I believe paeth forward filter will give the following
output for i. 5 10
bbp=1
0 1 1 1 1 1 1 1 1 1
10 1 1 1 1 1 1 1 1 1
10 1 1 1 1 1 1 1 1 1
10 1 1 1 1 1 1 1 1 1
10 1 1 1 1 1 1 1 1 1
bbp=3
0 1 2 3 3 3 3 3 3 3
10 10 10 3 3 3 3 3 3 3
10 10 10 3 3 3 3 3 3 3
10 10 10 3 3 3 3 3 3 3
10 10 10 3 3 3 3 3 3 3
Or I may be wrong.
Пн, 01 сен 2014, Henry Rich написал(а):
> Right. So this is the way to get the original from the forward filter. If
> it works.
>
> Henry Rich
>
> On 9/1/2014 9:48 PM, bill lam wrote:
> >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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> >
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