### Table 1: Dependency of the minimal surface area and the cmc surface period on the number of iterations for a xed discretization of the fundamental patch with 291 trian- gles. The minimization algorithm converges rapidly during the rst iterations; when the surface is close to its minimum the vertices try to move tangential to further decrease the energy and this motion is very slow. For the period problem and the nal surface these last minimization steps seem to have qualitatively no in uence, the intermediate time at which zero period occurs is very stable w.r.t. increasing number of iterations.

1997

Cited by 19

### Table 1. Information content of the different plenoptic subspaces with regard to the 3D motion estimation prob- lem

2003

"... In PAGE 6: ... 1b). We collected the motion constraint equations for all the plenoptic subspaces in Table1 , and we see that the cam- era that makes the motion estimation problem the easiest is the one that samples the whole plenoptic function (or a multi-perspective 3D slice of it for the case of planar mo- tion) because the motion estimation problem is reduced to a low-dimensional image registration problem as said before. Another important criteria is the range of directions (field of view) of the sensor.... In PAGE 6: ... To simplify the exposition we as- sume that the robot is only able to move on a planar, flat surface, thus the locomotion of the robot is limited to a hor- izontal planar motion, and that the camera designs under study are restricted sets of horizontally aligned pinhole line cameras. As summarized in Table1 in the previous section, we can see that we can extract the 3 planar motion param-... ..."

Cited by 4

### TABLE II Self-Motion Surface Boundary Data

1997

Cited by 12

### Table 1. Information content of the different plenoptic subspaces with regard to the 3D motion estimation prob- lem

2003

"... In PAGE 6: ... 1b). We collected the motion constraint equations for all the plenoptic subspaces in Table1 , and we see that the cam- era that makes the motion estimation problem the easiest is the one that samples the whole plenoptic function (or a multi-perspective 3D slice of it for the case of planar mo- tion) because the motion estimation problem is reduced to a low-dimensional image registration problem as said before. Another important criteria is the range of directions (field of view) of the sensor.... In PAGE 6: ... To simplify the exposition we as- sume that the robot is only able to move on a planar, flat surface, thus the locomotion of the robot is limited to a hor- izontal planar motion, and that the camera designs under study are restricted sets of horizontally aligned pinhole line cameras. As summarized in Table1 in the previous section, we can see that we can extract the 3 planar motion param- eters directly from the image data if we are able to capture Proceedings of the Ninth IEEE International Conference on Computer Vision (ICCV 2003) 2-Volume Set ... ..."

Cited by 4

### Table 1: Motion models

"... In PAGE 5: ... Clearly, a 2-D motion model does not uniquely correspond to one 3-D model; identical 2-D motion models may result from di erent assumptions about 3-D motion, surface and camera projection models. Table1 summarizes some parametric models for 2-D motion and provides possible underlying assumptions. The rst four models are illustrated in Fig.... In PAGE 6: ...5 (a) (b) (c) (d) Figure 2: Examples of parametric motion vector elds (sampled) and corresponding motion-compensated predictions of a centered square: (a) translation; (b) a ne; (c) projective linear; and (d) quadratic. See Table1 for model descriptions. pable of describing arbitrary 2-D motion elds.... In PAGE 6: ... O -lattice vectors of the motion eld can be approximated by suitable interpolation of the sampled eld [65]. In general, the interpolation kernel H ( Table1 ) has a small support, such that a motion vector is usually interpolated from at most four samples. The frequently used bilinear inter- polation kernel is a tensor product of horizontal and vertical 1-D triangular kernels.... In PAGE 6: ... Therefore, it can be expected that such elds can be e ciently represented using linear transforms followed by zeroing of high frequency components. For example, the polynomial transform given in the last row of Table1... In PAGE 7: ... To capture these second-order e ects, each motion trajectory must be modeled explicitly. For example, it may be represented by two vectors: instantaneous velocity _ x and acceleration x [13]: x( ) x(t) + _ x(t)( ? t) + x(t) 2 ( ? t)2: (5) Such a temporal modeling can be applied in addition to the spatial modeling described thus far in Table1 . Although representation of motion trajectory elds rather than displacement elds is advantageous in certain applications, larger amounts of motion information must be processed and/or transmitted [13].... In PAGE 8: ...g., a ne; Table1... In PAGE 9: ...2.3 Motion of regions Between the two extremes above, one can nd methods that apply motion models from Table1 to image regions. The motivation is to insure a more accurate modeling (smaller approximation error (6)) of motion elds than in the global motion case and a reduced number of parameters in comparison with the dense motion.... In PAGE 10: ... Thus, a more general image partitioning is neces- sary. The reasoning is that for objects with su ciently smooth 3-D surface and 3-D motion, the induced 2-D motion elds in the image plane can be suitably described by models from Table1 if applied to the area of object projection. A natural image partitioning can be provided by the image acquisition process itself.... In PAGE 12: ... 4.a) for di erent regions of support: (a) block-based (16 16 blocks); (b) pixel-based (globally- smooth as in (17)); and (c,d) region-based with a ne motion model ( Table1 ). For details of the region-based algorithm, see [20].... ..."

### Table 1: The True Motion and Surface Parameters, and a Summary of the Results of a Simulation That Converges to the True Solution.

1983

"... In PAGE 12: ... The image brightness function was generated using a multiplicative sinusoidal pattern (one that varies sinusoidally in both x and y directions), a 45 quot; field of view was assumed, and the image brightness gradients were computed analytically to avoid errors due to image brightness quantization and finite difference approximations of the brightness gradient. In practice, the brightness at inmge points in- two frames would be discretized first, and the gradient computed using finite difference methods, Table1 shows the true motion and surface paranleters, and the results of a simulation that converged to the true solution using the first scheme described earlier. In Table 2, the dual solution for the true motion and surface parameters, and the results of a simulation that converged to the dual solution are tabulated, In both cases, the solutions after various number of iterations are given.... ..."

Cited by 146

### Table 2: Surface Parameterization for business jet problem

1997

"... In PAGE 12: ... Six design variables were used whose associated mode shapes were combinations of 3 chordwise functions and 2 spanwise functions. The selected design variables result in a wing parameterization given by equation (36) and the functions fi and gj for this case are listed in Table2 . Note that the chordwise functions are given by a shear function (which is similar to a twist variable for small geometry perturbations), and two Hicks-Henne functions.... ..."

Cited by 29

### Table 2: Surface Parameterization for viscous wing problem

1998

Cited by 1

### Table 1. Theoretical expressions of surface displacements caused by slip motion on a plate boundary.

"... In PAGE 1: ... The method of geodetic data inversion In general, the viscoelastic surface displacements caused by slip motion along a plate bound- ary can be written in the form of hereditary integral in Eq. (1) of Table1 . Here, u indicates the total slip motion along the plate boundary , and GL is a viscoelastic slip response function.... ..."

### Table 1. Hierarchy of cameras with respect to the structure from motion problem

2002

Cited by 8