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Re: the Hilbert curve - is there any research into an image compression application of it? Split the image into RGB (or HSV) channels, stretch each of them int

Re: the Hilbert curve - is there any research into an image compression application of it? Split the image into RGB (or HSV) channels, stretch each of them into a stream using Hilbert curve mapping and then either try a lossless compression or a lossy JPEG/FFT-like one. A hunch says this could show some interesting results.

dvt 11y ago
There are probably little-to-no applications of Hilbert SFCs to image compression (in the sense of increasing compression ratio or something). The main benefit of using something like the Hilbert SFC is (2D) locality. That is, "close" points in D where D = [ d0,d1,d2,d3,d4,d5, ... dn] will also be "close" in D2, where D2 = [(x0,y0),(x0,y1)(x0,y2),...(xn,yn)]. NOTE: The converse does not hold. Closeness of points in the D2 plane does NOT guarantee closeness of points in D. Usually this has applications when dealing with things like file systems and databases. I've seen some people that argue that using something like Hilbert curves in compression algorithms will yield less compression-induced artifacts because the artifacts, as you can probably already guess, will "snake around" the image, being much harder to detect visually.
- ZeroGravitas 11y ago
  The Theora video codec (accidentally apparently) uses a hilbert curve for traversing it's superblocks.
- Someone 11y ago
  People also have toyed with the idea (and maybe even implemented it) to let the electron beam of a cathode ray tube trace out a Hilbert curve, or two mirrored side-by side. Advantage would be that you would not lose time in which you could have drawn pixels for vertical and horizontal blanking periods. Disadvantage would be that the hardware is a lot harder to make, more so if you want to dampen out oscillations near corners well.
theoh 11y ago
There's a recent overview of that kind of thing here: Scan Methods and Their Application in Image Compression Tarek Ouni and Mohamed Abid http://www.sersc.org/journals/IJSIP/vol5_no3/4.pdf http://www.sersc.org/journals/IJSIP/vol5_no3/4.pdf
eggy 11y ago
Wavelet transforms have been around for a while, and even used in JPEG 2000 for compression [1]. The article on Wikipedia does a great job of describing it. Hilbert transforms are involved. I learned of wavelet transforms when I was learning about fractals in the late 1990's. [1] https://en.wikipedia.org/wiki/Wavelet_transform https://en.wikipedia.org/wiki/Wavelet_transform

dvt 11y ago

There are probably little-to-no applications of Hilbert SFCs to image compression (in the sense of increasing compression ratio or something). The main benefit of using something like the Hilbert SFC is (2D) locality. That is, "close" points in D where D = [ d0,d1,d2,d3,d4,d5, ... dn] will also be "close" in D2, where D2 = [(x0,y0),(x0,y1)(x0,y2),...(xn,yn)]. NOTE: The converse does not hold. Closeness of points in the D2 plane does NOT guarantee closeness of points in D. Usually this has applications when dealing with things like file systems and databases. I've seen some people that argue that using something like Hilbert curves in compression algorithms will yield less compression-induced artifacts because the artifacts, as you can probably already guess, will "snake around" the image, being much harder to detect visually.

ZeroGravitas 11y ago
The Theora video codec (accidentally apparently) uses a hilbert curve for traversing it's superblocks.
Someone 11y ago
People also have toyed with the idea (and maybe even implemented it) to let the electron beam of a cathode ray tube trace out a Hilbert curve, or two mirrored side-by side. Advantage would be that you would not lose time in which you could have drawn pixels for vertical and horizontal blanking periods. Disadvantage would be that the hardware is a lot harder to make, more so if you want to dampen out oscillations near corners well.

theoh 11y ago

There's a recent overview of that kind of thing here: Scan Methods and Their Application in Image Compression Tarek Ouni and Mohamed Abid http://www.sersc.org/journals/IJSIP/vol5_no3/4.pdf http://www.sersc.org/journals/IJSIP/vol5_no3/4.pdf

eggy 11y ago

Wavelet transforms have been around for a while, and even used in JPEG 2000 for compression [1]. The article on Wikipedia does a great job of describing it. Hilbert transforms are involved. I learned of wavelet transforms when I was learning about fractals in the late 1990's. [1] https://en.wikipedia.org/wiki/Wavelet_transform https://en.wikipedia.org/wiki/Wavelet_transform