Filtering and Denoising

It is tempting to assume that a scan is the cloud you set out to acquire. It never is. A morning of TLS work inside a heritage church returns the masonry the conservator wants together with the scaffolding the contractor left in place, the surveyor who walked through the frame between two scan epochs, and the multi-path ghost of a polished marble cherub reflected onto a wall five metres behind it. On a typical TLS station somewhere between 0.5 and 3 percent of the returns are gross outliers, riding on a surface-thickening of one to three millimetres of Gaussian noise that the scanner's range jitter alone cannot avoid. Filtering separates the signal from the artefact, and it forces a dilemma this chapter will not pretend to resolve cleanly: a filter aggressive enough to remove the structured outliers a TLS scan accumulates is almost always aggressive enough to round a moulding profile or erode a tooled corner that the conservator needs preserved at sub-millimetre fidelity.

Filtering sits between acquisition and analysis in the processing pipeline. It receives the georeferenced and downsampled cloud of Chapter 5 and issues millions of neighbour queries against the spatial indexes of Chapter 4, and every later stage trusts its output: the normal estimation of Chapter 7 (on which the bilateral filter of this chapter itself relies), the registration of Chapter 8, and the surface reconstruction of Chapter 15 all degrade visibly when fed unfiltered data.

The chapter first separates the three noise types a filter must tell apart, then builds the method family outward from outlier removal (SOR and ROR) through isotropic smoothing (MLS and jet fitting), which averages equally in every direction and therefore rounds sharp features, to the edge-preserving and density-aware methods (bilateral filtering, WLOP, and guided filtering), which detect a feature and avoid smoothing across it, and closes with a practical pipeline for combining them.

Types of noise in point clouds

Choosing an appropriate filter requires understanding the type of noise present, and three categories cover almost every contaminating process encountered in practice. The first is Gaussian range noise: every LiDAR range measurement carries a small random error, typically millimetres to centimetres depending on the system, the target reflectivity, and the slant range. This noise affects every point and shifts each one slightly from its true position, and local averaging or surface fitting reduces it without much difficulty. The second category is gross outliers, points that lie metres or even kilometres from the true surface, caused by multi-path reflections, atmospheric scattering, sensor malfunctions, or birds and insects intersecting the beam. Outliers are typically isolated, with few or no neighbours near the true surface, which is the property that all outlier-rejection filters exploit. The third and most insidious category is mixed pixels. At depth discontinuities (the edge of a building against the sky, for example) the laser footprint straddles two surfaces at very different ranges, and the detector averages the returns to produce a "phantom" point between the two true surfaces. Mixed pixels are particularly difficult to remove because they form coherent structures, lines of phantom points along every edge, which can fool segmentation and classification algorithms into treating the artefact as a real geometric feature. The figure below sketches the three categories side by side.