Progressive Image Resolution

diagonal pixel or quad pixel interleaving facilitates bandwidth-defined digital imaging cruising


[Topically related to Fully Interleaved Scanning for infinite resolution on bandwidth-defined video; and Video Compression]

Bandwidth-restricted information connections may be used for remote activity simulations and zoom-searching in 3-D image-space cruising. By fully interleaving pixels on the diagonal in cartesian-coordinated (*) digital images -e.g. the Internet image formats maximized- image resolution may be progressively refined.

* (Other coordinates are similar but not as binary: equilateral-triangular-hexagonal is best-packed, and its interstitials have simple placement at triple density.)

From a given starting position in a surround-image, which may be left-right/up-down scanned, or left/right-diagonally, additional sub-diagonal or sub-vertical interleaved image resolution sampling is conveyed, which briefly avails shallow depth zooming to a factor-of-two, image-space penetration. As the improved resolution is used, a further factor-of-two sub-diagonal interleaved image resolution sampling is conveyed,- allowing the next factor-of-two image-space penetration. Ad infinitum.

For more narrowly constrained image-spaces, each succeeded factor of two image-space penetration also narrows the image-space field of view, thus maintaining a constant bandwidth requirement on image updates.

The interstitial pixel can be either direct-value, with its differential to its four adjacent neighbors, reducing them by its quarter; or its can be a difference itself to their average ... either way exhibits a little squirm as the progressive pixels overlap.


(In practical camera applications this may relate also to pixel luminance: Motion toward an object expands its angular perception without changing its own amplitude, but of pixels: Subpixel angles increase, brightening the pixel, until its image space exceeds the pixel. Compression schemes have several items of improvement for this, especially on schemes of tendencies-coefficients extraction with bit-slice level-progressive sampling and leading-zeroes compression:
  1. Pixels can be scanned faster than usual if each can be reset by the bit-slice sample value: Eventually within the usual pixel time, the low-order bits are scanned, but having been cumulated as well, thus also sub-least precision is attained, over several pixels.
  2. If the coeffixels, computed from pixels, were relocated uniquely (on cyclic base) across consecutive frames, placed uniformly across the time-base, and positive where these represent positive pixels, negatively where negative pixels, there is certain intrinsic reconstruction of the original image on the average, though temporally and bit-slice-layer enhancement-distorted. (However, in tight schemes these coeffixels are intermediate values not transmitted.)
  3. The least-precise receiver-display difference represents a wash larger than the pixel, to smooth the image where it was originally smooth or of less distinction than could be coded. (A difference of 2 stands distinctly above that wash.)
  4. The least-precise coeffixel increment represents an additional 0.35,-- this is especially important for single-bit-coded bit-sliced values, except if the total is zero, in which case it probably represents zero; 0.5 would be exactly the average but would be noticeable as sometimes additive, sometimes subtractive; 0.25 is half smaller, but also below design detectability: whence the intermediate value of 0.35, taken as below the average-between, to minimize that appearance of edge-ringing, less desireable than edge-softening.

Grand-Admiral Petry
'Majestic Service in a Solar System'
Nuclear Emergency Management

© 1998, 2012