Table 5 Summary of the multiscale hierarchy denoising method

Phase 1: Feature structural hierarchical segmentation

Cloth simulation filter (CSF) denoising

The advantage of the CSF method lies in its ability to effectively distinguish between non-ground points and ground points, thereby eliminating outliers.

Ground segmentation

Scenes: Steep slope/Relief/Flat

Advanced parameter setting:

Cloth resolution

Max iterations

Classification threshold

Cloth resolution: Refers to the mesh size of the cloth used to cover the terrain (the unit is the same as that of the point cloud). A higher cloth resolution results in a rougher DTM (Digital Terrain Model).

Max iterations: Refers to the maximum number of iterations for terrain simulation. 500 iterations are sufficient for most scenes.

Classification threshold: Refers to the threshold used to classify the point cloud into ground and non-ground parts based on the distance between the points and the simulated terrain. A value of 0.5 is suitable for most scenes.

Pass-through filter denoising

The purpose of the Pass-Through filter is to filter out points whose values along a specified dimension are not within a given range.

Ming and Qing Dynasties Official Architecture

Typical structure:

Brick and stone foundation

Colonnade

Dougong

Beam and rafter structure

Roof

Unique components of temple architecture:

Sculptures

Refer to the following data to set the required dimensions/height and apply through filtering for segmentation:

Specific point cloud data of the building structure.

Engineering Construction Practices.

Engineering Practices of the Qing Dynasty Department of Works.

Slope filter denoising

The slope filtering algorithm determines the flat or curved features of the point cloud surface by measuring the slope of each point in the point cloud, thereby filtering out noise points or other unnecessary points.

This method is suitable for denoising point clouds of inclined surfaces or flat areas, such as roofs and sloped ground.

The Gradient function in CloudCompare is used to calculate the gradient/slope/inclination of a scalar field.

The Gradient field can be computed using Euclidean distance.

By setting a slope threshold based on the gradient, it is possible to segment ground and non-ground points.

Phase 2: Large-scale denoising

Density-based spatial clustering of applications with noise (DBSCAN)

DBSCAN is a density-based clustering algorithm that can discover clusters of arbitrary shapes and effectively handle noise. It uses two parameters: the neighbourhood radius (ε) and the minimum number of points (MinPts), to control the density criteria for clustering, thereby determining whether data points belong to the same cluster.

Scope of application:

Entire heritage building/individual building structure.

It is capable of distinguishing areas with different densities in the visual area, differentiating between buildings and noise.

Density-based methods are applied in this study.

The first uses the DBSCAN programme from PCL.

Parameter settings:

Cluster Tolerance

Min Cluster Size

Max Cluster Size

Core Point MinPts

Parameter tuning should be performed according to the point cloud density and scale.

The second method is the density clustering algorithm provided by CloudCompare.

Parameter settings:

Local neighbourhood radius

(The programme is typically run with the default parameters.)

Phase 3: Small-scale denoising

Statistical outlier removal (SOR) filter

Statistical outlier removal (SOR) filters are a method for eliminating sparse outliers, considering average distances beyond the global mean and standard deviation as outliers, and trimming them from the dataset.

This method is suitable for denoising of small-scale complex structures.

Parameter settings:

Number of points to use for mean distance estimation: The number of points used for estimating the mean distance, typically set to 6 by default.

Standard deviation multiplier threshold (nSigma): The standard deviation multiplier threshold. When nSigma is set to 1, the maximum distance is calculated as the average plus nSigma times the standard deviation.

(max distance = average + nSigma*std. dev.)

Bilateral filter denoising

The Bilateral filtering algorithm, while removing noise, can preserve edge information in the point cloud of heritage buildings, which is crucial for maintaining the details and structure of the architecture.

This method is applicable to planar or curved point clouds of heritage buildings.

Parameter settings:

Spatial sigma (Variance of the normal distribution for the spatial part of the filter)

Scalar sigma (Variance of the normal distribution for the scalar part of the filter)

(The programme is typically run with the default system parameters.)