### Table 2 Correct localization rate as a function of sound type and distance for C2 con guration

"... In PAGE 26: ... In con guration C1, results show near-perfect reliability even at seven meter distance. For C2, we noted that the reliability depends on the sound type, so detailed results for different sounds are provided in Table2 , showing that only hand clap sounds cannot be reliably detected passed one meter. We expect that a human would have achieved a score of 100% for this reliability test.... ..."

### Table 2 Correct localization rate as a function of sound type and distance for C2 con guration

"... In PAGE 27: ...Table2 , showing that only hand clap sounds cannot be reliably detected passed one meter. We expect that a human would have achieved a score of 100% for this reliability test.... ..."

### Table 2. WER results for four different noise conditions using the P2 features. The figures in brackets indicate the 95% confidence intervals.

"... In PAGE 18: ....e., the P2 features. The WER results are listed for the conventional and the robust local distance function in Table 2. The results in Table2 indicate that the effectiveness of Acoustic Backing-off depends on the type of noise. For car noise, the improvement is statistically significant, and the WER is reduced by 48% when switching from a conventional to a robust local distance function.... ..."

### Table 1: Clustering results of five distance functions

2005

"... In PAGE 3: ...Table 1: Clustering results of five distance functions As shown in Table1 , EDR performs as well as DTW, ERP and LCSS. The poor clustering results of Euclidean distance confirm that it is very sensitive to local time shifting.... ..."

Cited by 21

### Table 4: Local recoding by inspection from Table 3

1999

"... In PAGE 4: ... 2.2 Optimum matching based on distance function The matching of households in Table4 was performed by inspection.Here we formulate the matching problem more precisely in order to perform the matching by computer.... In PAGE 5: ...Consider Table 2.Although the local recoding in Table4 was obtained from Table 3, Table 3 is already too coarse and it seems to be better to perform local recoding to the values of Table 2.Concerning the distance function, we might argue as follows.... ..."

Cited by 1

### Table 4: Local recoding by inspection from Table 3

1999

"... In PAGE 4: ... 2.2 Optimum matching based on distance function The matching of households in Table4 was performed by inspection. Here we formulate the matching problem more precisely in order to perform the matching by computer.... In PAGE 5: ...Consider Table 2. Although the local recoding in Table4 was obtained from Table 3, Table 3 is already too coarse and it seems to be better to perform local recoding to the values of Table 2. Concerning the distance function, we might argue as follows.... ..."

Cited by 1

### Table 1. Four Distance Functions from the Literature That We Have Investigated

in Peter Leven

"... In PAGE 6: ... In this approach, the distance function is defined as the length of the minimum RTR path connecting two configurations. For our experiments, we selected from the literature the four distance functions listed in Table1 . For the equations in this table, the robot has n joints, q and qprime are the two config- urations corresponding to different nodes in the roadmap, qi refers to the configuration of the ith joint, and p(q) refers to the workspace reference point p of the set of reference points A at configuration q.... In PAGE 6: ... (1996). Most of the distance functions defined in Table1 try to cap- ture the cost of a connection by using a measure defined only on the endpoints of the path. While this allows the value of the distance function to be calculated quickly, it does not suf- ficiently penalize the motion of the robot as it follows the path generated by the local planner.... ..."

### Table 1. Four Distance Functions from the Literature That We Have Investigated

"... In PAGE 7: ... In this approach, the distance function is defined as the length of the minimum RTR path connecting two configurations. For our experiments, we selected from the literature the four distance functions listed in Table1 . For the equations in this table, the robot has n joints, q and qprime are the two config- urations corresponding to different nodes in the roadmap, qi refers to the configuration of the ith joint, and p(q) refers to the workspace reference point p of the set of reference points A at configuration q.... In PAGE 7: ... (1996). Most of the distance functions defined in Table1 try to cap- ture the cost of a connection by using a measure defined only on the endpoints of the path. While this allows the value of the distance function to be calculated quickly, it does not suf- ficiently penalize the motion of the robot as it follows the path generated by the local planner.... ..."

### Table 2: Computation time and number of nodes of 10 di erent runs using the cubic spline repre- sentation (4 control points) in the example of Figure 7. the energy function. Indeed, for both distance and energy computations the position of several points and derivatives have to be computed along the curve. In the case of B ezier curves, these values depend on all the control points whereas in the case of splines, they depend on fewer control elements (2 control points and 2 control vectors- note that splines are a local representation). As the energy function and the distance function are called very often, the more expensive computations in the B ezier case a ect the total computation time. To verify this claim, we performed 200 random generations of deformations for each representation. Each deformation was then minimized and tested for the elasticity constraints. Most calls of the energy function occur during the energy minimization. For the splines, the total running time of the above experiment was 131 sec versus

### Table 1: Three commonly used M-estimators. 3.3 The Local Stage The aim of this stage is to reduce the in uence of er- roneous sections of the features: to perform this task, the residual error ri of curve Ci is computed by a ro- bust function of the distances fdi;jg1 j l0 i. We could take ri equal to the median of the fdi;jg, but once

"... In PAGE 4: ... These functions are very e cient, but are not suited to cases where the presence of outliers in the data is too large (experimentally, it must be kept below approximately 20%). Table1 lists three commonly used functions and their derivative. Among these estimators, some are more restrictive than others: when Tukey apos;s in uence function is null for residuals larger than a threshold c, Cauchy apos;s re- mains larger than zero while decreasing, whereas Hu- ber apos;s remains constant, equal to c.... In PAGE 5: ... Despite the bad accuracy of the model, the result is visually con- vincing. In order the reader to be aware of the parts of the curve which are less taken into account in the computation, we have drawn in black the points for which the residual is greater than c (c is de ned in Table1 ). Roughly speaking, these points are the ones for which the weight in the computation is decreased because their residual is too large.... ..."