. Author manuscript; available in PMC: 2013 Aug 12.

Published in final edited form as: ACM Trans Sens Netw. 2012 Jul;8(3):2240093. doi: 10.1145/2240092.2240093

Table IV.

Error Rates for ASAP in Steps 1 and 2 For the U.S. Map with n = 1,090 Cities, ρ = 0.032, and Number of Patches N ≈ 1200 Depending on the Noise Level

			Step 1 (Reflections)				Step 2 (Rotations)

η	deg	M	τ	$ε_{i n p}^{Z}$	$ε_{e i g}^{Z}$	$ε_{i n p}^{R}$	$ε_{e i g}^{R}$	$o u t l i e r s_{i n p}^{R}$	$o u t l i e r s_{e i g}^{R}$
>
0%	19	10228	0%	0.1%	0%	0.2	0.2	0.3%	0.1%
10%	19	10589	0%	0.2%	0%	1.7	1.2	0.8%	0.3%
20%	20	11299	0.1%	0.7%	0.1%	4	2.6	7.2%	2.5%
30%	20	11730	2.4%	2%	0.4%	7.7	4.2	21.1%	8.9%
35%	21	12165	7.1%	3%	1.3%	17.4	7.7	36.8%	18.8%
40%	22	12479	7.1%	5.5%	2.9%	18.3	8.3	44.2%	23.1%
45%	23	14305	8.8%	10.4%	6.9%	22.6	11.1	53.8%	32.0%
50%	23	15295	10.5%	16.1%	10.8%	26.8	12.2	61.7%	39.1%

M is the number of pairs of patches aligned (number of edges in the patch graph). τ denotes the percentage of patches incorrectly oriented, that is, the percentage of disagreements between ${\hat{z}}_{i}$ and z_i. $ε_{i n p}^{2}$ is the percentage of errors in the matrix $Z$ , that is, the percentage of disagreements between z_ij and $z_{i} z_{j}^{- 1}$ restricted to (i, j) ∈ E^P. $ε_{e i g}^{Z}$ is the percentage of disagreements between ${\hat{z}}_{i} {\hat{z}}_{j}^{- 1}$ and $z_{i} z_{j}^{- 1}$ also restricted to (i, j) ∈ E^P. $ε_{i n p}^{R}$ and $O u t l i e r s_{i n p}^{R}$ denote the average angle error (in degrees) and the number of outlier angles (errors above 10°) in θ_ij – (θ_i − θ_j) mod 2π for (i, j) ∈ E^P. $ε_{e i g}^{R}$ and $O u i l i e r s_{e i g}^{R}$ denote the average angle error (in degrees) and the number of outlier angles (errors above 10°) in ${\hat{θ}}_{i} - {\hat{θ}}_{j} - (θ_{i} - θ_{j})$ ) mod 2π for (i, j) ∈ E^P.