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

In modern surveying and 3D scanning, point cloud data (collections of three-dimensional coordinate points) are widely used. Point clouds obtained from drones, laser scanners, or photogrammetry can represent terrain and structures in great detail, but they often include noise (unwanted variation or outliers). Smoothing filters are used to appropriately process this noise and reproduce the original shape more smoothly.

There are various types of smoothing filters, among which the Gaussian Filter and the Median Filter are representative. In this article, we explain the theory and characteristics of these two filters and compare the differences in their effects when applied to point cloud data. We evaluate both from the perspectives of noise removal, edge (shape boundary) preservation, and computational cost, and consider which filter is suitable for different use cases such as urban scans, forest surveys, and architectural measurements. Finally, as an example of integrating these filters into modern point cloud processing workflows, we introduce a natural workflow using a solution called LRTK, which enables simple surveying and point cloud acquisition.

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

What is point cloud smoothing?

“Smoothing” refers to processing that evens out small bumps and variations in data. In point cloud data, smoothing is performed to suppress unwanted small fluctuations caused by measurement errors or sensor noise and to reproduce the shape of the object smoothly. For example, in a point cloud scanned from a ground surface, a road surface that should be flat may show small bumps due to sensor 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 extra points and jaggedness, subsequent processing (terrain analysis, 3D model generation, etc.) can proceed more stably. It is also necessary to balance edge preservation and noise reduction—reducing noise while retaining important shape features such as building edges and steep terrain. Appropriate smoothing improves surface reconstruction when generating meshes (polygon models) from point clouds and contributes to better data readability and analysis accuracy.

However, excessive smoothing can cause problems. If you smooth too much, fine details and edges in the point cloud can disappear, causing the shape to blur and accuracy to be degraded. Therefore, the degree of smoothing and the choice of method (filter) should be carefully selected based on the type of data and the intended purpose. Next, we will take a closer look at 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 the values around a target pixel by a Gaussian function according to distance and then averages them. This concept can be extended and applied to point cloud data. Specifically, when smoothing a given point, Gaussian weights are calculated based on the distances to neighboring points: closer points receive larger weights and farther 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 characteristic of the Gaussian Filter is that it is a linear filter, producing a gradual smoothing effect. The filter 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 broader area is blurred, smoothing out larger variations. By choosing an appropriate σ, you can balance noise reduction and shape preservation. However, note that setting σ too large makes the filter aggressive, potentially blurring and removing object edges and fine details.

The Gaussian Filter is well suited to averaging out random errors and slight sensor-induced fluctuations (so-called Gaussian noise). For example, it is effective for reducing minor noise on planar areas to make surfaces appear flatter or for reducing roughness on curved surfaces. Being a linear filter also makes the computational cost relatively manageable; the simple weighted average of neighboring points is easy to parallelize. With proper implementation, it can be applied quickly even to large point clouds containing many points.

On the other hand, the Gaussian Filter has challenges in edge preservation. Where the point cloud contains abrupt height changes or object boundaries, applying the filter can mix points from the high and low sides, blurring the boundary. For example, corners of buildings or points where the ground meets vegetation may become rounded by smoothing. This occurs because the Gaussian Filter weights only by distance and does not consider differences in point attributes (height, color, etc.). Therefore, if preserving sharp edges is important, consider the Median Filter or more advanced edge-preserving filters such as the bilateral filter.

Theory and characteristics of the Median Filter

The Median Filter is a non-linear smoothing method that uses the median of neighboring data. In image processing it is known to be effective at removing “salt-and-pepper” noise (isolated white and black pixels), and it can also be applied to point cloud data. The principle is simple: collect the positions (or values such as heights) of points in the neighborhood of 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 the rest, the Median Filter is suitable for removing outliers. For example, if a single mismeasured point is located much higher than its neighbors, taking the median will exclude that point since it lies outside the majority of neighboring values. As a result, the Median Filter effectively removes isolated noisy points while largely preserving the overall shape.

A major advantage of the Median Filter is that it can preserve edges relatively well. Because it uses the median instead of the mean, points on one face are not pulled toward the other face at a boundary. For instance, if plane A and plane B meet at a right angle, the Gaussian Filter may average points from both sides and round the corner. The Median Filter, however, will tend to select median points that lie on either plane A or plane B, so the edge remains sharp. For point clouds containing clear boundaries such as building corners or terrain steps, the Median Filter is therefore well suited to reducing noise while preserving shape.

However, as a non-linear filter, the Median Filter tends to be heavier in computational cost. Computing the median requires sorting (ranking) neighboring points, so for the same window size it can take longer than the simple average used by the Gaussian Filter. Also, when point clouds are unstructured (raw data without clear adjacency relationships), neighbor search itself can be time-consuming. That said, recent algorithmic improvements and parallel processing have made it possible to apply the Median Filter to large datasets at practical speeds.

There are also caveats with the Median Filter. Depending on the distribution of points within the filter window, the output may deviate from the actual shape. The median is only the middle value among neighbors and does not necessarily coincide with the average position of the original data. In some cases it can produce step-like artifacts where a smooth change is expected (the so-called staircase effect). Also, if an isolated outlier remains within the window, it may itself become the median and thus remain in the result. However, choosing 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 Filter and Median Filter

As we have seen, the Gaussian Filter and the Median Filter each have strengths and weaknesses. The main differences are summarized below.

• Noise removal characteristics: The Gaussian Filter is suitable for averaging out random fine noise to achieve smoothness. 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” noise.

• Edge preservation: 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, making boundaries easier to maintain. Therefore, when preserving shape detail is important, the Median Filter has the advantage.

• Degree of smoothing: The Gaussian Filter allows continuous control of smoothing strength via the σ parameter. This makes it easier to control the degree of smoothness, though excessive smoothing can remove necessary features. The Median Filter can adjust smoothing strength by changing the filter window size, but because the output is the median of neighboring points, it does not provide 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 weighted average. The Median Filter requires computing medians and can increase processing time on large datasets. Actual performance depends on implementation; recent parallel methods have enabled practical speeds for large point clouds.

• Effect on local density: The Gaussian Filter computes an average with surrounding points, so it does not change the number of points but tends to slightly homogenize local density variations. The Median Filter reduces local variance by moving outliers to positions consistent with neighboring points. Neither filter directly increases or decreases overall point density, but removing or relocating noisy points can make the distribution appear more uniform. Both filters do not generate missing-point interpolation, so to actually improve sparse regions you need separate interpolation or re-scanning.

Taking the above into account, the Gaussian and Median Filters are effective in different situations. In the next section, we consider which filter is appropriate for real-world use cases (urban environments, forest data, architectural measurement).

Examples of applying smoothing to point clouds

Urban scans (city point cloud data)

Point clouds captured from city streets and building exteriors contain many structures with clear edges, such as building ridgelines and curb edges. They also tend to include transient noise from moving vehicles and pedestrians, as well as outliers caused by reflections from glass or water surfaces. In many urban point cloud smoothing scenarios, the Median Filter is often more suitable. This is because the Median Filter is effective at removing isolated outliers while protecting edges. If corners or edges of buildings become blurred, the value of the survey data decreases; the Median Filter can reduce noise without degrading the shape.

Conversely, for large flat areas (e.g., roads or walls), applying a Gaussian Filter to smooth fine noise can also be effective. For example, Gaussian smoothing can even out fine measurement noise on a road surface to make it appear straighter and flatter. When applying a Gaussian Filter, however, use a small σ to avoid excessively blurring edges. In practice, a two-step approach is often used: first apply a Median Filter to remove obvious outliers, then apply a Gaussian Filter to smooth surfaces. In urban scans, the guideline is: use the Median Filter if edge preservation is a priority, and use the Gaussian Filter if surface smoothness is a priority.

Forest area point cloud data

Point clouds from forests or mountainous areas have points distributed very densely and irregularly due to countless leaves and branches. Structures at completely different heights—ground surface and canopy—coexist, and there may be isolated point noise from airborne particles or birds during measurement. For such datasets, initial outlier removal with a Median Filter is effective. Points that clearly float apart from their surroundings are eliminated by the median, reducing scattered false detections. In forests, many tiny points can be ambiguous (is it a leaf or noise?), and the Median Filter statistically removes points in improbable positions.

Since forests have few clear “edges,” applying a Gaussian Filter may not degrade shape as noticeably as in urban areas. For example, applying a Gaussian Filter to ground points can produce a smoother terrain model. The ground in forests often has roughness from grass and low vegetation, and appropriate σ smoothing can average out small bumps while preserving the overall trend. However, be careful: strong smoothing on tree point clouds can erase individual tree differences and cause adjacent trees or branches to merge. Because the Gaussian Filter blurs nearby points together, neighboring trees or foliage may fuse, complicating interpretation. Therefore, for forest data it is advisable to use the Median Filter for noise removal and use the Gaussian Filter for ground-surface smoothing, choosing the filter according to whether the target is trees or terrain. In general, avoid excessive smoothing in natural environments and retain necessary data characteristics by applying minimal filtering.

Architectural measurement point cloud data

Point clouds capturing building interiors or structures contain many artificial planes and straight edges such as walls, floors, columns, and beams. In architecture, precise measurement of dimensions and shapes is required, so high fidelity of edges and corners is important. If corners or angles (e.g., the right angle between wall and ceiling or the edge of a column) are rounded by smoothing, drawings or BIM models derived from the data will contain errors. Therefore, in architectural point clouds, noise removal using the Median Filter is particularly effective. The Median Filter can remove slight measurement noise on wall surfaces (points slightly offset from the plane) while preserving boundary lines between walls and columns. Outliers from window reflections or transient people and equipment are also easier to remove with a median-based filter.

Applying the Gaussian Filter to architectural point clouds requires caution. While high-quality laser scans still include minor noise on walls and floors that Gaussian smoothing can reduce to make surfaces appear more uniform, using too large a σ risks rounding door frames and sharp design elements. In architecture, the sharpness of corners is itself important information, so the disadvantages of detail loss often outweigh the smoothing benefits. Therefore, architectural measurement data should primarily use the Median Filter for outlier removal and keep smoothing to a minimum. If a Gaussian Filter is used, apply only very weak blur to reduce sensor-induced micro-roughness and carefully check that structural edges are not compromised.

Architectural point clouds are often limited in scope and relatively small in point count, so preserving accuracy is prioritized over processing time. In this respect, even if computational cost is somewhat higher, the median’s ability to protect edges makes it highly valuable. When post-processing point clouds captured on site, thoughtful filter selection will yield more accurate and usable deliverables.

Quantitative evaluation of smoothing effects and impact on density

It is also important to evaluate how much a filtered point cloud has improved relative to the original data or the true shape. One quantitative evaluation method is to compute errors by comparing the point cloud to reference measurements. For example, you can scan a known plane, apply a filter, and then compute the root mean square error (RMSE) of distances between points and the ideal plane. Generally, the Gaussian Filter is effective at reducing overall RMSE or standard deviation because it averages out small noise components. The Median Filter, by contrast, strongly reduces large errors and outlier-derived deviations by pulling extreme points back toward the original distribution. In other words, Gaussian tends to reduce mean error, while Median tends to reduce worst-case error. Specific improvement depends on the nature of the data and noise, so it is recommended to test filters on a small validation dataset before full-scale application.

A qualitative evaluation method is to visualize point clouds before and after smoothing and visually check surface smoothness and edge clarity. A Gaussian-filtered point cloud will look generally smooth and continuous, with roughness reduced. A Median-filtered point cloud will show edges remaining sharp while isolated noise points disappear, giving the impression that important features are preserved while noise is reduced. Examining behavior near edges will reveal that Gaussian smoothing can blur boundaries and place points at intermediate positions, whereas the Median Filter tends to keep points aligned with the original surfaces. These differences manifest in final deliverables (e.g., rendered images or model cross-sections): Gaussian smoothing yields a softer, more curved appearance, while Median smoothing yields a crisper, edge-defined appearance.

Finally, consider the effect of smoothing on point cloud density. Fundamentally, these filters move existing points without creating new ones or deleting them (except in rare cases where extreme outliers are effectively excluded by median calculation). Therefore, the overall average point density and point count do not change. Locally, however, removing or moving noisy points can smooth out density variations. For example, if a single protruding point is moved back onto the surrounding surface by smoothing, the space where the protrusion had been becomes a void, and surrounding surface points may appear slightly denser. Thus, after smoothing, point clouds often look more uniformly distributed because noise is reduced. Note, however, that smoothing cannot recover data in inherently undersampled regions; to improve point density you need separate interpolation or re-scanning.

Conclusion

The Gaussian Filter and the Median Filter are two fundamental methods for noise processing and smoothing of point cloud data. In this article we compared them in detail—from theoretical differences to noise reduction performance, edge preservation, 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 removing outliers while preserving important shapes. Which is better depends on the data and objectives; in many cases a staged combination of both filters can optimize the balance between noise removal and shape preservation.

In practice, deciding when and where to apply these filters is also important. Recently, tools and services have emerged that integrate point cloud acquisition and smoothing processing from end to end. One example is LRTK. With LRTK, you can acquire point clouds in the field using a smartphone or similar device and then apply noise removal and smoothing filters on the cloud, all without expensive dedicated software. This allows Gaussian and Median filtering to be executed seamlessly on the platform, greatly streamlining the workflow from surveying to data refinement.

Engineers who work with point cloud data should choose appropriate filters based on data characteristics, aiming to suppress noise while preserving shape. By leveraging modern solutions and workflows, you can quickly clean up field-acquired point clouds and put them to effective use. We hope this comparison helps you in that process.