Noisy data

If the point cloud is obtained from real sensors like laser range-scanners, laser profilers, or stereo cameras, the data will be corrupted in various ways. Therefore, in a second set of experiments, sensitivity of the feature histograms to noise is evaluated. Uniformly distributed noise is simulated by randomly translating vertices from a surface mesh inward or outward along the local surface normal. The level of noise is defined as the range of translations, measured in percent of the maximal object diameter¹. As an example, Figure 4(b) shows a surface mesh corrupted by the maximal level of noise we have tested (20%).

In Figure 5(a), we present plots of recognition rates for the six classifiers as a function of noise level. For the $\cal {E}$, $\chi_1^2$, ${\cal {K}}$, and ${\cal {L}}$ criteria, classification performance degrades rapidly with increasing noise. This is explained by the fact that the angular attributes $\alpha$, $\beta$, $\gamma$ are very sensitive to noise such that surface information is largely lost. Interestingly, these criteria reach a rather stable rate of between 10% and 15% correct classification. Some residual performance may be expected, as the distance attribute $\delta$ remains informative up to much higher noise levels. The $\chi_2^2$ and ${\cap}$ criteria, on the other hand, are a lot less sensitive to noise, exhibiting significantly lower performance at low noise and higher performance at high noise levels. Under realistic conditions of measurement (noise $<1\%$), however, the ${\cal {K}}$ and ${\cal {L}}$ criteria yield a reasonable recognition rate above 80%.