### Table 4. Results of Photometric Analysis

"... In PAGE 7: ...or the year (column 4). These are typically 0.0001 or 0.0002 mag and demonstrate the precision with which we measure the yearly means. Table4 gives the results of our photometric analyses. The semi-amplitudes are derived from sine-curve ts to the photometric data, assuming the planetary orbital periods given in Table 2, and serve as estimates of the maximum photometric variability possible at the orbital period.... In PAGE 7: ...etermined to high precision (i.e., 0:1%), our assessment of photometric semi-amplitude is not signi cantly altered if we permit the period of the sine curve to vary within several standard deviations of the period measurement error. All semi-amplitudes in Table4 are within 1 ? 2 of zero; i.e.... In PAGE 11: ... The standard deviation of the yearly means from the mean of the means, the measure of long-term variability, is 0.0008 mag ( Table4 ), signi cantly larger than the precision with which we typically measure the yearly means. To search for photometric pulsations at the value of the inferred orbital period of the planet, the year-to-year photometric variation was removed by shifting the data from each season to the mean brightness of the rst observing season.... In PAGE 11: ... Zero phase is the time of mid-transit for favorable orbital inclinations. The semi-amplitude of a sine-curve t to the data with the period xed to the planetary orbital period is 0:00011 0:00009 mag ( Table4 ). This result is a tighter constraint on variability than we were able to report in Paper II.... In PAGE 14: ... The standard deviation of the yearly mean magnitudes (Table 3, column 5) from the mean of the mean magnitudes is 0.0002 mag ( Table4 ), indicating no detectable long-term variations in 51 Peg. The photometric observations from the ve observing seasons are plotted in the top panel of Figure 4 against the orbital phase of the planetary companion computed with the ephemeris JDconj = 2; 450; 027:271 + 4:2310E (2) of Marcy (1998).... In PAGE 16: ...00016 0.00013 mag ( Table4 ), which is zero considering its uncertainty. The portion of the phase curve near the time of conjunction is replotted in the bottom panel of Figure 5, where two additional nights of intensive observations (not included in the top panel of Figure 5 for reasons listed previously) acquired with the 0.... In PAGE 18: ... The 210 nightly observations from these two observing seasons are plotted in Figure 6 (top panel) against the orbital phase of 1 Cnc b computed with the ephemeris JDconj = 2; 450; 206:04 + 14:649E (4) of Marcy (1998). Fourier analysis of these data at the planetary period gives a semi- amplitude of 0:00011 0:00009 mag ( Table4 ), a somewhat tighter constraint than we reported in Paper II, which used the old comparison star. Periodogram analysis of the data reveal no signi cant periodicities between 1 and 100 d.... In PAGE 20: ... The standard deviation of the yearly mean magnitudes from column 5 of Table 3 from the mean of the means, given as 0.0001 mag in Table4 , does not include the results of the fth and sixth observing seasons. The photometric observations from the six seasons are plotted modulo the planetary orbital period in the top panel of Figure 7.... In PAGE 20: ... The individual observations in seasons 1, 2, 5, and 6 have been adjusted so that their yearly means equal those of seasons 3 and 4. Fourier analysis of these data at the planetary period gives a semi-amplitude of 0:00011 0:00009 mag ( Table4 ), so any real light variation at this period must be extremely small. The portion of the phase curve near the time of conjunction is replotted in the bottom panel of Figure 7 with an expanded scale on the abscissa.... In PAGE 22: ... Fourier analysis of the adjusted data at the 116.67-d period gives a semi-amplitude of 0:00020 0:00011 ( Table4 ), in agreement with our results in Paper I. Periodogram analyses of the data reveal no signi cant periodicities between 1 and 200 d.... In PAGE 22: ...002 mag, but we suspect at least some of this to be a dimming of the comparison star. Therefore, the long-term variation in 70 Vir, given in Table4 as 0.0010 mag, is an upper limit.... In PAGE 24: ... Therefore, the long-term standard deviation of 0.0004 mag given in Table4 is an upper limit. The 242 nightly observations are plotted in the top panel of Figure 9 against the orbital phase of the planet computed with the ephemeris JDconj = 2; 449; 099 + 1035E (7) where the time of conjunction has been derived from an updated orbital ephemeris (Marcy 1998).... In PAGE 24: ...0 is our rst observing season. Fourier analysis on the planetary orbital period gives a semi-amplitude of 0:00048 0:00013 mag ( Table4 ), but this apparant variation is likely from variability in the comparison star, as discussed above. Therefore, the semi-amplitude on the planetary orbital period is an upper limit to variability in 47 UMa.... In PAGE 26: ...0002 mag; the standard deviation of the two yearly means from their mean is 0.0001 mag ( Table4 ). Therefore, we nd no evidence so far of any photometric variability in Gl 411.... In PAGE 27: ...0001 or 0.0002 mag ( Table4 ). For 47 UMa, we have shown that photometric variations on the 2.... In PAGE 29: ...f the star and planet. Hatzes et al. (1998) have searched for this re ected light of the planetary companion of 51 Peg in their high-resolution spectra. Their negative result implies that the planet is at least 2000 times fainter than the star, in agreement with the small semi-amplitude of our photometry listed in Table4 . We examine here the possibility that we might similarly detect in our photometry the re ected light from one of the short-period planets as the planet apos;s illumination changes the combined light as a function of orbital phase.... In PAGE 29: ....00008 mag. The precision of our photometry is approaching the precision needed to detect phase e ects of this magnitude. The semi-amplitudes of the photometric data and their errors listed in Table4 come directly from least-squares sine ts to the data on the planetary orbital periods.... In PAGE 29: ... This is when the dark, unlit hemisphere of the planet faces the earth. The semi-amplitude results in Table4 show that we have achieved the highest precision for Boo, 1 Cnc, and CrB. The phases of minimum of the sine ts to the photometry of these systems are 0.... In PAGE 30: ... However, the transit probabilities are very small for these last three systems (Table 4). Using the transit probabilites in Table4 , computed as the ratios of the stellar radii to the semi-major axes of the planetary orbits (Schneider 1996), we calculate the probability of nding at least one transit from among the six planets that have negative transit-search results. This is given by P (one transit) = 1 ? P (no transits) (8) where P (no transits) is the probabability of nding no transits.... In PAGE 30: ... This is given by P (one transit) = 1 ? P (no transits) (8) where P (no transits) is the probabability of nding no transits. This, in turn, is given by P (no transits) = P1(no transits) P2(no transits) ::: P6(no transit) (9) where Pi(no transits) is one minus the transit probability from Table4 . Then, P (no transits) = 0:61:... In PAGE 31: ....4. Year-to-Year Stellar Photometric Variations Our measure of year-to-year photometric variations is the standard deviation of a star apos;s yearly mean magnitudes (from Table 3) with respect to the mean of the yearly means. These standard deviations are given as long in column 3 of Table4 . We nd signi cant... ..."

### Table 8 Results of noise robustness experiments

"... In PAGE 4: ...2 (lexicon based on 7 matches, language model trained on 12 matches). Table8 shows the best results for the German YugNet match. Table 8 Results of noise robustness experiments ... ..."

### Table 3: Brightness variation due to focus change for four widely used lenses and their telecentric versions.

1995

"... In PAGE 17: ... This process is avoided in the telecentric case. Table3 summarizes our experiments on the photometric properties of the two con gurations. 4.... ..."

Cited by 7

### Table 2: Estimation of an inhomogeneous variation of the Potts model.

in Estimation of Markov Random Field prior parameters using Markov chain Monte Carlo Maximum Likelihood

"... In PAGE 13: .... Descombes, R. Morris, J. Zerubia, M. Berthod Parameters = 0:53 (N0 = 48070) = 0:5493 (N0 = 35699) Estimates ^ = 0:529 (hN0i = 48072) ^ = 0:5488 (hN0i = 35699) Sample Table 1: Estimation of the Potts model parameter To estimate we have to estimate a, b and c. The associated distribution is written: Pa;b;c(X) = 1 Z(a; b; c) exp 2 4? X c=fs;s0g2C a i + p 2 + b j + q 2 + c xs6 =xs0 3 5 : (26) This model can be written in the form of equation (1): Pa;b;c(X) = 1 Z(a; b; c) exp [?cN0(X) ? bN1(X) ? aN2(X)] ; (27) where: N0(X) = #X; the number of inhomogeneous cliques N1(X) = X inhomogeneous cliques j + q 2 = N0(X) j + q 2 inh:cl: N2(X) = X inhomogeneous cliques i + p 2 = N0(X) i + p 2 inh:cl: Table2 shows samples from this model and the parameters estimated from these samples.... ..."

### Table 2. Estimation of an inhomogeneous variation of the Potts model.

### Table 2. Robustness of Neurogenic Network Models to Variation in Initial Conditions, Prepattern

2002

"... In PAGE 3: ... each of the focal cells. For all three networks, we found solutions that were robust to this noise ( Table2 ). Simi- larly, both the augmented and reduced networks can The reduced, standard, and augmented versions of the select a single winner with very little initial bias in the network have 53, 63, and 69 such parameters, respec- prepattern by amplifying small amounts of noise (Table tively.... ..."

Cited by 7

### Table 1 Matching versions

"... In PAGE 6: ... Table 2 gives information on the amount of rejected points. As it can be seen from Table1 and Table 2, the amount of successfully matched points decreases and the percentage of detected blunders increases when (i) no geometric constraints are used (version 1), and (ii) grey level images are used (version 4). From the remaining versions, the ones using shifts result in more successful points because they are more stable (robust) than the one using the conformal transformation.... ..."

### Tables 1 and 2 summarize the results obtained with three views. Experiments with a larger number of views gave more accurate results. Experiments with real images indicate that images may be matched with an RMS error of about 0.5 pixels, which suggests that this is a realistic noise level. The results with synthetic data show that the algorithms are robust for noise levels well beyond this range.

1994

Cited by 126

### Table 2: Construction of 3D Models (H-2,3,4,5,6,7) us- ing image pairs: SM=matches after match strength com- putation, RM=matches after relaxation strategy, EM=robust matches after applying epipolar constraint, IE=Initial repro- jection error, FE= nal reprojection error after bundle ad- justment.

"... In PAGE 7: ...2 (see Figure 12). Statistics are summarized in Table2 . Al- though the initial reprojection error was very high for H5- model because the two images used in the 3D reconstruc- tion differed by a very small rotation, which is not very good for the working of the 3D reconstruction algorithm using epipolar constraint.... ..."

### Table 2 : Repeatability study : robustness against natural noise Scene

"... In PAGE 6: ...cene). Some examples are depicted on Fig. 7. For each image, 2 sections have been analyzed by a human expert and our algorithm in order to determine the centre position and the width of section. The errors introduced by our method (absolute value of differences between human measurements and filter responses) are presented in the Table 1 and Table2 . The error measured on the axis position and the curvilinear region width is from 1 to 2 pixels in many cases.... ..."