Determining Pixel Aspect Ratio (PAR)

[vampiredom]

This is a replacement for this discussion which was so zany and nonsensical. When scaling video to another size, it is essential to determine the pixel aspect ratio (PAR) of the source in order to do it properly.

If your source looks stretched or squeezed horizontally (objects look too fat or too skinny) then it most likely it has non-square pixels. If you don't know where your clip originated, determining PAR can be difficult.

Fortunately, only certain dimensions tend to have non-square pixels and most sources of these sizes tend to follow one of the standards.

If your image is not of the dimensions listed below, it is most likely square pixels (PAR = 1) and requires no special consideration. [such as 1920x1080, 1280x720, 1024x768, 640x480, 640x360, 480x360, etc.]

In addition to common DVD formats, I have also included SVCD and a few oddball "internet" resolutions with decent guesses as to their possible PAR. Please remember that, unless your source comes directly from a DVD or some known standard format, these are only "educated guesses", but educated guesses can often be better than stabbing in the dark.

For each resolution there are two possible PAR values listed: The "normal" (4:3) aspect, and "widescreen" (16:9)

Common non-square pixel formats and their Pixel Aspect Ratio (PAR)

NTSC
===================================================================
720x486   \
720x480    \ image appears slightly stretched -----> PAR = (10/11)
704x480    / image appears squeezed ---------------> PAR = (40/33)
352x240   /
-------------------------------------------------------------------
480x480   \
360x360    \ image appears squeezed ---------------> PAR = (15/11)
352x360    / image appears extremely squeezed -----> PAR = (60/33)
          /
-------------------------------------------------------------------
360x480   \
352x480    \ image appears extremely squeezed------> PAR = (20/11)
           / image appears ridiculously squeezed --> PAR = (80/33)
          /

PAL             
===================================================================
720x576   \
704x576    \ image appears slightly squeezed ------> PAR = (59/54)
352x288    / image appears extremely squeezed -----> PAR = (118/81)
360x288   /
-------------------------------------------------------------------
480x576 --- image appears extremely squeezed ------> PAR = (59/36)
        --- image appears ridiculously squeezed ---> PAR = (59/27)
480x384 --- image appears slightly squeezed -------> PAR = (59/54)
        --- image appears extremely squeezed ------> PAR = (118/81)
-------------------------------------------------------------------
360x576   \
352x576    \ image appears ridiculously squeezed---> PAR = (118/54)
           / image appears insanely squeezed-------> PAR = (236/81)
          /

HD (either NTSC or PAL)
===================================================================
1440x1080 \ 
960x720    \ --------------------------------------> PAR = (4/3)
1280x1080 -----------------------------------------> PAR = (3/2)

[vampiredom]

To convert a non-square pixel image into square pixels without cropping, multiply its width by the PAR. The height does not change. So…
704x480 @ 10/11 PAR would be 640x480 because:
704 * (10/11) = 640

Likewise,
720x576 @ 118/81 PAR would be 1049x576 because:
720 * (118/81) = 1048.8888888888888888888888888889

Just because a particular PAR conversion is "correct", however, it does not always mean it is the best choice.
Let's have a look at the example above, which gave use 1048.8888888888888888888888888889x576 for a widescreen PAL DVD. Setting a decimal width is impossible - and setting an odd width such as 1049 will cause problems in YUY2 and YV12 colorspaces. For YUY2, it must be evenly divisible by 2, while YV12 requires mod4. Our example of 1048 will work fine for both. So, in the real world:
720 * (118/81) = 1048

In cases where a video is 720 pixels wide (like all DV and DVD formats), the actual 4:3 or 16:9 area is only 704 pixels wide. This how it is possible, for example, for 720x480 and 704x480 to have the same height and pixel aspect ratio. When converting to square pixels from such sources, it is usually best to crop 8 pixels off of each side and start with a 704x480 box.

(Note: Some older professional NTSC formats may use 720x486. In which case, crop 4 pixels from the top and 2 from the bottom.)

In AviSynth terms, that's:

# assume a 720x576 source (PAL)
Crop(8,0,-8,0)

# assume a 720x480 source (NTSC)
Crop(8,0,-8,0)

# assume a 720x486 source (NTSC, like Matrox I-frame AVI files)
Crop(8,4,-8,-2)

So, let's do our PAL widescreen conversion again using the cropped numbers
704x576 @ 118/81 PAR would be 1024x576 because:
704 * (118/81) = 1025.5802469135802469135802469136 = ~1024

So, why not 1025 or 1026? If you are doing RGB formats only (such as making still images) this may be an OK choice.
However, with certain digital video formats, it is advantageous or requried for dimensions to be mod16.
1024 is also a standard computer monitor width, so it is a good choice for several reasons (and nobody will ever tell the difference).

In these examples, we will assume the target it YV12 and use dimensions that are mod4 (evenly divisible by 4) for output.

# We are assuming our input it NTSC 16:9 DVD in this example
# Note the decimal point values so that AviSynth returns a float instead of an integer
PAR = 40.0 / 33.0

# determine new width, make it mod4-safe for YV12
NewWidth = Round(width() * PAR) / 4 * 4
Spline36Resize(NewWidth, height())

[vampiredom]

To convert a square pixel image to a different PAR is easy. Divide the width by the PAR like such:

640x480 @ 10/11 PAR
640 / (10/11) = 704
704x480

The above example is rather simplistic. In many cases, when converting from square pixels, we'll want to scale the image overall. First we need to determine the scaling factor. To accomplish this, divide the source height by the target height:

SourceHeight / TargetHeight = ScalingFactor

1280x720 -> 704x480 @ 40/33 PAR
480 / 720 = 0.66666666666666666666666666666667

Once we have the scaling factor, apply that to both width and height of the source.
1280 * 0.66666666666666666666666666666667 = 853.33333333333333333333333333333
720 * 0.66666666666666666666666666666667 = 480

Now, divide the source width by the target PAR:
853.33333333333333333333333333333 / (40/33) = 704

From this, we can see that 1280x720 transforms perfectly to 704x480 for widescreen NTSC. The same is true for widescreen PAL:
576/720 = 0.8
1280 * 0.8 / (118/81) = 702.9
720 * 0.8 = 576

Well, almost perfectly in the case of PAL… but 702.9 is more than close enough to 704 to call it 704x576.

Sometimes, however. It is necessary or advantageous to crop or pad the source image when converting to from square pixels. Let's take the case of a 4928x3264 photograph that we want to format for 4:3 PAL DVD.

First, determine if the image - when scaled proportionately - will be wider or taller than the destination. The destination in this case is 720x576 @ 59/54 PAR. Lets' turn this to square pixels (we don't want to round it yet)

MaxWidth = 720 * (59/54) = 786.66666666666666666666666666667
MaxHeight = 576

From this, we'll get the effective Display Aspect Ratio of the target in square pixels:
TargetDAR = MaxWidth / MaxHeight = 1.3657407407407407407407407407407

Let's now compare this with the photograph:
SourceDAR = 4928/3264 = 1.5098039215686274509803921568627

From this, we can see that the DAR for the photo is larger, meaning it is wider than the Standard 720x576 4:3 PAL DVD.
We have the choice of cropping from the sides or letterboxing it (putting bars on the top and bottom of the image.) Let's try it both ways:

Cropping to fit another format

To determine the cropping, let's get the closest PAL-sized box within that image, in round pixels.
We'll use source image's height and the target format's DAR to determine that:
3264 * 1.3657407407407407407407407407407 = 4457.7777777777777777777777777776 = ~ 4458

Which gives us a cropped dimension of 4458x3264.

Is is best that this number is evenly divisible by 2. In this case, it is.
Were it not, we could have rounded up or down to the nearest 2. More than close enough for this kind of conversion.

Letterboxing to fit another format

Now, we'll do letterboxing instead of cropping. Width is easy here (Our target width will be 720) we only need to determine height.
First, we'll determine our scaling factor. In this case, this will be determined by the target and source widths.

TargetWidth / SourceWidth = ScalingFactor

ScalingFactor = 720 / 4928 = 0.1461038961038961038961038961039

Now, multiply the height by the scaling factor:
3264 * 0.1461038961038961038961038961039 = 476.88311688311688311688311688313

At this point, we are still dealing with square pixel values for the image. We need to apply the PAR to our new height:
476.88311688311688311688311688313 * (59/54) = 521.03896103896103896103896103897 = ~ 520

In AviSynth, we would do something like this to fit our photo into letterboxed PAL 4:3

# load the 4928x3264 image
ImageSource("bigphoto.jpg")

# resize and add borders to fill 720x576
Spline36Resize(720, 520)
AddBorders(0,28,0,28)

[vampiredom]

Most times, when converting from one non-square pixel format to another, we are converting PAL to NTSC or vice versa – or converting to/from a scaled format like SVCD. These types of standards conversions usually require only changing the height or width and leaving the other alone. Note: Any interlaced sources must be deinterlanced (or "bobbed") before scaling the height.

As far as scaling is concerned, these kinds of standards conversion are extremely easy and there really is no math required by the user:

# Restore a 480x480 SVCD to full size for DVD output
Spline36Resize(720,480)

# Scale the image from 720x480 NTSC -> PAL
Spline36Resize(720,576)

# Scale the image from 704x576 PAL -> NTSC
Spline36Resize(704,480)

Of course, for real NTSC<->PAL conversion, you need to choose a good deinterlacer and then convert the framerate from 60Hz <-> 50Hz, but we are only discussing scaling here.

Let's look at one case where we are not doing NTSC <-> PAL and where some math is required for the conversion.

Our source here will be HDV 1440x1080 @ PAR 4/3, which is widescreen. We will convert this to a 720x480 widescreen NTSC DVD two different ways; once with pillarboxing, and again with cropping.

First, we'll set the basic parameters common to both versions:

# Assume a 1440x1080 16:9 HDV source
SourceWidth  = width()
SourceHeight = height()
SourcePAR    = 1.333333

TargetWidth  = 720
TargetHeight = 480
TargetPAR    = 1.212121

Since the DAR of 720x480 widescreen DVD is slightly wider, the pillarboxed version will resize the video to 704x480 and add 8 pixel borders on each side. Here is VersionA:

# Scale factor based on heights = 0.444444
ScaleFactor  =  Float(TargetHeight) / Float(SourceHeight)

# Determine the width to scale to (no need to determine height)
ScaleWidth = Float(SourceWidth) * SourcePAR * ScaleFactor / TargetPAR

# Round to mod4 -> 704
ScaleWidth = Round(ScaleWidth * 4) / 4

# Determine the border size
PadX = (TargetWidth - ScaleWidth) / 2

VersionA = Spline36Resize(ScaleWidth, TargetHeight).AddBorders(PadX, 0, PadX, 0)

Now, if do it without adding borders, we'll have to crop a tiny bit from the top and bottom to preserve the aspect ratio accurately. We'll crop the source (as opposed to cropping the output) for a little more accuracy and increased performance. Here is VersionB:

# Scale factor based on widths = 0.5
ScaleFactor  =  Float(TargetWidth) / Float(TargetHeight)

# Determine the cropped height relative to the source
TargetDAR  = Float(TargetWidth) * TargetPAR / Float(TargetHeight)
CropHeight = Float(SourceWidth) * SourcePAR  / TargetDAR

# Round to mod2 -> 1056
CropHeight = Round(CropHeight * 2) / 2

# Determine the cropping amount for the top and bottom edges
CropY = (SourceHeight - CropHeight) / 2

VersionB = Crop(0,CropY,0,-CropY).Spline36Resize(TargetWidth, TargetHeight)

Both versions should be accurate conversions of the source.

[Keiyakusha]

Again this pure-math talks. Oh well, I'm not going to participate in such discussion again, just want to tell for those who hopefully will be able to read it below all this wall of text that there is plenty of dvds that are utilize full 720 pixels width and to get everything right needs to be resized like 720->853 without any cropping (and of course there is nothing to crop at all accept maybe ~2 semi-dark pixels which are normal and happens to be even on BD). Perhaps all american DVDs respect so called standards, I don't own any of such dvds so not sure, but this is not the case for other countries. And this is the case for pal-land too. So don't forget to use your eyes too, not pure math.

[vampiredom]

Originally Posted by Keiyakusha

So don't forget to use your eyes too, not pure math.

Absolutely. This is very true. The stuff I put in here is meant to be a starting point and not a one-size-fits all solution. I hinted at that at the top of the post: That the pixel dimensions are not an absolute guarantee of the PAR for any given clip. (Though I state that DVDs adhere to standards, I guess I should have said that they should adhere to such standards).

Originally Posted by Keiyakusha

there is plenty of dvds that are utilize full 720 pixels width and to get everything right needs to be resized like 720->853 without any cropping

Yes, many DVDs do ... and if you really want the full image, you should not crop. Using 853 for width, however, will only work out correctly with RGB, 852 would be a good choice for YUY2 or YV12.

I appreciate your comments. If you or anyone finds an error in what I've written here, please let me know so I can correct it. I am trying to provide some clear guidance in an orderly fashion to newbies, so as to possibly avoid pointless discussions like the one I mentioned previously.

[Keiyakusha]

Originally Posted by vampiredom

Using 853 for width, however, will only work out correctly with RGB, 852 would be a good choice for YUY2 or YV12.

Of course. Well, personally i'm not a fan of 852 too, I prefer anamorphic stuff

[Ghitulescu]

There is a lot of misunderstanding (and because of that also lots of misinformation) concerning the aspect ratio in general.
While some of them may derive from notations (SAR) and others from changes in standards and official recommendations (EBU), I think the bulk of misunderstandings comes from a very simple yet overlook issue: the difference between the framesize and the image size (which generally is smaller than the framesize, due to overscan, blanking, and various "safe" settings), and this concerns mainly the people using only the PC that do reencodings, these people having only PC-background.
There are only 2 DARs (FS and WS, 4:3 and 16 and 2 alternatives each (standard-analog, also called non-ITU, and ITU-R). However, since the material was processed maybe with a combination of digital (not necessarily ITU) and analog gear before editing (which also may influence the PAR), it is really difficult to find an one-for-all PAR/DAR solution. Depending on the source and its processing, all values may be correct, use your eyes and a PAR 1:1 display .

[TheSkiller]

Nice table!
There is however one point where I disagree with what the table states and that is the SVCD PAR.
The table assumes the 480x576/480 pixels used in SVCD make up a 4:3 frame. I'm pretty sure though, and that's also what I have observed capturing the output of DVD-Players playing a 480x576 test video, that these 480 pixels are simply a downsized version of 720 which means it has the same characteristics as 720 (wider than 4:3, scanline length is 53.333µs).
Therefore the PAR of PAL SVCD is 177/108 and the PAR of NTSC SVCD is 15/11.

Edit: Those are for 4:3 video, 16:9 is as follows: PAL 177/81 NTSC 60/33
It's actually just the PAR for 720,704 multiplied by 1.5.

[hello_hello]

Originally Posted by vampiredom

Fortunately, only certain dimensions tend to have non-square pixels and most sources of these sizes tend to follow one of the standards.

The problem is, they generally don't. At least not in my opinion. How were you able to come to a definitive conclusion they do?
(Edit) Sorry, I noticed in a later post you modified "tend to" with "should".
I don't think you can really generalise and say something like "crop to a width of 704 then use this pixel aspect ratio" etc. and know it'll be correct much of the time, because there's no way to know it will be. Admittedly if it's wrong it won't be out by much, but it can still be wrong. If only DVDs did all stick rigidly to some sort of standard.....

Personally I think DVDs (at least) are less likely to follow one of the standards than they are to follow them. My usual way of resizing DVDs is to use a straight 16:9 or 4:3 resize (I can't remember the exact PARs off the top of my head) then crop off only the necessary crud (or crop to mod16), encode what's left and at least 9 times out of 10 that'll be correct. I think DVDs which use the "official" PARs are the exception, not the norm, and I've come to this conclusion after comparing many old DVD encodes with their Bluray equivalent.

Anyway, being a GUI kind of guy I tend not to think about PAR all that much (I just choose non-ITU resizing, crop and encode) but for those times I do have to think about it, this resize calculator comes in quite handy as it'll let you choose between resize methods and it'll calculate the aspect ratio distortion for you as you crop. Yoda's Resize Calculator
At least with the calculator handy it's not necessary to remember a table of PARs.

[vampiredom]

Originally Posted by TheSkiller

Nice table!.

Thank you!

Originally Posted by TheSkiller

The table assumes the 480x576/480 pixels used in SVCD make up a 4:3 frame

Yeah, it really is all about the "should" thing. Of course, there is no way of knowing what somebody did when they made that SVCD and, if it was made from a DVD source, if the source was correct to begin with. However, I am pretty sure that most DVD players and player software will assume the same standard, so using this PARs in AviSynth will get you no worse results that you'd see when watching the original SVCD (or DVD, or whatever).

Originally Posted by hello_hello

I don't think you can really generalise and say something like "crop to a width of 704 then use this pixel aspect ratio" etc. and know it'll be correct much of the time, because there's no way to know it will be.

I can't. But, I can say that this is how it should work out. If somebody did not adhere to the standard then that is their error (and, if the error is bad enough, you'll have to compensate for it). Same point as above: This is only so that you can "restore" the frame size the way that a DVD/SVCD player would.

More and more, however, I believe that discs will be sticking to the standard... because, finally, most editing software is using the same standard, digital TV broadcasts are using the same standards, etc. For many years, it was not this way (I still remember Adobe using 0.9000 for NTSC in version CS3, etc.)

Heed Keiyakusha's words and you'll be fine: use your eyes, too!

[TheSkiller]

Originally Posted by vampiredom

Yeah, it really is all about the "should" thing. [...] However, I am pretty sure that most DVD players and player software will assume the same standard, so using this PARs in AviSynth will get you no worse results that you'd see when watching the original SVCD (or DVD, or whatever).

Yes, the "should" is what I'm talking about, maybe I didn't say clearly what I mean: SVCD should be using the PARs I stated because that's the way they are treated by standalone players (software players are always different, they always play "dumb" and resize only to either exactly 4:3 or 16:9 which is nothing specifically related to SVCD, it's the same for 720x... DVD). And it's also the way they are derived: It makes sense that a 480x576/480 video is derived by downsizing a 720x576/480 source since nothing is 480x... to begin with. For example in digital TV transmissions the incoming signal to the MPEG encoder is pretty much for sure always 720x576/480 (or even 486), and if the broadcast is done in super-duper low bitrate in reduced resolution, like 480x..., then the encoder takes those 720x... and resizes them to 480x.... The result is of course the same as the original 720x... video but horizontally squeezed, and therefore it is still covering an area wider than 4:3 or 16:9.


In conclusion, and that's my point, if you say a video of 720x... has those particular PARs mentioned in the table then you are ought say that a video of 480x... has those PARs I mentioned, otherwise it wouldn't be consistent. 720 is 1.5 times 480, so the PAR of 480 is also 1.5 times the PAR of 720.

[vampiredom]

In conclusion, and that's my point, if you say a video of 720x... has those particular PARs mentioned in the table then you are ought say that a video of 480x... has those PARs I mentioned, otherwise it wouldn't be consistent. 720 is 1.5 times 480, so the PAR of 480 is also 1.5 times the PAR of 720.

Thank you. I do see what you are saying.
** EDIT ** correct numbers now incorporated in the table ** EDIT **

[Asmodian]

Originally Posted by hello_hello

I think DVDs which use the "official" PARs are the exception, not the norm, and I've come to this conclusion after comparing many old DVD encodes with their Bluray equivalent.

Do you have a reason to assume the blurays do it correctly more often then DVDs?

[Keiyakusha]

Originally Posted by Asmodian

Do you have a reason to assume the blurays do it correctly more often then DVDs?

May I put it in the other way? How many anamorphic BDs you saw? I saw only the ones that use square pixels. So of course they are something that you can compare to.

[TheSkiller]

Originally Posted by vampiredom

480x480 -------------------------------------------> PAR = (15/11)
        --- image appears extremely squeezed ------> PAR = (50/33)
480x576 -------------------------------------------> PAR = (295/216)
        --- image appears ridiculously squeezed ---> PAR = (295/162)

Please let me know and I will revise it.

Sorry, those numbers are wrong, exept the first one. You forgot that PAL has 576 lines, not 480.

For example: (NTSC wide)
40/33 * 1.5 = 60/33

Now the test:
720 * 40/33 = 872.72
480 * 60/33 = 872.72

As you can see the 60/33 PAR is giving the same result for the 480 video as the 40/33 PAR does for the 720 video.

PAL:
59/54 * 1.5 = 177/108
...and so on.

It should look like this:

480x480 -------------------------------------------> PAR = (15/11)
        --- image appears extremely squeezed ------> PAR = (60/33)
480x576 -------------------------------------------> PAR = (177/108)
        --- image appears ridiculously squeezed ---> PAR = (177/81)

[Ghitulescu]

Originally Posted by Asmodian

Do you have a reason to assume the blurays do it correctly more often then DVDs?

Almost 100% of the BDs originated from film material use only a PAR of 1:1 throughout their process.

[vampiredom]

Originally Posted by TheSkiller

Sorry, those numbers are wrong, exept the first one. You forgot that PAL has 576 lines, not 480.

No, I didn't forget. I just started multiplying by the wrong number - just for the fun of it! Oops. Sorry 'bout that. I am putting the correct numbers in the table now. Thanks.

[hello_hello]

Originally Posted by Asmodian

Do you have a reason to assume the blurays do it correctly more often then DVDs?

I guess the square pixel thing has me assuming. I hope it's a reasonable one.

I'll admit I did some more thinking on this topic due to this thread, and I must admit that living in PAL-land there's a chance I'm making too quick an assumption the same thing also applies to NTSC DVDs. I have encoded quite a few of them, and I'm sure I've got a few lying around I'll be revisiting again due to this thread, but if the aspect ratio of Bluray discs can be taken as accurate, then in PAL-land at least, I'm absolutely certain by far the majority of discs use straight 16:9 or 4:3 resizing.

PAL actually has "digital" pixel aspect ratios, which differ from those vampiredom posted, and if memory serves me correctly they resize to exactly 16:9 or 4:3, although I'm not sure I actually understand them fully yet (cause of the 720 vs 704 width thing).
http://en.wikipedia.org/wiki/Pixel_a..._video_formats
They also seem to be the same pixel aspect ratios used in digital PAL SD TV.
http://en.wikipedia.org/wiki/Standar...ion#Resolution
Now didn't vampiredom post something about DVDs, digital TV and editing software all using the same standard?

For NTSC the PARs are always the same as those vampiredom posted so if NTSC discs do use straight 16:9 or 4:3 resizing the reason for it is something I'm still yet to learn.... maybe I'm just plain wrong about the way NTSC disc are resized.
I'm very tired at the moment though, I'll have to think about this some more tomorrow. In the meantime, comments anyone?

[TheSkiller]

Yes, as stated on the wiki page you linked, those are the official Rec.601 and "common digital" PARs. They differ in less than or about 1 pixel, it is actutally the 702<->704 issue (702 no typo). 702 because that is the very exact active image area in analog PAL. The "digital" PARs assumes 704 which is fine as well, since the difference is too small for any practical application (however 720 generic 4:3/16:9 resizing vs. PAR/ITU based resizing is).

See:

720 * 59/54 = 786.66
720 * 12/11 = 785.45

and

720 * 118/81 = 1048.88
720 * 16/11 = 1047.27

Nothing to worry about imo.