AN-1021: 基于MMSE的触摸屏应用多点校准算法 (Rev. 0)

AN-1021
ᆌᆩԴऻ
One Technology Way t P.O. Box 9106 t Norwood, MA 02062-9106, U.S.A. t Tel: 781.329.4700 t Fax: 781.461.3113 t www.analog.com
एᇀMMSE‫ةڦ‬ఄೡᆌᆩ‫ۅܠ‬ၯጚ໙݆
ፕኁǖNing Jia
०঻
၄‫پ‬ยԢ‫ܠ‬ᅜᅂৗೡत‫ة‬ఄೡरຍፕྺᆩࢽহ௬ăᅺഄ०
‫ࠓڦڇ‬ሰࢅዚ໯ዜኪ‫֡ڦ‬ፕᇱ૙Lj‫ۉ‬ፆ๕‫ة‬ఄೡ๟঄൱‫ׯ‬
Ԩ႙ยऺ‫ڦ‬๯჋ă඗ܸLj‫ۉ‬ፆ๕‫ة‬ఄೡ٪ሞ‫ڦ‬ऐႁ‫ܔ‬ഋဃ
ֶत໫‫ݣ‬ᅺጱLjᆖၚକ‫ة‬ఄೡׂิ‫ڦ‬XĂYፖՔăᅺُLj࢔
వॽ‫ة‬ఄೡ‫ڦ‬ፖՔᇑഄࢫ၂๖ೡ)ᅂৗೡ‫ྜ*ڪ‬ඇ‫ܔ‬ഋăࡤ
ᆶ‫ة‬ఄೡ‫ڦ‬ፌዕׂ೗‫้׍؜‬LjՂႷ๯ံኴႜၯጚ໙݆ă
ኍ‫ةܔ‬ఄೡ‫ڦ‬ঢ়‫ۆ‬ၯጚ໙݆๟ᅃዖएᇀෙ߲֖ቷ‫ڦۅ‬ෙ‫ۅ‬
ၯጚ໙݆ăኄዖঢ়‫ۆ‬ෙ‫ۅ‬ၯጚ໙݆ၳ୲ߛĂၳࡕࡻLj‫ړڍ‬
‫ة‬ఄೡড‫้ٷ‬LjႠీড‫گ‬ăԨᆌᆩԴऻኍ‫ۉܔ‬ፆ๕‫ة‬ఄ
ೡLj༵‫؜‬କᅃዖएᇀፌၭ਩‫ݛ‬ဃֶ(MMSE)‫ۅܠڦ‬ၯጚ໙
݆Lj֑ᆩෙ߲ᅜฉ‫֖ڦ‬ቷ‫ۅ‬ăຕბླྀ‫ํࢅڞ‬ᄓ਩ኤ௽LjԨ
໙݆‫ڦ‬৛‫܈‬ᆫᇀঢ়‫ۆ‬ෙ‫ۅ‬ၯጚ໙݆ă
Rev. 0
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Tel: 781.329.4700
www.analog.com
Fax: 781.461.3113
©2009 Analog Devices, Inc. All rights reserved.
Rev. 0 | Page 1 of 12
AN-1021
ᆌᆩԴऻ
ణ୤
०঻ ................................................................................................... 1
๖૩ ................................................................................................... 7
ຕბᇱ૙ .......................................................................................... 3
঳ஃ ................................................................................................... 8
ঢ়‫ۆ‬ෙ‫ۅ‬ၯጚ໙݆ ................................................................ 4
‫پ‬ஓኴႜ ........................................................................................... 8
एᇀMMSE‫ۅܠڦ‬ၯጚ໙݆ ................................................ 4
Պஓ ................................................................................................... 9
एᇀMMSE‫ۅܠڦ‬ၯጚ໙݆‫ݴڦ‬ဆ ................................... 6
֖੊࿔၅ ........................................................................................ 11
एᇀMMSE‫ۅܠڦ‬ၯጚ໙݆‫ڦ‬օየ ................................... 6
Rev. 0 | Page 2 of 12
AN-1021
ᆌᆩԴऻ
ຕბᇱ૙
཮1໯๖ࢤ෥ᇶႚ‫ڦ‬૙ၙዐ႐ྺO)ᇱ‫*ۅ‬Lj૙ၙӷ০ྺRă
्ۨ޿ࢤ෥ᇶႚ‫پ‬՗‫ڦ‬๟‫ة‬ఄೡူ‫ݛ‬ᅂৗೡ໯၂๖‫཮ڦ‬
ၟăઢ෥ྈᇶ՗๖ᆩࢽᄂጣᅂৗೡ໯๖ࢤ෥ᇶႚ৊ႜ‫ة‬ఄ
้Lj‫ة‬ఄೡׂิ‫ڦ‬ᅃፇ‫཮)ۅ‬ዐྺੲቧ‫ڦ‬၂๖*ăᅺُLj๴
‫ۉ‬ፆ๕‫ة‬ఄೡԨวऐႁ‫ܔ‬ഋဃֶࢅ໫‫ݣ‬ᅺጱ‫ڦ‬ᆖၚLjዘࠓ
ࢫ‫཮ڦ‬ၟሞ߳ፖՔዡฉ਩ᅜփཞ‫ڦ‬ᅺጱ჉ገĂೝᅎࢅ໫
‫ݣ‬ăၯጚ໙݆௬ଣ‫ڦ‬཈቟๟සࢆॽ‫ة‬ఄೡׂิ‫ڦ‬ፖՔገ࣑
‫ׯ‬৛ඓ‫پ‬՗໯๖཮ၟ‫ڦ‬ᅃፇፖՔă
ྺକՍᇀ‫ॆٷ‬૙঴ᅜฉ‫ݴ‬ဆLjփ‫्ݟ‬ยP’(x’, y’)ྺ‫ة‬ఄೡ኱থ
ׂิ‫ڦ‬ፖՔLjഄ‫ڪ‬ॏटፖՔ՗‫ٳ‬๕P’(Rcos θ0, Rsin θ0)ăଷྔ्
ยLjᇑP’(x’, y’)‫ܔ‬ᆌ‫ڦ‬૙ၙፖՔྺP(x, y)ă६ᇀP’(x’, y’)ᇑP(x, y)‫ڦ‬
࠲ဣLj੗‫ڥ‬ǖ
P(x, y) = P(KXRcos(θ0 + θ) + TX, KYRsin(θ0 + θ) + TY)
਍ෙঙࡧຕLj
cos(θ0 + θ) = cosθ0 cosθ − sinθ0 sinθ
त
sin(θ0 + θ) = sinθ0 cosθ + cosθ0 sinθ
੗‫ڥ‬ᅜူ‫ײݛ‬๕ǖ
⎧ x' = R cos θ 0
⎨ y ' = R sin θ
0
⎩
P (x , y )
⎧ x = K X R cos(θ 0 + θ ) + T X = K X R(cos θ 0 cos θ − sin θ 0 sin θ ) + T X
⎨ y = K R sin (θ + θ ) + T = K R(sin θ cos θ − cos θ sin θ ) + T
Y
0
Y
Y
0
0
Y
⎩
P(x, y)
ሶᆶ
O
O
⎧ x = cos θK X x'− sin θK X y '+T X
⎨ y = cos θK y '− sin θK x'+T
Y
Y
Y
⎩
ഄዐǖ
θĂKXĂKYĂTXࢅTY਩ྺ‫׉‬ຕă
08183-001
ยǖ
cosθKX = KX1
཮ 1. ‫ة‬ఄೡဃֶ
−sinθKX = KX2
ย٪ሞᅃ‫ۅ‬Ljഄ૙ၙፖՔྺP(x, y)Lj൐‫ة‬ఄೡׂิ‫ڦ‬ፖՔ
ྺP’(x’, y’)ă)P‫ۅ‬࿋ᇀࢤ෥ᇶႚฉLjᇑഄ‫ܔ‬ᆌ‫ڦ‬P’‫ۅ‬ሶ࿋ᇀ
ઢ෥ྈᇶฉă*ยP’(x’, y’) ჉ገθঙ‫܈‬Lj඗ࢫሞXࢅYዡ‫ݴ‬՚
໫‫ݣ‬KXࢅKYLj‫ݴ‬՚ೝᅎTXࢅTYLj੗ᅜ࣮‫ڟ‬ഄ૙ၙፖՔP(x,
y)ăၯጚ໙݆‫ڦ‬ణ‫ڦ‬๟ऺ໙ဣຕθĂKXĂKYĂTXࢅTYă඗
ࢫ੗૧ᆩኄၵဣຕ‫ةܔ‬ఄೡ኱থׂิ‫ڦ‬ፖՔ৊ႜၯጚă
TX = KX3
sinθKY = KY1
cosθKY = KY2
TY = KY3
ሶമຎ‫ײݛ‬๕੗߀ႀྺǖ
⎧ x = KX 1 x'+ KX 2 y '+ KX 3
⎨ y = KY y '+ KY y '+ KY
1
2
3
⎩
੗૧ᆩᅜฉ‫ײݛ‬๕ઠၯጚP’(x’, y’)Ljܸٗ‫ڟڥ‬P(x, y)ă‫ܔ‬ᇀXዡ
ࢅYዡܸჾLj߳‫ײݛ‬๕ዐ਩ࡤᆶෙ߲࿄ኪဣຕă
Rev. 0 | Page 3 of 12
AN-1021
ᆌᆩԴऻ
ঢ়‫ۆ‬ෙ‫ۅ‬ၯጚ໙݆!
एᇀMMSE‫ۅܠڦ‬ၯጚ໙݆
ཚࡗฉຎ‫ݴ‬ဆLj࿢்‫ڟڥ‬କXዡईYዡ‫ڦ‬ၯጚ‫ײݛ‬๕ă‫ܔ‬ᇀ
X ዡई Y ዡLj߳‫ײݛ‬๕਩ࡤᆶෙ߲࿄ኪဣຕăᅺُLjසࡕ
੗इ‫ڥ‬ෙ߲փ၎࠲֖ቷ‫ڦۅ‬႑တLjሶ੗ࠓॺ‫؜‬၍Ⴀ‫ײݛ‬
ፇLjཚࡗ঴‫ײݛ‬ઠइ‫ڥ‬࿄ኪဣຕ‫ڦ‬঴ă
ยෙ߲֖ቷ‫ڦۅ‬૙ၙፖՔྺ(x0, y0)Ă(x1, y1) ࢅ (x2, y2)Ljഄ‫ܔ‬
ᆌ‫֑ڦ‬ᄣፖՔྺ(x’0, y’0)Ă(x’1, y’1) ࢅ (x’2, y’2)LjሶXዡࢅYዡ
‫ײݛڦ‬๕‫ݴ‬՚ྺ
૧ᆩঢ়‫ۆ‬ෙ‫ۅ‬ၯጚ໙݆‫ڦڟڥ‬ဣຕLj੗ᅜॽෙ߲֖ቷ‫ۅ‬ၯ
ጚ‫ڟ‬૙ၙ࿋ዃă඗ܸLj‫ܔ‬ᇀփሞ֖ቷ‫޹ۅ‬ৎ‫ڦ‬ഄ໱‫ۅ‬Ljၯ
ጚႠీփฯ૙ၙLj‫ةړ‬ఄೡ၎‫ܔ‬ড‫้ٷ‬ᆮഄසُă๖૩և
‫ํڦݴ‬ᄓ঳ࡕཞᄣኤํକኄ߲࿚༶ăᅺُLj੗੊୯૧ᆩෙ
߲ᅜฉ‫֖ڦ‬ቷ‫ۅ‬Ljᅜइ‫ڥ‬ፌॅၯጚဣຕă
⎧ x0 = KX 1 x0' + KX 2 y 0' + KX 3
⎪
'
'
⎨ x1 = KX 1 x1 + KX 2 y1 + KX 3
'
⎪ x2 = KX 1 x2 + KX 2 y 2' + KX 3
⎩
ยᆶN + 1߲֖ቷ‫(ۅ‬N + 1 > 3)Ljഄ૙ၙፖՔྺ(x0, y0)Ă(x1,
y1)…(xN, yN)Lj൐ഄ‫ܔ‬ᆌ‫֑ڦ‬ᄣፖՔྺ(x’0, y’0)Ă(x’1, y’1)…
(x’N, y’N)Ljሶ၎ᆌ‫ײݛڦ‬๕සူǖ
⎧ x0 = KX 1 x0' + KX 2 y0' + KX 3
⎪
'
'
⎪ x1 = KX 1 x1 + KX 2 y1 + KX 3
⎨
M
⎪
⎪⎩ x N = KX 1 x N' + KX 2 y N' + KX 3
त
⎧ y0 = KY1 x0' + KY2 y0' + KY3
⎪
'
'
⎨ y1 = KY1 x1 + KY2 y1 + KY3
⎪ y = KY x ' + KY y ' + KY
1 2
2 2
3
⎩ 2
त
⎧ y0 = KY1 x0' + KY2 y0' + KY3
⎪
'
'
⎪ y1 = KY1 x1 + KY2 y1 + KY3
⎨
M
⎪
'
⎪⎩ y N = KY1 x N + KY2 y N' + KY3
एᇀُLj੗ॽᅜฉຎ‫߀ײݛ‬ႀྺਈንఇ๕ǖ
⎡ x0'
⎢ '
⎢ x1
⎢ x2'
⎣
y0' 1⎤ ⎡ KX 1 ⎤ ⎡ x0 ⎤
⎥
y1' 1⎥ • ⎢⎢ KX 2 ⎥⎥ = ⎢⎢ x1 ⎥⎥
y2' 1⎥⎦ ⎢⎣ KX 3 ⎥⎦ ⎢⎣ x2 ⎥⎦
⎡ x0'
⎢ '
⎢ x1
⎢ x2'
⎣
y0' 1⎤ ⎡ KY1 ⎤ ⎡ y0 ⎤
⎥
y1' 1⎥ • ⎢⎢ KY2 ⎥⎥ = ⎢⎢ y1 ⎥⎥
'
y2 1⎥⎦ ⎢⎣ KY3 ⎥⎦ ⎢⎣ y2 ⎥⎦
ጀᅪLj߳‫ײݛ‬ፇዐ‫ײݛڦ‬ຕ(N + 1)਩‫ٷ‬ᇀ࿄ኪဣຕ‫߲ڦ‬ຕ
(3)ă
त
੗९Lj࿢்‫ڦ‬ణ‫ڦ‬๟໙‫؜‬๢ࢇඇև(N + 1)߲֖ቷ‫ڦۅ‬ፌॅ
ၯጚဣຕăइ‫ڥ‬ፌॅဣຕ‫݆ݛڦ‬๟ፏთMMSEࡀሶăኄኟ
๟ኄዖ໙݆‫ྺ׬‬एᇀMMSE‫ۅܠڦ‬ၯጚ໙݆‫ڦ‬ᇱᅺ໯ሞă
ᅜXዡྺ૩Ljۨᅭᅃ߲ణՔࡧຕ
ሞُए‫إ‬ฉLj੗ᅜཚࡗ঴‫ײݛ‬໙‫؜‬ၯጚဣຕKX1ĂKX2Ă
KX3ĂKY1ĂKY2 ࢅ KY3ă
ཚࡗၩᇮ݆൱‫ڦڥ‬঳ࡕසူǖ
'
'
'
'
'
'
'
'
k = ( x0 − x2 )( y1 − y2) − (x1 − x2 )( y0 − y2 ) ሶ
ย!!!!!!!!!!!!!!!!!!
KX 1 =
KX 2 =
KX 3 =
KY1 =(
KY2 =
N
i =0
ഄዐLjFXྺ֖ቷ‫ڦۅ‬ဃֶೝ‫ࢅݛ‬ă
( x0 − x2 )( y1' − y2 ' ) − ( x1 − x2 )( y0' − y2' )
k
( x1 − x2 )( x1' − x2 ' ) − ( x0 − x2 )( x1' − x2' )
k
'
0
'
2 1
'
1 2
y (x x − x x ) +(y1' x0' x2 − x2' x0)+ (y2' x1' x0 − x0' x1)
k
y0 − y2)( x1' − x2 ') − ( y1 − y2
k
)( y
'
0
− y2' )
( y1 − y2 )(x0' − x2 ') −( y0 − y2 )(x1' − x2' )
KY3 =
(
FX = ∑ KX 1 xi' + KX 2 yi' + KX 3 − xi
k
y0'( x2' y1 − x1' y2 )+ (y1' x0' y2 − x2' y0) +(y2' x1' y0 − x0' y1)
k
Rev. 0 | Page 4 of 12
)
2
AN-1021
ᆌᆩԴऻ
KX1ĂKX2ࢅKX3‫ڦ‬ፌॅဣຕኸ๑ణՔࡧຕFXፌၭ‫ڦ‬ఫၵဣ
ຕăᅺُLj੗๑ᆩᅜူ‫ײݛ‬๕ǖ
ཚࡗၩᇮ݆൱‫ڦڥ‬঳ࡕසူǖ
ย
⎧ ∂FX
=0
⎪
⎪ ∂KX 1
⎪ ∂FX
=0
⎨
⎪ ∂KX 2
⎪ ∂FX = 0
⎪ ∂KX
3
⎩
न
N
⎧ ∂FX
=
2 xi' KX 1 xi' + KX 2 yi' + KX 3 − xi = 0
∑
⎪
∂
KX
i
0
=
1
⎪
N
⎪ ∂FX
= ∑ 2 yi' KX 1 xi' + KX 2 yi' + KX 3 − xi = 0
⎨
⎪ ∂KX 2 i=0N
⎪ ∂FX
'
'
⎪ ∂KX = ∑ 2 KX 1 xi + KX 2 yi + KX 3 − xi = 0
i =0
3
⎩
(
)
(
)
(
i =0
N
∑y
i =0
N
'2
i
∑y
i =0
'
i
⎡ KY1 ⎤
⎢ KY2 ⎥
⎢ KY ⎥
⎣ 3⎦
b1 =
∑y
∑y
, b = ∑ yi ,
2
c0 =
∑x x
∑x
c1 =
∑yx
∑y
, c = ∑ xi ,
2
d0 =
∑x y ,
∑x
d1 =
∑yx
∑y
, d = ∑ yi
2
'
i
'
i
,
'
i
' '
i i
'
i
'
i i
'
i
,
'2
i
'
i
'
i i
'
i
'
i i
'
i
a2 =
'
i
N
'
N
'
N
'
N
⎡ a0
⎢a
⎢ 1
⎢⎣a2
b0 1⎤ ⎡ KX 1 ⎤ ⎡c0 ⎤
b1 1⎥⎥ • ⎢⎢ KX 2 ⎥⎥ = ⎢⎢ c1 ⎥⎥
b2 1⎥⎦ ⎢⎣ KX 3 ⎥⎦ ⎢⎣c2 ⎥⎦
⎡a0
⎢a
⎢ 1
⎣⎢a2
b0 1⎤ ⎡ KY1 ⎤ ⎡d 0 ⎤
b1 1⎥⎥ • ⎢⎢ KY2 ⎥⎥ = ⎢⎢ d1 ⎥⎥
b2 1⎥⎦ ⎢⎣ KY3 ⎦⎥ ⎣⎢d 2 ⎦⎥
փవ݀၄Ljᅜฉ‫ײݛ‬ፇ‫߭ڦ‬๕ᇑമ௬ঢ়‫ۆ‬ෙ‫ۅ‬໙݆‫ײݛڦ‬ፇ
၎ཞǖ
⎡
' ⎤
⎤
xi' ⎥
⎢ ∑ xi xi ⎥
∑
i =0
⎡ KX 1 ⎤
⎢ iN=0
⎥
⎥
N
⎢ y' x ⎥
⎢
⎥
'⎥
=
BX
y
,
,
KX = ⎢ KX 2 ⎥
i i
∑
i
⎢∑
⎥
⎥
i =0
i =0
⎢ N
⎥
⎥
⎢⎣ KX 3 ⎥⎦
⎢ ∑ xi ⎥
N ⎥
⎢⎣ i =0 ⎥⎦
⎥⎦
, BY=
∑x y
∑x
'
i
'
i
त
N
⎡ x0'
⎢ '
⎢ x1
⎢ x2'
⎣
y0' 1⎤ ⎡ KX 1 ⎤ ⎡ x0 ⎤
⎥
y1' 1⎥ • ⎢⎢ KX 2 ⎥⎥ = ⎢⎢ x1 ⎥⎥
y2' 1⎥⎦ ⎢⎣ KX 3 ⎥⎦ ⎢⎣ x2 ⎥⎦
⎡ x0'
⎢ '
⎢ x1
⎢ x2'
⎣
y0' 1⎤ ⎡ KY1 ⎤ ⎡ y0 ⎤
⎥
y1' 1⎥ • ⎢⎢ KY2 ⎥⎥ = ⎢⎢ y1 ⎥⎥
y2' 1⎥⎦ ⎢⎣ KY3 ⎥⎦ ⎢⎣ y2 ⎥⎦
त
एᇀُLj੗ॽ߳‫ײݛ‬๕߀ႀྺਈንఇ๕3t,9#9Ljժ੗
ཚࡗ൱঴മຎ‫ײݛ‬ፇ໙‫؜‬ፌॅဣຕ,93−1t#9ă
ᇑXዡૌຼLjย
KY=
b0 =
'
i
i =0
)
N
∑x y ,
∑y
एᇀُLj੗ॽ‫ײݛ‬ፇ3t,9#9ࢅ3t,:#:‫ݴ‬՚߀ႀྺ
ย
∑ xi' yi'
a1 =
'
i
N
N
⎧⎛ N ' 2 ⎞
⎛ N ' '⎞
⎛ N '⎞
' '
⎪⎜ ∑ xi ⎟ KX 1 + ⎜ ∑ xi yi ⎟ KX 2 + ⎜ ∑ xi ⎟ KX 3 = ∑ xi xi
i
i
i
i
=
=
=
=
0
0
0
0
⎝
⎠
⎝
⎠
⎝
⎠
⎪
N
⎛ N '⎞
⎛ N '⎞
⎪⎛ N ' ' ⎞
' '
⎨ ⎜ ∑ xi yi ⎟ KX 1 + ⎜ ∑ yi ⎟ KX 2 + ⎜ ∑ yi ⎟ KX 3 = ∑ yi xi
i =0
⎠
⎝ i =0 ⎠
⎝ i =0 ⎠
⎪ ⎝ i =0
N
⎪
⎛ N '⎞
⎛ N '⎞
⎜ ∑ xi ⎟ KX 1 + ⎜ ∑ yi ⎟ KX 2 + N ⋅ KX 3 = ∑ xi
⎪
i =0
⎝ i =0 ⎠
⎝ i =0 ⎠
⎩
N
∑x
∑x ,
∑x
ഄዐLj!!!՗๖
Σ•
∑•
ᅜฉ‫ײݛ‬๕੗०ࣅྺ
⎡ N '2
⎢ ∑ xi
⎢ Ni=0
R = ⎢∑ xi' yi'
⎢ i =0
⎢ N
⎢ ∑ xi'
⎢⎣ i=0
'2
i
a0 =
⎡N ' ⎤
⎢∑ xi y i ⎥
⎢ i N= 0
⎥
⎢ y' y ⎥
∑
i i
⎢ i =0
⎥
⎢ N
⎥
⎢ ∑ yi ⎥
⎣⎢ i = 0
⎦⎥
඗ࢫन੗ཚࡗ൱঴‫ײݛ‬ፇ3 t ,: #:Lj໙‫؜‬:ዡ‫ڦ‬ፌॅဣ
ຕ,:3−1t#:ă
Rev. 0 | Page 5 of 12
AN-1021
ᆌᆩԴऻ
ሞُए‫إ‬ฉLj੗૧ᆩ၎ཞ‫ࠅڦ‬๕ऺ໙ဣຕ‫ڦ‬঳ࡕă
एᇀMMSE‫ۅܠڦ‬ၯጚ໙݆‫ڦ‬օየ
ย
ྜ‫ׯ‬एᇀMMSE‫ۅܠڦ‬ၯጚ໙݆‫ူڦ‬ଚօየǖ
1. ჋ስN +1 (N + 1 > 3)߲֖ቷ‫(ۅ‬x0, y0)Ă(x1, y1)…(xN,
yN)ă
2. ‫ةڟڥ‬ఄೡׂิ‫֖ڦ‬ቷ‫֑ڦۅ‬ᄣፖՔ(x’0, y’0)Ă(x’1, y’1)
…(x’N, y’N)ă
3. ૧ᆩԨᆌᆩԴऻߴ‫ࠅڦ؜‬๕Lj໙‫؜‬ၯጚဣຕKXࢅ!
!
KYăԈઔᅜူࠅ๕ǖ
k = (a0 − a2 )(b1 − b2 )− (a1 − a2 )(b0 − b2 )
ሶ
KX 1 =
KX 2 =
(c0 − c2 )(b1 − b2 )− (c1 − c2 )(b0 − b2 )
k
(c1 − c2 )(a0 − a2 )− (c0 − c2 )(a1 − a2 )
k = (a0 − a2 )(b1 − b2 )− (a1 − a2 )(b0 − b2 )
k
(c0 − c2 )(b1 − b2 )− (c1 − c2 )(b0 − b2 )
KX 1 =
b (a c − a c )+ b1 (a0c2 − a2c0 )+ b2 (a1c0 − a0c1 )
KX 3 = .0 2 1 1 2
k
k
KX 2 =
KY1
(d − d 2 )(b1 − b2 )− (d1 − d 2 )(b0 − b2 )
= 0
KX 3 =
KY2
(d − d 2 )(a0 − a2 )− (d 0 − d 2 )(a1 − a2 )
= 1
k
k
KY1 =
b (a d − a d )+ b1 (a0 d 2 − a2 d 0 )+ b2 (a1d 0 − a0 d1 )
KY3 = .0 2 1 1 2
k
KY2 =
एᇀMMSE‫ۅܠڦ‬ၯጚ໙݆‫ݴڦ‬ဆ
ཚࡗऺ໙a0Ăa1Ăa2Ǘb0Ăb1Ăb2Ǘc0Ăc1Ăc2ࢅd0Ăd1Ăd2੗
ᅜ݀၄Lj੗ॽa0Ăa1Ăa2‫ړ‬ፕएᇀෙዖփཞ‫ڦ݆ݛ‬x’i‫ेڦ‬඄
ೝ਩ኵLj੗ॽb0Ăb1Ăb2ੂፕएᇀෙዖփཞ‫ڦ݆ݛ‬y’i‫ेڦ‬඄
ೝ਩ኵăૌຼ‫ں‬Lj੗ॽc0Ăc1Ăc2‫ړ‬ፕएᇀෙዖփཞ‫ڦ݆ݛ‬
xi‫ेڦ‬඄ೝ਩ኵLjd0Ăd1Ăd2ሶ੗๫ྺएᇀෙዖփཞ‫ڦ݆ݛ‬
yi‫ेڦ‬඄ೝ਩ă
KY3 =
4.
ᆯᇀፌዕ‫ײݛ‬ፇᇑമ௬ঢ়‫ۆ‬ෙ‫ۅ‬໙݆‫ײݛڦ‬ፇਏᆶ၎ཞ߭
๕LjᅺُLj੗ॽएᇀMMSEࡀሶ‫ڦ‬໙݆๫ྺଷᅃዖෙ‫ۅ‬໙
݆ă඗ܸLjएᇀMMSE‫ڦ‬໙݆‫ڦ‬൶՚ሞᇀLjഄ֑ᆩ‫ڦ‬փ๟
ඪࢆ֖ቷ‫ڦۅ‬኱থ႑တLjܸ๟֖ቷ‫ेڦۅ‬඄ೝ਩႑တă࣑
ჾኮLjံᄲ໙‫؜‬N + 1߲኱থ֑ᄣ‫(ۅ‬x’0, y’0)Ă(x’1, y’1)…(x’N,
y’N)‫ڦ‬ෙ߲े඄ೝ਩‫(ۅ‬a0, b0)Ă(a1, b1)Ă(a2, b2)ăኄෙ߲े඄
ೝ਩‫ܔۅ‬ᆌ‫ڦ‬૙ၙፖՔྺ(c0, d0)Ă(c1, d1)ࢅ(c2, d2)ă੗९Lj
एᇀMMSE‫ڦ‬໙݆‫ڪ‬ၳᇀ‫ܔ‬ኄෙ߲े඄ೝ਩‫ܸۅ‬ჾ‫ڦ‬ঢ়‫ۆ‬
ෙ‫ۅ‬໙݆ă
Rev. 0 | Page 6 of 12
(c1 − c2 )(a0 − a2 )− (c0 − c2 )(a1 − a2 )
k
b.0 (a2c1 − a1c2 )+ b1 (a0c2 − a2c0 )+ b2 (a1c0 − a0c1
k
(d 0 − d 2 )(b1 − b2 )− (d1 − d 2 )(b0 − b2 )
k
(d1 − d 2 )(a0 − a2 )− (d 0 − d 2 )(a1 − a2 )
k
b.0 (a2 d1 − a1d 2 )+ b1 (a0 d 2 − a2 d 0 )+ b2 (a1d 0 − a0 d1 )
k
ሞኟ‫֡׉‬ፕዐLj૧ᆩၯጚဣຕ(KX, KY)ࢅူଚ‫ײݛ‬๕
ऺ໙P’(x’, y’)‫ڦ‬ၯጚ‫ۅ‬ă
⎧ x = KX 1 x ' + KX 2 y ' + KX 3
⎨
'
'
⎩ y = KY1 x + KY2 y + KY3
)
AN-1021
ᆌᆩԴऻ
๖૩
থူઠ‫ڦ‬ෙ߲ํᄓ‫ݴ‬՚֑ᆩঢ়‫ۆ‬ෙ‫ۅ‬໙݆ĂएᇀMMSE‫ڦ‬࿵
‫ۅ‬໙݆ࢅएᇀMMSE‫ڦ‬৵‫ۅ‬໙݆ǖ
1
2
3
ঢ়‫ۆ‬ෙ‫ۅ‬໙݆჋ስෙ߲֖ቷ‫ۅ‬Ljन཮2ዐ‫ۅڦ‬1Ă‫ۅ‬6ࢅ‫!ۅ‬
8ă၎ᆌ‫ڦ‬ၯጚဣຕྺǖ
KX1=+1.011238LjKX2=−0.003952LjKX3=−24.638760
KY1=+0.009894LjKY2=+1.005168LjKY3=−130.112700
૧ᆩᅜฉဣຕLjၯጚࢫ‫ڦ‬঳ࡕଚᇀ՗1ዐă
एᇀMMSE‫ڦ‬࿵‫ۅ‬໙݆჋ስ࿵߲֖ቷ‫ۅ‬Ljन཮2ዐ‫!ۅڦ‬
1Ă‫ۅ‬3Ă‫ۅ‬5Ă‫ۅ‬7ࢅ‫ۅ‬9ă၎ᆌ‫ڦ‬ၯጚဣຕྺǖ
KX1= +1.009899, KX2 = −0.002260, KX3 = −23.715720
KY1=+0.008494, KY2= +1.006247, KY3 = −121.821000
૧ᆩᅜฉဣຕLjၯጚࢫ‫ڦ‬঳ࡕଚᇀ՗2ዐă
एᇀMMSE‫ڦ‬৵‫ۅ‬໙݆჋ስ৵߲֖ቷ‫ۅ‬Ljन཮2ዐ‫!ۅڦ‬
1Ă‫ۅ‬2Ă‫ۅ‬3Ă‫ۅ‬4Ă‫ۅ‬5Ă‫ۅ‬6Ă‫ۅ‬7Ă‫ۅ‬8ࢅ‫ۅ‬9ă၎ᆌ‫!ڦ‬
ၯጚဣຕྺǖ
KX1= +1.011161, KX2 = −0.001887, KX3 = −25.777180
KY1=+0.009718, KY2= +1.006107, KY3 = −126.258100
૧ᆩᅜฉဣຕLjၯጚࢫ‫ڦ‬঳ࡕଚᇀ՗3ዐă
!
5
6
7
8
9
!
!
!
08183-002
4
཮ 2. ჋ስ֖ቷ‫ۅ‬
ස཮2໯๖Ljٗ‫ة‬ఄೡฉ჋ስକ৵߲‫ۅ‬ăഄ૙ၙፖՔྺ
(3931, 3849)Ă(2047, 3849)Ă(164, 3849)Ă(3931, 2047)Ă
(2047, 2047)Ă(164, 2047)Ă(3931, 246)Ă(2047, 246) ࢅ (164,
246)ă‫ة‬ఄೡׂิ‫ܔڦ‬ᆌ֑ᄣፖՔྺ(3927, 3920)Ă(2054,
3936)Ă(193, 3943)Ă(3911, 2119)Ă(2054, 2127)Ă(195,
2164)Ă(3915, 331)Ă(2050, 354)ࢅ(189, 371)ă၂඗Lj૙ၙፖ
Քᇑ‫ܔ‬ᆌ‫֑ڦ‬ᄣፖՔኮक़٪ሞट‫ڦٷ‬ဃֶă
!
!
!
!
!
՗1. ঢ়‫ۆ‬ෙ‫ۅ‬໙݆‫ڦ‬঳ࡕ
Point (X, Y)
૙ၙፖՔ
֑ᄣፖՔ
ၯጚፖՔ
ဃֶ
ဃֶೝ‫ࢅݛ‬
1
(3931, 3849)
(3927, 3920)
(3931, 3849)
(0, 0)
(276, 650)
2
(2047, 3849)
(2054, 3936)
(2037, 3846)
(−10, −3)
3
(164, 3849)
(193, 3943)
(155, 3835)
(−9, −14 )
4
(3931, 2047)
(3911, 2119)
(3922, 2039)
(−9, −8 )
5
(2047, 2047)
(2054, 2127)
(2044, 2028)
(−3, −19 )
6
(164, 2047)
(195, 2164)
(164, 2047)
(0, 0)
7
(3931, 246)
(3915, 331)
(3933, 242)
(+2, −4 )
8
(2047, 246)
(2050, 354)
(2047, 246)
(0, 0)
9
(164, 246)
(189, 371)
(165, 244)
(+1, −2)
1
2
3
4
5
6
7
8
9
(3931, 3849)
(3927, 3920)
(3933, 3856)
(2, 7)
(159, 418)
(2047, 3849)
(2054, 3936)
(2042, 3856)
(−5, +7)
(164, 3849)
(193, 3943)
(162, 3847)
(−2, −2 )
(3931, 2047)
(3911, 2119)
(3921, 2044)
(−10, −3 )
(2047, 2047)
(2054, 2127)
(2046, 2036)
(−1, −11)
(164, 2047)
(195, 2164)
(168, 2057)
(4, 10)
(3931, 246)
(3915, 331)
(3929, 245)
(−2, −1)
(2047, 246)
(2050, 354)
(2046, 252)
(−1, +6)
(164, 246)
(189, 371)
(166, 253)
(+2, +7)
1
2
3
4
5
6
7
8
9
(3931, 3849)
(3927, 3920)
(3938, 3856)
(7, 7)
(110, 363)
(2047, 3849)
(2054, 3936)
(2044, 3854)
(−3, +5)
(164, 3849)
(193, 3943)
(162, 3842)
(−2, −7)
(3931, 2047)
(3911, 2119)
(3925, 2044)
(−6, −3)
(2047, 2047)
(2054, 2127)
(2047, 2034)
(0, −13)
(164, 2047)
(195, 2164)
(167, 2053)
(3, 6)
(3931, 246)
(3915, 331)
(3932, 245)
(+1, −1)
(2047, 246)
(2050, 354)
(2046, 250)
(−1, +4)
(164, 246)
(189, 371)
(165, 249)
(+1,+3)
՗2. एᇀMMSE‫ڦ‬࿵‫ۅ‬໙݆‫ڦ‬঳ࡕ
Point (X, Y˅
૙ၙፖՔ
֑ᄣፖՔ
ၯጚፖՔ
ဃֶ
ဃֶೝ‫ࢅݛ‬
՗3. एᇀMMSE‫ڦ‬৵‫ۅ‬໙݆‫ڦ‬঳ࡕ
Point (X, Y˅
૙ၙፖՔ
֑ᄣፖՔ
ၯጚፖՔ
ဃֶ
ဃֶೝ‫ࢅݛ‬
Rev. 0 | Page 7 of 12
AN-1021
ᆌᆩԴऻ
঳ஃ!
‫پ‬ஓኴႜ!
සമຎํᄓ঳ࡕ໯๖Lj࿮ஃ֑ᆩనዖၯጚ໙݆LjၯጚፖՔ
਩ᇺᇺᆫᇀ኱থ֑ᄣፖՔăଷྔLjཚࡗԲডෙዖํᄓLj੗
‫؜ڥ‬ᅜူ঳ஃ
ᅜCᇕჾՊႀ‫ڦ‬ၯጚ໙݆‫پ‬ஓ९“Պஓ”և‫ݴ‬ăᆶෙ߲֖ቷ
‫้ۅ‬Lj‫پ‬ஓኴႜঢ়‫ۆ‬ෙ‫ۅ‬ၯጚ໙݆ăᆶෙ߲ᅜฉ‫֖ڦ‬ቷ‫ۅ‬
้Lj‫پ‬ஓኴႜएᇀMMSE‫ۅܠڦ‬ၯጚ໙݆ă‫پ‬ஓᅙཚࡗ
ADuC7026֪๬)ADuC7026๟ADIࠅິ‫؜‬೗‫ڦ‬ᅃ੼MCUׂ
೗*ăෙ߲๖૩ํᄓ‫ڦ‬঳ࡕ਩֑ᆩ޿‫پ‬ஓऺ໙‫ڟڥ‬ă
!
!
!
!
!
!
!
!
!
!
ঢ়‫ۆ‬ෙ‫ۅ‬ၯጚ໙݆ᆶዺᇀॽෙ߲֖ቷ‫ۅ‬ၯጚ‫ڟ‬૙ၙ࿋!
ዃăଷྔLj‫ܔ‬ᇀ੍ৎෙ߲֖ቷ‫ۅڦۅ‬LjഄႠీ՗၄‫!ݥ‬
‫ࡻ׉‬ă඗ܸLj‫ܔ‬ᇀփሞ֖ቷ‫޹ۅ‬ৎ‫ۅڦ‬Ljঢ়‫ۆ‬ෙ‫ۅ‬ၯ!
ጚ໙݆‫ڦ‬՗၄փฯ૙ၙăኄዖ໙݆‫ڦ‬ဃֶೝ‫ࢅݛ‬๟֪!
๬໯ᆩෙዖ໙݆ዐፌ‫ڦٷ‬ăᅺُLj‫ܔ‬ᇀ‫ة‬ఄೡ؅٫၎!
‫ܔ‬ড‫ڦٷ‬ᆌᆩLjঢ়‫ۆ‬ෙዖၯጚ໙݆ժ‫ڦࡻݥ‬჋ስă
‫ܔ‬ᇀగၵ‫)ۅ‬থৎ֖ቷ‫*ۅڦۅ‬LjएᇀMMSE‫ۅܠڦ‬ၯ!
ጚ໙݆‫ڦ‬՗၄փසঢ়‫ۆ‬ෙ‫ۅ‬ၯጚ໙݆ă඗ܸLj৽ኝ߲!
‫ة‬ఄೡઠੂLjएᇀMMSE‫ۅܠڦ‬ၯጚ໙݆‫ڦ‬ဃֶೝ‫!ݛ‬
ࢅၭᇀঢ়‫ۆ‬ෙ‫ۅ‬໙݆Ljᅺྺ໲૧ᆩକෙ߲ᅜฉ֖ቷ‫!ۅ‬
‫ڦ‬႑တăᅺܸLjጺ༹ܸჾLjഄႠీᆫᇀঢ়‫ۆ‬ෙ‫ۅ‬໙݆ă
‫ܔ‬ᇀएᇀMMSE‫ۅܠڦ‬ၯጚ໙݆Lj๑ᆩ‫֖ڦ‬ቷ‫ۅ‬ሁ!
‫ܠ‬LjႠీሁॅă
ํᄓ঳ࡕᇑຕბླྀ‫ڞ‬၎‫ࢇޙ‬ă
Rev. 0 | Page 8 of 12
AN-1021
ᆌᆩԴऻ
Պஓ
#define N
algorithm
9
// number of reference points for calibration
signed short int ReferencePoint[N][2];
// ideal position of reference points
signed short int SamplePoint[N][2];
// sampling position of reference points
double KX1, KX2, KX3, KY1, KY2, KY3;
// coefficients for calibration algorithm
void Do_Calibration(signed short int *Px, signed short int *Py) // do calibration for point
(Px, Py) using the calculated coefficients
{
*Px=(signed short int)(KX1*(*Px)+KX2*(*Py)+KX3+0.5);
*Py=(signed short int)(KY1*(*Px)+KY2*(*Py)+KY3+0.5);
}
int Get_Calibration_Coefficient()
algorithm: KX1, KX2, KX3, KY1, KY2, KY3
// calculate the coefficients for calibration
{
int i;
int Points=N;
double a[3],b[3],c[3],d[3],k;
if(Points<3)
{
return 0;
}
else
{
if(Points==3)
{
for(i=0; i<Points; i++)
{
a[i]=(double)(SamplePoint[i][0]);
b[i]=(double)(SamplePoint[i][1]);
c[i]=(double)(ReferencePoint[i][0]);
d[i]=(double)(ReferencePoint[i][1]);
}
}
else if(Points>3)
{
for(i=0; i<3; i++)
{
a[i]=0;
b[i]=0;
c[i]=0;
d[i]=0;
}
for(i=0; i<Points; i++)
Rev. 0 | Page 9 of 12
AN-1021
ᆌᆩԴऻ
{
a[2]=a[2]+(double)(SamplePoint[i][0]);
b[2]=b[2]+(double)(SamplePoint[i][1]);
c[2]=c[2]+(double)(ReferencePoint[i][0]);
d[2]=d[2]+(double)(ReferencePoint[i][1]);
a[0]=a[0]+(double)(SamplePoint[i][0])*(double)(SamplePoint[i][0]);
a[1]=a[1]+(double)(SamplePoint[i][0])*(double)(SamplePoint[i][1]);
b[0]=a[1];
b[1]=b[1]+(double)(SamplePoint[i][1])*(double)(SamplePoint[i][1]);
c[0]=c[0]+(double)(SamplePoint[i][0])*(double)(ReferencePoint[i][0]);
c[1]=c[1]+(double)(SamplePoint[i][1])*(double)(ReferencePoint[i][0]);
d[0]=d[0]+(double)(SamplePoint[i][0])*(double)(ReferencePoint[i][1]);
d[1]=d[1]+(double)(SamplePoint[i][1])*(double)(ReferencePoint[i][1]);
}
a[0]=a[0]/a[2];
a[1]=a[1]/b[2];
b[0]=b[0]/a[2];
b[1]=b[1]/b[2];
c[0]=c[0]/a[2];
c[1]=c[1]/b[2];
d[0]=d[0]/a[2];
d[1]=d[1]/b[2];
a[2]=a[2]/Points;
b[2]=b[2]/Points;
c[2]=c[2]/Points;
d[2]=d[2]/Points;
}
k=(a[0]-a[2])*(b[1]-b[2])-(a[1]-a[2])*(b[0]-b[2]);
KX1=((c[0]-c[2])*(b[1]-b[2])-(c[1]-c[2])*(b[0]-b[2]))/k;
KX2=((c[1]-c[2])*(a[0]-a[2])-(c[0]-c[2])*(a[1]-a[2]))/k;
KX3=(b[0]*(a[2]*c[1]-a[1]*c[2])+b[1]*(a[0]*c[2]-a[2]*c[0])+b[2]*(a[1]*c[0]a[0]*c[1]))/k;
KY1=((d[0]-d[2])*(b[1]-b[2])-(d[1]-d[2])*(b[0]-b[2]))/k;
KY2=((d[1]-d[2])*(a[0]-a[2])-(d[0]-d[2])*(a[1]-a[2]))/k;
KY3=(b[0]*(a[2]*d[1]-a[1]*d[2])+b[1]*(a[0]*d[2]-a[2]*d[0])+b[2]*(a[1]*d[0]a[0]*d[1]))/k;
return Points;
}
}
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AN-1021
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֖੊࿔၅
Vidales, Carlos E. “How to Calibrate Touch Screens, Embedded Systems Design.”Embedded.com, May 31, 2002. Embedded Systems
Design.May 27, 2009.
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AN-1021
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©2009 Analog Devices, Inc. All rights reserved. Trademarks and
registered trademarks are the property of their respective owners.
AN08183-0-7/09(0)
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