JP2022511883A - ビデオ符号化用の方法及び装置 - Google Patents
ビデオ符号化用の方法及び装置 Download PDFInfo
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Abstract
Description
本出願は2020年3月6日に出願された米国特許出願第16/812,000号「ビデオ符号化用の方法と装置」の優先権の利益を主張するものであり、当該出願は2019年3月9日に出願された米国仮出願第62/816,124号「適応変換係数ゼロアウト」の優先権の利益を主張するものである。先願発明の全開示はその全体が参照によって組み込まれる。
[技術分野]
本開示は、一般的にビデオ符号化に関連する実施形態を説明する。
M×NのTUでは、TUの左上のm×n(即ち、mnの積)領域で非ゼロ変換係数が保持される場合、直接行列乗算構造で実装された逆変換の係数あたりの乗算回数は、
は変換係数ベクトルを示し、Tは16×16変換行列である。続いて16×1変換係数ベクトル
が、入力ブロックXのスキャン順序(例えば、水平スキャン順序、垂直スキャン順序または対角スキャン順序)を用いて、4×4ブロックとして再編成される。より小さいインデックスを有する係数は、4×4係数ブロックのより小さいスキャンインデックスによって配置され得る。一部の実施形態では、バタフライ実装を有するハイパーキューブギブンズ変換(HyGT)を上記の行列乗算の代わりに用いて、NSSTの複雑さを低減することができる。
例えば、ゼロアウト方式は、1次元変換のうちの1つにのみ用いられ得る。一実施形態では、逆一次変換を、第1順序を用いて実行し、それによって、逆垂直変換を最初に、続いて逆水平変換を適用する。TBサイズは、32×32である。一例では、32長垂直変換はゼロアウト法を適用しない。したがって、32長逆垂直変換は、全ての中間データを計算するか、または中間ブロックの32行に保持する。32長逆水平変換は、ゼロアウト法を用いて、残余ブロックの左16列を計算または保持する。残余ブロックの残りの残余データは計算されず、ゼロになる(例えば、残りの残余データをゼロに設定することができる)。一例では、32長逆垂直変換は、ゼロアウト法を用いて中間ブロックの上位16行を計算または保持する。中間ブロックの残りの中間データは計算されず、ゼロになる(例えば、残りの中間データをゼロに設定することができる)。一方、32長逆水平変換は、ゼロアウト方式を適用しない。したがって、32長逆水平変換は、残余ブロックの32列の全ての残余データを計算または保持する。
残余ブロックの残りの残余データは、上記のように、計算されずゼロになる。
JEM:joint exploration model(共同探索モデル)
VVC:versatile video coding(多用途ビデオ符号化)
BMS:benchmark set(ベンチマークセット)
MV:Motion Vector(動きベクトル)
HEVC:High Efficiency Video Coding(高効率ビデオ符号化)
SEI:Supplementary Enhancement Information(補助強化情報)
VUI:Video Usability Information(ビデオ有用性情報)
GOP:Group of Pictures(画像群)
TU:Transform Units(変換ユニット)
PU:Prediction Units(予測ユニット)
CTU:Coding Tree Unit(符号化ツリーユニット)
CTB: Coding Tree Block(符号化ツリーブロック)
PB:Prediction Block(予測ブロック)
HRD:Hypothetical Reference Decoder(仮想参照デコーダ)
SNR:Signal Noise Ratio(信号ノイズ比)
CPU:Central Processing Unit(中央処理装置)
GPU:Graphics Processing Unit(グラフィックス処理装置)
CRT:Cathode Ray Tube(陰極線管)
LCD:Liquid-Crystal Display(液晶ディスプレイ)
OLED:Organic Light-Emitting Diode(有機発光ダイオード)
CD:Compact Disc(コンパクトディスク)
DVD:Digital Video Disc(デジタルビデオディスク)
ROM:Read-Only Memory(読み取り専用メモリ)
RAM:Random Access Memory(ランダムアクセスメモリ)
ASIC:Application-Specific Integrated Circuit(特定用途向け集積回路)
PLD:Programmable Logic Device(プログラマブル論理デバイス)
LAN: Local Area Network(ローカルエリアネットワーク)
GSM:Global System for Mobile communications(グローバル・システム・フォー・モバイル・コミュニケーションズ)
LTE:Long-Term Evolution(ロングタームエボリューション)
CANBus:Controller Area Network Bus(コントローラエリアネットワークバス)
USB:Universal Serial Bus(ユニバーサルシリアルバス)
PCI:Peripheral Component Interconnect(ペリフェラルコンポーネントインターコネクト)
FPGA:Field Programmable Gate Area(フィールドプログラマブルゲートエリア)
SSD:solid-state drive(ソリッドステートドライブ)
IC:Integrated Circuit(集積回路)
CU:Coding Unit(符号化ユニット)
本開示では、一部の例示的な実施形態を説明してきたが、本開示の範囲内にある、変更、変形、および様々な代替的な等価物が存在する。したがって、当業者は、本明細書に明示的に示されていない、または記載されていないが、本開示の原理を具現化し、したがってその趣旨および範囲内にある多数のシステムおよび方法に想到することができることが理解される。
付録I
4×4変換
付録II
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az, -bb, -as, -au, -bd, ax, ap, ay, -bc, -at, -at, -bc,
ay, ap, ax, -bd, -au, -as, -bb, az, aq, aw, -be,
-av, -ar, -ba, ba, ar, av, be, -aw, -aq, -az,
bb, as, au, bd, -ax, -ap, -ay, bc, at }
{ bo, ch,
-bv, -bh, -ca, cc, bj, bt, -cj, -bq, -bm, -cf,
bx, bf, by, -ce, -bl, -br, -ck, bs, bk, cd, -bz,
-bg, -bw, cg, bn, bp, ci, -bu, -bi, -cb,
cb, bi, bu, -ci, -bp, -bn, -cg, bw, bg, bz, -cd,
-bk, -bs, ck, br, bl, ce, -by, -bf, -bx,
cf, bm, bq, cj, -bt, -bj, -cc, ca, bh, bv,
-ch, -bo }
{ aj, ao,
-ak, -ai, -an, al, ah, am, -am, -ah, -al, an,
ai, ak, -ao, -aj, -aj, -ao, ak, ai, an, -al, -ah,
-am, am, ah, al, -an, -ai, -ak, ao, aj, aj,
ao, -ak, -ai, -an, al, ah, am, -am, -ah, -al, an,
ai, ak, -ao, -aj, -aj, -ao, ak, ai, an, -al, -ah,
-am, am, ah, al, -an, -ai, -ak, ao, aj }
{ bp, ck,
-bq, -bo, -cj, br, bn, ci, -bs, -bm, -ch, bt,
bl, cg, -bu, -bk, -cf, bv, bj, ce, -bw, -bi, -cd,
bx, bh, cc, -by, -bg, -cb, bz, bf, ca, -ca, -bf,
-bz, cb, bg, by, -cc, -bh, -bx, cd, bi, bw,
-ce, -bj, -bv, cf, bk, bu, -cg, -bl, -bt, ch,
bm, bs, -ci, -bn, -br, cj, bo, bq, -ck, -bp }
{ au, -be, -at,
-av, bd, as, aw, -bc, -ar, -ax, bb, aq, ay,
-ba, -ap, -az, az, ap, ba, -ay, -aq, -bb, ax,
ar, bc, -aw, -as, -bd, av, at, be, -au, -au,
be, at, av, -bd, -as, -aw, bc, ar, ax, -bb, -aq,
-ay, ba, ap, az, -az, -ap, -ba, ay, aq, bb,
-ax, -ar, -bc, aw, as, bd, -av, -at, -be, au }
{ bq, -ci, -bl,
-bv, cd, bg, ca, -by, -bi, -cf, bt, bn, ck,
-bo, -bs, cg, bj, bx, -cb, -bf, -cc, bw,
bk, ch, -br, -bp, cj, bm, bu, -ce, -bh, -bz, bz,
bh, ce, -bu, -bm, -cj, bp, br, -ch, -bk, -bw, cc,
bf, cb, -bx, -bj, -cg, bs, bo, -ck, -bn, -bt, cf,
bi, by, -ca, -bg, -cd, bv, bl, ci, -bq }
{ ae, -ag, -ad,
-af, af, ad, ag, -ae, -ae, ag, ad, af, -af,
-ad, -ag, ae, ae, -ag, -ad, -af, af, ad, ag, -ae,
-ae, ag, ad, af, -af, -ad, -ag, ae, ae, -ag, -ad,
-af, af, ad, ag, -ae, -ae, ag, ad, af, -af,
-ad, -ag, ae, ae, -ag, -ad, -af, af, ad, ag, -ae,
-ae, ag, ad, af, -af, -ad, -ag, ae }
{ br, -cf, -bg,
-cc, bu, bo, -ci, -bj, -bz, bx, bl, ck, -bm,
-bw, ca, bi, ch, -bp, -bt, cd, bf, ce, -bs,
-bq, cg, bh, cb, -bv, -bn, cj, bk, by, -by,
-bk, -cj, bn, bv, -cb, -bh, -cg, bq, bs, -ce, -bf,
-cd, bt, bp, -ch, -bi, -ca, bw, bm, -ck, -bl,
-bx, bz, bj, ci, -bo, -bu, cc, bg, cf, -br
}
{ av, -bb, -ap,
-bc, au, aw, -ba, -aq, -bd, at, ax, -az, -ar,
-be, as, ay, -ay, -as, be, ar, az, -ax,
-at, bd, aq, ba, -aw, -au, bc, ap, bb, -av,
-av, bb, ap, bc, -au, -aw, ba, aq, bd, -at,
-ax, az, ar, be, -as, -ay, ay, as, -be, -ar, -az,
ax, at, -bd, -aq, -ba, aw, au, -bc, -ap, -bb, av }
{ bs, -cc, -bi,
-cj, bl, bz, -bv, -bp, cf, bf, cg, -bo,
-bw, by, bm, -ci, -bh, -cd, br, bt, -cb, -bj,
-ck, bk, ca, -bu, -bq, ce, bg, ch, -bn,
-bx, bx, bn, -ch, -bg, -ce, bq, bu, -ca, -bk,
ck, bj, cb, -bt, -br, cd, bh, ci, -bm, -by,
bw, bo, -cg, -bf, -cf, bp, bv, -bz, -bl, cj,
bi, cc, -bs }
{ ak, -am,
-ai, ao, ah, an, -aj, -al, al, aj, -an, -ah,
-ao, ai, am, -ak, -ak, am, ai, -ao, -ah, -an,
aj, al, -al, -aj, an, ah, ao, -ai, -am, ak,
ak, -am, -ai, ao, ah, an, -aj, -al, al, aj, -an,
-ah, -ao, ai, am, -ak, -ak, am, ai, -ao, -ah,
-an, aj, al, -al, -aj, an, ah, ao, -ai,
-am, ak }
{ bt, -bz,
-bn, cf, bh, ck, -bi, -ce, bo, by, -bu,
-bs, ca, bm, -cg, -bg, -cj, bj, cd, -bp, -bx,
bv, br, -cb, -bl, ch, bf, ci, -bk, -cc, bq,
bw, -bw, -bq, cc, bk, -ci, -bf, -ch, bl, cb, -br,
-bv, bx, bp, -cd, -bj, cj, bg, cg, -bm,
-ca, bs, bu, -by, -bo, ce, bi, -ck, -bh, -cf,
bn, bz, -bt }
{ aw, -ay,
-au, ba, as, -bc, -aq, be, ap, bd, -ar,
-bb, at, az, -av, -ax, ax, av, -az, -at,
bb, ar, -bd, -ap, -be, aq, bc, -as, -ba, au, ay,
-aw, -aw, ay, au, -ba, -as, bc, aq, -be, -ap,
-bd, ar, bb, -at, -az, av, ax, -ax, -av,
az, at, -bb, -ar, bd, ap, be, -aq, -bc, as,
ba, -au, -ay, aw }
{ bu, -bw,
-bs, by, bq, -ca, -bo, cc, bm, -ce, -bk,
cg, bi, -ci, -bg, ck, bf, cj, -bh, -ch, bj,
cf, -bl, -cd, bn, cb, -bp, -bz, br, bx, -bt, -bv,
bv, bt, -bx, -br, bz, bp, -cb, -bn, cd, bl, -cf, -bj,
ch, bh, -cj, -bf, -ck, bg, ci, -bi, -cg, bk, ce,
-bm, -cc, bo, ca, -bq, -by, bs, bw, -bu }
{ aa, -aa,
-aa, aa, aa, -aa, -aa, aa, aa, -aa, -aa,
aa, aa, -aa, -aa, aa, aa, -aa, -aa, aa, aa, -aa,
-aa, aa, aa, -aa, -aa, aa, aa, -aa, -aa,
aa, aa, -aa, -aa, aa, aa, -aa, -aa, aa, aa, -aa,
-aa, aa, aa, -aa, -aa, aa, aa, -aa, -aa,
aa, aa, -aa, -aa, aa, aa, -aa, -aa, aa, aa, -aa,
-aa, aa }
{ bv, -bt,
-bx, br, bz, -bp, -cb, bn, cd, -bl, -cf,
bj, ch, -bh, -cj, bf, -ck, -bg, ci, bi, -cg, -bk,
ce, bm, -cc, -bo, ca, bq, -by, -bs, bw, bu, -bu,
-bw, bs, by, -bq, -ca, bo, cc, -bm, -ce,
bk, cg, -bi, -ci, bg, ck, -bf, cj, bh, -ch,
-bj, cf, bl, -cd, -bn, cb, bp, -bz, -br,
bx, bt, -bv }
{ ax, -av,
-az, at, bb, -ar, -bd, ap, -be, -aq, bc, as, -ba,
-au, ay, aw, -aw, -ay, au, ba, -as, -bc,
aq, be, -ap, bd, ar, -bb, -at, az, av, -ax,
-ax, av, az, -at, -bb, ar, bd, -ap, be, aq,
-bc, -as, ba, au, -ay, -aw, aw, ay, -au, -ba,
as, bc, -aq, -be, ap, -bd, -ar, bb, at, -az, -av,
ax }
{ bw, -bq,
-cc, bk, ci, -bf, ch, bl, -cb, -br, bv, bx,
-bp, -cd, bj, cj, -bg, cg, bm, -ca, -bs,
bu, by, -bo, -ce, bi, ck, -bh, cf, bn, -bz,
-bt, bt, bz, -bn, -cf, bh, -ck, -bi, ce, bo, -by,
-bu, bs, ca, -bm, -cg, bg, -cj, -bj, cd, bp, -bx,
-bv, br, cb, -bl, -ch, bf, -ci, -bk, cc, bq, -bw
}
{ al, -aj,
-an, ah, -ao, -ai, am, ak, -ak, -am, ai, ao,
-ah, an, aj, -al, -al, aj, an, -ah, ao, ai,
-am, -ak, ak, am, -ai, -ao, ah, -an, -aj, al, al,
-aj, -an, ah, -ao, -ai, am, ak, -ak, -am, ai, ao,
-ah, an, aj, -al, -al, aj, an, -ah, ao, ai,
-am, -ak, ak, am, -ai, -ao, ah, -an, -aj, al }
{ bx, -bn,
-ch, bg, -ce, -bq, bu, ca, -bk, -ck, bj, -cb,
-bt, br, cd, -bh, ci, bm, -by, -bw, bo, cg,
-bf, cf, bp, -bv, -bz, bl, cj, -bi, cc, bs,
-bs, -cc, bi, -cj, -bl, bz, bv, -bp, -cf, bf, -cg,
-bo, bw, by, -bm, -ci, bh, -cd, -br, bt, cb,
-bj, ck, bk, -ca, -bu, bq, ce, -bg, ch, bn,
-bx }
{ ay, -as,
-be, ar, -az, -ax, at, bd, -aq, ba, aw, -au,
-bc, ap, -bb, -av, av, bb, -ap, bc, au, -aw,
-ba, aq, -bd, -at, ax, az, -ar, be, as, -ay,
-ay, as, be, -ar, az, ax, -at, -bd, aq, -ba,
-aw, au, bc, -ap, bb, av, -av, -bb, ap, -bc,
-au, aw, ba, -aq, bd, at, -ax, -az, ar, -be,
-as, ay }
{ by, -bk,
cj, bn, -bv, -cb, bh, -cg, -bq, bs, ce, -bf,
cd, bt, -bp, -ch, bi, -ca, -bw, bm, ck, -bl,
bx, bz, -bj, ci, bo, -bu, -cc, bg, -cf, -br, br,
cf, -bg, cc, bu, -bo, -ci, bj, -bz, -bx, bl, -ck,
-bm, bw, ca, -bi, ch, bp, -bt, -cd, bf, -ce,
-bs, bq, cg, -bh, cb, bv, -bn, -cj, bk, -by }
{ af, -ad,
ag, ae, -ae, -ag, ad, -af, -af, ad, -ag, -ae, ae,
ag, -ad, af, af, -ad, ag, ae, -ae, -ag, ad, -af,
-af, ad, -ag, -ae, ae, ag, -ad, af, af, -ad,
ag, ae, -ae, -ag, ad, -af, -af, ad, -ag, -ae, ae,
ag, -ad, af, af, -ad, ag, ae, -ae, -ag, ad, -af,
-af, ad, -ag, -ae, ae, ag, -ad, af }
{ bz, -bh,
ce, bu, -bm, cj, bp, -br, -ch, bk, -bw, -cc, bf,
-cb, -bx, bj, -cg, -bs, bo, ck, -bn, bt, cf,
-bi, by, ca, -bg, cd, bv, -bl, ci, bq, -bq,
-ci, bl, -bv, -cd, bg, -ca, -by, bi, -cf, -bt, bn, -ck,
-bo, bs, cg, -bj, bx, cb, -bf, cc, bw,
-bk, ch, br, -bp, -cj, bm, -bu, -ce, bh, -bz }
{ az, -ap,
ba, ay, -aq, bb, ax, -ar, bc, aw, -as,
bd, av, -at, be, au, -au, -be, at, -av, -bd, as,
-aw, -bc, ar, -ax, -bb, aq, -ay, -ba, ap, -az, -az, ap,
-ba, -ay, aq, -bb, -ax, ar, -bc, -aw, as, -bd, -av, at,
-be, -au, au, be, -at, av, bd, -as, aw, bc,
-ar, ax, bb, -aq, ay, ba, -ap, az }
{ ca, -bf,
bz, cb, -bg, by, cc, -bh, bx, cd, -bi,
bw, ce, -bj, bv, cf, -bk, bu, cg, -bl,
bt, ch, -bm, bs, ci, -bn, br, cj, -bo,
bq, ck, -bp, bp, -ck, -bq, bo, -cj, -br, bn, -ci,
-bs, bm, -ch, -bt, bl, -cg, -bu, bk, -cf, -bv, bj, -ce,
-bw, bi, -cd, -bx, bh, -cc, -by, bg, -cb, -bz, bf, -ca
}
{ am, -ah,
al, an, -ai, ak, ao, -aj, aj, -ao, -ak, ai, -an,
-al, ah, -am, -am, ah, -al, -an, ai, -ak, -ao, aj,
-aj, ao, ak, -ai, an, al, -ah, am, am,
-ah, al, an, -ai, ak, ao, -aj, aj, -ao,
-ak, ai, -an, -al, ah, -am, -am, ah, -al, -an, ai, -ak,
-ao, aj, -aj, ao, ak, -ai, an, al, -ah, am
}
{ cb, -bi,
bu, ci, -bp, bn, -cg, -bw, bg, -bz, -cd, bk, -bs,
-ck, br, -bl, ce, by, -bf, bx, cf, -bm, bq,
-cj, -bt, bj, -cc, -ca, bh, -bv, -ch, bo, -bo, ch,
bv, -bh, ca, cc, -bj, bt, cj, -bq, bm, -cf,
-bx, bf, -by, -ce, bl, -br, ck, bs, -bk,
cd, bz, -bg, bw, cg, -bn, bp, -ci, -bu, bi, -cb }
{ ba, -ar,
av, -be, -aw, aq, -az, -bb, as, -au, bd, ax, -ap,
ay, bc, -at, at, -bc, -ay, ap, -ax, -bd, au, -as,
bb, az, -aq, aw, be, -av, ar, -ba, -ba, ar,
-av, be, aw, -aq, az, bb, -as, au, -bd,
-ax, ap, -ay, -bc, at, -at, bc, ay, -ap,
ax, bd, -au, as, -bb, -az, aq, -aw, -be, av, -ar,
ba }
{ cc, -bl,
bp, -cg, -by, bh, -bt, ck, bu, -bg, bx, ch,
-bq, bk, -cb, -cd, bm, -bo, cf, bz, -bi, bs, -cj,
-bv, bf, -bw, -ci, br, -bj, ca, ce, -bn, bn, -ce,
-ca, bj, -br, ci, bw, -bf, bv, cj, -bs, bi,
-bz, -cf, bo, -bm, cd, cb, -bk, bq, -ch, -bx, bg,
-bu, -ck, bt, -bh, by, cg, -bp, bl, -cc }
{ ac, -ab,
ab, -ac, -ac, ab, -ab, ac, ac, -ab, ab, -ac, -ac,
ab, -ab, ac, ac, -ab, ab, -ac, -ac, ab, -ab,
ac, ac, -ab, ab, -ac, -ac, ab, -ab, ac, ac,
-ab, ab, -ac, -ac, ab, -ab, ac, ac, -ab, ab, -ac,
-ac, ab, -ab, ac, ac, -ab, ab, -ac, -ac, ab,
-ab, ac, ac, -ab, ab, -ac, -ac, ab, -ab, ac }
{ cd, -bo,
bk, -bz, -ch, bs, -bg, bv, -ck, -bw, bh, -br, cg,
ca, -bl, bn, -cc, -ce, bp, -bj, by, ci, -bt, bf,
-bu, cj, bx, -bi, bq, -cf, -cb, bm, -bm, cb,
cf, -bq, bi, -bx, -cj, bu, -bf, bt, -ci, -by, bj,
-bp, ce, cc, -bn, bl, -ca, -cg, br, -bh,
bw, ck, -bv, bg, -bs, ch, bz, -bk, bo, -cd }
{ bb, -au,
aq, -ax, be, ay, -ar, at, -ba, -bc, av, -ap, aw,
-bd, -az, as, -as, az, bd, -aw, ap, -av,
bc, ba, -at, ar, -ay, -be, ax, -aq, au, -bb, -bb,
au, -aq, ax, -be, -ay, ar, -at, ba, bc, -av, ap,
-aw, bd, az, -as, as, -az, -bd, aw, -ap, av, -bc,
-ba, at, -ar, ay, be, -ax, aq, -au, bb }
{ ce, -br,
bf, -bs, cf, cd, -bq, bg, -bt, cg, cc, -bp,
bh, -bu, ch, cb, -bo, bi, -bv, ci, ca, -bn,
bj, -bw, cj, bz, -bm, bk, -bx, ck, by, -bl,
bl, -by, -ck, bx, -bk, bm, -bz, -cj, bw, -bj, bn, -ca,
-ci, bv, -bi, bo, -cb, -ch, bu, -bh, bp, -cc,
-cg, bt, -bg, bq, -cd, -cf, bs, -bf, br, -ce }
{ an, -ak,
ah, -aj, am, ao, -al, ai, -ai, al, -ao, -am, aj,
-ah, ak, -an, -an, ak, -ah, aj, -am, -ao, al,
-ai, ai, -al, ao, am, -aj, ah, -ak, an, an,
-ak, ah, -aj, am, ao, -al, ai, -ai, al, -ao,
-am, aj, -ah, ak, -an, -an, ak, -ah, aj, -am,
-ao, al, -ai, ai, -al, ao, am, -aj, ah,
-ak, an }
{ cf, -bu,
bj, -bl, bw, -ch, -cd, bs, -bh, bn, -by, cj, cb,
-bq, bf, -bp, ca, ck, -bz, bo, -bg, br, -cc,
-ci, bx, -bm, bi, -bt, ce, cg, -bv, bk, -bk,
bv, -cg, -ce, bt, -bi, bm, -bx, ci, cc, -br, bg,
-bo, bz, -ck, -ca, bp, -bf, bq, -cb, -cj, by,
-bn, bh, -bs, cd, ch, -bw, bl, -bj, bu, -cf }
{ bc, -ax,
as, -aq, av, -ba, -be, az, -au, ap, -at, ay, -bd,
-bb, aw, -ar, ar, -aw, bb, bd, -ay, at,
-ap, au, -az, be, ba, -av, aq, -as, ax, -bc,
-bc, ax, -as, aq, -av, ba, be, -az, au,
-ap, at, -ay, bd, bb, -aw, ar, -ar, aw, -bb,
-bd, ay, -at, ap, -au, az, -be, -ba, av, -aq, as,
-ax, bc }
{ cg, -bx,
bo, -bf, bn, -bw, cf, ch, -by, bp, -bg, bm,
-bv, ce, ci, -bz, bq, -bh, bl, -bu, cd, cj,
-ca, br, -bi, bk, -bt, cc, ck, -cb, bs, -bj,
bj, -bs, cb, -ck, -cc, bt, -bk, bi, -br, ca, -cj,
-cd, bu, -bl, bh, -bq, bz, -ci, -ce, bv, -bm, bg,
-bp, by, -ch, -cf, bw, -bn, bf, -bo, bx, -cg }
{ ag, -af,
ae, -ad, ad, -ae, af, -ag, -ag, af, -ae, ad, -ad,
ae, -af, ag, ag, -af, ae, -ad, ad, -ae, af, -ag,
-ag, af, -ae, ad, -ad, ae, -af, ag, ag,
-af, ae, -ad, ad, -ae, af, -ag, -ag, af, -ae, ad,
-ad, ae, -af, ag, ag, -af, ae, -ad, ad,
-ae, af, -ag, -ag, af, -ae, ad, -ad, ae, -af, ag
}
{ ch, -ca,
bt, -bm, bf, -bl, bs, -bz, cg, ci, -cb, bu,
-bn, bg, -bk, br, -by, cf, cj, -cc, bv,
-bo, bh, -bj, bq, -bx, ce, ck, -cd, bw,
-bp, bi, -bi, bp, -bw, cd, -ck, -ce, bx, -bq, bj,
-bh, bo, -bv, cc, -cj, -cf, by, -br, bk, -bg, bn,
-bu, cb, -ci, -cg, bz, -bs, bl, -bf, bm, -bt, ca,
-ch }
{ bd, -ba,
ax, -au, ar, -ap, as, -av, ay, -bb, be, bc,
-az, aw, -at, aq, -aq, at, -aw, az, -bc, -be, bb,
-ay, av, -as, ap, -ar, au, -ax, ba, -bd, -bd, ba,
-ax, au, -ar, ap, -as, av, -ay, bb, -be, -bc, az,
-aw, at, -aq, aq, -at, aw, -az, bc, be,
-bb, ay, -av, as, -ap, ar, -au, ax, -ba, bd }
{ ci, -cd,
by, -bt, bo, -bj, bf, -bk, bp, -bu, bz, -ce,
cj, ch, -cc, bx, -bs, bn, -bi, bg, -bl, bq,
-bv, ca, -cf, ck, cg, -cb, bw, -br, bm,
-bh, bh, -bm, br, -bw, cb, -cg, -ck, cf, -ca, bv,
-bq, bl, -bg, bi, -bn, bs, -bx, cc, -ch, -cj, ce,
-bz, bu, -bp, bk, -bf, bj, -bo, bt, -by, cd, -ci
}
{ ao, -an,
am, -al, ak, -aj, ai, -ah, ah, -ai, aj, -ak, al,
-am, an, -ao, -ao, an, -am, al, -ak, aj, -ai, ah,
-ah, ai, -aj, ak, -al, am, -an, ao, ao,
-an, am, -al, ak, -aj, ai, -ah, ah, -ai, aj,
-ak, al, -am, an, -ao, -ao, an, -am, al, -ak, aj,
-ai, ah, -ah, ai, -aj, ak, -al, am, -an, ao }
{ cj, -cg,
cd, -ca, bx, -bu, br, -bo, bl, -bi, bf, -bh, bk,
-bn, bq, -bt, bw, -bz, cc, -cf, ci, ck,
-ch, ce, -cb, by, -bv, bs, -bp, bm, -bj, bg,
-bg, bj, -bm, bp, -bs, bv, -by, cb, -ce, ch, -ck,
-ci, cf, -cc, bz, -bw, bt, -bq, bn, -bk, bh,
-bf, bi, -bl, bo, -br, bu, -bx, ca, -cd, cg, -cj
}
{ be, -bd,
bc, -bb, ba, -az, ay, -ax, aw, -av, au, -at, as,
-ar, aq, -ap, ap, -aq, ar, -as, at, -au, av,
-aw, ax, -ay, az, -ba, bb, -bc, bd, -be, -be, bd,
-bc, bb, -ba, az, -ay, ax, -aw, av, -au, at,
-as, ar, -aq, ap, -ap, aq, -ar, as, -at, au,
-av, aw, -ax, ay, -az, ba, -bb, bc, -bd, be }
{ ck, -cj,
ci, -ch, cg, -cf, ce, -cd, cc, -cb, ca, -bz, by,
-bx, bw, -bv, bu, -bt, bs, -br, bq, -bp, bo,
-bn, bm, -bl, bk, -bj, bi, -bh, bg, -bf, bf,
-bg, bh, -bi, bj, -bk, bl, -bm, bn, -bo, bp,
-bq, br, -bs, bt, -bu, bv, -bw, bx, -by, bz,
-ca, cb, -cc, cd, -ce, cf, -cg, ch, -ci, cj, -ck
}
}
ここで
{ aa, ab, ac, ad, ae, af, ag, ah, ai, aj, ak, al, am, an, ao, ap,
aq, ar, as, at, au, av, aw, ax, ay, az, ba, bb, bc, bd, be, bf, bg, bh, bi, bj,
bk, bl, bm, bn, bo, bp, bq, br, bs, bt, bu, bv, bw, bx, by, bz, ca, cb, cc, cd,
ce, cf, cg, ch, ci, cj, ck} =
{64,83,36,89,75,50,18,90,87,80,70,57,43,25,9,90,90,88,85,82,78,73,67,61,54,46,38,31,22,13,4,91,90,90,90,88,87,86,84,83,81,79,77,73,71,69,65,62,59,56,52,48,44,41,37,33,28,24,20,15,11,7,2}
付録III
4点DST-7
{
a, b, c, d }
{ c,
c, 0, -c }
{ d, -a,
-c, b }
{ b,
-d, c, -a }
ここで
{a, b, c, d} = { 29, 55, 74, 84}
8点DST-7
{
a, b, c, d, e, f, g, h,}
{ c,
f, h, e, b, -a, -d, -g,}
{ e,
g, b, -c, -h, -d, a, f,}
{
g, c, -d, -f, a, h, b, -e,}
{ h, -a,
-g, b, f, -c, -e, d,}
{ f, -e,
-a, g, -d, -b, h, -c,}
{ d,
-h, e, -a, -c, g, -f, b,}
{ b,
-d, f, -h, g, -e, c, -a,}
ここで
{a, b, c, d, e, f, g, h} = { 17, 32, 46, 60, 71, 78, 85, 86}
16点DST-7
{
a, b, c, d, e, f, g, h,
i, j, k, l, m, n, o, p,}
{ c,
f, i, l, o, o, l, i, f,
c, 0, -c, -f, -i, -l, -o,}
{
e, j, o, m, h, c, -b, -g, -l, -p, -k, -f,
-a, d, i, n,}
{ g,
n, l, e, -b, -i, -p, -j, -c, d, k, o,
h, a, -f, -m,}
{ i,
o, f, -c, -l, -l, -c, f, o, i, 0, -i, -o,
-f, c, l,}
{ k,
k, 0, -k, -k, 0, k, k, 0, -k, -k, 0,
k, k, 0, -k,}
{ m,
g, -f, -n, -a, l, h, -e, -o, -b, k, i, -d, -p,
-c, j,}
{ o,
c, -l, -f, i, i, -f, -l, c, o, 0, -o, -c,
l, f, -i,}
{ p, -a,
-o, b, n, -c, -m, d, l, -e, -k, f, j, -g,
-i, h,}
{ n, -e,
-i, j, d, -o, a, m, -f, -h, k, c, -p,
b, l, -g,}
{ l, -i,
-c, o, -f, -f, o, -c, -i, l, 0, -l, i, c,
-o, f,}
{ j,
-m, c, g, -p, f, d, -n, i, a, -k, l,
-b, -h, o, -e,}
{ h,
-p, i, -a, -g, o, -j, b, f, -n, k, -c, -e,
m, -l, d,}
{ f,
-l, o, -i, c, c, -i, o, -l, f, 0, -f,
l, -o, i, -c,}
{ d,
-h, l, -p, m, -i, e, -a, -c, g, -k, o, -n,
j, -f, b,}
{ b, -d,
f, -h, j, -l, n, -p, o, -m, k, -i, g, -e,
c, -a,}
ここで
{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p} = { 9, 17, 25, 33, 41, 49, 56,
62, 66, 72, 77, 81, 83, 87, 89, 90}
32点DST-7
{ a,
b, c, d, e, f, g, h, i,
j, k, l, m, n, o, p, q,
r, s, t, u, v, w, x, y,
z, A, B, C, D, E, F,}
{
c, f, i, l, o, r, u, x,
A, D, F, C, z, w, t, q,
n, k, h, e, b, -a, -d, -g, -j, -m, -p, -s, -v, -y, -B,
-E,}
{ e,
j, o, t, y, D, D, y, t,
o, j, e, 0, -e, -j, -o, -t, -y, -D, -D, -y, -t, -o, -j,
-e, 0, e, j, o, t, y, D,}
{ g,
n, u, B, D, w, p, i, b, -e, -l, -s,
-z, -F, -y, -r, -k, -d, c, j, q, x, E,
A, t, m, f, -a, -h, -o, -v, -C,}
{ i,
r, A, C, t, k, b, -g, -p, -y, -E, -v, -m,
-d, e, n, w, F, x, o, f, -c, -l, -u,
-D, -z, -q, -h, a, j, s, B,}
{ k,
v, F, u, j, -a, -l, -w, -E, -t, -i, b, m,
x, D, s, h, -c, -n, -y, -C, -r, -g, d, o,
z, B, q, f, -e, -p, -A,}
{ m,
z, z, m, 0, -m, -z, -z, -m, 0, m, z,
z, m, 0, -m, -z, -z, -m, 0, m, z, z,
m, 0, -m, -z, -z, -m, 0, m, z,}
{ o,
D, t, e, -j, -y, -y, -j, e, t, D, o,
0, -o, -D, -t, -e, j, y, y, j, -e, -t, -D, -o,
0, o, D, t, e, -j, -y,}
{ q,
E, n, -c, -t, -B, -k, f, w, y, h, -i, -z, -v,
-e, l, C, s, b, -o, -F, -p, a, r,
D, m, -d, -u, -A, -j, g, x,}
{ s,
A, h, -k, -D, -p, c, v, x, e, -n, -F, -m,
f, y, u, b, -q, -C, -j, i, B, r, -a, -t,
-z, -g, l, E, o, -d, -w,}
{ u,
w, b, -s, -y, -d, q, A, f, -o, -C, -h, m,
E, j, -k, -F, -l, i, D, n, -g, -B, -p, e,
z, r, -c, -x, -t, a, v,}
{ w,
s, -d, -A, -o, h, E, k, -l, -D, -g, p, z,
c, -t, -v, a, x, r, -e, -B, -n, i, F, j,
-m, -C, -f, q, y, b, -u,}
{ y,
o, -j, -D, -e, t, t, -e, -D, -j, o, y, 0, -y,
-o, j, D, e, -t, -t, e, D, j, -o, -y,
0, y, o, -j, -D, -e, t,}
{ A,
k, -p, -v, e, F, f, -u, -q, j, B, a, -z,
-l, o, w, -d, -E, -g, t, r, -i, -C, -b, y,
m, -n, -x, c, D, h, -s,}
{ C,
g, -v, -n, o, u, -h, -B, a, D, f, -w, -m,
p, t, -i, -A, b, E, e, -x, -l, q, s, -j,
-z, c, F, d, -y, -k, r,}
{ E,
c, -B, -f, y, i, -v, -l, s, o, -p, -r, m,
u, -j, -x, g, A, -d, -D, a, F, b, -C, -e,
z, h, -w, -k, t, n, -q,}
{ F, -a,
-E, b, D, -c, -C, d, B, -e, -A, f, z, -g,
-y, h, x, -i, -w, j, v, -k, -u, l, t, -m,
-s, n, r, -o, -q, p,}
{ D, -e,
-y, j, t, -o, -o, t, j, -y, -e, D, 0,
-D, e, y, -j, -t, o, o, -t, -j, y, e,
-D, 0, D, -e, -y, j, t, -o,}
{ B, -i,
-s, r, j, -A, -a, C, -h, -t, q, k, -z, -b,
D, -g, -u, p, l, -y, -c, E, -f, -v, o, m, -x,
-d, F, -e, -w, n,}
{ z, -m,
-m, z, 0, -z, m, m, -z, 0, z, -m, -m,
z, 0, -z, m, m, -z, 0, z, -m, -m, z,
0, -z, m, m, -z, 0, z, -m,}
{ x, -q,
-g, E, -j, -n, A, -c, -u, t, d, -B, m, k,
-D, f, r, -w, -a, y, -p, -h, F, -i, -o, z, -b,
-v, s, e, -C, l,}
{ v, -u,
-a, w, -t, -b, x, -s, -c, y, -r, -d, z, -q, -e,
A, -p, -f, B, -o, -g, C, -n, -h, D, -m, -i, E, -l,
-j, F, -k,}
{ t,
-y, e, o, -D, j, j, -D, o, e, -y,
t, 0, -t, y, -e, -o, D, -j, -j, D, -o, -e, y,
-t, 0, t, -y, e, o, -D, j,}
{ r,
-C, k, g, -y, v, -d, -n, F, -o, -c, u, -z,
h, j, -B, s, -a, -q, D, -l, -f, x, -w, e,
m, -E, p, b, -t, A, -i,}
{ p,
-F, q, -a, -o, E, -r, b, n, -D, s, -c, -m,
C, -t, d, l, -B, u, -e, -k, A, -v, f, j,
-z, w, -g, -i, y, -x, h,}
{ n,
-B, w, -i, -e, s, -F, r, -d, -j, x, -A, m,
a, -o, C, -v, h, f, -t, E, -q, c, k,
-y, z, -l, -b, p, -D, u, -g,}
{ l,
-x, C, -q, e, g, -s, E, -v, j, b, -n,
z, -A, o, -c, -i, u, -F, t, -h, -d, p, -B, y,
-m, a, k, -w, D, -r, f,}
{ j,
-t, D, -y, o, -e, -e, o, -y, D, -t, j, 0,
-j, t, -D, y, -o, e, e, -o, y, -D, t,
-j, 0, j, -t, D, -y, o, -e,}
{ h,
-p, x, -F, y, -q, i, -a, -g, o, -w, E, -z,
r, -j, b, f, -n, v, -D, A, -s, k, -c, -e,
m, -u, C, -B, t, -l, d,}
{ f,
-l, r, -x, D, -C, w, -q, k, -e, -a, g, -m,
s, -y, E, -B, v, -p, j, -d, -b, h, -n, t,
-z, F, -A, u, -o, i, -c,}
{ d,
-h, l, -p, t, -x, B, -F, C, -y, u, -q, m,
-i, e, -a, -c, g, -k, o, -s, w, -A, E, -D,
z, -v, r, -n, j, -f, b,}
{ b,
-d, f, -h, j, -l, n, -p, r, -t, v, -x, z,
-B, D, -F, E, -C, A, -y, w, -u, s, -q, o,
-m, k, -i, g, -e, c, -a,}
ここで {a, b, c, d, e,
f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, A, B, C, D, E, F
} = { 4, 9, 13, 17, 21, 26, 30, 34, 38, 42, 45, 50, 53, 56, 60, 63, 66, 68, 72,
74, 77, 78, 80, 82, 84, 85, 86, 88, 88, 89, 90, 90 }
4点DCT-8
{
a, b, c, d,}
{ b,
0, -b, -b,}
{ c, -b,
-d, a,}
{ d,
-b, a, -c,}
ここで
{a, b, c, d} = { 84,74,55,29}
8点DCT-8
{ a,
b, c, d, e, f, g, h,}
{ b,
e, h, -g, -d, -a, -c, -f,}
{ c,
h, -e, -a, -f, g, b, d,}
{
d, -g, -a, -h, c, e, -f, -b,}
{ e, -d,
-f, c, g, -b, -h, a,}
{ f,
-a, g, e, -b, h, d, -c,}
{ g,
-c, b, -f, -h, d, -a, e,}
{ h,
-f, d, -b, a, -c, e, -g,}
ここで
{a, b, c, d, e, f, g, h} = { 86,85,78,71,60,46,32,17}
16点DCT-8
{ a,
b, c, d, e, f, g, h, i,
j, k, l, m, n, o, p,}
{ b,
e, h, k, n, 0, -n, -k, -h, -e, -b, -b, -e, -h, -k, -n,}
{
c, h, m, -p, -k, -f, -a, -e, -j, -o, n, i,
d, b, g, l,}
{ d,
k, -p, -i, -b, -f, -m, n, g, a, h, o, -l, -e, -c,
-j,}
{ e,
n, -k, -b, -h, 0, h, b, k, -n, -e, -e, -n,
k, b, h,}
{ f,
0, -f, -f, 0, f, f, 0, -f, -f, 0, f,
f, 0, -f, -f,}
{ g, -n, -a,
-m, h, f, -o, -b, -l, i, e, -p, -c, -k, j,
d,}
{ h, -k,
-e, n, b, 0, -b, -n, e, k, -h, -h, k,
e, -n, -b,}
{ i, -h,
-j, g, k, -f, -l, e, m, -d, -n, c, o, -b,
-p, a,}
{ j, -e,
-o, a, -n, -f, i, k, -d, -p, b, -m, -g, h,
l, -c,}
{ k,
-b, n, h, -e, 0, e, -h, -n, b, -k, -k, b,
-n, -h, e,}
{ l,
-b, i, o, -e, f, -p, -h, c, -m, -k, a, -j,
-n, d, -g,}
{ m,
-e, d, -l, -n, f, -c, k, o, -g, b, -j, -p,
h, -a, i,}
{ n,
-h, b, -e, k, 0, -k, e, -b, h, -n, -n, h,
-b, e, -k,}
{ o, -k,
g, -c, b, -f, j, -n, -p, l, -h, d, -a, e,
-i, m,}
{ p,
-n, l, -j, h, -f, d, -b, a, -c, e, -g, i,
-k, m, -o,}
ここで
{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p} = {
90,89,87,83,81,77,72,66,62,56,49,41,33,25,17, 9}
32点DCT-8
{
a, b, c, d, e, f, g, h,
i, j, k, l, m, n, o, p,
q, r, s, t, u, v, w, x,
y, z, A, B, C, D, E, F,}
{
b, e, h, k, n, q, t, w,
z, C, F, -E, -B, -y, -v, -s, -p, -m, -j, -g, -d, -a, -c, -f, -i,
-l, -o, -r, -u, -x, -A, -D,}
{ c,
h, m, r, w, B, 0, -B, -w, -r, -m, -h, -c, -c, -h,
-m, -r, -w, -B, 0, B, w, r, m, h,
c, c, h, m, r, w, B,}
{ d,
k, r, y, F, -A, -t, -m, -f, -b, -i, -p, -w, -D,
C, v, o, h, a, g, n, u, B, -E,
-x, -q, -j, -c, -e, -l, -s, -z,}
{ e,
n, w, F, -y, -p, -g, -c, -l, -u, -D, A, r,
i, a, j, s, B, -C, -t, -k, -b, -h, -q, -z,
E, v, m, d, f, o, x,}
{ f,
q, B, -A, -p, -e, -g, -r, -C, z, o, d, h,
s, D, -y, -n, -c, -i, -t, -E, x, m, b, j,
u, F, -w, -l, -a, -k, -v,}
{ g,
t, 0, -t, -g, -g, -t, 0, t, g, g, t,
0, -t, -g, -g, -t, 0, t, g, g, t, 0, -t,
-g, -g, -t, 0, t, g, g, t,}
{ h,
w, -B, -m, -c, -r, 0, r, c, m, B, -w, -h, -h,
-w, B, m, c, r, 0, -r, -c, -m, -B, w,
h, h, w, -B, -m, -c, -r,}
{ i,
z, -w, -f, -l, -C, t, c, o, F, -q, -a, -r,
E, n, d, u, -B, -k, -g, -x, y, h, j,
A, -v, -e, -m, -D, s, b, p,}
{ j,
C, -r, -b, -u, z, g, m, F, -o, -e, -x, w,
d, p, -E, -l, -h, -A, t, a, s, -B, -i, -k, -D,
q, c, v, -y, -f, -n,}
{ k,
F, -m, -i, -D, o, g, B, -q, -e, -z, s, c,
x, -u, -a, -v, w, b, t, -y, -d, -r, A, f,
p, -C, -h, -n, E, j, l,}
{ l, -E, -h,
-p, A, d, t, -w, -a, -x, s, e, B, -o, -i,
-F, k, m, -D, -g, -q, z, c, u, -v, -b, -y,
r, f, C, -n, -j,}
{ m, -B, -c,
-w, r, h, 0, -h, -r, w, c, B, -m, -m,
B, c, w, -r, -h, 0, h, r, -w, -c, -B,
m, m, -B, -c, -w, r, h,}
{ n, -y, -c,
-D, i, s, -t, -h, E, d, x, -o, -m, z,
b, C, -j, -r, u, g, -F, -e, -w, p, l, -A, -a,
-B, k, q, -v, -f,}
{ o, -v,
-h, C, a, D, -g, -w, n, p, -u, -i, B,
b, E, -f, -x, m, q, -t, -j, A, c, F, -e,
-y, l, r, -s, -k, z, d,}
{ p, -s,
-m, v, j, -y, -g, B, d, -E, -a, -F, c, C,
-f, -z, i, w, -l, -t, o, q, -r, -n, u, k,
-x, -h, A, e, -D, -b,}
{ q, -p,
-r, o, s, -n, -t, m, u, -l, -v, k, w, -j,
-x, i, y, -h, -z, g, A, -f, -B, e, C, -d,
-D, c, E, -b, -F, a,}
{ r, -m,
-w, h, B, -c, 0, c, -B, -h, w, m, -r,
-r, m, w, -h, -B, c, 0, -c, B, h, -w,
-m, r, r, -m, -w, h, B, -c,}
{ s, -j,
-B, a, -C, -i, t, r, -k, -A, b, -D, -h, u,
q, -l, -z, c, -E, -g, v, p, -m, -y, d, -F, -f,
w, o, -n, -x, e,}
{
t, -g, 0, g, -t, -t, g, 0, -g, t, t,
-g, 0, g, -t, -t, g, 0, -g, t, t, -g,
0, g, -t, -t, g, 0, -g, t, t, -g,}
{
u, -d, B, n, -k, -E, g, -r, -x, a, -y, -q, h, -F,
-j, o, A, -c, v, t, -e, C, m, -l, -D,
f, -s, -w, b, -z, -p, i,}
{ v,
-a, w, u, -b, x, t, -c, y, s, -d,
z, r, -e, A, q, -f, B, p, -g, C, o,
-h, D, n, -i, E, m, -j, F, l, -k,}
{ w,
-c, r, B, -h, m, 0, -m, h, -B, -r, c, -w,
-w, c, -r, -B, h, -m, 0, m, -h, B, r,
-c, w, w, -c, r, B, -h, m,}
{ x,
-f, m, -E, -q, b, -t, -B, j, -i, A, u, -c,
p, F, -n, e, -w, -y, g, -l, D, r, -a,
s, C, -k, h, -z, -v, d, -o,}
{ y,
-i, h, -x, -z, j, -g, w, A, -k, f, -v, -B,
l, -e, u, C, -m, d, -t, -D, n, -c, s, E,
-o, b, -r, -F, p, -a, q,}
{ z,
-l, c, -q, E, u, -g, h, -v, -D, p, -b, m,
-A, -y, k, -d, r, -F, -t, f, -i, w, C, -o,
a, -n, B, x, -j, e, -s,}
{ A,
-o, c, -j, v, F, -t, h, -e, q, -C, -y, m,
-a, l, -x, -D, r, -f, g, -s, E, w, -k, b,
-n, z, B, -p, d, -i, u,}
{ B,
-r, h, -c, m, -w, 0, w, -m, c, -h, r, -B,
-B, r, -h, c, -m, w, 0, -w, m, -c, h,
-r, B, B, -r, h, -c, m, -w,}
{ C,
-u, m, -e, d, -l, t, -B, -D, v, -n, f, -c,
k, -s, A, E, -w, o, -g, b, -j, r, -z, -F,
x, -p, h, -a, i, -q, y,}
{ D,
-x, r, -l, f, -a, g, -m, s, -y, E, C,
-w, q, -k, e, -b, h, -n, t, -z, F, B,
-v, p, -j, d, -c, i, -o, u, -A,}
{ E,
-A, w, -s, o, -k, g, -c, b, -f, j, -n, r,
-v, z, -D, -F, B, -x, t, -p, l, -h, d, -a,
e, -i, m, -q, u, -y, C,}
{ F,
-D, B, -z, x, -v, t, -r, p, -n, l, -j, h,
-f, d, -b, a, -c, e, -g, i, -k, m, -o, q,
-s, u, -w, y, -A, C, -E,}
ここで
{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z,
A, B, C, D, E, F } = {90,90,89,88,88,86,85,84,82,80,78,77,74,72,68,66,63,60,56,53,50,45,42,38,34,30,26,21,17,13,
9, 4}
Claims (6)
- デコーダにおけるビデオ復号用の方法であって、
符号化されたビデオビットストリームから係数ブロックの符号化情報を復号するステップであって、前記符号化情報が前記係数ブロックのサイズを示すステップと、
前記係数ブロックの前記サイズに基づいて、逆一次変換の逆水平変換および逆垂直変換のうちの1つにおいて計算回数を削減するか否かを判定するステップであって、前記逆垂直変換が前記係数ブロックの変換係数を中間ブロックの中間データに変換し、前記逆水平変換が前記中間データを残余ブロックの残余データに変換するステップと、
前記逆一次変換を実行するステップであって、
前記逆垂直変換の前記計算回数を削減すると判定した場合、前記中間ブロックの前記中間データの上位16行が前記逆垂直変換によって計算され、前記中間ブロックの前記残りの中間データがゼロになり、
前記逆水平変換の前記計算回数を削減すると判定した場合、前記残余ブロックの前記残余データの左16列が前記逆水平変換によって計算され、前記残余ブロックの前記残りの残余データがゼロになる、ステップと、
前記残余データに基づいて前記残余ブロック内のサンプルを再構成するステップと、を含む方法。 - 前記逆水平変換および逆垂直変換のうちの1つは前記逆垂直変換であり、
前記判定するステップは、前記係数ブロックの前記サイズが32×64である場合、前記逆垂直変換の前記計算回数を削減すると判定するステップを含み、
前記逆一次変換を実行するステップは、前記逆一次変換を実行するステップであって、前記中間ブロックの前記中間データの前記上位16行が前記逆垂直変換によって計算され、前記中間ブロックの前記残りの中間データがゼロになる、ステップを含む、請求項1に記載の方法。 - 前記逆水平変換および逆垂直変換のうちの1つは前記逆水平変換であり、
前記判定するステップは、前記係数ブロックの前記サイズが32×64である場合、前記逆水平変換の前記計算回数を削減すると判定するステップを含み、
前記逆一次変換を実行するステップは、前記逆一次変換を実行するステップであって、前記残余ブロックの前記残余データの前記左16列が前記逆水平変換によって計算され、前記残余ブロックの前記残りの残余データがゼロになる、ステップを含む、請求項1に記載の方法。 - 前記逆水平変換および逆垂直変換のうちの1つは前記逆水平変換であり、
前記判定するステップは、前記係数ブロックの前記サイズが32×32である場合、前記逆水平変換の前記計算回数を削減すると判定するステップを含み、
前記逆一次変換を実行するステップは、前記逆一次変換を実行するステップであって、前記残余ブロックの前記残余データの前記左16列が前記逆水平変換によって計算され、前記残余ブロックの前記残りの残余データがゼロになり、前記中間ブロックの前記中間データは前記逆垂直変換によって計算される、ステップを含む、請求項1に記載の方法。 - 前記逆水平変換および逆垂直変換のうちの1つは前記逆垂直変換であり、
前記判定するステップは、前記係数ブロックの前記サイズが32×32である場合、前記逆垂直変換の前記計算回数を削減すると判定するステップを含み、
前記逆一次変換を実行するステップは、前記逆一次変換を実行するステップであって、前記中間ブロックの前記中間データの前記上位16行が前記逆垂直変換によって計算され、前記中間ブロックの前記残りの中間データがゼロになり、前記残余ブロックの前記残余データは前記逆水平変換によって計算される、ステップを含む、請求項1に記載の方法。 - 請求項1乃至5いずれか1項記載の方法を実行するように構成された処理回路を含む、ビデオ復号用の装置。
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