The Goldhill Pyramid

The binary image pyramid can be illustrated in terms of pyramid generation or of image reconstruction from the pyramid. The discussion here follows the order of pyramid construction. Read the page upwards to see the order of reconstruction.

Beginning with a square original picture...

the low pass channel is generated by removing every odd pel on every even line and every even pel on every odd line. The result is a picture with half as many pels as the original. Here it is shown rotated by 45 degrees with the diagonal lattice closed up onto a continuous square lattice (so it can be displayed without gaps).

The intervening pels from the original picture are predicted from this "lowpass" band, and the residue is coded as a difference signal. The difference image is

Next the process is repeated on the "diamond" lowpass band to yield another lowpass/highpass pair.

This pair are on a true square lattice because they contain one pel for every four in the original picture.

The process continues for eight bands, of which two more are shown here:

Of course, only the smallest/coarsest L band is coded; the decoder derives the others by upsampling L bands and filling in information from the appropriate H bands.

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