1、双线性插值法W(x)=1-(x),0≤[x≤1卷积核是一个三角形函数Y2y@02X.1AAy10W(x)P?2b+0
1、双线性插值法 W(x) =1−(x), 0 x 1 卷积核是一个三角形函数
1、双线性插值法A(x/4.y/4)=-?A(a+1,b+1)A(a,b+1)A(a,b)(xy)(a,b+1)(a+1,b+1)(x/4.y/4)A(atr.b)坐标映射(a,b)(a+1,b)原图像A放大后的图像B
1、双线性插值法
双线性插值法示意图YJ1J21112aX14y4x1- 4yp1-4xX222b21X
11 12 21 22 p Y X y1 y2 a b y 1- y x 1- x x2 x1 双线性插值法示意图
22ZZI(P)=I(i,j)*W(i,j)i-lIuWW1212IVW.W.1222122W =W(x,)W(y); Wiz =W(x,)W(y2)W(x)=1-△x; W(x,)=Ax; W(y)=1-Ay; W(y2)=AyAx= x-INT(x) △y= y-INT()I(P)= Wi./ +Wi2l12 +W21/21 +W22l2122=(1-Ax)(1- Ay)lu +(1-Ax)Ayl12 + △x(1-Ay)/21 +△xAy/22
= = = 2 1 2 1 ( ) ( , ) ( , ) i j I P I i j W i j = 21 22 11 12 I I I I I = 21 22 11 12 W W W W W ( ) ( ); ( ) ( ) 11 1 1 12 1 2 W =W x W y W =W x W y W(x ) =1−x ; W(x ) = x ; W(y ) =1−y ; W(y ) = y 1 2 1 2 x = x − INT(x) y = y − INT( y) 1 1 1 2 2 1 2 2 1 1 1 1 1 2 1 2 2 1 2 1 2 2 2 2 (1 )(1 ) (1 ) (1 ) ( ) x y I x yI x y I x yI I P W I W I W I W I = − − + − + − + = + + +
2、双三次卷积法·卷积核可以利用三次样条函数W(x)=1-2x2 +[xl3,01W2(x)=4-8+5x2-x,1≤x≤22≤Ws(x) = 0,yyXx,11121314X222:4x 232124Ay0W(x)X31323334X44414243x
2、双三次卷积法 • 卷积核可以利用三次样条函数 = = − + − = − + W x x W x x x x x W x x x x ( ) 0, 2 ( ) 4 8 5 , 1 2 ( ) 1 2 , 0 1 3 2 3 2 2 3 1