图像缩放是最常用的图像处理，在图像拉伸和取得图像略图中都要用到。图像缩放质量的好坏与图像像素插值方式有关，本文定义了常用的3种插值方式，即临近插值、线性插值和双立方插值方式：

type // 插值方式: 缺省(线性插值)，临近，线性，双立方 TInterpolateMode = (imDefault, imNear, imBilinear, imBicubic);

具体的缩放及其用到的插值过程代码如下：

过程定义： // 缩放图像，Alpha不透明度，IpMode插值方式 procedure ImageScale(var Dest: TImageData; const Source: TImageData; Alpha: Single = 1.0; IpMode: TInterpolateMode = imDefault); overload; // Source分别按比例ScaleX和ScaleY缩放到Dest的(x,y)坐标，其它参数同上 procedure ImageScale(var Dest: TImageData; x, y: Integer; const Source: TImageData; ScaleX, ScaleY: Single; Alpha: Single = 1.0; IpMode: TInterpolateMode = imDefault); overload; // TGraphic对象缩放到Dest procedure ImageScale(var Dest: TImageData; const Source: TGraphic; Alpha: Single = 1.0; IpMode: TInterpolateMode = imDefault); overload; procedure ImageScale(var Dest: TImageData; x, y: Integer; const Source: TGraphic; ScaleX, ScaleY: Single; Alpha: Single = 1.0; IpMode: TInterpolateMode = imDefault); overload; procedure ImageScale(var Dest: TImageData; const Source: TGpBitmap; Alpha: Single = 1.0; IpMode: TInterpolateMode = imDefault); overload; procedure ImageScale(var Dest: TImageData; x, y: Integer; const Source: TGpBitmap; ScaleX, ScaleY: Single; Alpha: Single = 1.0; IpMode: TInterpolateMode = imDefault); overload; 代码实现： (***************************************************************************** * typedef UINT ARGB * * ARGB GetBilinearColor(int x(*256), int y(*256), void* Scan0, UINT Stride) * * * * int x0 = x / 256 * * int y0 = y / 256 * * BYTE *pScan0 = Scan0 + y0 * Stride + y0 * 4 * * BYTE c[4][4] * * c[0] = *pScan0 // (x0, y0) * * c[1] = *(pScan0 + Stride) // (x0, y0+1) * * c[2] = *(pScan0 + 4) // (x0+1, y0) * * c[3] = *(PScan0 + Stride + 4) // (x0+1, y0+1) * * int u = x & 0xff * * int v = y & 0xff * * int m0 = (255-v) * (255-u) * * int m1 = v * (255-u) * * int m2 = (255-v) * u * * int m3 = v * u * * BYTE ARGB[4] * * for (int i = 0; i < 4; i ++) * * ARGB[i] = (c[0][i]*m0 + c[1][i]*m1 + c[2][i]*m2 + c[3][i]*m3) / 65536 * *****************************************************************************) procedure GetBilinearColor; asm and edx, 255 and ecx, 255 mov eax, BilinearTable movq mm0, [esi] // mm0 = C2(x+1, y) C0(x, y) movq mm1, mm0 add esi, [ebx].TImageData.Stride // [esi] = C3(x+1, y+1) C1(x, y+1) punpcklbw mm0, [esi] // mm0 = A1 A0 R1 R0 G1 G0 B1 B0 punpckhbw mm1, [esi] // mm1 = A3 A2 R3 R2 G3 G2 B3 B2 movq mm2, mm0 movq mm3, mm1 punpcklbw mm0, mm7 // mm0 = 00 G1 00 G0 00 B1 00 B0 punpcklbw mm1, mm7 // mm1 = 00 G3 00 G2 00 B3 00 B2 punpckhbw mm2, mm7 // mm2 = 00 A1 00 A0 00 R1 00 R0 punpckhbw mm3, mm7 // mm3 = 00 A3 00 A2 00 R3 00 R2 movq mm4, [eax+edx*8] pmullw mm4, [eax+ecx*8+256*8] psrlw mm4, 1 // 先除以2，否则后面的word有符号乘法会扩展符号位 movq mm5, mm4 punpckldq mm4, mm4 // mm4 = 00 m1 00 m0 00 m1 00 m0 punpckhdq mm5, mm5 // mm5 = 00 m3 00 m2 00 m3 00 m2 pmaddwd mm0, mm4 // mm0 = G1*m1+G0*m0 B1*m1+B0*m0 pmaddwd mm1, mm5 // mm1 = G3*m3+G2*m2 B3*m3+B2*m2 pmaddwd mm2, mm4 // mm2 = A1*m1+A0*m0 R1*m1+R0*m0 pmaddwd mm3, mm5 // mm3 = A3*m3+A2*m2 R3*m3+R2*m2 paddd mm0, mm1 // mm0 = G3n+G2n+G1n+G0n B3n+B2n+B1n+B0n paddd mm2, mm3 // mm2 = A2n+A2n+A1n+A0n R3n+R2n+R1n+R0n psrld mm0, 15 // mm0 = Gn/0x8000 Bn/0x8000 psrld mm2, 15 // mm2 = An/0x8000 Rn/0x8000 packssdw mm0, mm2 // mm0 = 00 An 00 Rn 00 Gn 00 Bn packuswb mm0, mm0 // mm0 = An Rn Gn Bn An Rn Gn Bn end; procedure GetNearColor; asm movd mm0, [esi] end; procedure GetBicubicColor; procedure SumBicubic; asm movd mm1, [esi] movd mm2, [esi+4] movd mm3, [esi+8] movd mm4, [esi+12] punpcklbw mm1, mm7 punpcklbw mm2, mm7 punpcklbw mm3, mm7 punpcklbw mm4, mm7 psllw mm1, 7 psllw mm2, 7 psllw mm3, 7 psllw mm4, 7 pmulhw mm1, [edi+edx+256*8] pmulhw mm2, [edi+edx] pmulhw mm3, [edi+eax+256*8] pmulhw mm4, [edi+eax+512*8] paddsw mm1, mm2 paddsw mm3, mm4 paddsw mm1, mm3 pmulhw mm1, mm5 paddsw mm0, mm1 add esi, [ebx].TImageData.Stride end; asm push edi mov edi, BicubicTable// edi = int64 uvTable (item * 16384) and edx, 255 // u = x & 255 shl edx, 3 // edx = u * 8 mov eax, edx // eax = -edx neg eax and ecx, 255 // v = y & 255 shl ecx, 3 // ecx = v * 8 pxor mm0, mm0 movq mm5, [edi+ecx+256*8] call SumBicubic movq mm5, [edi+ecx] call SumBicubic neg ecx movq mm5, [edi+ecx+256*8] call SumBicubic movq mm5, [edi+ecx+512*8] call SumBicubic paddw mm0, mm6 // argb += 4 psraw mm0, 3 // argb /= 8 packuswb mm0, mm0 pop edi end; function GetInterpolateProc(IpMode: TInterpolateMode; var Proc: TInterpolateProc): Integer; begin case IpMode of imNear: begin Result := 1; Proc := GetNearColor; end; imBicubic: begin Result := 4; Proc := GetBicubicColor; end else begin Result := 2; Proc := GetBilinearColor; end; end; end; procedure doScale(var Dest: TImageData; const Source: TImageData; Alpha: Single; IpMode: TInterpolateMode); var x, y, Width, Height: Integer; xDelta, yDelta: Integer; Radius, dstOffset: Integer; alphaI: Integer; src: TImageData; colorProc: TInterpolateProc; asm push esi push edi push ebx mov alphaI, 256 fild dword ptr alphaI fmul dword ptr Alpha fistp dword ptr alphaI// alphaI = alpha * 256.0 fwait mov edi, eax // edi = deat mov ebx, edx // ebx = source mov eax, ecx lea edx, colorProc call GetInterpolateProc mov esi, eax lea ecx, src // src = GetExpandData(source, radius, 0xffffffff) push ecx mov ecx, -1 mov edx, eax mov eax, ebx call GetExpandData shl esi, 7 // esi = radius * 128 mov eax, [ebx].TImageData.Width shl eax, 8 xor edx, edx idiv [edi].TImageData.Width mov xDelta, eax // xDelta = source.Width * 256 / dest.Width mov edx, eax add eax, esi mov x, eax // x = xDelta + Radius * 128 imul edx, [edi].TImageData.Width add eax, edx mov Width, eax // width = xDelta * dest.Width + x mov eax, [ebx].TImageData.Height shl eax, 8 xor edx, edx idiv [edi].TImageData.Height mov yDelta, eax // yDelta = source.Height * 256 / dest.Height add esi, eax mov y, esi // y = yDelta + Radius * 128 imul eax, [edi].TImageData.Height add eax, esi mov Height, eax // height = yDelta * dest.Height + y pxor mm7, mm7 mov ecx, 04040404h movd mm6, ecx punpcklbw mm6, mm7 mov eax, edi lea edx, src push edx call SetScaleRegs32 mov dstOffset, ebx pop ebx // ebx = src mov ecx, y cmp alphaI, 256 jae @@yLoopB // if (alpha >= 256) alphaScale else alphaBlendScale @@yLoopA: // for (; y < Height; y ++){ mov esi, ecx // { sar esi, 8 // esi = source.Scan0 + y / 256 * source.Stride imul esi, [ebx].TImageData.Stride add esi, [ebx].TImageData.Scan0 mov edx, x // for (; x < Width; x ++){ @@xLoopA: // { push esi push edx push ecx mov eax, edx sar eax, 8 shl eax, 2 add esi, eax // esi += (x / 256 * 4) call colorProc // mm0 = GetColor(src, esi, x, y) movd eax, mm0 // eax = ((mm0 >> 24) * alpha) >> 8 shr eax, 24 imul eax, alphaI shr eax, 8 movd mm1, [edi] // mm1 = *(ARGB*)edi punpcklbw mm0, mm7 punpcklbw mm1, mm7 psubw mm0, mm1 pmullw mm0, qword ptr ArgbTable[eax*8] psllw mm1, 8 paddw mm0, mm1 psrlw mm0, 8 packuswb mm0, mm7 // *(ARGB*)edi = ((mm0 - mm1) * ArgbTable[eax] + movd [edi], mm0 // mm1 * 256) / 256 add edi, 4 // edi += 4 pop ecx pop edx pop esi add edx, xDelta // x0 += xDelta cmp edx, Width jl @@xLoopA // } add edi, dstOffset // edi += dstOffset add ecx, yDelta // y0 += yDelta cmp ecx, Height jl @@yLoopA // } jmp @@Exit @@yLoopB: // for (; y < Height; y ++){ mov esi, ecx // { sar esi, 8 // esi = source.Scan0 + y / 256 * source.Stride imul esi, [ebx].TImageData.Stride add esi, [ebx].TImageData.Scan0 mov edx, x // for (; x < Width; x ++){ @@xLoopB: // { push esi push edx push ecx mov eax, edx sar eax, 8 shl eax, 2 add esi, eax // esi += (x / 256 * 4) call colorProc // mm0 = colorProc(src, esi, x, y) movd eax, mm0 // eax = mm0 >> 24 shr eax, 24 movd mm1, [edi] // mm1 = *(ARGB*)edi punpcklbw mm0, mm7 punpcklbw mm1, mm7 psubw mm0, mm1 pmullw mm0, qword ptr ArgbTable[eax*8] psllw mm1, 8 paddw mm0, mm1 psrlw mm0, 8 packuswb mm0, mm7 // *(ARGB*)edi = ((mm0 - mm1) * ArgbTable[eax] + movd [edi], mm0 // mm1 * 256) / 256 add edi, 4 // edi += 4 pop ecx pop edx pop esi add edx, xDelta // x0 += xDelta cmp edx, Width jl @@xLoopB // } add edi, dstOffset // edi += dstOffset add ecx, yDelta // y0 += yDelta cmp ecx, Height jl @@yLoopB // } @@Exit: emms mov eax, ebx call FreeImageData pop ebx pop edi pop esi end; procedure ImageScale(var Dest: TImageData; const Source: TImageData; Alpha: Single; IpMode: TInterpolateMode); begin if ImageEmpty(Dest) or ImageEmpty(Source) then Exit; DoScale(Dest, Source, Alpha, IpMode); end; procedure ImageScale(var Dest: TImageData; x, y: Integer; const Source: TImageData; ScaleX, ScaleY: Single; Alpha: Single; IpMode: TInterpolateMode); var src, dst: TImageData; begin if ImageEmpty(Source) then Exit; dst := GetSubImageData(Dest, x, y, Round(Source.Width * ScaleX), Round(Source.Height * ScaleY)); if dst.Scan0 = nil then Exit; if x < 0 then x := -Round(x / ScaleX) else x := 0; if y < 0 then y := -Round(y / ScaleY) else y := 0; src := GetSubData(Source, x, y, GetInfinity(dst.Width / ScaleX), GetInfinity(dst.Height / ScaleY)); DoScale(dst, src, Alpha, IpMode); end; procedure ImageScale(var Dest: TImageData; const Source: TGraphic; Alpha: Single; IpMode: TInterpolateMode); var src: TImageData; begin src := GetImageData(Source); DoScale(Dest, src, Alpha, IpMode); FreeImageData(src); end; procedure ImageScale(var Dest: TImageData; x, y: Integer; const Source: TGraphic; ScaleX, ScaleY: Single; Alpha: Single; IpMode: TInterpolateMode); var src: TImageData; begin src := GetImageData(Source); ImageScale(Dest, x, y, src, ScaleX, ScaleY, Alpha, IpMode); FreeImageData(src); end; procedure ImageScale(var Dest: TImageData; const Source: TGpBitmap; Alpha: Single; IpMode: TInterpolateMode); var src: TImageData; begin src := GetImageData(Source); ImageScale(Dest, src, Alpha, IpMode); FreeImageData(src); end; procedure ImageScale(var Dest: TImageData; x, y: Integer; const Source: TGpBitmap; ScaleX, ScaleY: Single; Alpha: Single; IpMode: TInterpolateMode); var src: TImageData; begin src := GetImageData(Source); ImageScale(Dest, x, y, src, ScaleX, ScaleY, Alpha, IpMode); FreeImageData(src); end;

临近插值过程很简单，就一句代码，而线性插值过程和双立方插值过程则较复杂，而且对于各像素的插值比例计算更是耗时，为了加快插值速度，线性插值过程和双立方插值过程都用了事先计算好的插值比例表，分别存放在BilinearTable变量和BicubicTable变量中，这2个变量的初始化是在单元的初始化代码中实现的（代码参见《Delphi图像处理 -- 图像像素结构与图像数据转换》第八部分）。

其中，通过调用SetBicubicSlope可改变双立方插值的效果，这个值一般在-0.5 -- -2.0之间，初始值为-0.75。

图像旋转过程也要用到上面的插值过程的。

关于线性插值原理，在GetBilinearColor过程前面有一段伪代码作为解释；为了帮助理解双立方插值方式，下面给出其纯Pascal的浮点版和整数版代码：

type TImageData = packed record Width: LongWord; // 图像宽度 Height: LongWord; // 图像高度 Stride: LongWord; // 图像扫描线字节长度 Scan0: Pointer; // 图像数据地址 end; // 浮点数版，Source四周的边界分别扩展了3 procedure BicubicScale(Source, Dest: TImageData); const A = -0.75; // 0.0 < BicuBicSlope <= 2.0 function BicubicFunc(x : double): double; var x2, x3: double; begin if x < 0 then x := -x; x2 := x * x; x3 := x2 * x; if x <= 1 then Result := (A + 2) * x3 - (A + 3) * x2 + 1 else if x <= 2 then Result := A * x3 - (5 * A) * x2 + (8 * A) * x - (4 * A) else Result := 0; end; function Bicubic(fx, fy: double): TRGBQuad; var x, y, x0, y0: Integer; fu, fv: double; pixel: array[0..3, 0..3] of PRGBQuad; afu, afv, aARGB, sARGB: array[0..3] of double; i, j: Integer; begin x0 := Trunc(floor(fx)); y0 := Trunc(floor(fy)); fu := fx - x0; fv := fy - y0; for i := 0 to 3 do begin for j := 0 to 3 do begin x := x0 - 1 + j; y := y0 - 1 + i; pixel[i, j] := PRGBQuad(LongWord(Source.Scan0) + y * Source.Stride + x shl 2); end; sARGB[i] := 0; end; afu[0] := BicubicFunc(1 + fu); afu[1] := BicubicFunc(fu); afu[2] := BicubicFunc(1 - fu); afu[3] := BicubicFunc(2 - fu); afv[0] := BicubicFunc(1 + fv); afv[1] := BicubicFunc(fv); afv[2] := BicubicFunc(1 - fv); afv[3] := BicubicFunc(2 - fv); for i := 0 to 3 do begin for j := 0 to 3 do aARGB[j] := 0; for j := 0 to 3 do begin aARGB[3] := aARGB[3] + afu[j] * pixel[i, j]^.rgbReserved; aARGB[2] := aARGB[2] + afu[j] * pixel[i, j]^.rgbRed; aARGB[1] := aARGB[1] + afu[j] * pixel[i, j]^.rgbGreen; aARGB[0] := aARGB[0] + afu[j] * pixel[i, j]^.rgbBlue; end; sARGB[3] := sARGB[3] + aARGB[3] * afv[i]; sARGB[2] := sARGB[2] + aARGB[2] * afv[i]; sARGB[1] := sARGB[1] + aARGB[1] * afv[i]; sARGB[0] := sARGB[0] + aARGB[0] * afv[i]; end; Result.rgbBlue := Max(0, Min(255, Round(sARGB[0]))); Result.rgbGreen := Max(0, Min(255, Round(sARGB[1]))); Result.rgbRed := Max(0, Min(255, Round(sARGB[2]))); Result.rgbReserved := Max(0, Min(255, Round(sARGB[3]))); end; var x, y: Integer; fx, fy: double; Offset: LongWord; p: PLongWord;//PRGBQuad; begin Offset := Dest.Stride - Dest.Width shl 2; p := PLongWord(Dest.Scan0); for y := 0 to Dest.Height - 1 do begin fy := (y + 0.4999999) * Source.Height / Dest.Height - 0.5; for x := 0 to Dest.Width - 1 do begin fx := (x + 0.4999999) * Source.Width / Dest.Width - 0.5; P^ := LongWord(Bicubic(fx, fy)); Inc(p); end; Inc(LongWord(p), Offset); end; end; const InterpolationRadius = 3; var BicubicUVTable: array[0..512] of Integer; procedure InitBicubicUVTable; const A = -0.75; function BicubicFunc(x : double): double; var x2, x3: double; begin if x < 0 then x := -x; x2 := x * x; x3 := x2 * x; if x <= 1 then Result := (A + 2) * x3 - (A + 3) * x2 + 1 else if x <= 2 then Result := A * x3 - (5 * A) * x2 + (8 * A) * x - (4 * A) else Result := 0; end; var I: Integer; begin for I := 0 to 512 do BicubicUVTable[I] := Round(256 * BicubicFunc(I * (1.0 / 256))); end; // 定点数版，Source四周的边界分别扩展了3 procedure BicubicScale(Source, Dest: TImageData); function Bicubic(x, y: Integer): TRGBQuad; var x0, y0, u, v: Integer; pixel: PRGBQuad; au, av, aARGB, sARGB: array[0..3] of Integer; i, j: Integer; begin u := x and 255; v := y and 255; pixel := PRGBQuad(LongWord(Source.Scan0) + (y div 256 - 1) * Source.Stride + ((x div 256 - 1) shl 2)); for i := 0 to 3 do sARGB[i] := 0; au[0] := BicubicUVTable[256 + u]; au[1] := BicubicUVTable[u]; au[2] := BicubicUVTable[256 - u]; au[3] := BicubicUVTable[512 - u]; av[0] := BicubicUVTable[256 + v]; av[1] := BicubicUVTable[v]; av[2] := BicubicUVTable[256 - v]; av[3] := BicubicUVTable[512 - v]; for i := 0 to 3 do begin for j := 0 to 3 do aARGB[j] := 0; for j := 0 to 3 do begin aARGB[3] := aARGB[3] + au[j] * pixel^.rgbReserved; aARGB[2] := aARGB[2] + au[j] * pixel^.rgbRed; aARGB[1] := aARGB[1] + au[j] * pixel^.rgbGreen; aARGB[0] := aARGB[0] + au[j] * pixel^.rgbBlue; Inc(LongWord(pixel), 4); end; sARGB[3] := sARGB[3] + aARGB[3] * av[i]; sARGB[2] := sARGB[2] + aARGB[2] * av[i]; sARGB[1] := sARGB[1] + aARGB[1] * av[i]; sARGB[0] := sARGB[0] + aARGB[0] * av[i]; Inc(LongWord(pixel), Source.Stride - 16); end; Result.rgbBlue := Max(0, Min(255, sARGB[0] div 65536)); Result.rgbGreen := Max(0, Min(255, sARGB[1] div 65536)); Result.rgbRed := Max(0, Min(255, sARGB[2] div 65536)); Result.rgbReserved := Max(0, Min(255, sARGB[3] div 65536)); end; var x, x0, y, xDelta, yDelta: Integer; w, h: Integer; Offset: LongWord; p: PLongWord; begin InitBicubicUVTable; p := PLongWord(Dest.Scan0); Offset := Dest.Stride - Dest.Width shl 2; yDelta := ((Source.Height - InterpolationRadius * 2) * 256) div Dest.Height; xDelta := ((Source.Width - InterpolationRadius * 2) * 256) div Dest.Width; y := (yDelta shr 1) - $80 + $200; x0 := (xDelta shr 1) - $80 + $200; h := Dest.Height * yDelta + y; w := Dest.Width * xDelta + x0; while y < h do begin x := x0; while x < w do begin P^ := LongWord(Bicubic(x, y)); Inc(x, xDelta); Inc(p); end; Inc(y, yDelta); Inc(LongWord(p), Offset); end; end;

另外，有关插值边界的处理，一般有2种办法，一是在插值过程中进行判断坐标是否超界而作相应的处理，二是舍弃边界部分，对于后者我是不主张的，因为那样是不完整的处理。我采用了扩展边框的办法进行边框插值处理，这样一来，虽然多了一道拷贝过程，却少了具体插值过程的坐标判断，二者抵消，插值速度应该是差不多的（据我测试，扩展边框办法在图像放大和旋转处理中速度还是略快一些），但是简化了插值代码。

下面是一个简单的图像缩放例子：

unit Main; interface uses Windows, Messages, SysUtils, Variants, Classes, Graphics, Controls, Forms, Dialogs, StdCtrls, jpeg, ExtCtrls, Menus, ImageUtils; type TMainForm = class(TForm) Image1: TImage; RadioButton1: TRadioButton; RadioButton2: TRadioButton; RadioButton3: TRadioButton; Button1: TButton; Image2: TImage; procedure FormCreate(Sender: TObject); procedure RadioButton1Click(Sender: TObject); procedure Button1Click(Sender: TObject); private { Private declarations } FMode: TInterpolateMode; public { Public declarations } end; var MainForm: TMainForm; implementation {$R *.dfm} procedure TMainForm.FormCreate(Sender: TObject); begin Image1.Picture.Bitmap.PixelFormat := pf24Bit; RadioButton2.Checked := True; RadioButton1Click(RadioButton2); end; procedure TMainForm.RadioButton1Click(Sender: TObject); var M: TInterpolateMode; Data: TImageData; begin M := TInterpolateMode(TRadioButton(Sender).Tag); if FMode <> M then begin FMode := M; Data := NewImageData(Image1.Width, Image1.Height, 0); ImageScale(Data, Image2.Picture.Graphic, 1.0, FMode); ImageDataAssignTo(Data, Image1.Picture.Bitmap); FreeImageData(Data); Image1.Invalidate; end; end; procedure TMainForm.Button1Click(Sender: TObject); begin Close; end; end.

运行效果图如下：

文章中使用GDI+版本下载地址和说明见《GDI+ for VCL基础 -- GDI+ 与 VCL》。

文章中所用数据类型及一些过程见《Delphi图像处理 -- 数据类型及内部过程》和《Delphi图像处理 -- 图像像素结构与图像数据转换》。

尽管我十分努力，但水平有限，错误在所难免，欢迎指正和指导。邮箱地址：

[email protected]

说明：本文代码于2010.5.20重新修订过，在处理过程中增加了一个Alpha参数，可实现半透明形式的图像缩放。