Sorry, I might use the wrong terminology. I meant the filter
that would give the original data from the output of the
forward filter, ie
data <--> m&backwad m&forward data
forward: (encode):
> Paeth(x) = Raw(x) - PaethPredictor(Raw(x-bpp), Prior(x), Prior(x-bpp))
backward (decode, back-feed, inverse, reverse):
> Raw(x) = Paeth(x) + PaethPredictor(Raw(x-bpp), Prior(x), Prior(x-bpp))
(value for element with negative index assumed 0)
You can see there are raw(..) in both side of the equation for
backward. Iteration or recursion seems needed and that is the reason
why I asked the question.
Пн, 01 сен 2014, Henry Rich написал(а):
> backward. 'paeth' is the paeth filter, which could be forward or backward,
> depending on use. Backward was what you wanted, no?
>
> Henry Rich
>
> On 9/1/2014 9:09 PM, bill lam wrote:
> >Just want to confirm, is you code for forward or backward
> >filter?
> >
> >Пн, 01 сен 2014, Henry Rich написал(а):
> >>Well, I said it was untested. It's just the framework. Here's a version
> >>that at least produces a result:
> >>
> >>
> >>y =. i. 5 10
> >>'height width'=: $y
> >>pixels=: ,y
> >>NB. convert to array, reverse, add bottom/right 0
> >>array =: ({.~ >:@$);.0 (height, width) $ pixels
> >>
> >>NB. x is unused,above), y is left,upper-left
> >>NB. Result is Paeth predictor
> >>paeth =: (({~ (i. <./)@:|@:(- +`-/)))@:(}.@,)
> >>NB. x is unused,above), y is left,upper-left
> >>NB. Result is (new pixel total,next upper-left (same as input 'above')
> >>pixels2x2 =: (256 | [ + 2 {. paeth)
> >>NB. y is is a pair of scanlines (current,above)
> >>NB. transpose, then decompress on each 2x2 producing a table of
> >>NB. (uncompressed value,above). Discard the above part, leaving a list
> >>scanlinepair =: 0 {"1 pixels2x2/\.@,.
> >>NB. Operate on each scanline-pair; reverse and remove added row/col
> >>xformimage =: 1 1&}.;.0 scanlinepair/\. array
> >>
> >>
> >>To support bpp you would need to keep an nx2 instead of a 2x2 history. Ecch.
> >>
> >>Henry Rich
> >>
> >>On 9/1/2014 11:04 AM, bill lam wrote:
> >>>I assume your code is for backward filter (from paeth to raw).
> >>>I tried with test data: y =. i. 5 10
> >>>'height width'=. $y
> >>>pixels=. ,y
> >>>
> >>>but it ran into error
> >>>|index error: scanlinepair
> >>>| xformimage=.1 1&}.;.0 scanlinepair/\.array
> >>>
> >>>Also the bpp meant comparison with bpp byte apart. this bpp can
> >>>be 1 to 7 depending on pixel format. so that each of the current
> >>>and above line can be reshaped or partition before processing
> >>>the 2x2 blocks.
> >>>
> >>>
> >>>Пн, 01 сен 2014, Henry Rich написал(а):
> >>>>Untested. Here is a framework. It's not pretty, but this
> >>>>computation is just not parallelizable.
> >>>>
> >>>>NB. convert to array, reverse, add bottom/right 0
> >>>>array =. ({.~ >:@$);.0 (height, width) $ pixels
> >>>>
> >>>>NB. y is 2x2 of (unused,above),:(left,upper-left)
> >>>>NB. Result is Paeth predictor
> >>>>paeth =. ({~ (i. <./)@:|@:(- +`-/))@:(}.@,)
> >>>>NB. y is 2x2 of (new pixel diff,above),:(left,upper-left)
> >>>>NB. Result is (new pixel total,next upper-left (same as input 'above')
> >>>>pixels2x2 =. ({. + 2 {. 256 | paeth)
> >>>>NB. y is is a pair of scanlines (current,above)
> >>>>NB. transpose, then decompress on each 2x2 producing a table of
> >>>>NB. (uncompressed value,above). Discard the above part, leaving a list
> >>>>scanlinepair =. 0 {"1 pixels2x2/\.@|:
> >>>>NB. Operate on each scanline-pair; reverse and remove added row/col
> >>>>xformimage =. 1 1&}.;.0 scanlinepair/\. array
> >>>>
> >>>>
> >>>>Henry Rich
> >>>>
> >>>>
> >>>>On 9/1/2014 1:44 AM, bill lam wrote:
> >>>>>Context for discussion, section 6.6 of this png rfc
> >>>>>
> >>>>>* http://tools.ietf.org/html/rfc2083
> >>>>>
> >>>>>The forward filter seems trivial, but the backward filter seems
> >>>>>tricky to me if not using loop. Any idea on a loop free
> >>>>>solution?
> >>>>>
> >>>>>
> >>>>>NB. Paeth Predictor
> >>>>>paeth=: 3 : 0
> >>>>>p=. +/ 1 1 _1 * y
> >>>>>y{~ (i.<./) |p-y
> >>>>>)
> >>>>>
> >>>>>forward=: 4 : 0
> >>>>>prev=. 10$ 3 5 8
> >>>>>iy=. i.10
> >>>>>pae=. 256&| iy - paeth"1 ((-x)}.(x#0),iy),.prev,.((-x)}.(x#0),prev)
> >>>>>)
> >>>>>
> >>>>> 3 forward''
> >>>>>253 252 250 3 3 3 3 3 3 3
> >>>>> 4 forward''
> >>>>>253 252 250 0 1 0 4 2 0 6
> >>>>>
> >>>>>NB. backward ??
> >>>>>NB. 4 backward 4 forward ''
> >>>>>
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> >>>
> >>----------------------------------------------------------------------
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> >
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