Comparing 3D Descriptors for Local Search of Craniofacial Landmarks

Below we provide the values of expected local accuracy curves as defined in Section 2 of the ISVC main paper, for each descriptor-landmark pair, varying the search radius rS from 1 to 200 mm. Landmarks with bilateral symmetry (left and right) were merged together by considering each a separate instance of the same test. The descriptor template for each landmark was computed as the median descriptor from a training set, created by means of 6-fold cross-validation. To compute the scores s(v), the descriptor template was compared with the one of each vertex using (minus) the Euclidean distance (i.e. considering each descriptor as a point in N -dimensional space, being N the descriptor length). The only exception was the case of spin images, where we used the (2D) cross-correlation, as suggested in the original paper. Nonetheless, we should mention that results using Euclidean distance (with the descriptor normalized to sum the unit) were similar to those using cross-correlation. Tables 1, 2 and 3 summarize the results. Each cell describes the first plateau of the expected local accuracy curve: the number on the top indicates its median value and the ones below (in parentheses) indicate its limits. Recall that the plateau is only searched for rS values below the first peak of GL. The plateau range was determined as the region for which eL did not vary more than 10%. The best descriptor for each landmark is highlighted in boldface and those with no significant difference to it are indicated with an asterisk. For example, in Table 2 the best descriptor for the inner-eye corners (en) is SI; if we constrain the search to a radius below 22 mm we can expect to locate each of the inner-eye corners at 1.7 mm from their correct (ground truth) position. Clearly, the great majority of landmarks must be constrained to a local search range for all six descriptors and only a few of them could be used globally (e.g. n, prn, pg, sn). We also explored the influence of the neighborhood size used for the computation of the descriptors, testing for rN = 20 mm (Table 1), rN = 30 mm (Table 2) and rN = 40 mm (Table 3).