Ideal conditions

Under ideal conditions, the test objects' surfaces are completely exposed to the sensor and sensed data are free of noise. Table 1 shows the achieved recognition rates and times for the six criteria [cf. Section 4]. The measured times include all steps from drawing feature samples to the output of the best matching object model. Generating the surface mesh is not included. Almost perfect classification has been achieved by the ${\cal {K}}$ and ${\cal {L}}$ criteria. Interestingly, the $\chi_2^2$ criterion performs dramatically weaker than the $\chi_1^2$ criterion. Apparently, the weighting of histogram differences by the reciprocal of the trained histogram value alone is much more reliable than taking also the estimate from the small test sample into account [cf. Equations (13), (14)].

Correct classification and confusion rates between all pairs of objects are shown in Figure 3. All classifiers work well for simple shapes like cube or sphere. Interestingly, the objects that are difficult to classify differ drastically across the criteria. On the other hand, the $\cap$ and $\chi_2^2$ criteria exhibit a strikingly similar pattern of classification performance. This similarity will also be retained in all the other tests of the classifiers we report below. The same similarity holds for the best, the ${\cal {K}}$ and ${\cal {L}}$ criteria.