There are a wide variety of applications for LPS; most of them are explained in detail in [2]. Here are several that pertain directly to image processing.
LPS was originally developed to aid development of computer graphics image synthesis, especially fractal creation (see [1]). By rendering pixels in the LPS order, a low resolution indication of the eventual picture is almost immediately visible. Slow computers or ambitious programmers otherwise produce images that can take hours to see--starting with the extremely boring topmost rows of pixels.
The pixel ordering for image rendering suggests an image file format. The initial portion of such a file gives a low resolution image; subsequent portions fill in the details.
Because LPS is linear, the pixels that are rendered earliest can be magnified (``fat pixels'') to cover the entire image area very early. Subsequent pixels can be magnified by smaller factors, eventually not magnified at all. If there are constant patches in the image, the later pixels often make no difference to the image appearance--they do not need to be rendered or stored at all. This observation leads to a lossless image compression technique for text and line-drawing images that is competitive with run-length encoding but has the useful property that a prefix of the compressed file is a lossy compression of the entire image.
The results of image morphology operations (dilation, erosion, opening, closing) can be rapidly approximated by performing the basic operations in LPS order. For some applications, an approximation that takes only 15% of the total time may be sufficient.
The table T can be used as a halftone
mask. Fig. 3 shows an
image with the first 968 of the pixels
marked. This is the dot pattern associated with
an LPS mask at gray level 0.125 (where 1.0 indicates
black).
Images can be searched to locate objects (``Where's Waldo?'') or gather image statistics, such as histogram estimation. An infinite version of LPS is appropriate for Monte Carlo integration.
