"... In PAGE 6: ... All manual designs required more samples than the learned controller, but produced controllers that, visually and quantitatively, were significantly inferior to our learned controller. In Table1 , we show the number of samples and the percentage of input space coverage of each controller. For this comparison, we only consider the catch task, ignoring the stand task.... ..."

"... In PAGE 12: ...are listed in Table2 . It can be seen from the table that a reduction of variance by as much as a factor of 3 has been achieved.... ..."

"... 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].... ..."