input data. In particular, we propose using star-convexity, a family of structured nonconvex functions that are unimodal on all lines that pass through a global minimizer, as our geometric constraint for reshaping loss landscapes, leading to (1) extra novel hinge losses appended to the original loss and (2) near-optimal predictions. We demonstrate the state-of-the-art performance using DLC with existing network architectures for the tasks of training recurrent neural networks (RNNs), 3D point cloud registration, and multimodel image alignment.

HBSP: a hybrid bilinear and semidefinite programming approach for aligning partially overlapping point clouds

In many applications, there is a need for algorithms that can align partially overlapping point clouds while remaining invariant to corresponding transformations. This research presents a method that achieves these goals by minimizing a binary linear assignment-least squares (BLALS) energy function. First, we reformulate the BLALS problem as the minimization of a quadratic function with quadratic and linear constraints through variable substitution. By utilizing semidefinite relaxation and the convex envelope of bilinear monomials, we relax the problem to create a lower bound that can be solved using linear assignment and low-dimensional semidefinite programming. Additionally, we develop a branch-and-bound (BnB) algorithm that only branches over the transformation variable, which enhances convergence. Experimental results show that, compared to state-of-the-art approaches, the proposed method is robust against non-rigid deformation and outliers when the outliers are separate from the inliers. However, its robustness decreases when outliers are mixed with inliers. The run time of our method is relatively high due to the need to solve a semidefinite program in each iteration of the BnB algorithm.

BA-CLM: A Globally Consistent 3D LiDAR Mapping Based on Bundle Adjustment Cost Factors

Constructing a globally consistent high-precision map is essential for the application of mobile robots. Existing optimization-based mapping methods typically constrain robot states in pose space during the graph optimization process, without directly optimizing the structure of the scene, thereby causing the map to be inconsistent. To address the above issues, this paper presents a three-dimensional (3D) LiDAR mapping framework (i.e., BA-CLM) based on LiDAR bundle adjustment (LBA) cost factors. We propose a multivariate LBA cost factor, which is built from a multi-resolution voxel map, to uniformly constrain the robot poses within a submap. The framework proposed in this paper applies the LBA cost factors for both local and global map optimization. Experimental results on several public 3D LiDAR datasets and a self-collected 32-line LiDAR dataset demonstrate that the proposed method achieves accurate trajectory estimation and consistent mapping.

Clique-like Point Cloud Registration: A Flexible Sampling Registration Method Based on Clique-like for Low-Overlapping Point Cloud

Three-dimensional point cloud registration is a critical task in 3D perception for sensors that aims to determine the optimal alignment between two point clouds by finding the best transformation. Existing methods like RANSAC and its variants often face challenges, such as sensitivity to low overlap rates, high computational costs, and susceptibility to outliers, leading to inaccurate results, especially in complex or noisy environments. In this paper, we introduce a novel 3D registration method, CL-PCR, inspired by the concept of maximal cliques and built upon the SC2-PCR framework. Our approach allows for the flexible use of smaller sampling subsets to extract more local consensus information, thereby generating accurate pose hypotheses even in scenarios with low overlap between point clouds. This method enhances robustness against low overlap and reduces the influence of outliers, addressing the limitations of traditional techniques. First, we construct a graph matrix to represent the compatibility relationships among the initial correspondences. Next, we build clique-likes subsets of various sizes within the graph matrix, each representing a consensus set. Then, we compute the transformation hypotheses for the subsets using the SVD algorithm and select the best hypothesis for registration based on evaluation metrics. Extensive experiments demonstrate the effectiveness of CL-PCR. In comparison experiments on the 3DMatch/3DLoMatch datasets using both FPFH and FCGF descriptors, our Fast-CL-PCRv1 outperforms state-of-the-art algorithms, achieving superior registration performance. Additionally, we validate the practicality and robustness of our method with real-world data.

High-Throughput and Accurate 3D Scanning of Cattle Using Time-of-Flight Sensors and Deep Learning

We introduce a high-throughput 3D scanning system designed to accurately measure cattle phenotypes. This scanner employs an array of depth sensors, i.e., time-of-flight (ToF) sensors, each controlled by dedicated embedded devices. The sensors generate high-fidelity 3D point clouds, which are automatically stitched using a point could segmentation approach through deep learning. The deep learner combines raw RGB and depth data to identify correspondences between the multiple 3D point clouds, thus creating a single and accurate mesh that reconstructs the cattle geometry on the fly. In order to evaluate the performance of our system, we implemented a two-fold validation process. Initially, we quantitatively tested the scanner for its ability to determine accurate volume and surface area measurements in a controlled environment featuring known objects. Next, we explored the impact and need for multi-device synchronization when scanning moving targets (cattle). Finally, we performed qualitative and quantitative measurements on cattle. The experimental results demonstrate that the proposed system is capable of producing high-quality meshes of untamed cattle with accurate volume and surface area measurements for livestock studies.

Advancing Global Pose Refinement: A Linear, Parameter-Free Model for Closed Circuits via Quaternion Interpolation

Global pose refinement is a significant challenge within Simultaneous Localization and Mapping (SLAM) frameworks. For LIDAR-based SLAM systems, pose refinement is integral to correcting drift caused by the successive registration of 3D point clouds collected by the sensor. A divergence between the actual and calculated platform paths characterizes this error. In response to this challenge, we propose a linear, parameter-free model that uses a closed circuit for global trajectory corrections. Our model maps rotations to quaternions and uses Spherical Linear Interpolation (SLERP) for transitions between them. The intervals are established by the constraint set by the Least Squares (LS) method on rotation closure and are proportional to the circuit's size. Translations are globally adjusted in a distinct linear phase. Additionally, we suggest a coarse-to-fine pairwise registration method, integrating Fast Global Registration and Generalized ICP with multiscale sampling and filtering. The proposed approach is tested on three varied datasets of point clouds, including Mobile Laser Scanners and Terrestrial Laser Scanners. These diverse datasets affirm the model's effectiveness in 3D pose estimation, with substantial pose differences and efficient pose optimization in larger circuits.

Accurate Registration of Cross-Modality Geometry via Consistent Clustering

The registration of unitary-modality geometric data has been successfully explored over past decades. However, existing approaches typically struggle to handle cross-modality data due to the intrinsic difference between different models. To address this problem, in this article, we formulate the cross-modality registration problem as a consistent clustering process. First, we study the structure similarity between different modalities based on an adaptive fuzzy shape clustering, from which a coarse alignment is successfully operated. Then, we optimize the result using fuzzy clustering consistently, in which the source and target models are formulated as clustering memberships and centroids, respectively. This optimization casts new insight into point set registration, and substantially improves the robustness against outliers. Additionally, we investigate the effect of fuzzier in fuzzy clustering on the cross-modality registration problem, from which we theoretically prove that the classical Iterative Closest Point (ICP) algorithm is a special case of our newly defined objective function. Comprehensive experiments and analysis are conducted on both synthetic and real-world cross-modality datasets. Qualitative and quantitative results demonstrate that our method outperforms state-of-the-art approaches with higher accuracy and robustness. Our code is publicly available at https://github.com/zikai1/CrossModReg.

Rigid point cloud registration based on correspondence cloud for image-to-patient registration in image-guided surgery

BACKGROUND

Image-to-patient registration aligns preoperative images to intra-operative anatomical structures and it is a critical step in image-guided surgery (IGS). The accuracy and speed of this step significantly influence the performance of IGS systems. Rigid registration based on paired points has been widely used in IGS, but studies have shown its limitations in terms of cost, accuracy, and registration time. Therefore, rigid registration of point clouds representing the human anatomical surfaces has become an alternative way for image-to-patient registration in the IGS systems.

PURPOSE

We propose a novel correspondence-based rigid point cloud registration method that can achieve global registration without the need for pose initialization. The proposed method is less sensitive to outliers compared to the widely used RANSAC-based registration methods and it achieves high accuracy at a high speed, which is particularly suitable for the image-to-patient registration in IGS.

METHODS

We use the rotation axis and angle to represent the rigid spatial transformation between two coordinate systems. Given a set of correspondences between two point clouds in two coordinate systems, we first construct a 3D correspondence cloud (CC) from the inlier correspondences and prove that the CC distributes on a plane, whose normal is the rotation axis between the two point clouds. Thus, the rotation axis can be estimated by fitting the CP. Then, we further show that when projecting the normals of a pair of corresponding points onto the CP, the angle between the projected normal pairs is equal to the rotation angle. Therefore, the rotation angle can be estimated from the angle histogram. Besides, this two-stage estimation also produces a high-quality correspondence subset with high inlier rate. With the estimated rotation axis, rotation angle, and the correspondence subset, the spatial transformation can be computed directly, or be estimated using RANSAC in a fast and robust way within only 100 iterations.

RESULTS

To validate the performance of the proposed registration method, we conducted experiments on the CT-Skull dataset. We first conducted a simulation experiment by controlling the initial inlier rate of the correspondence set, and the results showed that the proposed method can effectively obtain a correspondence subset with much higher inlier rate. We then compared our method with traditional approaches such as ICP, Go-ICP, and RANSAC, as well as recently proposed methods like TEASER, SC2-PCR, and MAC. Our method outperformed all traditional methods in terms of registration accuracy and speed. While achieving a registration accuracy comparable to the recently proposed methods, our method demonstrated superior speed, being almost three times faster than TEASER.

CONCLUSIONS

Experiments on the CT-Skull dataset demonstrate that the proposed method can effectively obtain a high-quality correspondence subset with high inlier rate, and a tiny RANSAC with 100 iterations is sufficient to estimate the optimal transformation for point cloud registration. Our method achieves higher registration accuracy and faster speed than existing widely used methods, demonstrating great potential for the image-to-patient registration, where a rigid spatial transformation is needed to align preoperative images to intra-operative patient anatomy.

SGRTmreg: A Learning-Based Optimization Framework for Multiple Pairwise Registrations

Point cloud registration is a fundamental task in computer vision and graphics, which is widely used in 3D reconstruction, object tracking, and atlas reconstruction. Learning-based optimization and deep learning methods have been widely developed in pairwise registration due to their own distinctive advantages. Deep learning methods offer greater flexibility and enable registering unseen point clouds that are not trained. Learning-based optimization methods exhibit enhanced robustness and stability when handling registration under various perturbations, such as noise, outliers, and occlusions. To leverage the strengths of both approaches to achieve a less time-consuming, robust, and stable registration for multiple instances, we propose a novel computational framework called SGRTmreg for multiple pairwise registrations in this paper. The SGRTmreg framework utilizes three components-a Searching scheme, a learning-based optimization method called Graph-based Reweighted discriminative optimization (GRDO), and a Transfer module to achieve multi-instance point cloud registration.Given a collection of instances to be matched, a template as a target point cloud, and an instance as a source point cloud, the searching scheme selects one point cloud from the collection that closely resembles the source. GRDO then learns a sequence of regressors by aligning the source to the target, while the transfer module stores and applies the learned regressors to align the selected point cloud to the target and estimate the transformation of the selected point cloud. In short, SGRTmreg harnesses a shared sequence of regressors to register multiple point clouds to a target point cloud. We conduct extensive registration experiments on various datasets to evaluate the proposed framework. The experimental results demonstrate that SGRTmreg achieves multiple pairwise registrations with higher accuracy, robustness, and stability than the state-of-the-art deep learning and traditional registration methods.

Mutual Voting for Ranking 3D Correspondences

Consistent correspondences between point clouds are vital to 3D vision tasks such as registration and recognition. In this paper, we present a mutual voting method for ranking 3D correspondences. The key insight is to achieve reliable scoring results for correspondences by refining both voters and candidates in a mutual voting scheme. First, a graph is constructed for the initial correspondence set with the pairwise compatibility constraint. Second, nodal clustering coefficients are introduced to preliminarily remove a portion of outliers and speed up the following voting process. Third, we model nodes and edges in the graph as candidates and voters, respectively. Mutual voting is then performed in the graph to score correspondences. Finally, the correspondences are ranked based on the voting scores and top-ranked ones are identified as inliers. Feature matching, 3D point cloud registration, and 3D object recognition experiments on various datasets with different nuisances and modalities verify that MV is robust to heavy outliers under different challenging settings, and can significantly boost 3D point cloud registration and 3D object recognition performance.

Accelerating Globally Optimal Consensus Maximization in Geometric Vision

Branch-and-bound-based consensus maximization stands out due to its important ability of retrieving the globally optimal solution to outlier-affected geometric problems. However, while the discovery of such solutions caries high scientific value, its application in practical scenarios is often prohibited by its computational complexity growing exponentially as a function of the dimensionality of the problem at hand. In this work, we convey a novel, general technique that allows us to branch over an n-1 dimensional space for an n-dimensional problem. The remaining degree of freedom can be solved globally optimally within each bound calculation by applying the efficient interval stabbing technique. While each individual bound derivation is harder to compute owing to the additional need for solving a sorting problem, the reduced number of intervals and tighter bounds in practice lead to a significant reduction in the overall number of required iterations. Besides an abstract introduction of the approach, we present applications to four fundamental geometric computer vision problems: camera resectioning, relative camera pose estimation, point set registration, and rotation and focal length estimation. Through our exhaustive tests, we demonstrate significant speed-up factors at times exceeding two orders of magnitude, thereby increasing the viability of globally optimal consensus maximizers in online application scenarios.

Match Normalization: Learning-Based Point Cloud Registration for 6D Object Pose Estimation in the Real World

In this work, we tackle the task of estimating the 6D pose of an object from point cloud data. While recent learning-based approaches have shown remarkable success on synthetic datasets, we have observed them to fail in the presence of real-world data. We investigate the root causes of these failures and identify two main challenges: The sensitivity of the widely-used SVD-based loss function to the range of rotation between the two point clouds, and the difference in feature distributions between the source and target point clouds. We address the first challenge by introducing a directly supervised loss function that does not utilize the SVD operation. To tackle the second, we introduce a new normalization strategy, Match Normalization. Our two contributions are general and can be applied to many existing learning-based 3D object registration frameworks, which we illustrate by implementing them in two of them, DCP and IDAM. Our experiments on the real-scene TUD-L Hodan et al. 2018, LINEMOD Hinterstoisser et al. 2012 and Occluded-LINEMOD Brachmann et al. 2014 datasets evidence the benefits of our strategies. They allow for the first-time learning-based 3D object registration methods to achieve meaningful results on real-world data. We therefore expect them to be key to the future developments of point cloud registration methods.

Instant Segmentation and Fitting of Excavations in Subsurface Utility Engineering

Using augmented reality for subsurface utility engineering (SUE) has benefited from recent advances in sensing hardware, enabling the first practical and commercial applications. However, this progress has uncovered a latent problem - the insufficient quality of existing SUE data in terms of completeness and accuracy. In this work, we present a novel approach to automate the process of aligning existing SUE databases with measurements taken during excavation works, with the potential to correct the deviation from the as-planned to as-built documentation, which is still a big challenge for traditional workers at sight. Our segmentation algorithm performs infrastructure segmentation based on the live capture of an excavation on site. Our fitting approach correlates the inferred position and orientation with the existing digital plan and registers the as-planned model into the as-built state. Our approach is the first to circumvent tedious postprocessing, as it corrects data online and on-site. In our experiments, we show the results of our proposed method on both synthetic data and a set of real excavations.

Comparison of Point Cloud Registration Techniques on Scanned Physical Objects

This paper presents a comparative analysis of six prominent registration techniques for solving CAD model alignment problems. Unlike the typical approach of assessing registration algorithms with synthetic datasets, our study utilizes point clouds generated from the Cranfield benchmark. Point clouds are sampled from existing CAD models and 3D scans of physical objects, introducing real-world complexities such as noise and outliers. The acquired point cloud scans, including ground-truth transformations, are made publicly available. This dataset includes several cleaned-up scans of nine 3D-printed objects. Our main contribution lies in assessing the performance of three classical (GO-ICP, RANSAC, FGR) and three learning-based (PointNetLK, RPMNet, ROPNet) methods on real-world scans, using a wide range of metrics. These include recall, accuracy and computation time. Our comparison shows a high accuracy for GO-ICP, as well as PointNetLK, RANSAC and RPMNet combined with ICP refinement. However, apart from GO-ICP, all methods show a significant number of failure cases when applied to scans containing more noise or requiring larger transformations. FGR and RANSAC are among the quickest methods, while GO-ICP takes several seconds to solve. Finally, while learning-based methods demonstrate good performance and low computation times, they have difficulties in training and generalizing. Our results can aid novice researchers in the field in selecting a suitable registration method for their application, based on quantitative metrics. Furthermore, our code can be used by others to evaluate novel methods.

Fully automated structured light scanning for high-fidelity 3D reconstruction via graph optimization

Convenient and high-fidelity 3D model reconstruction is crucial for industries like manufacturing, medicine and archaeology. Current scanning approaches struggle with high manual costs and the accumulation of errors in large-scale modeling. This paper is dedicated to achieving industrial-grade seamless and high-fidelity 3D reconstruction with minimal manual intervention. The innovative method proposed transforms the multi-frame registration into a graph optimization problem, addressing the issue of error accumulation encountered in frame-by-frame registration. Initially, a global consistency cost is established based on point cloud cross-multipath registration, followed by using the geometric and color differences of corresponding points as dynamic nonlinear weights. Finally, the iteratively reweighted least squares (IRLS) method is adopted to perform the bundle adjustment (BA) optimization of all poses. Significantly enhances registration accuracy and robustness under the premise of maintaining near real-time efficiency. Additionally, for generating watertight, seamless surface models, a local-to-global transitioning strategy for multiframe fusion is introduced. This method facilitates efficient correction of normal vector consistency, addressing mesh discontinuities in surface reconstruction resulting from normal flips. To validate our algorithm, we designed a 3D reconstruction platform enabling spatial viewpoint transformations. We collected extensive real and simulated model data. These datasets were rigorously evaluated against advanced methods, roving the effectiveness of our approach. Our data and implementation is made available on GitHub for community development.

Accurate global and local 3D alignment of cryo-EM density maps using local spatial structural features

Advances in cryo-electron microscopy (cryo-EM) imaging technologies have led to a rapidly increasing number of cryo-EM density maps. Alignment and comparison of density maps play a crucial role in interpreting structural information, such as conformational heterogeneity analysis using global alignment and atomic model assembly through local alignment. Here, we present a fast and accurate global and local cryo-EM density map alignment method called CryoAlign, that leverages local density feature descriptors to capture spatial structure similarities. CryoAlign is a feature-based cryo-EM map alignment tool, in which the employment of feature-based architecture enables the rapid establishment of point pair correspondences and robust estimation of alignment parameters. Extensive experimental evaluations demonstrate the superiority of CryoAlign over the existing methods in terms of both alignment accuracy and speed.

Tooth Alignment Network Based on Landmark Constraints and Hierarchical Graph Structure

Automatic tooth alignment target prediction is vital in shortening the planning time of orthodontic treatments and aligner designs. Generally, the quality of alignment targets greatly depends on the experience and ability of dentists and has enormous subjective factors. Therefore, many knowledge-driven alignment prediction methods have been proposed to help inexperienced dentists. Unfortunately, existing methods tend to directly regress tooth motion, which lacks clinical interpretability. Tooth anatomical landmarks play a critical role in orthodontics because they are effective in aiding the assessment of whether teeth are in close arrangement and normal occlusion. Thus, we consider anatomical landmark constraints to improve tooth alignment results. In this article, we present a novel tooth alignment neural network for alignment target predictions based on tooth landmark constraints and a hierarchical graph structure. We detect the landmarks of each tooth first and then construct a hierarchical graph of jaw-tooth-landmark to characterize the relationship between teeth and landmarks. Then, we define the landmark constraints to guide the network to learn the normal occlusion and predict the rigid transformation of each tooth during alignment. Our method achieves better results with the architecture built for tooth data and landmark constraints and has better explainability than previous methods with regard to clinical tooth alignments.

HTMC: hierarchical tolerance mask correspondence for human body point cloud registration

Point cloud registration can be solved by searching for correspondence pairs. Searching for correspondence pairs in human body point clouds poses some challenges, including: (1) the similar geometrical shapes of the human body are difficult to distinguish. (2) The symmetry of the human body confuses the correspondence pairs searching. To resolve the above issues, this article proposes a Hierarchical Tolerance Mask Correspondence (HTMC) method to achieve better alignment by tolerating obfuscation. First, we define various levels of correspondence pairs and assign different similarity scores for each level. Second, HTMC designs a tolerance loss function to tolerate the obfuscation of correspondence pairs. Third, HTMC uses a differentiable mask to diminish the influence of non-overlapping regions and enhance the influence of overlapping regions. In conclusion, HTMC acknowledges the presence of similar local geometry in human body point clouds. On one hand, it avoids overfitting caused by forcibly distinguishing similar geometries, and on the other hand, it prevents genuine correspondence relationships from being masked by similar geometries. The codes are available at https://github.com/ChenPointCloud/HTMC.

An Error Estimation System for Close-Range Photogrammetric Systems and Algorithms

Close-range photogrammetry methods are widely used for non-contact and accurate measurements of surface shapes. These methods are based on calculating the three-dimensional coordinates of an object from two-dimensional images using special digital processing algorithms. Due to the relatively complex measurement principle, the accurate estimation of the photogrammetric measurement error is a non-trivial task. Typically, theoretical estimations or computer modelling are used to solve this problem. However, these approaches cannot provide an accurate estimate because it is impossible to consider all factors that influence the measurement results. To solve this problem, we propose the use of physical modelling. The measurement results from the photogrammetric system under test were compared with the results of a more accurate reference measurement method. This comparison allowed the error to be estimated under controlled conditions. The test object was a flexible surface whose shape could vary smoothly over a wide range. The estimation of the measurement accuracy for a large number of different surface shapes allows us to obtain new results that are difficult to obtain using standard approaches. To implement the proposed approach, a laboratory system for the error estimation of close-range photogrammetric measurements was developed. The paper contains a detailed description of the developed system and the proposed technique for a comparison of the measurement results. The error in the reference method, which was chosen to be phasogrammetry, was evaluated experimentally. Experimental testing of the stereo photogrammetric system was performed according to the proposed technique. The obtained results show that the proposed technique can reveal dependencies that may not be detected by standard approaches.

Hunter: Exploring High-Order Consistency for Point Cloud Registration With Severe Outliers

After decades of investigation, point cloud registration is still a challenging task in practice, especially when the correspondences are contaminated by a large number of outliers. It may result in a rapidly decreasing probability of generating a hypothesis close to the true transformation, leading to the failure of point cloud registration. To tackle this problem, we propose a transformation estimation method, named Hunter, for robust point cloud registration with severe outliers. The core of Hunter is to design a global-to-local exploration scheme to robustly find the correct correspondences. The global exploration aims to exploit guided sampling to generate promising initial alignments. To this end, a hypergraph-based consistency reasoning module is introduced to learn the high-order consistency among correct correspondences, which is able to yield a more distinct inlier cluster that facilitates the generation of all-inlier hypotheses. Moreover, we propose a preference-based local exploration module that exploits the preference information of top- k promising hypotheses to find a better transformation. This module can efficiently obtain multiple reliable transformation hypotheses by using a multi-initialization searching strategy. Finally, we present a distance-angle based hypothesis selection criterion to choose the most reliable transformation, which can avoid selecting symmetrically aligned false transformations. Experimental results on simulated, indoor, and outdoor datasets, demonstrate that Hunter can achieve significant superiority over the state-of-the-art methods, including both learning-based and traditional methods (as shown in Fig. 1). Moreover, experimental results also indicate that Hunter can achieve more stable performance compared with all other methods with severe outliers.

DPCN++: Differentiable Phase Correlation Network for Versatile Pose Registration

Pose registration is critical in vision and robotics. This article focuses on the challenging task of initialization-free pose registration up to 7DoF for homogeneous and heterogeneous measurements. While recent learning-based methods show promise using differentiable solvers, they either rely on heuristically defined correspondences or require initialization. Phase correlation seeks solutions in the spectral domain and is correspondence-free and initialization-free. Following this, we propose a differentiable solver and combine it with simple feature extraction networks, namely DPCN++. It can perform registration for homo/hetero inputs and generalizes well on unseen objects. Specifically, the feature extraction networks first learn dense feature grids from a pair of homogeneous/heterogeneous measurements. These feature grids are then transformed into a translation and scale invariant spectrum representation based on Fourier transform and spherical radial aggregation, decoupling translation and scale from rotation. Next, the rotation, scale, and translation are independently and efficiently estimated in the spectrum step-by-step. The entire pipeline is differentiable and trained end-to-end. We evaluate DCPN++ on a wide range of tasks taking different input modalities, including 2D bird's-eye view images, 3D object and scene measurements, and medical images. Experimental results demonstrate that DCPN++ outperforms both classical and learning-based baselines, especially on partially observed and heterogeneous measurements.

Accurate Global Point Cloud Registration Using GPU-Based Parallel Angular Radon Spectrum

Accurate robot localization and mapping can be improved through the adoption of globally optimal registration methods, like the Angular Radon Spectrum (ARS). In this paper, we present Cud-ARS, an efficient variant of the ARS algorithm for 2D registration designed for parallel execution of the most computationally expensive steps on Nvidia™ Graphics Processing Units (GPUs). Cud-ARS is able to compute the ARS in parallel blocks, with each associated to a subset of input points. We also propose a global branch-and-bound method for translation estimation. This novel parallel algorithm has been tested on multiple datasets. The proposed method is able to speed up the execution time by two orders of magnitude while obtaining more accurate results in rotation estimation than state-of-the-art correspondence-based algorithms. Our experiments also assess the potential of this novel approach in mapping applications, showing the contribution of GPU programming to efficient solutions of robotic tasks.

SC 2-PCR++: Rethinking the Generation and Selection for Efficient and Robust Point Cloud Registration

Outlier removal is a critical part of feature-based point cloud registration. In this article, we revisit the model generation and selection of the classic RANSAC approach for fast and robust point cloud registration. For the model generation, we propose a second-order spatial compatibility (SC 2) measure to compute the similarity between correspondences. It takes into account global compatibility instead of local consistency, allowing for more distinctive clustering between inliers and outliers at an early stage. The proposed measure promises to find a certain number of outlier-free consensus sets using fewer samplings, making the model generation more efficient. For the model selection, we propose a new Feature and Spatial consistency constrained Truncated Chamfer Distance (FS-TCD) metric for evaluating the generated models. It considers the alignment quality, the feature matching properness, and the spatial consistency constraint simultaneously, enabling the correct model to be selected even when the inlier rate of the putative correspondence set is extremely low. Extensive experiments are carried out to investigate the performance of our method. In addition, we also experimentally prove that the proposed SC 2 measure and the FS-TCD metric are general and can be easily plugged into deep learning based frameworks.

Fully automatic tracking of native glenohumeral kinematics from stereo-radiography

The current work introduces a system for fully automatic tracking of native glenohumeral kinematics in stereo-radiography sequences. The proposed method first applies convolutional neural networks to obtain segmentation and semantic key point predictions in biplanar radiograph frames. Preliminary bone pose estimates are computed by solving a non-convex optimization problem with semidefinite relaxations to register digitized bone landmarks to semantic key points. Initial poses are then refined by registering computed tomography-based digitally reconstructed radiographs to captured scenes, which are masked by segmentation maps to isolate the shoulder joint. A particular neural net architecture which exploits subject-specific geometry is also introduced to improve segmentation predictions and increase robustness of subsequent pose estimates. The method is evaluated by comparing predicted glenohumeral kinematics to manually tracked values from 17 trials capturing 4 dynamic activities. Median orientation differences between predicted and ground truth poses were 1.7∘ and 8.6∘ for the scapula and humerus, respectively. Joint-level kinematics differences were less than 2∘ in 65%, 13%, and 63% of frames for XYZ orientation DoFs based on Euler angle decompositions. Automation of kinematic tracking can increase scalability of tracking workflows in research, clinical, or surgical applications.

Point cloud completion in challenging indoor scenarios with human motion

Combining and completing point cloud data from two or more sensors with arbitrarily relative perspectives in a dynamic, cluttered, and complex environment is challenging, especially when the two sensors have significant perspective differences while the large overlap ratio and feature-rich scene cannot be guaranteed. We create a novel approach targeting this challenging scenario by registering two camera captures in a time series with unknown perspectives and human movements to easily use our system in a real-life scene. In our approach, we first reduce the six unknowns of 3D point cloud completion to three by aligning the ground planes found by our previous perspective-independent 3D ground plane estimation algorithm. Subsequently, we use a histogram-based approach to identify and extract all the humans from each frame generating a three-dimensional (3D) human walking sequence in a time series. To enhance accuracy and performance, we convert 3D human walking sequences to lines by calculating the center of mass (CoM) point of each human body and connecting them. Finally, we match the walking paths in different data trials by minimizing the Fréchet distance between two walking paths and using 2D iterative closest point (ICP) to find the remaining three unknowns in the overall transformation matrix for the final alignment. Using this approach, we can successfully register the corresponding walking path of the human between the two cameras' captures and estimate the transformation matrix between the two sensors.

LiDAR-Based Maintenance of a Safe Distance between a Human and a Robot Arm

This paper demonstrates the capabilities of three-dimensional (3D) LiDAR scanners in supporting a safe distance maintenance functionality in human-robot collaborative applications. The use of such sensors is severely under-utilised in collaborative work with heavy-duty robots. However, even with a relatively modest proprietary 3D sensor prototype, a respectable level of safety has been achieved, which should encourage the development of such applications in the future. Its associated intelligent control system (ICS) is presented, as well as the sensor's technical characteristics. It acquires the positions of the robot and the human periodically, predicts their positions in the near future optionally, and adjusts the robot's speed to keep its distance from the human above the protective separation distance. The main novelty is the possibility to load an instance of the robot programme into the ICS, which then precomputes the future position and pose of the robot. Higher accuracy and safety are provided, in comparison to traditional predictions from known real-time and near-past positions and poses. The use of a 3D LiDAR scanner in a speed and separation monitoring application and, particularly, its specific placing, are also innovative and advantageous. The system was validated by analysing videos taken by the reference validation camera visually, which confirmed its safe operation in reasonably limited ranges of robot and human speeds.

Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimization

We propose the first general and scalable framework to design certifiable algorithms for robust geometric perception in the presence of outliers. Our first contribution is to show that estimation using common robust costs, such as truncated least squares (TLS), maximum consensus, Geman-McClure, Tukey's biweight, among others, can be reformulated as polynomial optimization problems (POPs). By focusing on the TLS cost, our second contribution is to exploit sparsity in the POP and propose a sparse semidefinite programming (SDP) relaxation that is much smaller than the standard Lasserre's hierarchy while preserving empirical exactness, i.e., the SDP recovers the optimizer of the nonconvex POP with an optimality certificate. Our third contribution is to solve the SDP relaxations at an unprecedented scale and accuracy by presenting [Formula: see text], a solver that blends global descent on the convex SDP with fast local search on the nonconvex POP. Our fourth contribution is an evaluation of the proposed framework on six geometric perception problems including single and multiple rotation averaging, point cloud and mesh registration, absolute pose estimation, and category-level object pose and shape estimation. Our experiments demonstrate that (i) our sparse SDP relaxation is empirically exact with up to 60%- 90% outliers across applications; (ii) while still being far from real-time, [Formula: see text] is up to 100 times faster than existing SDP solvers on medium-scale problems, and is the only solver that can solve large-scale SDPs with hundreds of thousands of constraints to high accuracy; (iii) [Formula: see text] safeguards existing fast heuristics for robust estimation (e.g., [Formula: see text] or Graduated Non-Convexity), i.e., it certifies global optimality if the heuristic estimates are optimal, or detects and allows escaping local optima when the heuristic estimates are suboptimal.

Fuzzy Cluster-Based Group-Wise Point Set Registration With Quality Assessment

This article studies group-wise point set registration and makes the following contributions: "FuzzyGReg", which is a new fuzzy cluster-based method to register multiple point sets jointly, and "FuzzyQA", which is the associated quality assessment to check registration accuracy automatically. Given a group of point sets, FuzzyGReg creates a model of fuzzy clusters and equally treats all the point sets as the elements of the fuzzy clusters. Then, the group-wise registration is turned into a fuzzy clustering problem. To resolve this problem, FuzzyGReg applies a fuzzy clustering algorithm to identify the parameters of the fuzzy clusters while jointly transforming all the point sets to achieve an alignment. Next, based on the identified fuzzy clusters, FuzzyQA calculates the spatial properties of the transformed point sets and then checks the alignment accuracy by comparing the similarity degrees of the spatial properties of the point sets. When a local misalignment is detected, a local re-alignment is performed to improve accuracy. The proposed method is cost-efficient and convenient to be implemented. In addition, it provides reliable quality assessments in the absence of ground truth and user intervention. In the experiments, different point sets are used to test the proposed method and make comparisons with state-of-the-art registration techniques. The experimental results demonstrate the effectiveness of our method. The code is available at https://gitsvn-nt.oru.se/qianfang.liao/FuzzyGRegWithQA.

Collaborative 3D Scene Reconstruction in Large Outdoor Environments Using a Fleet of Mobile Ground Robots

Teams of mobile robots can be employed in many outdoor applications, such as precision agriculture, search and rescue, and industrial inspection, allowing an efficient and robust exploration of large areas and enhancing the operators' situational awareness. In this context, this paper describes an active and decentralized framework for the collaborative 3D mapping of large outdoor areas using a team of mobile ground robots under limited communication range and bandwidth. A real-time method is proposed that allows the sharing and registration of individual local maps, obtained from 3D LiDAR measurements, to build a global representation of the environment. A conditional peer-to-peer communication strategy is used to share information over long-range and short-range distances while considering the bandwidth constraints. Results from both real-world and simulated experiments, executed in an actual solar power plant and in its digital twin representation, demonstrate the reliability and efficiency of the proposed decentralized framework for such large outdoor operations.

GraphReg: Dynamical Point Cloud Registration With Geometry-Aware Graph Signal Processing

This study presents a high-accuracy, efficient, and physically induced method for 3D point cloud registration, which is the core of many important 3D vision problems. In contrast to existing physics-based methods that merely consider spatial point information and ignore surface geometry, we explore geometry aware rigid-body dynamics to regulate the particle (point) motion, which results in more precise and robust registration. Our proposed method consists of four major modules. First, we leverage the graph signal processing (GSP) framework to define a new signature, i.e., point response intensity for each point, by which we succeed in describing the local surface variation, resampling keypoints, and distinguishing different particles. Then, to address the shortcomings of current physics-based approaches that are sensitive to outliers, we accommodate the defined point response intensity to median absolute deviation (MAD) in robust statistics and adopt the X84 principle for adaptive outlier depression, ensuring a robust and stable registration. Subsequently, we propose a novel geometric invariant under rigid transformations to incorporate higher-order features of point clouds, which is further embedded for force modeling to guide the correspondence between pairwise scans credibly. Finally, we introduce an adaptive simulated annealing (ASA) method to search for the global optimum and substantially accelerate the registration process. We perform comprehensive experiments to evaluate the proposed method on various datasets captured from range scanners to LiDAR. Results demonstrate that our proposed method outperforms representative state-of-the-art approaches in terms of accuracy and is more suitable for registering large-scale point clouds. Furthermore, it is considerably faster and more robust than most competitors. Our implementation is publicly available at https://github.com/zikai1/GraphReg.

High-fidelity standard model reconstruction and verification of an airliner based on point clouds

Computational fluid dynamics (CFD) numerical simulation as the primary research tool is particularly essential for its credibility during the aerodynamic design of aircraft. To further promote CFD verification and validation on the airliner, a high-fidelity model reconstruction of the airliner is fundamental. Based on this, we put forward a novel framework, to our best knowledge, to reconstruct a high-fidelity standard model for an airliner efficiently, and the feasibility and accuracy of these reconstructed models are accessed by the CFD simulation-based validation method. First and foremost, a laser scanner was placed at each station around the airliner to scan and acquire multiview point clouds. Afterwards, the truncated least-squares-based algorithm was adopted to register these point clouds entirely. Additionally, we fitted the nonuniform rational basis spline surface based on the least-squares progressive and iterative approximation algorithm. Finally, CFD simulation results were compared and analyzed with the aerodynamic data obtained by the aircraft manufacturer under the same Mach number of the uniform model. It turns out that the coincidence between them is high, and the changing trend is basically consistent. Hence, this method is highly feasible and can establish a high-fidelity standard model of an airliner with unified high and low speeds so that its appearance, test data, and research results can be adopted as the standard data for CFD verification and validation.

A Practical O(N2) Outlier Removal Method for Correspondence-Based Point Cloud Registration

Point cloud registration (PCR) is an important and fundamental problem in 3D computer vision, whose goal is to seek an optimal rigid model to register a point cloud pair. Correspondence-based PCR techniques do not require initial guesses and gain more attentions. However, 3D keypoint techniques are much more difficult than their 2D counterparts, which results in extremely high outlier rates. Current robust techniques suffer from very high computational cost. In this paper, we propose a polynomial time ( O(N²), where N is the number of correspondences.) outlier removal method. Its basic idea is to reduce the input set into a smaller one with a lower outlier rate based on bound principle. To seek tight lower and upper bounds, we originally define two concepts, i.e., correspondence matrix (CM) and augmented correspondence matrix (ACM). We propose a cost function to minimize the determinant of CM or ACM, where the cost of CM rises to a tight lower bound and the cost of ACM leads to a tight upper bound. Then, we propose a scale-adaptive Cauchy estimator (SA-Cauchy) for further optimization. Extensive experiments on simulated and real PCR datasets demonstrate that the proposed method is robust at outlier rates above 99 percent and 1  ∼ 2 orders faster than its competitors. The source code will be made publicly available in https://ljy-rs.github.io/web/.

Fast and Robust Iterative Closest Point

The iterative closest point (ICP) algorithm and its variants are a fundamental technique for rigid registration between two point sets, with wide applications in different areas from robotics to 3D reconstruction. The main drawbacks for ICP are its slow convergence, as well as its sensitivity to outliers, missing data, and partial overlaps. Recent work such as Sparse ICP achieves robustness via sparsity optimization at the cost of computational speed. In this paper, we propose a new method for robust registration with fast convergence. First, we show that the classical point-to-point ICP can be treated as a majorization-minimization (MM) algorithm, and propose an Anderson acceleration approach to speed up its convergence. In addition, we introduce a robust error metric based on the Welsch's function, which is minimized efficiently using the MM algorithm with Anderson acceleration. On challenging datasets with noises and partial overlaps, we achieve similar or better accuracy than Sparse ICP while being at least an order of magnitude faster. Finally, we extend the robust formulation to point-to-plane ICP, and solve the resulting problem using a similar Anderson-accelerated MM strategy. Our robust ICP methods improve the registration accuracy on benchmark datasets while being competitive in computational time.