Video Viewing Challenge/Puzzle

[Dave Haynie]

Here’s a simple exercise for your mathematics, one I alluded to long ago. If you want to understand compressed video, you’re going to have to expand your mental and mathematical model to explain this. And it’s very basic.

ATSC. US digital HDTV. Like DVD, it uses MPEG-2. There are a few delivery formats, but the two common ones are 1280×720/60p (demanded by ABC’s ESPN division, and they have a point… I filmed soccer for some years, always found 720p superior to 1080i) and 1920×1080/60i. These formats contain, respectively, 5.3 and 6 times the information of DVD video at 480/60i.

Well encoded DVD runs at an average of around 8Mb/s. The peak available bandwidth for ATSC is 19.4Mb/s, and most actual network broadcasts are around 15Mb/s. So here’s the problem for you: no one anywhere denies that HDTV as broadcast in the USA and viewed on a proper modern display is much better than DVD. And yet, we’re talking about 6x as much information in only about twice the bitrate, and it’s exactly the same algorithm.. no AVC magic here. Your mathematics, as presented, will claim that DVD is far, far better. But it’s not even close.

That’s the cognitive psychology aspect here… unless you have an accurate mathematical model of the brain, you can’t make absolutely predictions based on the mathematics of video compression. Which is why this has been an engineering problem, not a science problem: engineering = science + art.

-Dave

[John Bean]

Dave

Let’s see how the simple mathematical model for estimating the Q factor in your suggested scenario.

1080p AVC video at 15 Mb/s:

CF = (1920p*1080p) * 24 bpp * 24 fps / 15 Mbs
= 79.626

Q <~ 1 / CF
Q <~ 1 / 80

480p-MPEG2 at 8 Mb/s:
CF = (( (720p*480p) * 24 bpp * 24 fps) / 8 Mbs) * ( 5 / 3)
= 41.472

UF = (1920*1080) / (720*480)
= 5.53846

CF*UF = 230.1

Q <~ 1 / (CF * UF)
Q <~ 1 / 230

=>1/80 vs 1/230

Clearly, using simple mathematics we see that a 1080p-AVC video at 15 Mb/s is going to be far superior than its 480p-MPEG2 upscaled counterpart.

Cheers!

[Dave Haynie]

Dude… try actually reading. ATSC is MPEG-2, identical in every way to the MPEG-2 used on DVD. Only it’s somewhere between 12Mb/s and 19Mb/s or so (depends on the number of SD secondary channels they drop into that MPEG-2 transport stream; I have not seen more than four, but the physical limit is a total of 32).

So do your calculations, but it’s MPEG-2 in both. One is 8Mb/s and 720×480/60i, one is say 15Mb/s (or so it for each) and 1920×1080/60i or 1280×720/60p (same basic issues for PAL, of course).

-Dave

[John Bean]

Dave,

For the same reason why you need an UPSCALING FACTOR, in order to compare videos of different frame rates, you also need a FRAME-RATE SCALING factor. Otherwise, it is like comparing apples and oranges.

Consider a 1080-60p and 1080-30p video both at 15 Mbs.

It is clear here that the video 1080-30p will be less compressed than the 1080-60p at the same bitrate. But if I wanted to compare these two videos, then I would need to adjust the frame rates for one of the videos.

So if I adjust the 1080-60p to 30p, that will result in a 60/30=2 times increase in the BITRATE. The way to understand it is this: I need to compare 2 frames from the 60p video to 1 frame from the 30p video. So that is 2 times the bit-rate for a 60p video in comparison to a 30p video.

So the 1080-60p adjusted to 30p will be equivalent if we adjust the BITRATE to 2*15Mbs=30Mbs.

Define FF=frame-rate scaling factor

FF = (TARGET FRAME-RATE) / (INITIAL FRAME-RATE)

ABRF = adjusted bitrate for frame rate conversion = BR * FF

As well, I also will assume we can go convert from 60i to 30p with no affects to Q. This is a valid assumption when the UPPER and LOWER fields are taken from the same PROGRESSIVE source frame in time.

So lets use simple math again!

480-60i 8 Mbs:
CF = (720p*480p) * 24 bpp * 30 fps / 8 Mbs
CF = 31.104

UF = (1920*1080) / (720*480)
UF = 5.54846

CF*UF = 31.104 * 5.54846 = 172.5792

Q <~ 1 / (CF * UF)
Q <~ 1 / 173

1080-60i 15 Mbs:
CF = (1920p*1080p) * 24 bpp * 30 fps / 15 Mbs
CF = 99.532

Q <~ 1 / 100

720-60p 15 Mbs:

FF = 60 / 30 = 2
ABRF = 15 Mbs * 2 = 30 Mbs

CF = (1280p*720p) * 24 bpp * 60 fps / 30 Mbs
CF = 44.2368

UF = (1920*1080) / (1280*720)
UF = 2.25

CF*UF = 44.2368 * 2.25 = 99.53

Q <~ 1 / (CF * UF)
Q <~ 1 / 100

=>1 / 173 vs 1/100 vs 1 / 100

So clearly, using simple math again, we see that in terms of these Q factors:

1080-60i-15Mbs == 720-60p-15Mbs >> 480-60i-8Mbs

Math is so much fun!!!

Cheers!