Gaussian Filter vs Median Filter: Comparing the Effects of Point Cloud Smoothing

In modern surveying and 3D scanning, point cloud data (a collection of three-dimensional coordinate points) is widely used. Point clouds obtained from drones, laser scanners, or photogrammetry can represent terrain and structures in fine detail, but they also tend to include noise (unwanted variations and outliers). Smoothing filters are used to appropriately process this noise and restore the original shape smoothly.

There are various types of smoothing filters, among which the Gaussian filter and the Median filter are representative. This article explains the theory and characteristics of these two filters and compares the differences in effects when applied to point cloud data. We evaluate them in terms of noise removal, edge (shape boundary) preservation, and computational cost, and consider which filter is suitable for each use case such as urban scanning, forest surveying, and architectural measurement. Finally, as an example of introducing these filters into modern point cloud processing workflows, we naturally introduce a solution called LRTK that enables simple surveying and point cloud acquisition.

First, let’s look at what point cloud smoothing is, and why and for what purpose it is needed.

What is point cloud smoothing

Smoothing refers to the process of evening out small bumps and variations in data. In point cloud data, smoothing is performed to suppress unnecessary small fluctuations caused by measurement error or sensor noise, and to reproduce the object’s shape smoothly. For example, in a point cloud scanned from the ground, a road surface that should be flat may become finely bumpy due to instrument noise. Applying a smoothing filter can even out those bumps and bring the data closer to the actual road surface.

The purpose of smoothing is not limited to mere noise removal. By removing extraneous points and jaggedness, subsequent processing (such as terrain analysis or 3D model generation) can proceed more stably. It is also necessary to balance noise reduction with edge preservation—reducing only the noise while retaining important shape features such as building edges or steep terrain. Appropriate smoothing improves surface reconstruction when generating a mesh (polygon model) from point clouds, and contributes to better data readability and analysis accuracy.

However, excessive smoothing can cause problems. If you smooth too much, the fine details and edges in the point cloud may disappear, blurring the shape and degrading accuracy. Therefore, deciding the appropriate degree of smoothing and which method (filter) to use must be selected carefully according to the data type and purpose. Next, we will examine in detail the principles and characteristics of two representative smoothing filters: the Gaussian filter and the Median filter.

Theory and characteristics of the Gaussian filter

The Gaussian filter is an averaging process that uses weights following a Gaussian (normal) distribution. Originally known as Gaussian blur in image processing, it weights surrounding pixel values according to a Gaussian function based on distance from the target pixel and averages them. This idea can be extended and applied to point cloud data. Specifically, when smoothing a given point, Gaussian weights are calculated based on distances to neighboring points; closer points receive larger weights and more distant points smaller weights, and the weighted average position is computed. Moving the point to that average position suppresses local noise and yields a smoother point cloud.

A key characteristic of the Gaussian filter is that it is a linear filter that produces a gentle smoothing effect. The filter’s strength can be adjusted by the Gaussian distribution’s standard deviation (σ). With a small σ, only very close neighbors are averaged, removing only fine noise; with a large σ, a wider area is blurred and larger undulations are evened out. Choosing an appropriate σ allows you to balance noise reduction and shape preservation. However, be careful that making σ too large makes the filter aggressive, potentially blurring and removing edges and fine details of the object.

The Gaussian filter is suitable for averaging out random errors and sensor-induced small fluctuations (so-called Gaussian noise). For example, it is effective for reducing slight noise on planar areas to make surfaces closer to flat, or for smoothing roughness on curved surfaces. Because it is a linear filter, its computational cost can be relatively modest; the simple weighted average is easy to parallelize. With proper implementation, it can be applied quickly even to large-scale point clouds containing many points.

On the other hand, the Gaussian filter has challenges in edge preservation. If there are abrupt height changes or object boundaries in the point cloud, applying the filter in those regions can mix high-side and low-side points, averaging them and blurring the boundary. For example, corners of buildings or the contact area between ground and trees—places that should be sharply separated—can become rounded by smoothing. This is because the Gaussian filter weights only by distance and does not consider differences in point attributes (such as height or color). Therefore, when it is necessary to keep edges sharp, consider using the Median filter described below or more advanced edge-preserving filters (for example, the bilateral filter).

Theory and characteristics of the Median filter

The Median filter is a nonlinear smoothing method that takes the median of neighboring data. In image processing, it is known to be effective for removing salt-and-pepper noise (isolated white and black pixel noise), and it can be applied to point cloud data as well. The principle is simple: collect the positions (or values such as heights) of neighboring points for the target point, compute their median, and replace the target point with that median position. Because the median is less affected by values that differ extremely from others (outliers), the Median filter is suitable for removing outliers. For example, if a single mismeasured point is far higher than its surroundings, taking the median will exclude it because it deviates from the majority of neighboring points. As a result, it is possible to effectively remove isolated noisy points while largely preserving the overall shape during point cloud smoothing.

A major advantage of the Median filter is its relatively good edge preservation. Because it uses the median rather than the mean, points on different surfaces do not get drawn into an intermediate value at boundary areas where surfaces intersect. In an extreme case where plane A and plane B meet at a right angle, a Gaussian filter may average A-side and B-side points and round the corner. The Median filter, however, tends to select a median that lies on either plane A or plane B, so the edge is more likely to remain sharp. Because of this property, the Median filter is suitable for noise reduction while preserving shape in point clouds that include distinct boundaries such as building corners or terrain steps.

On the other hand, because the Median filter is a nonlinear filter, it tends to be somewhat heavier in computational cost. Finding the median requires sorting (ranking) neighboring points, so for the same window (neighborhood) size it can take longer than a Gaussian filter that simply computes a weighted average. Also, for unstructured point clouds (raw data without clear adjacency), searching for neighbors itself can be time-consuming. However, recent algorithmic improvements and parallel processing make it possible to apply the Median filter at practical speeds even to large-scale data.

There are caveats to the Median filter. Depending on the point distribution within the filter window, the output may deviate from the actual shape. The median is, after all, an intermediate value among neighbors and may not coincide with the original average position. In some cases, it can introduce staircase-like steps where smooth variation should occur (the so-called staircase effect). Also, if isolated outliers remain within the window, such a point itself can be chosen as the median. However, selecting an appropriate window size (neighborhood range) and applying the filter iteratively when necessary can mitigate these issues. Overall, the Median filter is a useful tool in point cloud processing, offering a good balance between edge preservation and noise reduction.

Comparison between Gaussian and Median filters

As we have seen, Gaussian and Median filters each have strengths and weaknesses. The main differences can be summarized as follows.

• Noise removal characteristics: The Gaussian filter is suitable for averaging out random fine noise to smooth data. The Median filter excels at removing extreme outliers (impulse noise). In other words, the former is good at reducing overall roughness, while the latter is good at eliminating isolated “point-like” noise.

• Edge preservation capability: The Median filter can keep edges relatively sharp. The Gaussian filter tends to blur edges, whereas the Median filter prevents points from different surfaces from mixing, so boundaries are more likely to be maintained. Therefore, when you want to preserve shape details, the Median filter is superior.

• Degree of smoothing: The Gaussian filter allows continuous adjustment of smoothing strength via the σ value. This makes it easy to control the degree of smoothness, but if applied too strongly, important features may be lost. The Median filter can adjust smoothing strength by changing the filter window size, but because the output becomes the median of neighboring points, it does not offer as fine-grained continuous control as the Gaussian filter.

• Computational cost: Generally, the Gaussian filter tends to be more computationally efficient because it only requires a simple weighted average. The Median filter requires median computation, which can increase processing time for large datasets. Actual performance depends on implementation, and recent parallel processing techniques have achieved practical speeds for large point clouds.

• Effect on local density: The Gaussian filter computes an average with surrounding points, so the point cloud density itself does not change, though variations in local density tend to become somewhat more uniform. The Median filter reduces local variation as outliers are assimilated (positions replaced) with surrounding points, thereby decreasing local spread. In other words, neither filter directly changes point count or overall density, but removing or mitigating noisy points can make the data appear more uniformly distributed.

Considering the above, Gaussian and Median filters work effectively in different situations. The next section discusses which filter is suitable in actual use cases (urban environments, forest data, architectural measurement).

Examples of applying smoothing to point clouds

Urban scanning (city) point cloud data

Point clouds obtained by 3D scanning city streets and building exteriors contain many structures with clear edges such as building ridgelines and curb lines. They also tend to include temporary point cloud noise from moving objects like vehicles and pedestrians, and outliers from reflections on glass or water surfaces. For such urban point clouds, the Median filter is often suitable. Because the Median filter protects edges while effectively removing isolated outliers, it maintains the value of survey data by reducing noise without blurring building corners and edges.

On the other hand, for wide flat areas (for example, roads or wall surfaces), applying a Gaussian filter to smooth fine noise can also be effective. For example, using a Gaussian filter to smooth fine measurement noise on a road surface makes the road appear straighter and flatter. However, when applying a Gaussian filter, set σ relatively small to avoid over-blurring at edges. In practice, a two-step process—first using a Median filter to remove obvious outliers, then applying a Gaussian filter to smooth surfaces—is sometimes used. In urban scanning, a useful guideline is: emphasize the Median filter when edge preservation is important, and use the Gaussian filter when smooth surfaces are the priority.

Forest area point cloud data

Point clouds from laser scanning forests or mountainous areas have points distributed very densely and irregularly due to countless tree leaves and branches. They contain structures at completely different heights, such as ground (terrain surface) and canopy (forest top), and often include isolated point noise from atmospheric particles or birds during measurement. For such datasets, removing outliers with the Median filter is effective. Points that are clearly floating relative to their surroundings are eliminated by the median, reducing scattered false-detection points. In forests, there are many tiny points that are difficult to classify as leaves or mere noise, but the Median filter can statistically remove points that are unlikely positions.

Meanwhile, because clear “edges” are less common in forest point clouds, applying a Gaussian filter may not degrade shapes as noticeably as in urban areas. For example, applying a Gaussian filter to ground points can produce a smooth terrain model. In forested areas, ground points are often rough due to grass and undergrowth, but Gaussian smoothing with a suitable σ can average out fine irregularities while preserving overall undulation trends. However, be careful: strongly smoothing the tree point clouds themselves (canopy or trunk) may erase differences between individual trees and cause adjacent trees’ point clouds to merge. Because the Gaussian filter blurs nearby points, neighboring trees or branches may fuse, making interpretation difficult. Therefore, for forest data, it is desirable to use the Median filter for noise removal and the Gaussian filter for ground-surface smoothing, choosing the filter according to the target (tree vs terrain). In general, avoid excessive smoothing in natural environments and limit filtering to what is necessary to preserve real data characteristics.

Architectural measurement point cloud data

Point clouds measuring building interiors or structures include many planar surfaces and linear edges of man-made objects such as walls, floors, columns, and beams. In architecture, it is required to accurately capture these dimensions and shapes, so high fidelity of edges and corners in point cloud processing is important. For example, if the right angle where wall and ceiling meet or the corner of a column becomes rounded, the drawings or BIM models derived from them will contain errors. Therefore, noise removal with the Median filter is particularly effective for architectural point clouds. The Median filter can remove slight measurement noise on wall surfaces (points slightly floating from the plane) while keeping wall-column boundary lines sharp. It also easily removes distant outliers from reflections on window glass or people and equipment that briefly appear in scans, thanks to median-based filtering.

On the other hand, applying the Gaussian filter to architectural point clouds requires caution. Even with high-quality laser scans, walls and floors include small noises, and reducing those with Gaussian smoothing can make surfaces look more uniform. However, setting σ slightly too large risks rounding door frames and other sharply detailed design elements. In architecture, the sharpness of corners itself is often important information, so the disadvantages of detail loss often outweigh the smoothing benefits. Therefore, architectural measurement data should generally follow a policy of removing noisy points primarily with a Median filter and limiting smoothing to the minimum necessary. If using a Gaussian filter, apply only a very weak blur to remove sensor-induced fine roughness and carefully verify that structural edges are not compromised.

Architectural point clouds often cover limited areas with relatively fewer points, so accuracy preservation is prioritized over processing time. This further increases the value of the Median filter, which protects edges even if it costs somewhat more compute. When post-processing point clouds acquired on site, thoughtful filter selection like this yields more accurate and manageable deliverables.

Quantitative evaluation of smoothing effects and influence on density

It is also important to evaluate how much the filtered point cloud has improved relative to the original data or the true shape. One quantitative evaluation example is to compute errors by comparing the point cloud to original measurements. For instance, you can apply a filter to point cloud data scanned from a known plane and then compute the root mean square error (RMSE) of distances between points and the ideal plane. In general, the Gaussian filter is effective at reducing overall RMSE and standard deviation because it averages out small noise components. The Median filter strongly pulls large outliers back toward the original distribution, so it substantially reduces maximum errors and outlier-induced deviations. In other words, the Gaussian filter tends to excel at reducing average error, while the Median filter contributes more to reducing worst-case errors. However, the exact amount of improvement depends on the data characteristics and the noise type, so in actual projects it is recommended to compare error metrics before and after filtering on small validation datasets.

A qualitative evaluation method is to visualize point clouds before and after smoothing and visually check surface smoothness and edge sharpness. A point cloud smoothed by a Gaussian filter gives an overall smooth and continuous impression with reduced coarse roughness. By contrast, a Median-filtered point cloud retains sharp edges while removing noise points, giving the impression that important areas remain crisp while noise is reduced. Inspecting behavior near edges in detail shows that Gaussian filtering can blur boundaries between different surfaces or place points at intermediate positions, whereas the Median filter keeps points aligned with the original surfaces. These differences appear in final deliverables (for example, rendered images or model cross-sections): Gaussian smoothing tends to yield soft, curved appearances, while Median smoothing yields sharper, well-defined edges.

Finally, consider the effect of smoothing on point cloud density. Fundamentally, these filters only move existing points and do not create new points or delete existing ones (except in extreme cases where outliers are excluded in median calculations and thus effectively removed). Therefore, the overall average point density and point count do not change. However, locally the removal or movement of noise points can make density distribution appear smoother. For example, if a single protruding point is moved back onto a nearby surface by smoothing, the space where that protruding point was becomes a void, and the surrounding surface points may appear slightly denser. In this way, filtered point clouds better conform to surfaces and exhibit reduced point spread. Note, however, that filters cannot compensate for areas with originally insufficient observation density; to actually increase point cloud density you need interpolation or re-scanning.

Summary

Gaussian and Median filters are the two fundamental methods for noise processing and smoothing of point cloud data. This article compared them in detail from theoretical differences to noise removal performance, edge preservation capability, computational efficiency, application examples, and evaluation methods. To recap, the Gaussian filter is excellent at reducing overall roughness through smooth averaging, while the Median filter is superior at eliminating outliers while preserving important shapes. Which is better depends on the data and the purpose; in some cases combining both in staged processing can optimize the balance between noise removal and shape preservation.

In practice, when to and where to apply these filters is also important. Recently, tools and services that provide an integrated workflow from point cloud acquisition to smoothing processing have emerged. One example is LRTK. With LRTK, you can acquire point clouds on-site via simple surveying with a smartphone and perform noise removal and smoothing filter processing on the cloud. Without expensive dedicated software, Gaussian and Median filtering of point clouds can be executed seamlessly on the LRTK platform, dramatically streamlining the workflow from surveying to data shaping.

Engineers who will handle point cloud data should choose appropriate filters according to data characteristics and aim to suppress noise while preserving shape. Make use of modern solutions to quickly clean up field-acquired point clouds and put them to effective use. I hope this comparison will assist you in that endeavor.