[XviD-devel] Other clip with Bframes, quality vs size
Christoph Lampert
xvid-devel@xvid.org
Sun, 18 Aug 2002 19:19:48 +0200 (CEST)
This message is in MIME format. The first part should be readable text,
while the remaining parts are likely unreadable without MIME-aware tools.
Send mail to mime@docserver.cac.washington.edu for more info.
---595374472-1970848293-1029691188=:15624
Content-Type: TEXT/PLAIN; charset=US-ASCII
The last clip, this time Michael's favourite "Dogma" Clip. actually it's
rather interesting:
The first one is as before: bpp versus PSNR again.
You see the great gap between PSNR 46 and 52, which is in fact between
Pframes' quant=3 and Pframes quant=4. This is most likely because of
prequantized input material.
I guess most parts of the material was encoded at quantizer 3 before, so
encoding at quant=3 again gives almost perfect reconstruction.
But my topic is PSNR<->bpp for B-frames, and because of the huge gap you
can't see anything, so there is a second plot (...lower.png) which shows
just the results for quant 4 and higher.
There you see that sometimes Bframes are better and sometimes not. Great,
what a statement! You cannot tell which max_bframes value would be best to
choose from this plot.
So there is another plot, where not max_bframes gets different colors, but
bquant_ratio (Dogma-bquantratio.png). Here the colors mean:
Red+line: max_bframes=0 (so bquant doesn't matter)
green: bquant_ratio = 100 result: always worse then non-bframes
blue: bquant_ratio = 150 result: always better than non-bframes
purple:bquant_ratio = 200 result: even better in some cases
turquoise: ratio = 250 result: best, in many cases (!)
ratio=80 was left out, because it's clearly inferior.
So, what parameters to choose for an arbitrary file?
I don't have the faintest idea...
gruel
P.S. Be aware that these just the _average_ values. Of course
P-frames quality is better than B-frames quality for ratio>100 and not
only average value, but standard deviation has to be taken into
account. I did those plots, too, but they are not help, either.
--
Christoph H. Lampert chl@math,uni-bonn,de | Diese Signature wurde maschi-
Beringstr. 6, Raum 14 Tel. (0228) 73-2948 | nell erstellt und bedarf
Sprechstunden: keine, aber meistens da | keiner Unterschrift. AZ 27B-6
---595374472-1970848293-1029691188=:15624
Content-Type: IMAGE/png; name="Dogma-quality-vs-size.png"
Content-Transfer-Encoding: BASE64
Content-ID: <Pine.LNX.4.21.0208181919480.15624@lieb.math.uni-bonn.de>
Content-Description:
Content-Disposition: attachment; filename="Dogma-quality-vs-size.png"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---595374472-1970848293-1029691188=:15624
Content-Type: IMAGE/png; name="Dogma-quality-vs-size-lower.png"
Content-Transfer-Encoding: BASE64
Content-ID: <Pine.LNX.4.21.0208181919481.15624@lieb.math.uni-bonn.de>
Content-Description:
Content-Disposition: attachment; filename="Dogma-quality-vs-size-lower.png"
iVBORw0KGgoAAAANSUhEUgAAAoAAAAHgBAMAAADH/8HXAAAABGdBTUEAALGP
C/xhBQAAABJQTFRF////AAAA/wAAAMAAAID/wAD/+205ZgAAADh0RVh0U29m
dHdhcmUAWFYgVmVyc2lvbiAzLjEwYSAgUmV2OiAxMi8yOS85NCAoUE5HIHBh
dGNoIDEuMindFS5JAAAMT0lEQVR4nO2dzZLjKhJGkau8l98gpyJm3xF1Z++4
172vmOn3f5Yx6A8kIQkSZJN8xxG22wLUdSJBP4a0UgAAAAAAAADwalp1u7Wv
/k8UTKPlQWA87VNe8+r/RME0OvpMADa32vhXSGFfJ31q6wMwQRgeGwm2drTa
wrJC69/erL1d3yVt/Ed2duluaTd2EgQESiWrwO2dyAACmUBgDi5BpSFwAQQy
gUAmEMgEAplAIBMIZAKBTCCQCQQygUAmFFQaAhdQUGkIXEBBpSFwAQWVhsAF
FFQaAhdQUGkIXEBBpSFwAQWVhsAFFFQaAhdQUGkIXEBBpSFwTtilMAQugEAm
EMgEAplAIBMIZAKBTCCQCQQygUAmEMiEwopD4BwKKw6BcyisOATOobDiEDiH
wopD4BwKKw6BcyisOATOobDiEDiHwopD4BwKKw6BcyisOATOCLwUhsA5CQQ+
P7qZN11CAAjcZCmwaQdn8lesr8AX2A5r/Z8RqJ8hcJOFwMakLLK2NnUlMAoS
uOZG5zsZYxBj4C6rBxH9uA15OyBwk1WBzc0ciBuMgfvgPHAGBDKBQCYQyIQC
y0PgDAosD4EzKLA8BM6gwPIQOIMCy0PgDAosD4EzKLA8BM6gwPIQOIMCy0Pg
DAosD4EzKLA8BLqEXgpD4AwIZAKBTCCQCQQygUAmEMgEAplAIBMIZAKBTCi0
AgS6UGgFCHSh0AoQ6EKhFSDQhUIrQKALhVaAQBcKrQCBLhRaAQJdKLQCBLpQ
aAUIdKHQChDoEHwpDIEuEMgEAplAIJMvCq0BgTaXC26o8kAEMvnST79CakCg
A+knCIzGjIDf3yEGIdCmO4QgAqMh8wyB0VB4Fb/AIX1MRQK7Hvx43APqeAWO
6WOqE3h/PpT6eT6O4BU4po+pSCCZ5/v9/ny+Xo/V8Qmc0sdUlDeGzHMXgYcC
cMPNlD6mngjsr4O7MZAbgUP6mAoFdrDHwD59TE0CKaYSzgMnKKYSBI6E343W
QOAIBDKhqFoQOEJRtSBwIK4HQ+AIBDKBQCYUVw0CByiuGgT2RPZgCByAQCYU
WQ8CeyiyHgQq9aHiezAEKgjk8vH9Hd+DIVB1EUixlSHQCIzuwRDYAYFMKLom
BBoouiYEauJ7MAQaIJAJxVeFQA3FV4VAxerBEKiBQCYQyIQYdesW+NG90Nq2
qzo0xbJmgY/HP+bV04N/Ds2wrFng/eOfb/3qEXhsjm/VAu9dBNL6ZkTgHne1
JRBj4C79kiTOSUzdAnsgkAnN/p1ordxIdQL7lUoHgcBFD+7Wyh0FApcCEYEH
6VZzkfPZL4yBx+nWE5LzWdByf03NAn/pAHR7cFjGDk3NAv+jI3A2BCICj/P9
Px2C5H4IgQEYWcRsBAKZjawI1MkSzMfdi1yBGt6FsFoT2AzpOqrI2pFBYDuk
6xiydnB38dYQt4GFwMZ8ZMWg7LQnxKq95qYxcWcLZO3izWH34PWDiH7cVA1p
TzIJ1PlObkpo2pPPx2P6B7Gbq+888PP5GCF2cxUK/JwE7vfg3QRGFQpUIQJ3
U2hVKNAaA2m/+N636/UJtKHuZaOfIgK3GHrwhiWMgVtchgluxzLdrVK1QOoF
Hk22uEblAs1S18PJFteoWeBldlkSRc0Cv54CPz73y21SscDLl3tZ4nA4NCsW
SETuhbGNd8OcygTa004vW2OgNzTnVCbQnvh8oY1yiEAP1hkfbZXDGOjBikBK
0mBlAq0xkH8331CVQGfmH6VpsyqBztxTStNmXQKt2c+JenBlAq0IhMAI7DGQ
PGUwQ/UY3gCEwGP4BAZPkq5VIPk2IAIP4T+EQOAurIyfCyoVSMlaq08gL2Xq
gvoE8jJ+LqhTIKVrrUKBCgK5JOzBEMilSoGUsK1KBDqzX1IGYC0CnflXEBiB
Pf2KUjZciUAnAilly5UINGNgklxZcyoRaOi/EqGkjdYk8OduRkJK2mhNAn9f
7yp1D65K4OPPXUEgg7VMRWxqEmgOxYkDsCaB3ZoaCIymE0iJW/ULbIXljenW
1KQOQL/AMX2MFIFdBJ4ncEwfI0sgpW7VJ3BKHyMrbwwlbW3DzZQ+RkwEapL3
4M2DiMC8MZS8xS2BAvPGUPIWKzoPVDl6MARyqUbggZOYgz+A4VKVwL0APPYT
LC61CDQXcnsCY3JP1CLw0LRKROAGBwRiDNwhwzG4LoGUo1EIZFKRwCw9GAIN
Yb/B4lCRQPKvQgr7FSCHegReNpZxhf0OlYNwgVb2kkvXUVdP9hCBPqz8OaTu
v+5q/XIDY6CPKYPTZeiojGSLa0gXqGyBpqPGXPBuIF3gOAaS2hgDGQgXOEGZ
2q1FYJ7LEFWPQMrVMAQyqUTgl+fzD3bLggXaqe58QyAEbjGd8el8s2t0cwZZ
SBbo5ptdBRG4xRSB3nyzELjB9fF7eEv59iJYoHMnJhuSBdp3YrIhWaCCQBbO
nZhsCBaoybO4xqYGgTl7sHCBmVYn2cgWmGlxjU0FArMGoHSBGghkQllbh0Am
8gXm7cFCBdrJ2iAwguvRn07iI1OgnayN8u5JpsDrdbyRkLkHCxX48/lzxq0s
jUyB1s1UyrynFYHtIK3gtCef6rOfz0uZ97QU2Dw/ulnbyhT4eHQCc/fgFYFt
q5ohAvVzkQLHn6ah3PtZCNT5TtrG2lpq2pMuAml9I+dHwS3W3Oh8J+PHxY6B
V3U1An09mPOz9C7eg8hNFZ32pJ+V4B0Ck02U3hJYctqTPsLItzlnBM4oU2Af
geTbnCwEhQrs5wZmP4kRK7AHAplQ/l0IFXjSdZwSLvCEHixU4FnXcUqqQPc6
zl4eZy0gToNkgWMPthZoWtNW0yBUoEELNJNjrMuO6U5rIiQLpKHHIgLjoKev
778wBsaie3DyHrtAlkAnvozADwgMwRnhSGXosQuECfycCcyPMIFWBC6WCPPX
xa0hTKCVqGhxIQyBQSyWCCdYG7yGWIGIQCbLNeoQGIIvy0RyhAo841Zqh1CB
dNqeBAm0vus9LwAlCbRmG9B5exUk8CUBKEngFIF04l4FCRzHwNNOYTSCBA6c
2YFFCiRvuugciBE43oi5+PNt50COwOFWIPXTEk5CjsD+ZvRWxvccyBHYRyBB
YBz9GHjqKYxGjMCO4RQmdbptP8IE0vAmccJ3P7IETufQZwWgMIE0vkMEhvN4
/D2+xxgYQfdrF+NC15OQJPDvu7KXWp+DHIGX/5rbWZ+ff+FSLgr6/fuuEIHR
XC4Xc+DFGBhOd8ilf1/PvQrukCCwO+l7BuAPBMYxnPOdeyewwy9wSB9TgMDx
suOdInBMH/P+AqfLjncSOKaPeX+BL8UncEofU2remDPYcDOlj0EEbiLiIPJK
IJCJiPPAVyJJ4AtOYiCQjSCBr7iQEyUQEcgFAuPJswrpCMULND+cDoHxmC8z
M63EPEL5Au93hQhk0H2dDoHRdGPg6yhe4KuBQCYQyKRogfnT6uxTtMDzZgH6
KVrg558/r/4vFC7wmju12D5lC0QE8jBj4EtuYk0ULdAAgTxecyN/oniBiEAG
5kQaAuNJntM4grIFZs/Ru0/ZAhGBPHAzQQAQyAQCmUAgk7IFvu7bzBEIZFKs
QH0r64UzOkaKFGjO//T6LkRgHOYKRH+fBIFxmGvg0xKbbFOmwOfjHb7S1JQp
8A2ugQcKFPgusddRoMB3Gf06ShT4TgFYpEBEIA+MgaKAQCYrAlvVmHQdWPJ/
hKXAptX5JqZtELjJUmDbDh/fCskb81IWAnW+ky7jTr8VaU/8rLlpTNz1H2MM
3GX1IKIfN9UPhRC4ifcofFP9wRgCNynuPPCdbmVpyhP4BhOKbMoT+AZT2mzK
E4gI5IExUBgQyKQogdbvt74NRQm8vtOt6J6iBL5hAJYlEBHIBGOgQCCQCQQy
gUAmEMgEAplAIBMIZAKBTCCQCQQygUAmEMgEAplAIBMIZAKBTCCQCQQygUAm
EMgEAplAIBMIZAKBTCCQCQQygUAmEMgEAplAIBMIZAKBTCCQCQQyqVtggr8N
Apn4BbYVrFjPKXBMH3NKmKudHa22sKzQ+rc3a29z/m1j+hgI3MT3t03pY5ob
2MAr0E4fA2IYU2iBOMYkbgAAAEA4/UFEvwi8nhsOkRnPNMZMoK0SeDzu/7om
p8Cucf0iMAL7vy5rBLbt8CJRYJtd4K3PRatECuz/utxjYJ8JVKDAYWjPKNDK
BCowka+T5xQAAAAAAIBY/g/ObtPwIp0f0wAAAAd0SU1FB9IIEhEGFuYoGMEA
AAAwdEVYdFNvZnR3YXJlAGdudXBsb3QgTGludXggdmVyc2lvbiAzLjcgcGF0
Y2hsZXZlbCAxCoOB67EAAAAASUVORK5CYII=
---595374472-1970848293-1029691188=:15624
Content-Type: IMAGE/png; name="Dogma-bquantratio.png"
Content-Transfer-Encoding: BASE64
Content-ID: <Pine.LNX.4.21.0208181919482.15624@lieb.math.uni-bonn.de>
Content-Description:
Content-Disposition: attachment; filename="Dogma-bquantratio.png"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---595374472-1970848293-1029691188=:15624--