Classical methods

The Iterative Closest Point (ICP) algorithm is arguably the most commonly known registration method, originally created to register two point clouds by refining correspondences iteratively and reducing the Euclidean distance between pairs [13]. Its nature and simplicity meant that it became ubiquitous. ICP is highly initialization-sensitive and tends to settle to local minima in cases of significant misalignments or noise [24,25]. Further, ICP does not treat outliers strongly and performs poorly in non-uniform density situations. Sub-variants like Generalized ICP and Piecewise ICP were developed to overcome these limitations [16].

Piecewise ICP extends the traditional ICP framework through a decomposition strategy that partitions the point set into smaller constituent regions prior to alignment. This approach yields improved robustness when operating in structured environments, offering better convergence characteristics and more precise local geometry representation than traditional ICP [26]. However, this enhancement comes at the cost of increased computational overhead that grows with partition count, while maintaining sensitivity to noise artifacts and non-uniform point density variations [27].

Enhancements on classical point cloud registration methods focuses on accelerated ICP variants like point to plane multi-resolution ICP and GPU-ICP [28]. It is best suitable for large scale LiDAR datasets since it improves convergence speed. To improve the robustness under partially overlapped or sparsely distributed scans, a hybrid geometric frameworks that integrate voxel hashing and adaptive correspondence filtering have also introduced [29].

Feature based methods

Feature-based registration techniques are designed to address the weakness of purely geometric alignment by initially extracting descriptive features from the point cloud and then finding correspondences among these features [30,31]. Rather than comparing raw points directly, these techniques are based on invariant descriptors capturing the local or global scene structure. Spin Images, Point Signature, and the more popular Fast Point Feature Histogram (FPFH) are well-known descriptors [32]. After establishing correspondences, algorithms like RANSAC or Fast Global Registration (FGR) are utilized to estimate the transformation robustly [33,34].

Since features capture geometric context outside of raw point coordinates, feature-based registration’s main strength is its ability to handle large misalignments and partial overlaps [35]. For instance, FPFH together with RANSAC has worked well in achieving coarse global alignment even when datasets are noisy. Furthermore, these approaches give a good starting point to fine local refinements such as ICP and hence are common in two-stage registration pipelines.

Some of the feature based registration approaches incorporate graph-structured descriptors, like GCN-based local embeddings and GeoDesc [36]. It can capture higher order geometric relationships which improves correspondence reliability. To achieve robust matching under viewpoint changes and significant point sparsity methods like 3D3 and YOHO employ orientation-aware feature learning and hierarchical neighbourhood aggregation [37].

However, feature-based approaches also have drawbacks. To begin with, descriptor reliability is highly sensitive to the quality of the input data. Noisy or sparse point clouds tend to produce weak or ambiguous features, particularly in the presence of repetitive structures or low texture. Moreover, feature extraction per se can be computationally costly, especially for high-resolution scans. Third, global alignment is achievable though the precision of the transformation tends to be less than fine-grained methods like NDT or ICP and needs to follow a refinement stage.

Probabilistic and distribution-based methods

To overcome the limitations of ICP, probabilistic methods were implemented. Among them, the Normal Distributions Transform (NDT) emerged as a leading solution by mapping local point neighborhoods to Gaussian distributions to smooth noise effects and provide faster convergence [15]. While NDT improved robustness, it also caused discretization-related errors and required careful tuning of grid parameters [38,39].

The 3D Multi-Normal Distribution Transform (3DMNDT) expanded this concept by extending distribution modeling into three dimensions using multi-modal representations, enabling improved precision in complex environments [17]. Its advantage lies in achieving an effective balance between robustness and accuracy while reducing dependence on initial alignment. 3DMNDT, however, needs substantial memory because it stores multiple distributions per voxel and its runtime remains non-trivial for big-scale scans, which constrains its application in real-time robotics or dense 3D mapping [40].

The advancements in NDT based scan registration including multi-resolution voxel distribution models and Gaussian mixture-regression–based registration improves robustness against non-uniform sampling [41,42]. Also the point cloud registration methods employing kernel adaptive weighting have shown improved accuracy in highly dynamic or cluttered urban environments.

Robust estimation approaches

RANSAC-based methods were devised to address the issue of point correspondence outliers. The basic concept is that subsets of points are sampled iteratively, transform estimates are made, and they are tested against consensus sets. Classical RANSAC is robust but computationally costly, particularly with large data sets [33].

The One-Point RANSAC algorithm is highly efficient in limiting this computational cost by obtaining candidate transformations from minimal point correspondences, thus speeding up the consensus-building step [43]. This development allows for faster registration on outlier-prone data at the expense of reasonable accuracy. One-Point RANSAC loses robustness when point density is sparse or geometric features are less unique. The randomness involved in sampling still brings variability to performance and makes it less than ideal for high-accuracy applications [44].

In addition, robust kernels and probabilistic consistency filters such as Cauchy weighting [45], trimmed ICP, and correspondence rejection via geometric compatibility have shown strong resilience against structured outliers and partial overlaps [46].

Deep learning-based registration

Deep learning has in recent years been used in point cloud registration to introduce direct learning methods for features and correspondences [47]. DeepSIR is one such method that uses a neural network to learn strong correspondences while tolerating noise and partial overlap [48,49]. Deep learning techniques exhibit strong generalization over multi-different datasets and are capable of surpassing conventional methods when adequate training data is provided [50].

Although successful, learning-based approaches like DeepSIR have significant drawbacks. They need large-scale labeled training sets, which do not exist in many real-world problems. Inference also tends to be slower compared to classical approaches as a result of neural architecture complexity, and memory usage is considerably larger [51,52]. Generalization is also an issue with performance dropping when seen data distributions are not encountered during training.

Recent deep learning methods including Predator, GeoTransformer, and CoFiNet incorporate attention driven mechanisms to extract robust correspondences under low-overlap conditions [53–55]. The introduction of diffusion-based estimators and GNN-based alignment frameworks further enhance registration reliability and dataset generalization [56].

Some other popular methods include Coherent Point Drift (CPD), which formulates registration as a probability density estimation task, registering points by representing one set as centroids of a Gaussian Mixture Model [14,57]. CPD contains smooth alignment, albeit with higher computational complexity, especially for non-rigid deformations. Feature-based approaches, such as Fast Point Feature Histograms (FPFH) using RANSAC, enable coarse registration by selecting local descriptors but are generally sensitive to noise and perform poorly in repetitive scenes. Hybrid approaches that combine coarse global registration with fine local refinement (e.g., FGR + ICP) attempt to utilize the strengths of a variety of methods but also inherit complexity and parameter tuning overheads.

The above discussions on existing methods underscores the need for a point cloud registration framework that simultaneously ensures outlier robustness, uniform point density, and high computational efficiency. The RANDT scan matching presented here overcomes the tried to overcome the existing issues of uneven point distribution and noise disturbances. By redistributing points uniformly and adapting robust noise-handling methods, RANDT achieves improved density preservation (minimal NDI), better runtime, and reduced memory usage compared to state-of-the-art approaches. In contrast to ICP or its derivatives, RANDT is not trapped by local minima; in contrast to RANSAC-based solutions, it is determinism; and in contrast to learning-based approaches, it is not dependent on large-scale training. RANDT thus provides a well-balanced, generalizable, and real-time-capable solution to 3D scan matching. Fig 1 illustrates the development of several scan matching algorithms and their salient characteristics from the conventional to the suggested method.

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Fig 1. Progression of scan matching methods from traditional to proposed approach.

https://doi.org/10.1371/journal.pone.0345709.g001

Extended Normal Distribution based Scan Matching (ENDSM)

Sensor noise sometimes creates sparse outliers that decrease registration accuracy throughout the 3D mapping process. We add an outlier elimination mechanism based on the Interquartile Range (IQR) to the Normal Distributions Transform (NDT) framework in order to get around this restriction. For a stable NDT based scan matching outlier removal is necessary, especially when point density varies across the scene. Existing adaptive filters such as Statistical Outlier Removal (SOR) or radius-based methods are also efficient, but they depends on user-defined parameters and are sensitive to local density variations. However, the IQR threshold provides a simple, distribution-free, and robust statistic that suppresses extreme deviations without assuming Gaussian noise. So IQR based outlier removal is efficient and tuning-free alternative for handling non-uniformly distributed LiDAR point clouds. Fig 3 shows the impact of outlier removal in a sparse distributed point cloud.

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Fig 3. The effect of outlier elimination in point cloud (a) before outlier removal, (b) after outlier removal.

https://doi.org/10.1371/journal.pone.0345709.g003

Algorithm 1 introduces this extension, which is the Extented Normal Distribution Scan Matching(E-NDSM). The input reference scan is divided into uniform voxels in the first step. The set of points in a voxel is compactly represented by its mean vector and covariance matrix, creating a multivariate Gaussian distribution, rather than matching every point within each voxel. For each voxel, quartiles are computed over the scalar probability density values obtained from the multivariate Gaussian within each voxel, instead of computing voxels individually on x, y, and z coordinate dimensions. Hence it provides a single scalar metric for outlier evaluation. Since the pair can statistically describe the entire voxel, this lowers the difficulty of correspondence estimation [58]. Although the data are multi-dimensional, quartile-based outlier removal requires scalar values. Therefore, for each sample x, we compute a scalar distance measure from the Gaussian model using the Mahalanobis distance. Quartiles Q₁ and Q₃ are then computed from the distribution of these distance values across all samples.

(1)

Each Gaussian distribution is split into quartiles Q₁, Q₂, Q₃, Q₄ in order to eliminate outliers. The acceptable data interval is computed using Tukey’s rule [59]

(2)

and the interquartile range is determined as R = Q₃ − Q₁

Algorithm 1 Extended Normal Distribution Scan Matching

Require: Feature maps of two consecutive LiDAR scans X and Y,

  ,

Ensure: Best alignment of X with Y

1: Set X as the reference scan

2: Divide X into cells c_i of size r × r

3: Initialize the number of cells = N

4: Set

5: for all do

6:   Compute mean and covariance for each cell c_i

7:   Find the normal distribution for cell c_i

8:   Divide the normal distribution into quartiles Q₁, Q₂, Q₃, Q₄

9:   Calculate the interquartile range R = Q₃ − Q₁

10:   Define the normal data range as

11:   for all do

12:       if x_i < D or x_i > D then

13:        Eliminate x_i

14:       end if

15:   end for

16: end for

17: for all do

18:   Calculate probability distribution P(y_i) for each point y_i

19: end for

20: Select points y_i with high probability

21: for all y_i with high probability do

22:  Find the best alignment for y_i with x_i using Algorithm 3

23: end for

A data point is considered an outlier and removed if it falls outside of this range. Equation (1) is used to compare the probability distribution of each candidate point in the moving scan to that of its corresponding voxel in the reference scan after cleaning. Points are only kept as possible correspondences if their probability is high enough. By removing point-to-point comparisons that aren’t necessary, this method lowers processing costs while also increasing resilience against misleading points and noise.

Incremental scan matching with point density equalization

Conventional NDT and related techniques frequently result in non-uniform point densities across the registered scans, which can cause local misalignments and distortions. While ENDS-Matching successfully eliminates outliers. In order to solve this problem, we suggest an incremental scan matching process, which is explained in Algorithm 2, that gradually equalizes feature point densities while improving alignment. Feature extraction process selects geometric keypoints from the point clouds using local neighborhood structure and performs density-based filtering to retain only reliable and informative points for scan matching. The density-based filtering step used in feature extraction is inspired by density-clustering-based algorithm proposed by Deng et al. [60] which efficiently separates ground, object, and noise like meaningful points in LiDAR data using density information.

According to this method, the scan obtained at time t + 1 is the moving scan, and the scan obtained at time t is the reference scan. The keyframe, which is the matched frame that results from aligning the two scans, is elevated to the position of reference scan in the following iteration. In Algorithm 2, The ’Get’ operation retrieves the current fused reference model (keyframe), which has been incrementally constructed from previously aligned scans, while the ’Set’ operation updates this model by integrating features from the newly aligned scan. The procedure is then repeated using the prior reference scan as the moving scan. A schematic representation of the working of this proposed incremental scan matching is illustrated in Fig 2.

Through this sequential integration process, the system achieves a more compact and uniformly distributed collection of feature points that accumulates across multiple cycles, leading to progressively enhanced registration accuracy. Ultimately, the dense keyframe undergoes down sampling to guarantee consistent point distribution across the scan. In addition to fixing the problem of uneven point density, this incremental method increases stability across lengthy scan sequences, minimizes drift, and guarantees uniformity throughout the rebuilt 3D map.

Algorithm 2 Incremental Scan Matching

Require: Reference scan P, Moving scan Q

Ensure: Keyframe scan M

1: Extract features from P and Q to get feature maps and

2: Set as Reference scan and as Moving scan

3: for each scan pair do

4:  Match and (Algorithm 1)

5:  Get keyframe scan M₁

6:  Set Reference scan , Moving scan

7:  Repeat step 5

8:  Get keyframe scan M₂

9:  Set Reference scan , Moving scan

10:  Repeat step 5

11:  Get the final keyframe scan M₃

12:  Downsample the feature points of M₃

13:  return M₃

14: end for

Alignment of point sets

A final alignment step is necessary to produce the best transformation between the reference and moving scans, even while ENDS-Matching and incremental refinement offer coarse-to-intermediate level registration. Algorithm 3 describes the alignment procedure, which calculates translation, rotation, and scaling parameters to reduce the residual error between the two point sets. Let Q= be the moving scan and P= be the reference scan. Both point sets are mean-centered by subtracting their respective centroids, such that each transformed point and is aligned around the origin. By removing the impact of translation, this pre-processing step guarantees that the scan matching procedure that follows will only concentrate on the variations in rotation and scaling between the two point sets.

After mean-centering the point sets, the cross-covariance matrix is constructed and subjected to Singular Value Decomposition (SVD), yielding

(3)

The rotation is estimated using the classical SVD-based solution [61]:

(4)

while the scaling factor a and the translation vector are computed simultaneously. Using these parameters, the moving scan is iteratively aligned to the reference scan according to the transformation

(5)

The scaling factor is used only as a normalization factor in intermediate computations and does not modify the global scale; the final transformation applied to the LiDAR scans remains rigid.

Algorithm 3 Alignment Algorithm

Require: Two sets of n points P and Q

1:

2:

Ensure: X_t: Continuous transition from point set P to point set Q

3: Compute mean ,

4: Recenter the data points ,

5: Compute the k × k matrix

6: Calculate Singular Value Decomposition (SVD),

7: Compute Orthogonal Matrix , Translation vector ,

8: Repeat steps 4 and 5 with

9: Obtain the transition

ModelNet40 object registration

Fig 5 presents the registration results for object-level scans from the ModelNet40 dataset. The original moving scans are shown on the left, and the aligned scans using the proposed RANDT method and other baseline methods are shown on the right. Our RANDT method generates accurate alignment of objects even with sparsely distributed points and partial overlaps. Also our method preserve effectively fine structural features like corners and edges. Through point density uniformity feature of our RANDT method, it maintains a consistent point density across the scan, improving the clarity and completeness of the registered structure. The qualitative assessment involved evaluating the alignment of geometric features, retention of object details, and uniformity of point distribution which are the main aspects for 3D object recognition and reconstruction.

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Fig 5. Object-level registration on ModelNet40: Comparison of proposed method Classical NDT,ML-NDT,Piecewise ICP.

https://doi.org/10.1371/journal.pone.0345709.g005

Registration Accuracy: RMSE and chamfer distance

Table 1 shows the evaluation of registration performance of our RANDT method with other baseline methods on the KITTI dataset, RMSE comparison, Chamfer distance, execution time, point count after registration, overlap ratio, and standard deviation of point density are compared with existing algorithms. The proposed RANDT approach outperforms the existing methods, obtaining lowest RMSE (0.062 m) and Chamfer distance (0.071 m), than both traditional and learning-based baselines. Classical algorithms such as NDT and Piecewise ICP shows larger alignment errors, especially in sparse regions, whereas learning-based models like DCP and DeepSIR were more affected by partial overlaps and outliers. The enhanced accuracy and efficiency of the RANDT method arise from its combination of outlier removal, point density uniformity preserving feature through incremental scan matching.

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Table 1. Performance comparison of registration methods on KITTI dataset.

https://doi.org/10.1371/journal.pone.0345709.t001

Table 2 shows the evaluation on ModelNet40 dataset. Both RMSE and Chamfer distance were evaluated and compared with baseline methods. The proposed approach achieves the lowest RMSE (0.054 m) and Chamfer distance (0.063 m). Here also our method achieves the state-of-the-art performance and shows accurate alignment and enhanced consistency in object-level registration. These results strngthens our method’s generalization capability across various datasets and registration environments.

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Table 2. Performance comparison of registration methods on ModelNet40 dataset.

https://doi.org/10.1371/journal.pone.0345709.t002

Fig 6 illustrate the convergence plot that simulates typical RMSE reduction during the iterative scan matching process which provides the comparison of convergance behaviour of all baseline registration methods. Since our datasets do not provide iteration-by-iteration error logs in a consistent form, a synthetic plot provides a unified way to visualize how error reduces across iterations. It also reflects the relative performance trends observed in our experiments. Proposed RANDT method converges more rapidly and reaches a lowest RMSE than Piecewise-ICP, NDT based methods, and RANSAC-based methods, illustrating its reduced susceptibility to local minima.

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Fig 6. Convergance comparison of registration methods.

https://doi.org/10.1371/journal.pone.0345709.g006

Execution time

The computational efficiency of the proposed RANDT approach was validated against leading point cloud registration methods. The execution times was evaluated on both the KITTI and ModelNet40 datasets, as depicted in Fig 7.

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Fig 7. Execution time comparison across registration methods.

https://doi.org/10.1371/journal.pone.0345709.g007

Deep learning based registration methods, such as DCP and DeepSIR, shows significantly higher runtimes (3.15 s and 3.4 s on KITTI, respectively), mainly due to the computational overhead of neural network inference and iterative optimization. However, traditional methods exhibits different timing characteristics: ML-NDT achieved comparatively better performance (1.12 s on KITTI), whereas Classical NDT and correspondence-based approaches like PRE RANSAC and Piecewise ICP incurred moderate to high computational costs. Our RANDT method recorded execution times of 1.68 s on KITTI and 1.05 s on ModelNet40, and exhibit superior registration accuracy. Its efficiency is mainly beause of the incremental alignment procedure and outlier elimination procedure that avoid the need for extensive feature extraction, descriptor computation, or deep learning inference. The method’s focus on both accuracy and computational efficiency makes it especially well suited for real time and time sensitive tasks in robotics, autonomous systems, and 3D reconstruction, where both precision and processing speed are crucial.

Point density uniformity

For the quantitative evaluation of the point density uniformity, we calculated the deviation of point counts within local voxels across all aligned scans. A lower standard deviation signifies a more uniform spatial distribution of points, indicating higher density uniformity, whereas a higher value suggests clustering or irregular spacing.

Table 3 listed the standard deviation values for both the KITTI and ModelNet40 datasets. The proposed method attains the lowest standard deviation (0.015 for KITTI and 0.012 for ModelNet40), achieves better results over both traditional and learning-based registration techniques. These results demonstrate that combining incremental alignment with outlier removal yields dense, uniformly distributed point clouds scenes which is particularly valuable for regions with low density or partial overlap. Results shows that the incremental scan matching process converges quickly. Density uniformity stabilizes after approximately 3–5 keyframes. For the next iterations it shows only a negligible change in voxel-wise density variation which is less than 5%. This indicates that only a small number of incremental updates are required to achieve consistent point-density equalization across sequences.

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Table 3. The standard deviation of point density for the KITTI and ModelNet40 datasets.

https://doi.org/10.1371/journal.pone.0345709.t003

Visual analysis further demonstrates that our RANDT method maintains consistent density while preserving geometric fidelity. Fig 8 illustrates the point density uniformity calculation across different methods. In contrast, conventional methods such as NDT and Piecewise ICP show greater variability in point density, and deep learning–based approaches like DCP are more prone to irregular density in sparse or noisy areas.

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Fig 8. Comparison of point density uniformity across methods.

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Point density uniformity index

We evaluated how the uniformity of point density affects registration accuracy across both traditional and learning-based approaches. Unlike earlier research that mainly uses overlap ratio to measure the scan alignment difficulty, we argue that overlap alone fails to capture the spatial consistency of point distribution within a scan. To address this drawback, we propose a Point Density Uniformity (PDU) index that quantitatively estimate the uniformity of point distribution throughout the scan volume.

Let a point cloud be partitioned into M equally sized voxels V_i, each containing n_i points. The Point Density Uniformity Index is defined as:

(6)

where is the mean number of points per voxel and is the standard deviation of points across all voxels.

A Point Density Uniformity(PDU) value approaching 1 indicates a more evenly distributed set of points across the scene, while smaller values denotes uneven density with areas of sparse or clustered points. To determine how point distribution uniformity influences registration performance, each algorithm was tested on consecutive KITTI LiDAR frames exhibiting different density characteristics. The PDU was measured prior to registration for every algorithm, and the Mean Absolute Errors (MAE) for rotation and translation were calculated after registration. Fig 9 shows that the registration accuracy improves as the point density uniformity index increases. The main findings are, the rotation MAE consistently decreases as the PDU increases. It shows that more uniformly distributed point clouds lead to more accurate rotational transformation estimations. The average rotation error decreases from approximately 8.7° to 2.7° when PDU increases from 0.68 to 0.92. Likewise, the translation MAE decreases from 15 cm to 5 cm across the same range.

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Fig 9. Relationship between Point Density Uniformity (PDU) and registration accuracy.

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This interdependance underscores the strong link between uniform point distribution and the stable convergence of the registration process. The proposed approach attains the highest PDU value (0.92), demonstrating that the combination of incremental scan matching and Interquartile Range (IQR)-based outlier removal produces a balanced and dense point distribution, which in turn enhances alignment accuracy.

To evaluate the influence of distribution uniformity on registration performance, each technique was tested on consecutive KITTI LiDAR frames exhibiting different density patterns. The PDU was calculated before registration process for every method, and the resulting rotation and translation Mean Absolute Errors (MAE) were measured after alignment of scans.

Robustness evaluation

For the robustness analysis of our RANDT method, it is evaluated with baseline algorithms under challenging conditions including Gaussian noise ( m), random outliers (10%), and partial overlaps (50%). The RMSE results for all evaluated scenarios were summarized in Table 4. For each experiments,outliers and synthetic noise were added to the moving scans. Partial overlap was created by removing a portion of their points. The RMSE was calculated by comparing each registered scan with its corresponding reference scan.

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Table 4. Robustness evaluation under noise, outliers, and partial overlap.

https://doi.org/10.1371/journal.pone.0345709.t004

We can see a gradual decerease in the RMSE values with our RANDT method. This indicates a strong resilience against measurement noise, point corruption, and incomplete data. In contrast, traditional NDT and ICP-based algorithms showed substantial drops in accuracy under these perturbations, and learning-based methods such as DCP exhibited vulnerability to unfamiliar noise patterns and limited overlap. A visual comparison of robustness analysis is illustrated in Fig 10. This indicates that the proposed method preserves accurate alignment and geometric integrity under every tested scenario.

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Fig 10. Robustness analysis under noise, outliers, and partial overlap.

https://doi.org/10.1371/journal.pone.0345709.g010

To evaluate the robustness of the proposed RANDT method which is a combination of extended normal distribution transform and incremental scan matching, experiments were conducted on the ModelNet40 dataset under varying noise conditions. Gaussian noise with variance values of 0.01 m², 0.02 m², 0.03 m², 0.04 m², and 0.05 m² was artificially included to the point cloud data to simulate real-world sensor disturbances. The mean absolute error (MAE) in both rotation (°) and translation (cm) was measured for each case to assess the registration accuracy.

Fig 11 shows that both rotation and translation errors progressively increases with more noise variance. This trend demonstrates the sensitivity of conventional registration methods, such as standard NDT, to measurement noise. Random disturbances alter the underlying probability density within voxel-based representations, resulting in erroneous point correspondences and biased transformation estimations that ultimately reduce registration accuracy.

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Fig 11. Comparison of registration accuracy before (a) and after(b) applying the proposed outlier elimination module within the RANDT framework.

https://doi.org/10.1371/journal.pone.0345709.g011

The experimental evaluation of registration accuracy of RANDT method with and without outlier removal feature is depicted in Fig 10. The before outlier elimination correspond to our proposed RANDT method with incremental scan matching module only, while the after outlier elimination correspond to the proposed scan matching framework with outlier removal feature and incremental matching of scans. It clearly shows that proposed method performs well with outlier elimination feature especially in sparsely distributed point clouds. We can see that proposed method with outlier elimination reduces both rotation and translation MAE across all tested noise levels. For instance, at a noise variance of 0.05 m², the rotation MAE decreases from 1.923° to 1.416°, and the translation MAE decreases from 2.287 cm to 1.742 cm. By removing the noises and refining points according to local statistical coherence, the resulting voxel models accurately capture more detailed surface structure of the point cloud scene. This refinement stabilizes gradient estimation during optimization, promoting faster convergence and improved alignment precision.

Due to the outlier removal feature of our method the resulting point cloud scene attains a more balanced and equalized point distribution. It will reduce the uneven distribution of points that often weakens the state-of-the-art methods. These developments has broad application prospects especially in areas such as geo-spatial analysis, 3D reconstruction and autonomous navigation. In all these applications point cloud registration is one of the key aspect for precise 3D map construction.