### Table 4: Convergence range of different algorithms for affine mo- tion.

"... In PAGE 5: ... The experiments are similar to the ones for the rigid motion (table 3), we registered the source and target images while varying the synthetic affine motion until the methods fail to find the motion. Each motion parameter is evaluated independently, Table4 summarizes the results of applying our CCRE algorithm as well as the other MI schemes. The values shown are the maximum capture range (from a zero initial guess) for each parameter in each algorithm.... ..."

### Table 1: Iteration counts for iterative solutions of FIT2P. Algo- rithm switched phase at step 17.

"... In PAGE 22: ... The results for FIT2P are tabulated in Table 1. Table1 : Iteration counts for iterative solutions of FIT2P. Algo- rithm switched phase at step 17.... In PAGE 23: ...Indeed, as shown in Table1 , the number of PCG iterations taken to solve the normal equations generally increases as the IPM converges to a solution. On the other hand, when the two-phase algorithm switches to the RAE system (which occurs at the 17th IPM step), the number of SQMR iterations taken to solve the preconditioned RAE system generally decreases as the IPM solution converges.... ..."

### Table 1: Overview of IAI Projects

2002

"... In PAGE 16: ... Within this deliverable D11 all IAI projects have been reviewed and mapped to a high-level process matrix in order to (1) provide for a wider and more strongly industry-relevant scope, and (2) start providing a roadmap of IFC development, as a major spin-off effect of the work, Further work and recommendations will be done in the subsequent deliverables D12 and D13. Table1 below summarises the IAI projects, their status and targeted IFC release. Table 1: Overview of IAI Projects ... In PAGE 17: ... Hence, this process can become a core capability in the object model that all disciplines should use during a facilities lifecycle. Means of Escape (IAI Project AR-4) As mentioned in Table1 above, this project has been superseded by project CS-4. Initially, it has targeted 2 stages.... ..."

### Table 3: Convergence analysis information for adjoint Newton algorithm in experiment 1

in Application of a New Adjoint Newton Algorithm to the 3-D ARPS Storm Scale Model Using Simulated Data

"... In PAGE 34: ... After 18 iterations, the cost function decreased 8 orders of magnitude when the ANA is used. We construct Table3 for iterations 1 to 5 and 14 to 18. This table indicates that the ANA has a fast linear convergence rate for the rst 5 iterations with average M = 8:77 while its convergence rate slows down for the last ve iterations where average M = 1:79.... In PAGE 41: ...he retrieved and corresponding reference elds for experiments 1 and 2, respectively. Corr. denotes correlation coe cient. Table3 . Convergence analysis information for adjoint Newton algorithm in experiment 1.... ..."

### Table 2. The constrained affine projection algorithm. CAP Algorithm

### Table 1. Influence of the number of allowed errors x on the false acceptance ratio PFA for n = 37 and Pb = 0.01

2007

"... In PAGE 11: ... And because only the first k rounds of the fast bit exchanges contribute to the security, the false acceptance ratio will increase with decreasing k. This property is demonstrated for both distance bounding protocols in Table1 . In this numerical example, n = 37 and the bit error rate Pb is 0.... In PAGE 11: ...b is 0.01. The error correcting codes for our noise resilient MAD protocol have been selected following [16]. The results in Table1 clearly show that the false acceptance ratio increases significantly with the number x of allowed errors. One can also notice that the false acceptance ratio is remarkably smaller in our noise resilient MAD protocol (several orders of magnitude).... In PAGE 12: ... As demonstrated above, to decrease the false acceptance ratio, one has to allow fewer bit errors (denoted by x) for a fixed number n of rounds, or increase the number of rounds (without changing x). Table1 shows that the false acceptance ratio is remarkably higher in the Hancke and Kuhn protocol. The main reason is that an attacker has a 3 4 prob- ability of guessing a response correctly in the Hancke and Kuhn protocol, but only a 1 2 probability in our noise resilient MAD protocol.... ..."

Cited by 1

### Table 1. A comparison with expected geometric values of results obtained using the present projective algorithm, the DROID Euclidean algorithm, and the affine specialisation (discussed in Section 7). For the projective structure the cross-ratio measurement was made before transformation to the Euclidean frame, and the remaining measures after. For the affine structure, the cross-ratio and ratio measurements were made before transformation to the Euclidean frame, and the remaining measures after. 128 points were used to compute the transformation to the Euclidean frame. The point error is the average distance between a transformed point and the veridical Euclidean point, in the Euclidean frame. Coplanarity is a mean value for the two faces of the reference object.

1997

"... In PAGE 12: ... The transfor- mation can be determined using the coordinates of five or more points in the Quasi-Euclidean and Eu- clidean frames (Semple amp; Kneebone 1952) (we em- ploy all 128 points on the reference object in a least- squares computation), where direct physical measure- ment on the reference object provides the Euclidean coordinates. Comparison between the expected and measured values in columns 3 and 4 of Table1 provides an over- all assessment of the quality of the recovered projec- tive structure, by showing cross-ratios computed be- fore transformation to the Euclidean coordinate frame and other measurements like collinearity and copla- narity made after the transformation to ensure that all such measurements are in a single reference coordi- nate frame. The collinearity measure a80 a81 a86 a82a81 a72 a249 a193 a81 a72 a26 a93 a155 a11a83 a72 a53a84a81 a163 and the coplanarity measure a226 a81 a85a81a86a26a87a53a84a86a82a81 a72 a163 a193 a81 a72 a249 a93 a155 a54a83 a72 were obtained by using SVD to obtain the prin- cipal axes a208 a90 a251 a90 a21 together with the variance a81 a163 , a81 a249 , a81 a26 of point positions along each axis.... In PAGE 12: ... Note that all measures converge as more im- ages are considered. Column 6 of Table1 also provides a comparison with a local implementation of the DROID system (Harris 1987; Harris amp; Pike 1987) which computes... In PAGE 15: ...a111a122a116a61a110a179a111a114a128a73a116a112a123a127a129a38a113a6a119a95a130a61a124a15a113a95a130a112a119a6a123 a92 a196 system, although the latter has the stronger con- straints and utilises accurate camera calibration. Table1 shows that both at initialisation and at a later stage in the sequence, all the evaluation mea- sures are similar. Note the accuracy of recovered structure: the structure is accurate to within 1mm, after transformation to a Euclidean frame, for an object at a distance of 80cm.... In PAGE 19: ....4. Summary The experimental results for affine structure echo the conclusions already listed in Section 6: viz. that the quality of structure is the same for uncalibrated and calibrated systems (see Table1 ), and that structure im- proves over time. However, it is worth recalling our introductory re- marks about the significant advantages affine structure presents over projective structure in terms of the extra invariants available, invariants which appear to offer more scope for interaction with the environment than does the fundamental invariant in projective structure, the cross-ratio.... ..."

Cited by 112

### Table 1: Performance of the Subscribe and Access protocols using Affine and Projective coordinates.

"... In PAGE 6: ... We first ran the protocols using both of these coordinates to determine which type will result in faster performance. The com- putation times corresponding to different parts of the Subscribe and Access protocols are shown in Table1 . The parts of the protocols that we measured are: Client subscribe: (i) construction of a commitment to a message and a ZKPK that the commitment is well formed and (ii) ver- ification of the validity of the authentication token received from the server.... ..."

### Table 2: Overview of 42 processes and its affinity to the PKI-technology PKI almost indispensable Superiority of PKI not clearly evident

"... In PAGE 8: ...3.3 D2: Advantages for Business Processes A cluster analysis (see Table2 ) on the basis of the average values and its standard deviations of the facet answer (1.... ..."

### Table 1: Point conversion complexity: M is squaring or multipli- cation; and I is inversion. From \ To Affine Projective Jacobian Chudnovsky Modified

"... In PAGE 9: ... In order to use mixed coordinates it is sometimes necessary to convert a point representation from one coordinate system to an- other to have the input in the required format for the addition or doubling algorithm. Table1 shows that conversion from Affine co- ordinates to any of the other coordinate systems is very efficient be- cause the conversions only consist of setting all of the Z, Z2 and Z3 coordinates to one and the aZ4 coordinate to a (the elliptic curve parameter). Conversion to or from Projective coordinates is ineffi- cient because of the inversion required, as is converting from any of the other coordinate systems to Affine coordinates.... ..."