Restoration tips: Kush Gauge™

KUSH GAUGE™

What is the Kush Gauge™?

It's a rule of thumb to calculate the needed bitrate for H.264 encoded video; it was written by Kush Amerasinghe, a computer scientist. In this context, the word "gauge" means "a device used to make measurements"

How does it work?

Quoting Kush's document:

"to estimate the optimal H.264 bit rate value that would give what is considered “good quality” results for a given video, you could multiply the target pixel count by the frame rate; then multiply the result by a factor of 1, 2 or 4, depending on its motion rank; and then multiply that result by 0.07 (the constant, Ed.) to get the bit rate in bps (divide that by 1,000 to get a kbps estimate or by 1,000,000 to get a Mbps estimate)."

The Kush Gauge™ formula:

width x height x FPS x motion rank x constant = final bitrate in bps

Practical example:

1280 × 720 @24fps, medium motion (rank 2):

1280 × 720 × 24 × 2 × 0.07 = 3,096,576 bps = ~ 3000 kbps

"In case of CBR, a value close to this estimate can be used. In case of VBR, a value that is about 75% of the estimate can be used as a target and a value about 150% of it can be used as the maximum rate. This VBR gap greatly depends on the nature of the content and the ability to absorb the bit rate spikes in the target playback environment."

What is the motion rank?

The amount of motion could be called “motion rank”; from Kush's document:

"As a general rule, try to simplify it into three ranks: Low, Medium, High. To define these ranks in real-world terms:
• Low motion is a video that has minimal movement. For example, a person talking in front of a camera without moving much while the camera itself and the background is not moving at all.
• Medium motion would be some degree of movement, but in a more predictable and orderly manner, which means some relatively slow camera and subject movements, but not many scene changes or cuts or sudden snap camera movements or zooms where the entire picture changes into something completely different instantaneously.
• High motion would be something like the most challenging action movie trailer, where not only the movements are fast and unpredictable but the scenes also change very rapidly."

What's about the constant:

from Kush's document:

"I sought to develop a base number ... (that) can produce real-world bit-rate estimates. After numerous experiments, I noticed a certain pattern of what could be considered a “constant” or base value (for most commonly used video frame-size and frame-rate ranges). When rounded off, that value is 0.07 bps per pixel, per frame, per motion rank value."

Andrea's Corollary to the Kush Gauge™:

To calculate video bitrate for a codec different from H.264, the Kush Gauge costant value should be changed accordingly to the codec used.

(these constant values will be threated in the next post)

Comments, improvements, corrections are welcome!

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Reference (PDF documents):

H.264 FOR THE REST OF US (page 21)

prologue: DON'T (always) TRUST COMPANIES!

Following many HDTV and internet broadcaster advices, a "studio quality" transmission for an H.264 1080p transmission could be achieved with a bitrate of a mere 6mbps; if we use the Kush Gauge formula, we can see that this is true only if the motion factor is lower than medium... for 16/9 sport material at 29.97fps, for example, a 17.4mbps bitrate is needed!

ANDREA'S COROLLARY TO THE KUSH GAUGE™

To calculate video bitrate for a codec different from H.264, the Kush Gauge costant value should be changed accordingly to the codec used.

Other lossy video codecs (apart H.264/MPEG-4 part 10, or AVC)

Even if AVC is widely used, also thanks to the x.264 open source encoder, there are many other codecs still in use nowadays; the main ones are:

• MPEG-2 - used in many DTV and HDTV broadcasting, in DVD and sometimes in BD
• VC-1 - used sometimes in BD; once used in HD-DVD
• H.265, or HEVC - new codec, used in particular for 4K/UHD

There are also many other ones - H.263 (divx/xvid), MPEG-1 (VCD), WMV9 - that are slowly replaced by newer (or better) ones.

So, let's focus on the main three alternative codecs to AVC.

VC-1

Quality is really similar to AVC; but it has some technical features missing or worst than AVC; the constant will therefore be set at 0.075 - sligthly worse than AVC.

HEVC

New codec, still in development; few serious comparisons were made, and it seems that bitrate gain could vary from 35% to over 70%; based on past studies, it could be difficult to believe that; if an AVC encoded video had a bitrate factor of 100, HEVC could achieve the same video quality at 30... so, to be fair, I'll put it at 60 - 40% gain - so the constant will be set for the moment at 0.042; this is obviously a value that will change in time, whenever more deep comparisons will be conducted, and newer encoders will be developed.

MPEG-2

This is the most known and valid alternative to AVC; widely used aroud the globe thanks mostly to DVD and DVB, it will be used for many years to come.

And it's the most difficult to rate in comparison to AVC... According to many, AVC have the same quality of MPEG-2 at half the bitrate; so, if MPEG-2 bitrate factor is 100, AVC should be 50 - setting the constant at 0.14.

Is it true? Well, probably in many cases it could be, but there are so many variables that plays against or in favour of this, that a simple, unique value is difficult to set at the moment.

Comparison papers state that average AVC bitrate gain is around 55.4%; this value is mainly calculated using PSNR as main video quality valutation. But it's known now that modern video codecs (including MPEG-2) rely on the fact that human vision could be "tricked" more easily than measurement; therefore, this value should not be taken as an absolute truth; infact, following tests results that used SSIM, when MPEG-2 and AVC have the same subjective quality, AVC gain is lower.

Some HDTV stations claims that their MPEG-2 1080i broadcasting have a perfect quality at 6/8mpbs; obviously it's not true; even if in some cases this bitrate is more than enough - news, weather reports, soap operas, studio transmissions - it is not the case for movies, or worst for sport!

In their defense, there were great improvements in the latest year in MPEG-2 encoders, gaining more than 30% in bitrate Vs. the first encoders; plus, some technique "borrowed" from the H.264 format helped to achieve extraordinary results - in comparison to old MPEG-2 encoders, of course.

Speaking about software encoders, these is not always true; despite the fact that there were improvements, they were not so outstanding as hardware encoders of broadcast level...

So, at the end, I think it's fair to set the constant for MPEG-2 at 0.136 - considering AVC bitrate gain between 40 and 55%: this constant could be lowered to 0.116 - setting the AVC gain at 40% - only for evaluating existing encoded material that was produced with industry level hardware encoders, like DVD, BD or HDTV material, as it's a matter of fact that those kind of encoders work better than available software ones that we could use at home.

FINAL NOTES:

As the Kush Gauge is a "rule of thumb" and not a law, of course also these constants are approximate; nevertheless, this rule should be used with the most part of video sources, but must still be used with a grain of salt!

ANDREA'S COROLLARY TO THE KUSH GAUGE™

To calculate video bitrate for a codec different from H.264, the Kush Gauge costant value should be changed accordingly to the codec used.

To obtain a good quality video:

width x height x FPS x motion rank x

• 0.045 for HEVC
• 0.075 for VC-1
• 0.136 for MPEG-2

= final bitrate in bps

or higher should be used* to obtain a good quality result.

exception: a source material, made using industry standard MPEG-2 hardware decoder, must have a bitrate* higher than

width x height x FPS x motion rank x 0.116

to be considered of good quality.

*CBR or VBR average bitrate

CHECKING QUALITY OF A GIVEN VIDEO MPEG-2 ENCODED SOURCE:

HD-NET is known to have a fairly good quality; let's take "Escape from New York": its actual resolution is 1920x804, FPS is 29.97fps and motion factor could be set at 2, so:

1920 x 804 x 29.97 x 2 x 0.116 = 10,733,268 = ~10.73mbps

or, according to higher constant value,

1920 x 804 x 29.97 x 2 x 0.136 = 12,583,832 = ~12.58mbps

as it's bitrate is 17.2mbps, its quality could be considered very good!

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Also WOWOW, a japanese HDTV station, has a good quality; "Indiana Jones and the Temple of Doom" has an actual resolution of 1920x816, FPS is 23.976fps and motion factor could be set at 2, so:

1920 x 816 x 23.976 x 2 x 0.116 = 8,714,773 = ~8.71mbps

or, according to higher constant value,

1920 x 816 x 23.976 x 2 x 0.136 = 10,217,320 = ~10.22mbps

as its bitrate is 19.9mbps, its quality could be considered really high!

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"Matrix Reloaded" is a movie full of action; so a motion factor of 4 is considered - even if probably a 3 should be quite good.

NTSC DVD:

720 x 480 x 29.97 x 4 x 0.136 = 5,634,551 = ~5.63mbps

average bitrate is 6.34mbps, so its quality is good.

PAL DVD:

720 x 576 x 25 x 4 x 0.136 = 5,640,192 = ~5.64mbps

average bitrate is 6.5mbps, so its quality is slightly better than the NTSC DVD.

Comments, improvements, corrections are welcome!

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References:

PDF documents

The Kush Gauge - H.264 FOR THE REST OF US (page 21)

SUBJECTIVE QUALITY ASSESSMENT OF THE EMERGING
AVC/H.264 VIDEO CODING STANDARD

EBU Technical Report 008 - HDTV Contribution Codecs

Using AVC/H.264 and H.265 expertise to boost MPEG-2 efficiency

BBC Guidelines - Technical and Delivery Standards for Worldwide

Comparison of the Coding Efficiency of Video Coding Standards

Thanks for this information, Andrea. I'm reading up on the Kush Gauge now.