高質(zhì)量的快速圖像縮放――二次線性插值和三次卷積插值

1、高質(zhì)量的快速的圖像縮放二次線性插值和三次卷積插值限制條件:為了便于討論，這里只處理32bit的ARGB顏色;代碼使用C+;涉及到匯編優(yōu)化的時(shí)候假定為x86平臺;使用的編譯器為vc2005;為了代碼的可讀性,沒有加入異常處理代碼;測試使用的CPU為AMD64x2 4200+(2.37G) 和 Intel Core2 4400(2.00G);速度測試說明:只測試內(nèi)存數(shù)據(jù)到內(nèi)存數(shù)據(jù)的縮放測試圖片都是800*600縮放到1024*768; fps表示每秒鐘的幀數(shù),值越大表示函數(shù)越快A: 近鄰取樣插值、二次線性插值、三次卷積插值 縮放效果對比 原圖 近鄰取樣縮放到0.6倍 近鄰取樣縮放到1.6倍 二次線

2、性插值縮放到0.6倍 二次線性插值縮放到1.6倍 三次卷積插值縮放到0.6倍 三次卷積插值縮放到1.6倍 原圖 近鄰取樣縮放到8倍 二次線性插值縮放到8倍 三次卷積插值縮放到8倍 二次線性插值(近似公式)近鄰取樣插值縮放簡單、速度快，但很多時(shí)候縮放出的圖片質(zhì)量比較差(特別是對于人物、景色等)，圖片的縮放有比較明顯的鋸齒；使用二次或更高次插值有利于改善縮放效果；B: 首先定義圖像數(shù)據(jù)結(jié)構(gòu):#define asm _asmtypedef unsigned char TUInt8; / 0.255struct TARGB32 /32 bit color TUInt8 b,g,r,a; /a is a

3、lpha;struct TPicRegion /一塊顏色數(shù)據(jù)區(qū)的描述，便于參數(shù)傳遞 TARGB32* pdata; /顏色數(shù)據(jù)首地址 long byte_width; /一行數(shù)據(jù)的物理寬度(字節(jié)寬度)； /abs(byte_width)有可能大于等于width*sizeof(TARGB32); long width; /像素寬度 long height; /像素高度;/那么訪問一個(gè)點(diǎn)的函數(shù)可以寫為：inline TARGB32& Pixels(const TPicRegion& pic,const long x,const long y) return ( (TARGB32*)(TUInt8*

4、)pic.pdata+pic.byte_width*y) )x;二次線性差值C: 二次線性插值縮放原理和公式圖示: 縮放后圖片 原圖片 (寬DW,高DH) (寬SW,高SH)縮放映射原理: (Sx-0)/(SW-0)=(Dx-0)/(DW-0) (Sy-0)/(SH-0)=(Dy-0)/(DH-0) = Sx=Dx*SW/DW Sy=Dy*SH/DH聚焦看看(Sx,Sy)坐標(biāo)點(diǎn)(Sx,Sy為浮點(diǎn)數(shù))附近的情況； 對于近鄰取樣插值的縮放算法，直接取Color0顏色作為縮放后點(diǎn)的顏色；二次線性插值需要考慮(Sx,Sy)坐標(biāo)點(diǎn)周圍的4個(gè)顏色值Color0Color1Color2Color3，把(Sx

5、,Sy)到ABCD坐標(biāo)點(diǎn)的距離作為系數(shù)來把4個(gè)顏色混合出縮放后點(diǎn)的顏色；(u=Sx-floor(Sx); v=Sy-floor(Sy); 說明:floor函數(shù)的返回值為小于等于參數(shù)的最大整數(shù) ) 二次線性插值公式為: tmpColor0=Color0*(1-u) + Color2*u; tmpColor1=Color1*(1-u) + Color3*u; DstColor =tmpColor0*(1-v) + tmpColor2*v; 展開公式為: pm0=(1-u)*(1-v); pm1=v*(1-u); pm2=u*(1-v); pm3=u*v; 則顏色混合公式為: DstColor =

6、Color0*pm0 + Color1*pm1 + Color2*pm2 + Color3*pm3;參數(shù)函數(shù)圖示：二次線性插值函數(shù)圖示對于上面的公式，它將圖片向右下各移動(dòng)了半個(gè)像素，需要對此做一個(gè)修正；= Sx=(Dx+0.5)*SW/DW-0.5; Sy=(Dy+0.5)*SH/DH-0.5;而實(shí)際的程序,還需要考慮到邊界(訪問源圖片可能超界)對于算法的影響,邊界的處理可能有各種方案(不處理邊界或邊界回繞或邊界飽和或邊界映射或用背景顏色混合等;文章中默認(rèn)使用邊界飽和來處理超界);比如: 邊界飽和函數(shù): /訪問一個(gè)點(diǎn)的函數(shù)，(x,y)坐標(biāo)可能超出圖片邊界； /邊界處理模式:邊界飽和inline

7、 TARGB32 Pixels_Bound(const TPicRegion& pic,long x,long y) /assert(pic.width0)&(pic.height0); bool IsInPic=true; if (x=pic.width ) x=pic.width -1; IsInPic=false; if (y=pic.height) y=pic.height-1; IsInPic=false; TARGB32 result=Pixels(pic,x,y);if (!IsInPic) result.a=0;return result;D: 二次線性插值縮放算法的一個(gè)參考實(shí)

8、現(xiàn)：PicZoom_BilInear0該函數(shù)并沒有做什么優(yōu)化，只是一個(gè)簡單的浮點(diǎn)實(shí)現(xiàn)版本；inline void Bilinear0(const TPicRegion& pic,float fx,float fy,TARGB32* result) long x=(long)fx; if (xfx) -x; /x=floor(fx); long y=(long)fy; if (yfy) -y; /y=floor(fy); TARGB32 Color0=Pixels_Bound(pic,x,y); TARGB32 Color2=Pixels_Bound(pic,x+1,y); TARGB32 Co

9、lor1=Pixels_Bound(pic,x,y+1); TARGB32 Color3=Pixels_Bound(pic,x+1,y+1); float u=fx-x; float v=fy-y; float pm3=u*v; float pm2=u*(1-v); float pm1=v*(1-u); float pm0=(1-u)*(1-v); result-a=(pm0*Color0.a+pm1*Color1.a+pm2*Color2.a+pm3*Color3.a); result-r=(pm0*Color0.r+pm1*Color1.r+pm2*Color2.r+pm3*Color3.

10、r); result-g=(pm0*Color0.g+pm1*Color1.g+pm2*Color2.g+pm3*Color3.g); result-b=(pm0*Color0.b+pm1*Color1.b+pm2*Color2.b+pm3*Color3.b); void PicZoom_Bilinear0(const TPicRegion& Dst,const TPicRegion& Src) if ( (0=Dst.width)|(0=Dst.height) |(0=Src.width)|(0=Src.height) return; unsigned long dst_width=Dst.

11、width; TARGB32* pDstLine=Dst.pdata; for (unsigned long y=0;yDst.height;+y) float srcy=(y+0.)*Src.height/Dst.height-0.5; for (unsigned long x=0;x16; long y=y_1616; TARGB32 Color0=Pixels_Bound(pic,x,y); TARGB32 Color2=Pixels_Bound(pic,x+1,y); TARGB32 Color1=Pixels_Bound(pic,x,y+1); TARGB32 Color3=Pixe

12、ls_Bound(pic,x+1,y+1); unsigned long u_8=(x_16 & 0xFFFF)8; unsigned long v_8=(y_16 & 0xFFFF)8; unsigned long pm3_16=(u_8*v_8); unsigned long pm2_16=(u_8*(unsigned long)(255-v_8); unsigned long pm1_16=(v_8*(unsigned long)(255-u_8); unsigned long pm0_16=(255-u_8)*(255-v_8); result-a=(pm0_16*Color0.a+p

13、m1_16*Color1.a+pm2_16*Color2.a+pm3_16*Color3.a)16); result-r=(pm0_16*Color0.r+pm1_16*Color1.r+pm2_16*Color2.r+pm3_16*Color3.r)16); result-g=(pm0_16*Color0.g+pm1_16*Color1.g+pm2_16*Color2.g+pm3_16*Color3.g)16); result-b=(pm0_16*Color0.b+pm1_16*Color1.b+pm2_16*Color2.b+pm3_16*Color3.b)16); void PicZoo

14、m_Bilinear1(const TPicRegion& Dst,const TPicRegion& Src) if ( (0=Dst.width)|(0=Dst.height) |(0=Src.width)|(0=Src.height) return; long xrIntFloat_16=(Src.width)16)/Dst.width+1; long yrIntFloat_16=(Src.height)16)/Dst.height+1; const long csDErrorX=-(11); const long csDErrorY=-(11); unsigned long dst_w

15、idth=Dst.width; TARGB32* pDstLine=Dst.pdata; long srcy_16=csDErrorY; long y; for (y=0;yDst.height;+y) long srcx_16=csDErrorX; for (unsigned long x=0;xdst_width;+x) Bilinear1(Src,srcx_16,srcy_16,&pDstLinex); /border srcx_16+=xrIntFloat_16; srcy_16+=yrIntFloat_16; (TUInt8*&)pDstLine)+=Dst.byte_width;

16、/速度測試:/=/ PicZoom_BilInear1 17.7 fps/F: 邊界訪問超界的問題二次線性插值需要考略邊界訪問超界的問題，我們可以將邊界區(qū)域和內(nèi)部區(qū)域分開處理，這樣就可以優(yōu)化內(nèi)部的插值實(shí)現(xiàn)函數(shù)了：比如不需要判斷訪問超界、減少顏色數(shù)據(jù)復(fù)制、減少一些不必要的重復(fù)坐標(biāo)計(jì)算等等inline void Bilinear2_Fast(TARGB32* PColor0,TARGB32* PColor1,unsigned long u_8,unsigned long v_8,TARGB32* result) unsigned long pm3_16=u_8*v_8; unsigned long

17、 pm2_16=(u_88)-pm3_16; unsigned long pm1_16=(v_88)-pm3_16; unsigned long pm0_16=(1a=(pm0_16*PColor00.a+pm2_16*PColor01.a+pm1_16*PColor10.a+pm3_16*PColor11.a)16); result-r=(pm0_16*PColor00.r+pm2_16*PColor01.r+pm1_16*PColor10.r+pm3_16*PColor11.r)16); result-g=(pm0_16*PColor00.g+pm2_16*PColor01.g+pm1_1

18、6*PColor10.g+pm3_16*PColor11.g)16); result-b=(pm0_16*PColor00.b+pm2_16*PColor01.b+pm1_16*PColor10.b+pm3_16*PColor11.b)16); inline void Bilinear2_Border(const TPicRegion& pic,const long x_16,const long y_16,TARGB32* result) long x=(x_1616); long y=(y_1616); unsigned long u_16=(unsigned short)(x_16);

19、unsigned long v_16=(unsigned short)(y_16); TARGB32 pixel4; pixel0=Pixels_Bound(pic,x,y); pixel1=Pixels_Bound(pic,x+1,y); pixel2=Pixels_Bound(pic,x,y+1); pixel3=Pixels_Bound(pic,x+1,y+1); Bilinear2_Fast(&pixel0,&pixel2,u_168,v_168,result); void PicZoom_Bilinear2(const TPicRegion& Dst,const TPicRegion

20、& Src) if ( (0=Dst.width)|(0=Dst.height) |(0=Src.width)|(0=Src.height) return; long xrIntFloat_16=(Src.width)16)/Dst.width+1; long yrIntFloat_16=(Src.height)16)/Dst.height+1; const long csDErrorX=-(11); const long csDErrorY=-(11); unsigned long dst_width=Dst.width; /計(jì)算出需要特殊處理的邊界 long border_y0=-csDE

21、rrorY/yrIntFloat_16+1; /y0+y*yr=0; y0=csDErrorY = y=-csDErrorY/yr if (border_y0=Dst.height) border_y0=Dst.height; long border_x0=-csDErrorX/xrIntFloat_16+1; if (border_x0=Dst.width ) border_x0=Dst.width; long border_y1=(Src.height-2)16)-csDErrorY)/yrIntFloat_16+1; /y0+y*yr y=(height-2-csDErrorY)/yr

22、if (border_y1border_y0) border_y1=border_y0; long border_x1=(Src.width-2)16)-csDErrorX)/xrIntFloat_16+1; if (border_x1border_x0) border_x1=border_x0; TARGB32* pDstLine=Dst.pdata; long Src_byte_width=Src.byte_width; long srcy_16=csDErrorY; long y; for (y=0;yborder_y0;+y) long srcx_16=csDErrorX; for (

23、unsigned long x=0;xdst_width;+x) Bilinear2_Border(Src,srcx_16,srcy_16,&pDstLinex); /border srcx_16+=xrIntFloat_16; srcy_16+=yrIntFloat_16; (TUInt8*&)pDstLine)+=Dst.byte_width; for (y=border_y0;yborder_y1;+y) long srcx_16=csDErrorX; long x; for (x=0;x8; TARGB32* PSrcLineColor= (TARGB32*)(TUInt8*)(Src

24、.pdata)+Src_byte_width*(srcy_1616) ; for (unsigned long x=border_x0;x16; TARGB32* PColor1=(TARGB32*)(TUInt8*)(PColor0)+Src_byte_width); Bilinear2_Fast(PColor0,PColor1,(srcx_16 & 0xFFFF)8,v_8,&pDstLinex); srcx_16+=xrIntFloat_16; for (x=border_x1;xdst_width;+x) Bilinear2_Border(Src,srcx_16,srcy_16,&pD

25、stLinex);/border srcx_16+=xrIntFloat_16; srcy_16+=yrIntFloat_16; (TUInt8*&)pDstLine)+=Dst.byte_width; for (y=border_y1;yDst.height;+y) long srcx_16=csDErrorX; for (unsigned long x=0;x=2;SH=2)證明這個(gè)公式不會造成內(nèi)存訪問超界: 要求Dx=DW-1時(shí): sx+1=int( (dw-1)/dw*(dw-1) ) +1 = (sw-1) 有: int( (sw-1)*(dw-1)/dw ) =sw-2 (sw-1

26、)*(dw-1)/dw (sw-1) (dw-1) /dw1 (dw-1) Src.width)|(2Src.height) return; long xrIntFloat_16=(Src.width-1)16)/Dst.width; long yrIntFloat_16=(Src.height-1)16)/Dst.height; unsigned long dst_width=Dst.width; long Src_byte_width=Src.byte_width; TARGB32* pDstLine=Dst.pdata; long srcy_16=0; for (unsigned lon

27、g y=0;y8; TARGB32* PSrcLineColor= (TARGB32*)(TUInt8*)(Src.pdata)+Src_byte_width*(srcy_1616) ; long srcx_16=0; for (unsigned long x=0;x16; Bilinear_Fast_Common(PColor0,(TARGB32*)(TUInt8*)(PColor0)+Src_byte_width),(srcx_16 & 0xFFFF)8,v_8,&pDstLinex); srcx_16+=xrIntFloat_16; srcy_16+=yrIntFloat_16; (TU

28、Int8*&)pDstLine)+=Dst.byte_width; G: 模擬單指令多數(shù)據(jù)處理利用單指令多數(shù)據(jù)處理的MMX指令一般都可以加快顏色的運(yùn)算；在使用MMX改寫之前，利用32bit寄存器(或變量)來模擬單指令多數(shù)據(jù)處理；數(shù)據(jù)儲存原理:一個(gè)顏色數(shù)據(jù)分量只有一個(gè)字節(jié),用2個(gè)字節(jié)來儲存單個(gè)顏色分量的計(jì)算結(jié)果，對于很多顏色計(jì)算來說精度就夠了；那么一個(gè)32bit寄存器(或變量)就可以儲存2個(gè)計(jì)算出的臨時(shí)顏色分量；從而達(dá)到了單個(gè)指令兩路數(shù)據(jù)處理的目的;單個(gè)指令兩路數(shù)據(jù)處理的計(jì)算:乘法： (0x00AA*a)16) | (0x00BB*a) = 0x00AA00BB * a可見只要保證0x00AA*

29、a和0x00BB*a都小于(116)那么乘法可以直接使用無符號數(shù)乘法了加法: (0x00AA+0x00CC)16) | (0x00BB+0x00DD) = 0x00AA00BB + 0x00CC00DD可見只要0x00AA+0x00CC和0x00BB+0x00DD小于(18; unsigned long pm2_8=u_8-pm3_8; unsigned long pm1_8=v_8-pm3_8; unsigned long pm0_8=256-pm1_8-pm2_8-pm3_8; unsigned long Color=*(unsigned long*)(PColor0); unsigned

30、 long BR=(Color & 0x00FF00FF)*pm0_8; unsigned long GA=(Color & 0xFF00FF00)8)*pm0_8; Color=(unsigned long*)(PColor0)1; GA+=(Color & 0xFF00FF00)8)*pm2_8; BR+=(Color & 0x00FF00FF)*pm2_8; Color=*(unsigned long*)(PColor1); GA+=(Color & 0xFF00FF00)8)*pm1_8; BR+=(Color & 0x00FF00FF)*pm1_8; Color=(unsigned

31、long*)(PColor1)1; GA+=(Color & 0xFF00FF00)8)*pm3_8; BR+=(Color & 0x00FF00FF)*pm3_8; *(unsigned long*)(result)=(GA & 0xFF00FF00)|(BR & 0xFF00FF00)8); inline void Bilinear_Border_Common(const TPicRegion& pic,const long x_16,const long y_16,TARGB32* result) long x=(x_1616); long y=(y_1616); unsigned lo

32、ng u_16=(unsigned short)(x_16); unsigned long v_16=(unsigned short)(y_16); TARGB32 pixel4; pixel0=Pixels_Bound(pic,x,y); pixel1=Pixels_Bound(pic,x+1,y); pixel2=Pixels_Bound(pic,x,y+1); pixel3=Pixels_Bound(pic,x+1,y+1); Bilinear_Fast_Common(&pixel0,&pixel2,u_168,v_168,result); void PicZoom_Bilinear_C

33、ommon(const TPicRegion& Dst,const TPicRegion& Src) if ( (0=Dst.width)|(0=Dst.height) |(0=Src.width)|(0=Src.height) return; long xrIntFloat_16=(Src.width)16)/Dst.width+1; long yrIntFloat_16=(Src.height)16)/Dst.height+1; const long csDErrorX=-(11); const long csDErrorY=-(11); unsigned long dst_width=D

34、st.width; /計(jì)算出需要特殊處理的邊界 long border_y0=-csDErrorY/yrIntFloat_16+1; /y0+y*yr=0; y0=csDErrorY = y=-csDErrorY/yr if (border_y0=Dst.height) border_y0=Dst.height; long border_x0=-csDErrorX/xrIntFloat_16+1; if (border_x0=Dst.width ) border_x0=Dst.width; long border_y1=(Src.height-2)16)-csDErrorY)/yrIntFlo

35、at_16+1; /y0+y*yr y=(height-2-csDErrorY)/yr if (border_y1border_y0) border_y1=border_y0; long border_x1=(Src.width-2)16)-csDErrorX)/xrIntFloat_16+1; if (border_x1border_x0) border_x1=border_x0; TARGB32* pDstLine=Dst.pdata; long Src_byte_width=Src.byte_width; long srcy_16=csDErrorY; long y; for (y=0;

36、yborder_y0;+y) long srcx_16=csDErrorX; for (unsigned long x=0;xdst_width;+x) Bilinear_Border_Common(Src,srcx_16,srcy_16,&pDstLinex); /border srcx_16+=xrIntFloat_16; srcy_16+=yrIntFloat_16; (TUInt8*&)pDstLine)+=Dst.byte_width; for (y=border_y0;yborder_y1;+y) long srcx_16=csDErrorX; long x; for (x=0;x8; TARGB32* PSrcLineColor= (TARGB32*)(TUInt8*)(Src.pdata)+Src_byte_width*(srcy_1616) ; for (unsigned long x=border_x0;x16; TARGB32* PColor1=(TARGB32*)(TUInt8*)(PColor0)+Src_byte_width); Bilinear_Fast_Common(PColor0,PColor1,(srcx_16 & 0x