This paper presents an improved methodology for point cloud registration using curvature-based feature descriptors. The core contribution is the adoption of the Umbrella Curvature method for curvature estimation, evaluated against the standard Surface Variance approach under various noise conditions. To enhance robustness, local variance features are introduced alongside curvature, forming a composite descriptor for more reliable point matching. Registration is performed using a modified Iterative Closest Point (ICP) algorithm leveraging these features. Extensive experiments demonstrate that Umbrella Curvature significantly improves alignment accuracy, particularly under high noise, and that the proposed feature aggregation further enhances robustness. Some limitations in specific geometric configurations are discussed.
performance compared to traditional eigenvalue-based techniques.
Earlier, Pauly et al. [
Alternative curvature estimation strategies include fit- tested on Google Colab, with the code structured into ting local surfaces to point sets. Zhang et al. [15] pro- modular functions to ensure clarity and reproducibility. posed estimating curvature by fitting normal sections in Public datasets and annotated notebooks were used to multiple directions, ofering improved stability compared facilitate consistent experimentation. to direct covariance analysis. Such methods, however, typically incur higher computational costs. 3.1. Data Acquisition
Neighbor Selection. Accurate curvature estimation
strongly depends on the choice of neighboring points. The datasets were sourced from the Stanford 3D Scanning
Park et al. [16] introduced the Elliptic Gabriel Graph Repository1, a well-known benchmark containing
high(EGG) for selecting neighbors that better capture local resolution 3D scans. Three objects were selected—Bunny,
geometric relationships. Friedman et al. [
Point Cloud Feature Extraction. Beyond hand-crafted the selected objects.
features, learning-based methods such as Xiang et al. [
Registration Algorithms. The Iterative Closest Point KD-Tree-based search for retrieving the nearest
neigh(ICP) algorithm [
Other works, like Bae and Lichti [
Summary. Overall, while many approaches leverage curvature and variance for analysis, the combination 3.3. Curvature Estimation of umbrella curvature estimation, local variance filtering, and noise-robust feature aggregation within an ICP We implemented and compared two curvature estimaframework remains relatively unexplored. This paper tion methods: Surface Variance Curvature and Umbrella aims to systematically study and validate these contribu- Curvature. tions under noisy conditions.
Umbrella Curvature [
min ∑︀3
=1 UM = ∑︁ ⃒ ⃒ − =1 ⃒⃒ ‖ − ‖ · ⃒⃒ ⃒ ⃒
and is the surface normal. The normalized displacement vectors are projected onto the normal vector, and vature value.
To assess robustness, Gaussian noise was synthetically added to point clouds. Two noise-resilient curvature methods were developed.
new_points = neighbors − median(neighbors)
The second, Umbrella-3, applies a sliding window median filter to the neighborhood: 1: ← 2: Initialize
neighbors of
5: 6: 7: end for
Update with [] filtered [] ← median()
Point cloud alignment was performed using a modified version of ICP. Traditional ICP uses proximity-based cortheir absolute projections are summed to obtain the cur- pairs, stabilized or when a maximum number of iterations respondence; we instead introduced feature-based match- three served as sources. Registration performance was ing using curvature and local variance.
In the first variant (ICP-Curvature), for each source point , nearest target neighbors are found. The neigh- lap of aligned scans. bor with the most similar curvature is selected if the diference is below a threshold 1.
(1) (2) after curvature-based selection, local variance is also compared. The match is accepted only if the variance diference is below a second threshold 2.
Rigid transformations were computed using Singular Value Decomposition (SVD). After computing and centering the centroids of the correspondence pairs, the covariance matrix was formed, and SVD was applied: = ︂[ 0 1 ︂]
To balance accuracy, robustness, and speed, parameters were chosen based on prior work and empirical tuning. For curvature estimation, = 8 neighbors were used. In the Umbrella method, cosine similarity ensured even distribution. ICP correspondence search used = 50 neighbors, while local variance was computed using 1000 points.
Thresholds for feature matching were set to 1 = 2 = 0.0001, based on analysis of feature value distributions. The median filter window for Umbrella-3 was set to size 5. ICP typically ran for 50–100 iterations, with early stopping if no improvement was observed. Some tests downsampled 50% of the points to study eficiency.
To validate the efectiveness of the proposed methods, we conducted a series of experiments on several real-world point clouds. These experiments used both clean and synthetically noised data, enabling evaluation under diverse conditions. We focused on quantitative comparisons and visual inspections to assess registration quality.
lecting four scans per object (Bunny, Armadillo, Dragon). One scan was chosen as the target, while the other measured using the mean Euclidean distance between matched point pairs (registration error) and visual over
Algorithm 1 ICP using Curvature Feature 1: Initialize empty correspondence sets. 2: for each point in source point cloud do 3: Find nearest neighbors of in target point cloud. 4: For each neighbor, compute curvature diference. 5: Select neighbor with minimum curvature diference. 6: if curvature diference ≤ 1 then 7: Add (, ) to correspondence set. 8: end if 9: end for 10: Estimate optimal transformation from correspondences. 11: Apply transformation to source cloud. 12: Repeat until convergence.
Algorithm 2 ICP using Curvature and Local Variance 1: Initialize empty correspondence sets. 2: for each point in source point cloud do 3: Find nearest neighbors of in target point cloud. 4: For each neighbor, compute curvature diference. 5: Select neighbor with minimum curvature diference. 6: if curvature diference ≤ 1 then 7: Compute local variance at and . 8: if variance diference ≤ 2 then 9: Add (, ) to correspondence set. 10: end if 11: end if 12: end for 13: Estimate optimal transformation from correspondences. 14: Apply transformation to source cloud. 15: Repeat until convergence.
Variation. As summarized in Tables 1 to 3, Umbrella Cur- hood size in the curvature computation. Experiments vature generally produced lower registration errors and using = 8 and = 100 neighbors (Tables 8 to 10) required fewer ICP iterations. Visualizations in Figures 1 showed that while a larger neighborhood occasionally to 9 confirm that this method better preserves geometric led to faster convergence, it also risked oversmoothing details during alignment. Nonetheless, failure cases oc- the geometry. We therefore adopted = 8 as the default curred when the initial misalignment was large or when to maintain local detail. diferent regions of the object had similar curvature char- Finally, we tested robustness to noise by adding Gausacteristics—such as the Bunny’s head and back. sian perturbations to the source point clouds. Variants
To evaluate computational eficiency, we downsam- of the Umbrella curvature method—including median pled the point clouds to 50% of their original size. As centering (Umbrella2), local filtering (Umbrella3), and shown in Table 4, this introduced only a small increase the combination of Umbrella3 with local variance—were in error, suggesting that downsampling ofers a practical compared. Results, shown in Tables 11 to 13 and Figtrade-of between speed and accuracy. ures 10 to 12, indicate that both Umbrella2 and Umbrella3
We also explored enhancements to the base curvature improve noise resilience. The most robust variant, Umdescriptor. Adding a local variance feature improved reg- brella3 with local variance, achieved very low registration istration accuracy in most cases, particularly in regions errors in several cases, although some visually incorrect with ambiguous curvature but difering point dispersion alignments occurred under heavy noise—highlighting (see Tables 5 to 7). For the Dragon model, however, the the limits of local variance in such conditions. efect was inconsistent, indicating that the benefit may In summary, the experiments demonstrate that Umbe data-dependent. brella curvature outperforms Surface Variation for point Another important factor was the choice of neighbor- cloud registration, particularly when combined with local variance or median filtering. These improvements remain efective across clean, downsampled, and noisy data, confirming the proposed method’s robustness and accuracy.
This work investigated the use of curvature-based features to enhance point cloud registration, particularly under challenging conditions such as noise and partial data. The proposed approach combined Umbrella Curvature estimation with local variance filtering, and extended the traditional ICP algorithm using feature-driven matching strategies.
The experimental results highlighted several key findings. Umbrella Curvature consistently outperformed Surface Variation in providing reliable and discriminative geometric descriptors, leading to lower registration errors and faster convergence. The addition of local variance proved useful in distinguishing between regions with similar curvature, especially when those regions originated from diferent parts of the object. Moreover, the robustness of the method was significantly improved by incorporating median-based centering and local filtering prior to curvature estimation. Even when point clouds were downsampled to half their original size, the registration remained accurate and eficient, demonstrating the method’s scalability.
Despite these promising results, some limitations were observed. A low numerical registration error did not always imply correct alignment, particularly in cases involving large initial misalignments or symmetric geometries. Additionally, while local variance was helpful in clean data scenarios, its efectiveness diminished under strong noise. The method also encountered dificulties when dealing with large flat surfaces or repeated structures that exhibit similar curvature patterns.
Looking ahead, future work will explore the integration of global geometric descriptors or semantic segmentation to improve performance in ambiguous regions. Adaptive strategies for selecting neighborhood sizes based on local point density and noise characteristics may also enhance accuracy. Furthermore, extending the method to non-rigid registration tasks—where local deformations occur—presents an exciting direction. Finally, learning-based curvature estimation could be investigated as a means to further improve robustness and generalization.
In conclusion, the results confirm that combining welldesigned curvature descriptors with local statistical features can lead to substantial improvements in point cloud registration, even under noisy and incomplete conditions.
During the preparation of this work, the authors used ChatGPT, Grammarly in order to: Grammar and spelling check, Paraphrase and reword. After using this tool/service, the authors reviewed and edited the content as needed and take full responsibility for the publication’s content.
Bunny Armadillo Dragon
Umbrella Method Surface Variance Umbrella Method Surface Variance Umbrella Method Surface Variance Noise + Umbrella Noise + Umbrella2
Noise + Umbrella3 Noise + Umbrella3 + local variance