### Table 14: Example 7, Shape-from-shading problem, third order scheme, Godunov numerical Hamiltonian

"... In PAGE 21: ... Because the exact solution of case (a) is a piecewise bi-linear polynomial and the exact solution of case (b) is a bi-quadratic polynomial, the numerical solutions by the third order scheme are accurate up to round-off errors. Table14 indicates that the errors for both cases are round-off errors, and the iteration numbers in Table 14 demonstrate the fast... In PAGE 21: ... Because the exact solution of case (a) is a piecewise bi-linear polynomial and the exact solution of case (b) is a bi-quadratic polynomial, the numerical solutions by the third order scheme are accurate up to round-off errors. Table 14 indicates that the errors for both cases are round-off errors, and the iteration numbers in Table14 demonstrate the fast... ..."

### Table 1 Goodness-of-fit of the three models of the interaction of shape from shading and contour

"... In PAGE 14: ... In addition, the noise increases with contour contrast, a result that is less intuitive. The performance of the three models can be com- pared in the Table1 where smaller absolute values of the log-likelihood indicate better fits. From this table, we can see that the model based on internal noise fits the data substantially less well than the nested model, even though it has more degrees of freedom.... ..."

### TABLEREPRESENTSRESULTSFORTHE MORE COMPLIGUEDSHAPE.THE METHODS ARENAMEDAS FOLLOWS: sfs: SHAPE-FROM-SHADING. msfi: MULXWUZSOLLWION~LWE-FROM-SHADING. sfii: SHAPE-FROM-SHADING WITHTHEINTEGRABILITYCONSTRAINT. msfsi: MUL~RE~OL~~ON SHAPEFROMSHADINGWlTHTHEINTEGRABLLITYCONSTRAINT.

### Table II. Comparison of three algorithms on three datasets using noise-free images: i) shape-from-shading only by mini- mizing E2 in Eq.(7), ii) hybrid method by minimizing E3 in Eq.(10), iii) hybrid method by enforcing bounds as in Section 3.2. Each entry has a pair of error measurements for the re- covered height field. The first one is the mean error while the second one is the RMS error. All numbers are given in the unit of a pixel.

2005

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### Table 3.11: Example 6, Shape-from-shading problem, Lax-Friedrichs numerical Hamiltonian, x = y = 1.

### Table 3.12: Example 7, Shape-from-shading problem, third order scheme, Godunov numer- ical Hamiltonian

### Table 3.10: Example 6, Shape-from-shading problem, Godunov numerical Hamiltonian. case 1 (smooth) case 2 (non-smooth)

### Table 1 Error measurement and comparison with other Shape from Shading algorithms [20]

2005

"... In PAGE 9: ...( Table1 ). It appears that our method gives better result than several light source directions.... ..."

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### Table 1. Quality and computational complexity of our algorithm, applied to all the ten Yale faces. Ten columns correspond to the ten faces. The first row contains asymmetry estimates of the faces (we subtract the lowest element). The second row contains the quality estimates, measured via an inverse normalized distance between the estimated and actual depths. The third row contains the quality estimates with statistical Carte- sian shape from shading (assuming constant albedo as in the work of Atick et al. [11]). The last row contains running times (in seconds) of our algorithm on all ten faces

2004

"... In PAGE 9: ... We scale the ground truth solution at the end, so that it will have the same mean as the estimated depth. In Table1 we provide asymmetry estimates for all ten Yale DB faces along with quality and computational complexity estimates of the results. Asymmetry is measured via a Frobenius distance between normalized (to mean gray level 1) frontally illuminated face F and its reflect R.... In PAGE 9: ...rom the image I and are given directly (without using z) by Eq. (9). In the last row of Fig. 4, we show results for the face number 6 in the Yale database, which has the worst reconstruction quality (see Table1... ..."

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### Table 1: Probabilistic Relevance Propagation Algorithms Method k Neighbors is pis

"... In PAGE 3: ... In particular, the framework can recover most existing link-based algorithms. Table1 shows a family of relevance propagation algorithms which are covered by our general framework. As can be seen from the table, PageRank and its extensions are special cases of the framework.... ..."

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