C. Gotsman / Constant-time Filtering

11 (a) (b) (c) (d) (e) (f) Figure 6: Using Gaussian ltering to warp an image: (a) A s a m p l e 256 256 pixel black and white checkerboard image. Each colored square in the image has 8 8 pixels. (b) Point sampled w a r p o f (a) with warp functions x(uu v) = 256u=v, y(uu v) = v. (c) Gaussian kernel shapes required to lter the warp at some texture p ositions. The ellipses are tri-parametric-(aa bb) deformations of a circle of unit-pixel radius. Note that the smaller ellipses (in the lower rows) are signiicantly rotated f r om an axis-aligned orientation. (d) Warp of (a) with Gaussian constant-time ltering using our method. Kernels with parameters outside the implemented r ange were r educed to the implemented p arameter ranges. (e-f) Preeltered versions of the image (a) with the basis kernels (a.4) and (a.8) of Fig. 3, used to obtain (d). The borders, always problematic when ltering with kernels with large support, have been cut away.