There is currently significant interest in freeform, curve-based authoring of graphic images. In particular, "diffusion curves" facilitate graphic image creation by allowing an image designer to specify naturalistic images by drawing curves and setting colour values along either side of those curves. Recently, extensions to diffusion curves based on the biharmonic equation have been proposed which provide smooth interpolation through specified colour values and allow image designers to specify colour gradient constraints at curves. We present a Boundary Element Method (BEM) for rendering diffusion curve images with smooth interpolation and gradient constraints, which generates a solved boundary element image representation. The diffusion curve image can be evaluated from the solved representation using a novel and efficient line-by-line approach. We also describe "curve-aware" upsampling, in which a full resolution diffusion curve image can be upsampled from a lower resolution image using formula evaluated orrections near curves. The BEM solved image representation is compact. It therefore offers advantages in scenarios where solved image representations are transmitted to devices for rendering and where PDE solving at the device is undesirable due to time or processing constraints.

Sketch based image coding decomposes an input image into a piece-wise smooth approximation image and a residual image. Image compression by gradient field integration follows this model, but differs by generating the approximation image from gradient data along edge contours and regularly sampled low resolution image data. This allows direct and efficient calculation of an approximation image which is smooth between edges. In this paper, we describe the image compression by gradient field integration approach, together with a low complexity implementation intended for near visually lossless compression of mixed content images. The implementation uses gradient field integration by scanline convolution, simple edge data extraction, DCT residual image coding and is block-based; it is suited to compression of images containing sharp edges occurring along pixel borders. Compression results are provided indicating potential gains from this method.

The paper is concerned with digital halftoning by error diffusion. It discusses error diffusion where the error distribution from a pixel to the next scanline, resulting from the complete processing of the current scanline, approximates a standard Cauchy distribution, having the form (1//spl pi/)1/(1+x/sup 2/). Such error diffusion is capable of generating sparse halftone patterns, which are free of worm artifacts, no matter how sparse the halftone patterns. It is argued that the well spread sparse halftone patterns are due to the remarkable properties of this particular distribution: the distribution is radially balanced, being equal within equiangular radial slices; and further, the distribution maintains this radial balance under self-convolution, spreading in proportion to the degree of self-convolution. Approximating this error distribution is an effective tool for designing error diffusion masks.