### Table 5. Summary of timing estimates for convolution architectures

in By

2001

"... In PAGE 10: ...able 4. Mapping report summary for derivative estimator design ................................46 Table5 .... In PAGE 71: ...2.2 Direct computation design Direct computation architectures compatible with the HWS interfaces might take several forms, noted DC-1 to DC-4 for reference to Table5 . The simplest internal logic would result from directly addressing a 16 x 16 array of multiply/add circuits to compute a single output, requiring explicitly writing each 16x16 sub-image to the HWS (DC-1).... ..."

### Table 3. Performance results after merging implementation steps. Note the decrease in convolution time is a result of early exit from loops based on zero values remaining in the kernel array.

"... In PAGE 9: ... This saves four write/read transfers. Table3 shows the results of implementing this optimization. The ifftcols value goes to zero because this function is now embedded in the fftcols routine.... ..."

### Table 1: Discretization errors in the convolution integral, taken at the point of maximum error in the curvature approximation along a unit circle ( = 0:2).

1998

"... In PAGE 7: ...cales). Growth of these singularities is even more severe for non-monotonic kernels. Any numerical approximation to the convolution of second order and higher derivatives, therefore, will require many discrete points within jxj lt; to accurately approximate to the convolution. Table1 provides evidence for this tendency, where the error between the exact convolution integral of @2K8=@x2 with f and @2K8=@y2 with f and our numerical approximations to these quantities is quite large, even with many discrete points within . 3 DETERMINING THE INTERFACE TOPOLOGY It is di cult to obtain high-order accurate approximations to n and when the interface is represented by a color function with a steep transition region.... In PAGE 8: ... The divergence in (3) can also be approximated by convolving f with the second derivatives of the kernel as was done in [AP95]. However, as shown in Table1 , the relative error asso- ciated with discretizing the convolution of the kernel second derivatives with f can be an order of magnitude larger than the relative error associated with discretizing the convolution of the kernel rst derivatives with f. Furthermore, at least for the case shown in Table 1,... ..."

Cited by 3

### Table 2: Center-Weighted Vectors

1994

"... In PAGE 4: ...Table 2: Center-Weighted Vectors Table2 lists the 5 one-dimensional center-weighted convolution kernels which are used to create the 25 two-dimensional 5-by-5 convolution kernels. The names of these one-dimensional kernels are mnemon- ics for Level, Edge, Spot, Wave, and Ripple.... ..."

Cited by 23

### Table 4: Center-Weighted Vectors

1994

"... In PAGE 8: ...Table 4: Center-Weighted Vectors Table4 lists the 5 one-dimensional center-weighted convolution kernels which are used to create the two- dimensional 5-by-5 convolution kernels. The names of these one-dimensional kernels are mnemonics for Level, Edge, Spot, Wave, and Ripple.... ..."

Cited by 8

### Table 1. Frames per second for various configurations of the algorithm on height fields of size a179a13a180a33a181a52a182a37a179a62a180a11a181 and a180a11a183a11a184a52a182a48a180a88a183a11a184 , using a a185a46a182a30a185 convolution kernel. HW/No PT: Hardware implementation , pixel texturing disabled. HW/SWPT: Hardware implementation with software pixel texturing. SW: Software implementation. Sizes are in pixels.

2000

"... In PAGE 9: ... 5.1 Frame Rates Table1 reports the frame rates for three configurations: The hardware implementa- tion without pixel textures, which gives incorrect images but has times closest to those likely if pixel texturing were indeed supported, the hardware implementation with soft- ware pixel textures, which provides a lower bound on the frame rate, and the software implementation. The frame rates of Table 1 are those required to generate the raster images of caus- tics from raster images of height fields.... In PAGE 9: ...1 Frame Rates Table 1 reports the frame rates for three configurations: The hardware implementa- tion without pixel textures, which gives incorrect images but has times closest to those likely if pixel texturing were indeed supported, the hardware implementation with soft- ware pixel textures, which provides a lower bound on the frame rate, and the software implementation. The frame rates of Table1 are those required to generate the raster images of caus- tics from raster images of height fields. Running times for height field generation on an Infinite Reality Onyx 2 are 178 frames per second for a a10 a83a60a174a41a175 a10 a83a60a174 heightfield with one impulse (plus four reflected impulses), and 64 frames per second for a a83a60a176a102a177a36a175a69a83a60a176a102a177 heightfield with three impulses (plus 12 reflected impulses).... In PAGE 9: ... Running times for height field generation on an Infinite Reality Onyx 2 are 178 frames per second for a a10 a83a60a174a41a175 a10 a83a60a174 heightfield with one impulse (plus four reflected impulses), and 64 frames per second for a a83a60a176a102a177a36a175a69a83a60a176a102a177 heightfield with three impulses (plus 12 reflected impulses). From Table1 , it is clear that interactive rates of between 9 and 15 frames per second can be achieved on the Infinite Reality for a height field of size a83a60a176a60a177a91a175a178a83a60a176a60a177 . On the Indigo 2, the frame rate drops to between three and four frames per second which, while not interactive, is still reasonable.... ..."

Cited by 27

### Table 3.1: Consistency errors for the evaluation of curvature on regularized 2D data for di erent sizes of h and increasing stencil width l of the L2-projection and the convolution with derivatives of smoothing kernels, respectively. We see that the consistency error is rather independent of the grid-size, i.e. decreasing h does not decrease the error if l is kept xed. If the value of l is increased by a factor 2 we see that the error is decreased by approximately a factor 1=4.

### Table 3.2: Consistency errors for the evaluation of curvature on regularized 3D data for di erent sizes of h and increasing stencil width l of the L2-projection and the convolution with derivatives of smoothing kernels, respectively. If the value of l is increased by a factor 2 we see that the error is decreased by approximately a factor 1=4. Moreover for xed l the error is rather independent of h.

### Table I). The table lists the image used, the blurring kernel applied in convolution, and the details of the additive noise process including the distribution, the standard deviation ( ) of the additive noise, and the SNR. The results shown reflect the optimal regularization parameter as computed via cross- validation. Although attaining a high SNR does not necessarily imply that the subjective quality of the restored image is superior [11], [21], we seek results that at least improve, and that do not degrade the SNR. The SNR of a noisy image is defined by

1999

Cited by 6

### Table 1: Filter kernels of B-spline type obtained by recursively convolving box lters. All lters h in this table have support [?L; L] and are normalized to one. Convolutions f h are represented as nite linear combinations of repeated integrals of f.

1998

"... In PAGE 12: ... This yields the following sequence of bell-shaped lters of B-spline type: ~bn(x) = n (2L)n n X i=0(?1)i n i ij(x) (25) where i = 2i?n n L and i = 1 : : : n . In Table1 the rst few functions of this type are given explicitly in the form of Def. 13.... In PAGE 12: ... 13. The expressions for f h contained in Table1 result by applying relation (23).... In PAGE 14: ... These techniques can be applied to the new algorithm without any modi cation. In Table1 various lter kernels of B-spline type are shown. The convolution value for the most simple lter kernel { the box lter { is given as the di erence of the rst-order sums at just two di erent locations.... ..."

Cited by 8