### Table 2. The comparison of 3D reconstruction measurement data of a resistance. NURBS curves MDP

2006

"... In PAGE 6: ... Detailed comparison of matching results obtained with these methods is given in table 1. Table2 gives a comparison of 3D measurement results of the resistance. 6.... ..."

### Table 2: 3D point reconstruction error for the RADIUS image data.

2000

"... In PAGE 24: ... Our algorithm recovered 61 correspondence rooftop polygon points, all of them correct (Figures 11 and 12). The corresponding 3D points reconstructed by the al- gorithm are reported in Table2 . This experiment uses the ground truth 3D data supplied in the model board 1 data set Here we only reported the comparisons between the reconstructed 3D points and their ground truth data for those 3D points whose ground truth coordinates are available.... In PAGE 24: ... This experiment uses the ground truth 3D data supplied in the model board 1 data set Here we only reported the comparisons between the reconstructed 3D points and their ground truth data for those 3D points whose ground truth coordinates are available. From Table2 , we can see that for some image correspondences such as 20, 21, 34, 35, 36, 49, 50, and 57, the trian- gulated 3D points have large errors although their correspondences are determined correctly by our algorithm. This is due mainly to the errors in the locations of rooftop polygon points, since it is well known that these 2D errors have a significant effect on the triangulated 3D data, especially when there are only two images [17].... ..."

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### Table 3: Baseline accuracy of the 3D reconstruction pro-

1996

"... In PAGE 6: ... The accuracy of each reconstructed roof polygon was then determined by comparing it with its 3D ground truth counterpart in terms of center-line distance and inter-vertex distances. Table3 reports, for each image, the median of the center-line polygon distances between reconstructed and ground truth polygons for that image. Also reported are the me- dians of the planimetric #28horizontal#29 and altimetric... In PAGE 7: ... For pairs of detected and ground truth polygons having the same number of vertices, the set of inter- vertex planimetric and altimetric errors were com- puted, and the medians of those measurements are shown in Table 4, broken down by the image in which the 2D polygons feeding the reconstruction process were hypothesized. Unlike the baseline er- ror data from Table3 , where the horizontal accu- racy of reconstructed polygon vertices was better than their vertical accuracy, here the situation is reversed, strongly suggesting that the planimetric component of reconstructed vertices is more sen- sitive to inaccuracies in the 2D polygon detection process than the altimetric component. This result is consistent with previous observations that the... ..."

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### Table 4: Evaluation of actual reconstruction accuracy. Median planimetric and altimetric errors (in meters) between reconstructed 3D polygon vertices and ground truth roof vertices for the two different modes of processing.

"... In PAGE 37: ...5 Distance (in meters) Figure 18: Building detector sensitivity vs. 3D polygon accuracy, computed as the median of center-line distances between reconstructed 3D polygons and ground truth polygons For pairs of detected and ground truth polygons having the same number of vertices, the set of inter-vertex planimetric and altimetric errors were computed, and the medians of those measurements are shown in Table4 , broken down by the image in which the 2D polygons feeding the reconstruction process were hypothesized. Unlike the baseline error data from Table 3, where the horizontal accuracy of reconstructed polygon vertices was better than their vertical accuracy, here the situation is reversed, strongly suggesting that the planimetric component of reconstructed vertices is more sensitive to inaccuracies in the 2D polygon detection process than the altimetric component.... ..."

### Table 1 Comparison between volume rendering and polygon rendering applications Volume rendering Polygon rendering

"... In PAGE 4: ...(see Table1 ) show that the calculation of rendering primitives and the rendering thereof introduce a considerable latency: on average, it takes 222.9 ms to render one frame.... ..."

### Table 1: Qualitative comparison of 3-D digital curve representation schemes.

1997

"... In PAGE 15: ... Thus, of the four methods only CQ satis es the projection property. Table1 compares the four 3-D digital curve representation schemes according to requirements (a) through (f). (g) One way to de ne the distance between the discrete chain and the original continuous curve is according to the maximum distance between any chain lattice point and the curve.... ..."

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### Table 1: Qualitative comparison of 3-D digital curve representation schemes.

1998

"... In PAGE 8: ...he projection property is that QRijl = RijQl, i.e., the projection of a 3-D chain onto a plane perpendicular to any one of the coordinate system axes should be identical to the 2-D digital representation of the projection of the continuous curve onto that plane. Table1 compares Grid Intersect Quantization (GIQ), Thinned Cube Quantization (TCQ)... ..."

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### Table 1: Cylinder data 2D and 3D

"... In PAGE 51: ... Value Par. Value M 50 S 300 N 400 Z 400 50 m 1:569 10?6 s=m t 4 10?3s t0 4 10?3s min 100 m min 2:3 10?4 s=m tmin 0 s t0;min 0s 1:5 1 0:5 2 0:75 v 4 vt0 2 Table1 : Image and parameter domain settings. The FCE-algorithm is used for fast detection of the interesting regions in parameter domain resulting from GRT.... In PAGE 60: ...10 80 0.5 Table1 : Line parameters. p is the slope, is the o set, and is the curve amplitude.... In PAGE 67: ... Most parameters, however, will a ect the Emission and Transmission contributions in the same way (through ij only), and therefore the model and its output is considered adequate for the purpose of identifying areas in the E-T plane where one source is dominating. From Table1 it is seen that the blank scan contribution to the noise as expected is only a small fraction of the transmission for same duration, the ratio being well ex- plained by the average attenuation of the (central part of) the 20 cm Cylinder phantom. For all practical purposes, therefore, the application of a 20 minutes blank scan will ensure that the blank scan contribution is negligible since the cases where a longer transmission scan might be ap- plied are those with a higher attenuation.... In PAGE 72: ... This table give parameters valid for any practically used value of NEC and Tt. Table1 Estimated model constants. Case Mode a [k counts] b [ ] c [sec] Cylinder 2D 47.... In PAGE 72: ... In the Cylinder (2D) case the blank scan parameter d has also been estimated from reconstructed images corres- ponding to varying blank scan length Tb, and the estimated value is d = 0:96. By comparison with the parameter c from Table1 the transmission scan in the cylinder case (2D) is seen to contribute approximately 6.7 times more to the variance than a blank scan with the same duration, c... In PAGE 73: ... In the Brain phantom (3D) case and in case MN two emission and two transmission scans were measured, thus both emission and transmission parameters have been es- timated. The parameters are listed in Table1 . Despite the approximations made for deriving the models Figures 3 and 4 demonstrate an excellent match between the meas- ured data and the model for many decades of NEC.... In PAGE 74: ... This implies that the sum of the emisssion and transmission term are given by V E2 = a RNEC(T ? Tt) + c Tt (12) Thus, with respect to the total noise level, the optimum duration of the transmission scan is given by Tt = T 1 + q a cRNEC (13) Figure 7 shows the normalized variance of the individual noise terms and their sum as a function of transmission scan time Tt. The Figure corresponds to the parameters found in Table1 for the Brain Phantom (3D) and the sum of the transmission scan time and emission scan time is arbitrarily set to 1800 sec. In Figure 7 it is assumed that RNEC = 1000 counts per slice per sec, which gives an op- timized normalized variance of 0.... In PAGE 78: ... The slow methods can be accelerated some by implementing multiplication with the transpose of the system matrix (adjoint operator) as a backprojection integral, but note that this implies that the approximation of the system matrix will be di erent in the forward and the backprojection part. Machine Fast ART Slow ART Fast EM Slow EM Fast LSCG Slow LSCG Pentium 26 sec 2218 sec 17 sec 5776 sec 17 sec 5250 sec Onyx 16 sec 1306 sec 16 sec 2722 sec 16 sec 2715 sec Table1 Time usage for 20 iterations of EM and LSCG.... In PAGE 82: ... Example 1 In the rst example the (synthetic) sinogram has 125 101 samples and the reconstructed image has 101 101 samples. In Table1 the reconstruction times on both machines are shown for the fast and the slow method as well as the ratio between the execution times (slow/fast). Times are measured for ART, EM, and the LSCG- method, when EM and LSCG were running (arbitrar- ily) 20 iterations, and ART 20 full iterations, i.... In PAGE 83: ... The sparse system matrix for this transformation geo- metry required approximately 13 MBytes, and each iteration requires approximately one second. Machine Type ART EM LSCG Fast 26 sec 17 sec 17 sec Pentium Slow 2218 sec 5776 sec 5250 sec Ratio 85 340 309 Fast 16 sec 16 sec 16 sec SGI Onyx Slow 1306 sec 2722 sec 2715 sec Ratio 82 170 170 Table1 Time usage for 20 iterations of EM and LSCG. For ART the timeis for 20 full iterations, i.... ..."

### Table 1. Ambiguity in reconstruction of symmetric curves: A single view is not enough for re- construction of general symmetric curves, except for case (a) of Figure 2, but sufficient for planar symmetric curves. Two or more views are needed for reconstruction of generally shaped sym- metric curves.

2004

"... In PAGE 8: ... For curves with general shapes, the solution is always unique. To conclude Section 3, we summarize all cases of symmetric curves studied so far in Table1 , in terms of ambiguities in reconstruction from one or two views. 8 We have also tried other distances such as L1-distance and C1-distance.... ..."

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### Table 1. Median planimetric and altimetric errors (in meters) between reconstructed 3D polygon vertices and ground truth roof vertices.

1996

"... In PAGE 11: ... altimetric (vertical) components. The median dis- tance errors are shown in Table1 , broken down by the image in which the 2D polygons feeding the reconstruction process were hypothesized. The results suggest that the planimetric component of reconstructed vertices is more sensitive to inaccu- racies in the detection and triangulation process than the altimetric component.... ..."

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