How to Remove Noise and Improve Accuracy of Point Cloud Data with a Gaussian Filter

Basics of Point Cloud Processing and the Noise Problem

Point cloud data obtained from 3D scanners, LiDAR, photogrammetry, and the like record real-world coordinates as a collection of many points. Point clouds contain shape information of the target, but they also inevitably include noise introduced during acquisition. For example, consider surveying terrain with a laser scanner. Due to the surface reflection characteristics, sensor measurement errors, and environmental factors (rain, dust, interference from sunlight, etc.), points can be recorded at positions that deviate from the true surface. When scanning structures, lasers can scatter on steel edges or GPS reception can be poor in some locations, causing positional variation and introducing inaccurate points often called “shadow points.”

As obtained, point clouds contain noise points and outliers of varying sizes, which, if left untreated, adversely affect subsequent analysis and modeling accuracy. For example, estimating surfaces from a noisy point cloud can produce local anomalous bumps and dips, making accurate volume calculations or shape identification difficult. In construction site verification, comparing design drawings with acquired point clouds is used to assess construction accuracy, but noisy point clouds can inflate errors and lead to incorrect judgments. Therefore, noise removal and smoothing are very important steps in point cloud processing.

Why Noise Removal and Smoothing Are Necessary

There are several clear advantages to removing noise and smoothing point cloud data.

• Reduction of measurement error: Averaging out variations caused by sensor measurement errors (random noise) brings each point’s position closer to the actual geometry. This can improve the overall accuracy of the point cloud data.

• Improved shape discriminability: With noise removed, planes and curved surfaces are represented more smoothly and edges and boundaries become clearer. This makes it easier to understand terrain undulation or structural shapes both visually and analytically. For example, slope gradients or road undulations can be more accurately assessed on smoothed data than on noisy data.

• Reliability in as-built verification: On construction sites, differences between the design surface and the current point cloud are used to calculate cut-and-fill volumes or check as-built dimensions. If the point cloud contains a lot of noise, the difference calculations can pick up fine, unnecessary errors and lead to unnecessary rework. A smoothed point cloud makes it easier to capture true deviations, improving the reliability of as-built verification.

• Efficiency of data processing: Removing obvious outliers (points far removed from the rest) reduces the load on subsequent processing. Cleaned point clouds are smaller than raw noisy data, shortening processing times on PCs or in the cloud.

For these reasons, it is recommended to apply appropriate filters for noise removal and smoothing after point cloud acquisition. Below, we focus on the method known as the Gaussian filter and explain smoothing for point clouds.

What Is a Gaussian Filter?

A Gaussian filter is a smoothing filter that uses weighting based on the Gaussian (normal) distribution. It originated in image processing and is commonly known as “Gaussian blur.” For example, applying a Gaussian filter to a 2D image smooths the image by averaging the pixel values around a target pixel with weights given by a Gaussian distribution. The center pixel receives the highest weight, and weights decrease exponentially with distance, so a Gaussian filter can reduce noise while preserving edges to some extent. Compared to a simple uniform average, it better preserves the original shape and is effective against random noise (other than impulse noise) in images.

Extending this Gaussian-weighted smoothing concept to 3D point clouds yields Gaussian-filter-based point cloud smoothing. Because point clouds lack a regular pixel grid like images, you first gather the points in each point’s neighborhood and compute a Gaussian-weighted average over that set. In a Gaussian filter, nearer points receive larger weights and farther points smaller weights, producing an averaged coordinate. This smooths local bumps and produces a smoother point cloud representation.

The Gaussian function’s standard deviation σ (sigma) determines the filter strength: larger σ smooths over a wider area (stronger smoothing). However, if σ is too large, fine details of the original shape (edges and small undulations) will be lost, so choosing an appropriate value is important.

Applying a Gaussian Filter to Point Clouds and Neighborhood Search

When applying a Gaussian filter to point cloud data, defining the neighborhood region—which points to average—and how to compute it are key. Two representative neighborhood search methods are below.

• k-Nearest Neighbors (k-NN): For each target point, search for the k spatially nearest neighbor points and use that set for smoothing. For example, you might set “the 20 nearest points for each point,” and weight their contributions based on distance. k-NN is easy to implement and guarantees a fixed number of local points, but if the point cloud’s density is uneven, it may include distant points or be confined to a very small area.

• Radius Neighbors: Define a radius R a priori and gather points that fall within that sphere (in 3D) or circle (in 2D). For example, collect points within a 50 cm radius and apply Gaussian weights to them. Radius-based neighborhoods determine the smoothing region by a physical distance scale, so smoothing is not dependent on point density. However, depending on point sparsity, the number of neighbors can vary widely, which may produce uneven results.

For the points gathered by these neighborhood searches, apply a Gaussian function such as w = exp(-(d^2)/(2σ^2)) for distance d to calculate weights and compute the average. In practice, spatial indices like KD-tree are commonly used to efficiently search neighbors for each point. The resulting weighted average is used to update the original point’s position to a smoothed new position, or to output a new point cloud.

A benefit of the Gaussian filter is that it is less influenced by outliers than a simple average. Distant anomalous points (outliers) receive extremely small Gaussian weights, so their contribution to the average becomes negligible (implementations may also set a threshold distance beyond which neighbors are not considered). Conversely, points within the normal neighborhood are averaged appropriately, reducing small jitter and producing smoothness.

One caveat is that if an edge (a step or corner) lies within the neighborhood, the filter can round off that edge. For example, smoothing a corner where two walls meet at a right angle can blur the boundary between the two surfaces. If preserving important edges is required, use a smaller neighborhood radius or σ, or mask edge regions to exclude them from smoothing.

Effects and Accuracy Improvements of Gaussian Filtering in Civil Engineering

Let’s consider the practical effects Gaussian smoothing can have in surveying and structural measurement in civil engineering.

First, in terrain surveying (e.g., as-built management for cut-and-fill). Scanning slopes and development areas with drones or ground-based LiDAR yields large terrain point clouds, but noise points from vegetation, machinery, and people are often mixed in. Applying Gaussian smoothing/removal makes the terrain point cloud represent the actual smooth surface, producing a terrain model with fine bumps removed. This improves cut-and-fill volume calculations and enables earthwork quantity estimates that are less influenced by extraneous noise. In slope gradient measurements, locations that appeared to have sharp gradients due to noise stabilize after smoothing and reflect actual average gradients. In the field, this clarifies comparisons with design values and helps determine corrective actions more accurately.

Next, in structural measurement (e.g., bridge or tunnel inspections). High-precision point cloud scans capture tiny surface irregularities and defects on concrete, but they also include sensor noise. For example, a tunnel wall scan may have millimeter-scale noise across the surface, making a wall that should be smooth appear rough. Gaussian filtering smooths out this unwanted roughness so that truly significant defects (for example bulging or delamination) stand out. In bridge scans, areas other than fine details like rivets and bolts become smoother, making it easier to grasp overall deformation or sagging. Gaussian smoothing is especially useful for assessing large-scale planarity (“Is this deck flat overall?”) because it is not affected by random outlier points and yields stable flatness evaluation results.

Thus, point clouds smoothed with a Gaussian filter reduce noise-induced error components and improve analysis accuracy. In some validation cases, comparing RMSE (root mean square error) to a reference plane before and after smoothing shows post-smoothing errors reduced to less than half. For as-built verification workflows compliant with specifications, combining positional correction using control points with smoothing can further enhance the final delivered product’s quality.

Comparing Gaussian Filters with Other Filtering Methods

There are many methods for denoising point clouds besides the Gaussian filter, each with its own characteristics. Here we compare the Gaussian filter with two representative alternatives: the median filter and surface fitting (plane fitting) smoothing.

• Median filter: The median filter removes the influence of outliers by taking the median of the neighborhood points. In image processing it’s often used to remove salt-and-pepper noise; in point clouds you can compute the median for x, y, and z coordinates of the neighborhood and set the new point position accordingly. Its advantage is that a single extreme outlier does not affect the median, so it is very robust to impulse-like noise. It is effective in small neighborhoods for removing isolated spurious points. However, its drawback is that because it uses the median rather than an average, its smoothing effect on small fluctuations is weaker than a Gaussian filter. If the neighborhood window is too large, edges can still become rounded or points can be moved to positions that do not exist in reality.

• Surface fitting (Moving Least Squares, etc.): Surface fitting smoothing fits a virtual surface (or plane) to each point’s neighborhood and reprojects points onto that surface. A typical example is the Moving Least Squares (MLS) method. Instead of averaging, MLS computes a locally optimal geometric surface from noisy points, achieving smoothing that follows the original geometry. Its advantage is that for data containing planes or smooth surfaces, it can produce very smooth, high-precision results and thoroughly remove fine noise. This is particularly effective where clear surfaces exist, as those surfaces are more faithfully reproduced. However, disadvantages include high computational cost and longer processing time, and when multiple different surfaces (e.g., at edges) are present in the neighborhood, averaging can blur the geometry. The algorithm is also more complex and harder to implement.

In summary, the Gaussian filter is a simple, weighted-average smoothing method that balances ease of implementation and strong random-noise reduction. The median filter is effective at removing extreme outliers, while surface-fitting methods are suitable for high-precision surface reconstruction. In practice, multiple filters are often combined in stages. For example, a typical workflow might remove obvious outliers with Statistical Outlier Removal, then apply a Gaussian filter to smooth fine noise—leveraging the strengths of each filter.

Filter Processing to Efficiently Handle Point Clouds Acquired with LRTK

Recently, [LRTK](https://lrtk.lefixea.com) has emerged as an easy-to-use, high-precision surveying system using smartphones and has attracted attention in civil engineering surveying. LRTK combines a cm-level GNSS receiver (RTK) that connects to a smartphone with the smartphone’s built-in LiDAR scanner, allowing detailed point cloud data with absolute coordinates to be captured simply by walking the site. Filter processing plays an important role in efficiently handling the point cloud data obtained in this way.

Smartphone-based point cloud scans are easier to acquire than traditional laser scanners but often produce very large point sets and include smartphone-LiDAR-specific noise. LRTK uploads the acquired data to the cloud and automatically performs point cloud noise removal and unnecessary point reduction. For example, duplicate points from multiple scans and dynamic objects such as people and vehicles are detected and removed in the cloud to generate a clean, organized point cloud. Combining Gaussian-filter smoothing further reduces variability on terrain and structure surfaces, producing high-quality point clouds. As a result, data sizes are reduced and subsequent analyses (e.g., as-built heatmap display or earthwork calculations) become more accurate and faster.

Filtered LRTK point clouds have fewer false positives due to noise, allowing immediate onsite use of measurement results. For example, when displaying an as-built heatmap on a smartphone right after scanning to compare with the design, a noise-free point cloud produces clear color distributions, making it easy to identify excess/deficit earth or construction errors at a glance. Workflows that used to require returning to a desktop PC for manual noise removal can be completed automatically on site with LRTK, leading to significant operational efficiency gains.

Conclusion: A New Workflow Combining Smartphone RTK, Point Cloud Scanning, and Gaussian Smoothing

This article explained Gaussian-filter-based noise removal and smoothing for point cloud data, from basic concepts to practical applications. The Gaussian filter, which reduces inevitable noise in point cloud data and improves data accuracy and usability, is a highly useful tool in civil surveying and 3D scanning. It contributes to correcting measurement errors and improving the accuracy of as-built verification, making it valuable to both field engineers and researchers.

Recently, a practical workflow combining smartphones with RTK positioning and 3D scanning—“smartphone RTK × point cloud scanning”—has been implemented. LRTK is a representative example, enabling anyone on site to quickly acquire high-precision point clouds and automatically perform filter processing such as Gaussian smoothing. This simplifies the whole process from acquisition to analysis and enables much faster accuracy checks and as-built confirmations than traditional methods.

Noise processing that used to take time in specialized software can now be completed on site by introducing systems like LRTK. The workflow that combines the reliability of smartphone RTK positioning, the detail of point cloud scanning, and the smoothing effect of Gaussian filters will strongly support DX (digital transformation) in the civil engineering and construction industries. If you are facing issues with point cloud noise or processing time at your site, consider using Gaussian filtering alongside introducing modern smartphone-based point cloud solutions such as LRTK.