Noise in 3D Laser Range Scanner Data Xianfang Sun ∗ Cardiff University, UK Beihang University, China Paul L. Rosin † Cardiff University, UK Ralph R. Martin ‡ Cardiff University, UK Frank C. Langbein § Cardiff University, UK ABSTRACT This paper discusses noise in range data measured by a Konica Mi- nolta Vivid 910 scanner. Previous papers considering denoising 3D mesh data have often used artificial data comprising Gaussian noise, which is independently distributed at each mesh point. Measure- ments of an accurately machined, almost planar test surface indicate that real scanner data does not have such properties. An initial char- acterisation of real scanner noise for this test surface shows that the errors are not quite Gaussian, and more importantly, exhibit signif- icant short range correlation. This analysis yields a simple model for generating noise with similar characteristics. We also exam- ine the effect of two typical mesh denoising algorithms on the real noise present in the test data. The results show that new denoising algorithms are required to effectively remove real scanner noise. Keywords: 3D laser scanner, correlation analysis, Fourier analy- sis, noise modeling. Index Terms: G.1.2 [Numerical Analysis]: Approximation— Approximation of surfaces and contours; I.3.5 [Computer Graph- ics]: Computational Geometry and Object Modeling—Curve, sur- face, solid, and object representations 1 I NTRODUCTION Noise is ubiquitous in measured data. Surface mesh models built using measurement data obtained using 3D range scanners neces- sarily contains some type of noise. To remove the noise in sur- face mesh models, many mesh denoising algorithms have been de- veloped, for example [1, 3, 4, 5, 6, 8, 9, 13, 14, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27] and other references therein. In evaluating the effectiveness of denoising algorithms both visual and numeri- cal comparisons are used [20]. For meshes corresponding to real scanned data, however, we can in most cases only perform visual comparisons, because ground truth data required for evaluation are almost always unavailable. However, to provide a more objective evaluation and more thorough testing, numerical comparisons are required. Having synthetic models of real scanner noise would be useful for evaluating denoising algorithms. Any synthetic model used for evaluating denoising algorithms should take an exact model surface and add noise, which is to be removed by the algorithms. The noise should have the same char- acteristics as noise in real measurement data. Experimentally, mea- surement noise is often assumed to be Gaussian in wide range of disciplines. Thus, various mesh denoising algorithms have been developed based on the Gaussian noise assumption [1, 6], while others used synthetic models with Gaussian white noise (that is, independent Gaussian noise per mesh vertex) in evaluation of their algorithms [3, 13, 20, 26, 27]. However, real 3D laser scanner noise is, in practice, not quite Gaussian according to our observations, and ∗ e-mail: Xianfang.Sun@cs.cardiff.ac.uk † e-mail: Paul.Rosin@cs.cardiff.ac.uk ‡ e-mail: Ralph.Martin@cs.cardiff.ac.uk § e-mail: F.C.Langbein@cs.cardiff.ac.uk is correlated at adjacent mesh points. Shen [18] has also previously observed that real measurement noise on edges does not exactly fol- low the pattern prescribed by a random number generator, and has given a new method of generating synthetic edge noise. One approach to understanding system noise is to combine noise models for the components of the measurement system. For ex- ample, an optical sensor is used, and intensity noise models for optical sensors have been discussed in the literature [10]. However, depth values are not computed directly from intensity values, but instead triangulation is used after locating pixels of maximum in- tensity. Other sources of noise might include optical components such as the lens, the mirror (and its drivers), and laser, as well as electronic noise. Furthermore, numerical errors may also arise in the proprietary software used to calculate positions. Ultimately, es- pecially as we do not have access to all the components of a com- mercial system, and even if we did, the noise coming from some components may not be well characterised, we suggest that such a componentwise modeling approach is not practical. Instead, there- fore, we simply consider the overall noise present in the output of the scanner. In this paper, we show that the measurement noise in a flat area does not follow the common assumption of Gaussian white noise, and we analyse real measurement noise from a 3D range scanner. We also give a method to synthesise noise with similar character- istics. We then discuss the different results obtained by applying certain denoising algorithms to remove real scanner noise, and syn- thetic Gaussian white noise. The aim of this paper is to bring the attention of the mesh processing community to the fact that real scanner noise is not independent Gaussian noise per mesh ver- tex—any algorithm evaluation and development should be based on more realistic assumptions about 3D scanner noise. The remainder of this paper is organised as follows. Section 2 discusses our approach to acquisition of the test data we used to characterize noise. We explain the choice of test specimens and various data preprocessing procedures, and discuss our assumptions about the shape of the underlying test surface. In Section 3 we anal- yse the noise in the test data based on a quasi-statistical approach to describe the distribution and correlation of the scanner noise. We further employ the discrete Fourier transform to characterise the scanner noise. Section 4 describes artificial noise synthesis based on this analysis using the inverse discrete Fourier transform. Sec- tion 5 presents the results of using two typical mesh denoising al- gorithms to demonstrate the difficulties of removing real scanner noise, compared to removing synthetic Gaussian white noise. Fi- nally, Section 6 concludes this paper. 2 DATA ACQUISITION AND PREPROCESSING 2.1 Data Acquisition We describe in this section the methods used to acquire noisy data using a commercial scanner, and a standard test object. The ap- proach was to use a highly accurate test object, so that any noise in the measurements would be attributable to the scanner, and not to the test piece itself. The scanner we used in our test was a Konica Minolta Vivid 910, which has a specified point accuracy of 50μ m. Boehnen and Flynn [2] reviewed several different 3D scanners, and found that that Konica Minolta Vivid 910 was the most accurate scanner in a