Design of an enhanced feature point matching algorithm utilizing 3D laser scanning technology for sculpture design

3D laser scanning data

For effective model design, 3D laser scanning technology requires accurate acquisition and processing of point cloud data. Raw data from 3D laser scanners often entail large volumes, high residuals, unstructured and uneven sampling distributions, and incompleteness. Post-processing is essential before the data can be used in design applications. Key advancements in the intelligent processing of point cloud data encompass point cloud data model integration (Tian et al., 2021), data quality enhancement, data characterization and extraction (Chen et al., 2024), and data model reconstruction (Chen et al., 2018).

Wang et al. (2022) explores external data acquisition methods of terrestrial 3D laser scanning technology from an engineering perspective, summarizing the advantages, disadvantages, and corresponding scopes of application for each technique. Kang et al. (2023) discusses point cloud data acquisition and processing technologies for the Nanjing subway tunnel project, yielding high-quality point cloud data. Benchekroun (2022) applies 3D laser scanning to cultural heritage sites, examining heritage buildings’ rapid laser scanning method. It rapidly scans the National Southwest United University site, offering a reference for archiving and digitizing historical relics and sites.

Despite its speed and sampling density advantages over traditional methods, 3D laser scanning produces point cloud data with high redundancy, nonlinear error distribution, and incompleteness, challenging intelligent processing. Wang, Yin & Jing (2023) investigates standard point cloud filtering algorithms based on the PCL library to address these issues, analyzing algorithm parameter settings for optimal filtering effects. It identifies the best waveform algorithm and proposes a hybrid approach combining Gaussian filtering.

For complex building point cloud data segmentation challenges such as low efficiency, poor noise resistance, and low accuracy, Xu, Li & Chen (2022) focuses on building roof structures. The method improves efficiency by collecting and comparing accurate building point cloud data.

Feature point matching algorithm based on 3D laser scanning technology

The growing advancement of 3D laser scanning technology has led to an expansion of its application areas. Mi et al. (2023) reports the application of this technology in obtaining substantial point cloud data of pit enclosure walls. Through meticulous point cloud processing and modeling, the study conducted in-depth deformation analysis using advanced software. The technology excelled in matching feature points and accurately revealing three-dimensional overall deformation and two-dimensional local deformation of the pit enclosure wall. Additionally, the study compared the differences between the two monitoring techniques regarding deformation magnitude and monitoring accuracy, providing critical data support for engineering practice. However, McDonald, Robinson & Tian (2022) reveals that while 3D scanning demonstrates clear benefits in scope and efficiency for pit monitoring, it lags behind traditional monitoring methods regarding accuracy and interference level, which introduces potential bias in monitoring outcomes.

Integrating 3D laser scanning technology and building information modeling technology has emerged as a significant research focus in the architectural field. Scholars are exploring novel intelligent construction quality inspection methods and assessment techniques for more precise corrective system design. Yue et al. (2024) employs 3D laser scanning technology to match feature points for construction quality inspection. Xu et al. (2023) explores terrestrial 3D laser scanners in building stereoscopy, collecting 3D spatial data of target building surfaces. The study suggests extracting the building’s center axis from the point cloud using a random sample consensus algorithm to fit straight lines and an overall least squares method to fit planes, achieving precise feature point matching for building flatness and perpendicularity.

Wang et al. (2021) introduces a comprehensive assessment of wall flatness through 3D laser scanning. By calculating the curvature of wall contour lines and analyzing the relationship between curvature features and flatness, efficient feature point matching of the wall point cloud was achieved using the least squares method. Moreover, Yao et al. (2022) utilizes SIFT operator (Pan et al., 2024) and ORB operator (Yang et al., 2019) to extract image features from infrared and visible images for image matching, although large rotation angles between images may reduce matching accuracy. Huang et al. (2023) suggests a stereo-matching method based on bootstrap image and adaptive support domain, offering less operational difficulty but lower resistance to varying illumination conditions. Wei & Meng (2023), Wu & Chiu (2023), Guo et al. (2024) proposes a pattern of matching light and color information features to achieve image matching with better effects; however, the matching effect may need validation for pictures with poor quality.

Despite the advancements in feature point matching methods, specific challenges persist, particularly in specialized application scenarios such as sculpture design. Sculptures often exhibit complex and variable shapes, making direct measurement nearly unfeasible. In response to this issue, this article introduces an innovative nearest point iteration algorithm grounded in the principle of feature point matching. The algorithm aims to enhance efficiency and accuracy in feature point matching, offering robust technical support for 3D modeling and shape correction analysis within sculpture design.

Feature point pairs

In 3D laser scanning technology, feature points are crucial identification markers in 3D stitching. In this article, feature points are designated as the overlapping region between two viewpoints of the sculpture under examination. Using a three-dimensional laser scanning system, two local surfaces of the sculpture are scanned to obtain physical point cloud data for both surfaces.

To ensure the accuracy of these measurements, the feature point sets of the two distinct local surfaces are pre-established. These sets are defined as follows:

(1) $$M=\{m_i\},i=q,2,...,k$$

(2) $$N=\{n_i\},i=1,2,...,k.$$

Then, according to the spatial feature invariance of the feature points, n sets of matching point pairs $U=\{u_i,u_i\in M\}$ and $V=\{v_i,v_i\in N\}$ can be obtained. U and V are the subsets of the 3D data point sets obtained under the two surfaces, respectively, and $u_i$ and $v_i$ are one-to-one correspondences. On this basis, according to the principle of 3D data stitching technique, let the rotation matrix R and translation vector T satisfy the following objective function to obtain the minimum value:

(3) $$e^2(R,T)={\displaystyle \frac{1}{n}\sum _{i=1}^n||v_i-(R\times u_i+T)|{|}^2.}$$

To obtain the coordinate transformation matrix, according to the feature point sets $X=\{x_i\},i=1,2,...,n$ and $Y=\{y_i\},i=1,2,...,n$ in two views of 3D space, the rotation matrix R and translation matrix can be obtained by the following Singular Value Decomposition (SVD) decomposition method, which ensures that the splicing is free from aberrations and has relatively high accuracy. Thus, Eq. (3) can be varied under the SVD decomposition method as:

(4) $$e^2(R,T)={\displaystyle \frac{1}{n}||Y-R\times X-T\times H^T|{|}^2}$$where $H=\{1,1,...,1{\}}^T$, and according to the regular array (Eq. (5)):

(5) $$K=I-{\displaystyle \frac{1}{n}H\times H^T}$$

SVD analysis can be performed using $K^2=K^T=K$ and $P={\displaystyle \frac{1}{n}Y\times K\times X^T}$ to obtain R. For spatial point sets, the calculation is done separately:

(6) $$u_x={\displaystyle \frac{1}{n}\sum _{i=1}^n{x}_i}$$

(7) $$u_y={\displaystyle \frac{1}{n}\sum _{i=1}^n{y}_i.}$$

Calculate the translation vector $T=u_y-R\times u_x$. After obtaining R and T, any point $y_i$ in the feature point set Y can be transformed into X by the following equation:

(8) $$y_i=x_i\times R+T.$$

The two data sets are eventually transformed to the same coordinate system, resulting in a coarse splice.

Precise splicing and iterative matching

Following the initial rough splicing and rapid real-time matching of 3D laser scanning images, the process leverages the initial matching point pairs derived from feature points to establish the splicing position of the two local surfaces as the starting point for localization. The specific process is shown in Fig. 3. To achieve iterative matching for precise stitching, enhancements are made to the existing ICP algorithm. The rough feature point pairs are filtered based on a distance threshold, ensuring that only points within the correct matching region are included in the exact matching point pairs.

Although conventional ICP algorithms may suffer from slow computation speeds, this limitation is addressed by setting a specific neighborhood dimension as the distance threshold and calculating distances between any two points within that range. This approach significantly reduces splicing time and accelerates computation by processing only point cloud data within the neighborhood that falls within the small distance threshold.

Therefore, in this article, we propose to use the mean square distance between two points as the metric of the distance between nearest neighbors and let $X^{m-1}=\{x_i\},i=1,2,...,r$ and $Y^{m-1}=\{y_i\},i=1,2,...,r$ be the data point sets of the nearest points obtained in m-1 iterations, respectively. Then the mean square distance between the point sets $X^{m-1}$ and $Y^{m-1}$ is:

(11) $$S={\displaystyle \frac{1}{r}\sum _{i=1}^r||x_i-y_i|{|}^2}$$where r is the number of point cloud data in the overlapping surfaces, and the convergence speed of the algorithm can be significantly accelerated by using this nearest point distance metric. Therefore, the error threshold S is set in the iterative matching, and the coordinate transformation matrices $R_0$ and $T_0$ the 3D data splicing are solved. The coordinate transformations of the two groups of point cloud data are carried out according to the initial coordinate transformation relationship. Finally, the distance between the two groups of point cloud data after the transformations is obtained $S_1$. According to the distance threshold constraints, the closest matching point pairs in the two groups of matching point clouds are searched. After eliminating the invalid matching pairs, the closest matching pairs are then optimized using the four-element algorithm with correction coefficients to solve for the transformation parameters $R_1$ and $T_1$. The above two sets of point cloud data are transformed again using $R_1$ and $T_1$, the distance between them after this transformation is found out at $S_2$. If $S_2$ is less than the initial threshold S, then stop searching. Otherwise, the search continues until $S_i$ is smaller than the initial threshold. Eventually, the most accurate feature point match is found when the search stops.

Evaluation indicators

To assess the accuracy of alignment, this study employs two metrics: mean rotation angle error (MRAE) and mean translation error (MTE). MRAE is utilized to quantify the degree of deviation in the rotation angle during the registration process. This error value is obtained by calculating the rotational angle errors at multiple measurement points and then averaging them. MTE, on the other hand, describes the translational discrepancy between the measurement results and the reference values. This type of error can be expressed as the average of the translational differences between all measurement and reference values. In evaluating registration accuracy, the mean translation error provides insights into the positional offsets generated during registration. Generally, a smaller mean translation error indicates more precise registration results, while a larger error may suggest significant deviations in the registration process. Assuming there are a total of n measurements, the formula for calculating MRAE is as follows:

(12) $$\mathrm{M}\mathrm{R}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{n}\sum _i^n{\displaystyle \frac{|R_i-T_i|}{T_i}}}$$where $R_i$ is the actual output angle and $T_i$ is the theoretical output angle.

The formula for MTE is as follows:

(13) $$MTE={\displaystyle \frac{1}{n}\sum _{i=1}^n|M_i-Value|}$$where $M_i$ is the actual measured value and value is the reference value.

Comparative analysis

By examining the overlapping region of two views of a sculpture, an advanced 3D measurement system is employed to capture the two local surfaces precisely, enabling the alignment and comparison of feature points. Successful feature alignment offers high-quality initial values for the subsequent ICP algorithm throughout the alignment process, playing a pivotal role in enhancing overall alignment accuracy. Given the influence of the sampling interval on the volume of point cloud data, tests are conducted at various intervals to assess the matching success rates of different algorithms and the number of feature points. The results displayed in Fig. 4 are obtained through thorough comparisons and experimental analyses.

The figure illustrates a strong correlation between the matching success rate and the sampling interval. When the distance threshold is relatively tiny, the matching accuracy of both algorithms is low. This is because a minimal threshold limits the number of matching points. As the distance threshold increases, the matching accuracy of the FM-ICP-FPM algorithm rapidly improves and reaches an optimum within a specific threshold range. In contrast, the traditional ICP algorithm exhibits slower improvement in matching accuracy when the distance threshold is significant, and it is prone to being affected by incorrect matching points. Across all tested distance thresholds, the matching accuracy of the FM-ICP-FPM algorithm is higher than that of the traditional ICP algorithm. By introducing feature point matching and gradient histogram feature vectors, the FM-ICP-FPM algorithm enhances the accuracy and robustness of matching. Especially when the distance threshold is moderate, this algorithm can screen out more precise matching points, thereby improving the overall matching accuracy. Notably, the FM-ICP-FPM algorithm proposed in this article demonstrates superior performance at sampling intervals of 200 and 300, achieving a success rate of 100%—considerably higher than the 83% peak success rate of the SIFT-ORB-FPM algorithm. This finding indicates that the FM-ICP-FPM algorithm boasts exceptional accuracy and stability in feature point matching and alignment, offering a promising and practical approach to 3D reconstruction and alignment.

After a comprehensive analysis of the impact of sampling intervals on the success rate of feature point matching, this section proceeds to select several representative sampling intervals and conduct comparative tests on the MRAE and MTE performance metrics across different algorithms. As depicted in Fig. 5, the proposed FM-ICP-FPM algorithm demonstrates clear superiority across all metrics. It is evident from the figure that the performance of LS-FPM, SIFT-ORB-FPM, and GI-ASD-FPM in terms of MRAE and MTE is notably inferior to that of the FM-ICP-FPM algorithm.

A notable observation emerges from the data: as the number of sampling points increases from 200 to 300, the MRAE and MTE performance metrics of the compared algorithms undergo a marked decline. Specifically, while the GI-ASD-FPM algorithm demonstrates improvements relative to LS-FPM and SIFT-ORB-FPM, its performance still sees a significant drop, with the MTE rising from 201 at a sampling interval of 200 to 479 at an interval of 300. In stark contrast, the FM-ICP-FPM algorithm stands out, achieving a remarkable matching success rate of 100% at a sampling interval of 200. Moreover, its MTE of 154 and MRAE of 0.065 are considerably lower than those of the other algorithms, highlighting its superior performance in terms of accuracy and reliability.

This result demonstrates that the FM-ICP-FPM algorithm effectively minimizes alignment error and enhances alignment accuracy while maintaining a high matching success rate. These findings offer a more reliable and efficient approach to feature point matching and correction system design in sculpture creation.

Feature point matching efficiency test

Figure 5 provides an in-depth look at the performance of the proposed FM-ICP-FPM algorithm at a sampling interval of 200, illustrating its accuracy before and after ICP alignment integration. The figure shows that the alignment accuracy significantly improves after performing two-by-two ICP fine alignment on four pairs of point clouds and optimizing the ICP algorithm.

Initially, the feature-matching alignment stage achieves a certain degree of alignment, yet its accuracy remains constrained. However, by merging the initial alignment results from feature matching with the standard ICP algorithm, more precise alignment results are achieved. This is due to the iterative optimization of the transformation matrix by the ICP algorithm, which leads to a more accurate point cloud alignment.

Notably, the FM-ICP-FPM algorithm delivers initial solid values for the subsequent ICP algorithm during the feature matching stage, facilitating the ICP algorithm’s rapid convergence to the optimal solution and further enhancing alignment accuracy. As a result, the combination of the feature matching and ICP algorithms enables the proposed FM-ICP-FPM algorithm to achieve high-precision 3D point cloud alignment without compromising alignment speed.

This section presents two experiments to thoroughly assess the FM-ICP-FPM algorithm’s operational efficiency in handling the 3D laser scanning image matching task. In Experiment E1, the number of core feature points of 3D laser scanning images to be matched is equivalent to the number of matching point pairs. In Experiment E2, the number of core feature points of 3D laser scanning images to be matched is double that of the matching point pairs.

Under the conditions of Experiment E1, as depicted in Fig. 6A, it is evident that the elapsed time required for image matching increases proportionally as the number of core feature points of the 3D laser scanning image to be matched gradually rises from 10 to 70. Notably, when the number of core feature points and matching point pairs reaches 70, the FM-ICP-FPM algorithm’s matching time is a mere 423 ms, with an MTE of 201 mm.

Conversely, in Experiment E2, illustrated in Fig. 7B, as the number of core feature points increases from 40 to 50 and the corresponding matching point pairs rise from 20 to 25, the matching elapsed time sees a noticeable jump from 204 to 256 ms. At the same time, the MTE climbs from 121 mm to 152 mm. This increase in matching elapsed time is attributed to the substantial increase in the number of matching point pairs, which poses challenges in memory and cache management.

Figure 7C demonstrates the results of the MRAE metrics for both experimental setups. It is evident that as the number of matching points increases, the MRAE also rises, although the MRAE in E1 consistently remains lower than that in E2. Despite the increasing matching points, the overall time to address the 3D laser scanning image matching problem remains efficient.