graphics - Algorithm for fast Drop shadow in GDI+

Question

What is an efficient way to add a drop-shadow to an image in GDI?

Right now i start with my image:

i use ImageAttributes and a ColorMatrix to draw the image's alpha mask to a new image:

colorMatrix = (
    ( 0,  0,  0, 0, 0),
    ( 0,  0,  0, 0, 0),
    ( 0,  0,  0, 0, 0),
    (-1, -1, -1, 1, 0),
    ( 1,  1,  1, 0, 1)
    );

i then apply a Gaussian Blur convolution kernel, and offset it slightly:

And then i draw my original image back over top:

Problem is that it's just too slow, it takes about 170ms to generate the image with drop-shadow, verses 2ms without the drop-shadow (70x slower):

• with drop shadow: 171,332 μs
• without drop shadow: 2,457us

When a user (e.g. me) is scrolling through a list of items, that extra 169ms delay is very noticeable.

---

You can ignore the code below, it doesn't add anything to the question, or the answer:

class function TImageEffects.GenerateDropShadow(image: TGPImage;
        const radius: Single; const OffsetX, OffsetY: Single; const Opacity: Single): TGPBitmap;
var
    width, height: Integer;
    alphaMask: TGPBitmap;
    shadow: TGPBitmap;
    graphics: TGPGraphics;
    imageAttributes: TGPImageAttributes;
    cm: TColorMatrix;
begin
{
    We generate a drop shadow by first getting the alpha mask. This will be a black
    sillouette on a transparent background. We then blur the black "shadow" by the amounts
    given.
    We then draw the original image on top of it's own shadow.
}

{
    http://msdn.microsoft.com/en-us/library/aa511280.aspx
    Windows Vista User Experience -> Guidelines -> Aesthetics -> Icons

    Basic Flat Icon Shadow Ranges

    Flat icons
    Flat icons are generally used for file icons and flat real-world objects,
    such as a document or a piece of paper.

    Flat icon lighting comes from the upper-left at 130 degrees.

    Smaller icons (for example, 16x16 and 32x32) are simplified for readability.
    However, if they contain a reflection within the icon (often simplified),
    they may have a tight drop shadow. The drop shadow ranges in opacity from
    30-50 percent.
    Layer effects can be used for flat icons, but should be compared with other
    flat icons. The shadows for objects will vary somewhat, according to what
    looks best and is most consistent within the size set and with the other
    icons in Windows Vista. On some occasions, it may even be necessary to
    modify the shadows. This will especially be true when objects are laid over
    others.
    A subtle range of colors may be used to achieve desired outcome. Shadows help
    objects sit in space. Color impacts the perceived weight of the shadow, and
    may distort the image if it is too heavy.

    Blend mode: Multiply
    Opacity: 22% to 50% - depends on color of the item.
    Angle: 130 to 120, use global light
    Distance: 3 (256 thru 48x), Distance = 1 (32x, 24x)
    Spread: 0
    Size: 7 (256x thru 48x), Spread = 2 (32x, 24x)
}
    width := image.GetWidth;
    height := image.GetHeight;

    //Get bitmap to hold final composited image and shadow
    Result := TGPBitmap.Create(width, height, PixelFormat32bppARGB);

    //Use ColorMatrix methods to "draw" the alpha image.
    alphaMask := TImageEffects.GetAlphaMask(image);
    try
        //Blur the black and white shadow image
//      shadow := TImageEffects.BoxBlur(alphaMask, radius);
        shadow := TImageEffects.GaussianBlur(alphaMask, radius); //because Gaussian Blur is linearly-separable into two 1d kernels, it's actually faster than the box blur
    finally
        alphaMask.Free;
    end;

    //Draw
    graphics := TGPGraphics.Create(Result);
    try
        //Draw the "shadow", using the passed in opacity value.
        {
            Color transformations are of the form
        c =  (r, g, b, a)
        c' = (r, g, b, a)
        c' = c*M
            = (r, g, b, a, 1) * (0 0 0 0 0)  //r
                                      (0 0 0 0 0)  //g
                                      (0 0 0 0 0)  //b
                                      (1 1 1 1 0)  //a
                                      (0 0 0 0 1)  //1
        }

        imageAttributes := TGPImageAttributes.Create;
    {   cm := (
                ( 1, 0, 0, 0,   0),
                ( 0, 1, 0, 0,   0),
                ( 0, 0, 1, 0,   0),
                ( 0, 0, 0, 0.5, 0),
                ( 0, 0, 0, 0,   1)
            );}
        cm[0, 0] :=  1; cm[0, 1] :=  0; cm[0, 2] :=  0; cm[0, 3] := 0;       cm[0, 4] := 0;
        cm[1, 0] :=  0; cm[1, 1] :=  1; cm[1, 2] :=  0; cm[1, 3] := 0;       cm[1, 4] := 0;
        cm[2, 0] :=  0; cm[2, 1] :=  0; cm[2, 2] :=  1; cm[2, 3] := 0;       cm[2, 4] := 0;
        cm[3, 0] :=  0; cm[3, 1] :=  0; cm[3, 2] :=  0; cm[3, 3] := Opacity; cm[3, 4] := 0;
        cm[4, 0] :=  0; cm[4, 1] :=  0; cm[4, 2] :=  0; cm[4, 3] := 0;       cm[4, 4] := 1;


        imageAttributes.SetColorMatrix(
                cm,
                ColorMatrixFlagsDefault,
                ColorAdjustTypeBitmap);
        try
            graphics.DrawImage(shadow,
                        MakeRectF(OffsetX, OffsetY, width, height), //destination rectangle
                        0, 0, //source (x,y)
                        width, height, //source width, height
                        UnitPixel,
                        ImageAttributes);

            //Draw original image over-top of it's shadow
            graphics.DrawImage(image, 0, 0);
        finally
            imageAttributes.Free;
        end;
    finally
        graphics.Free;
    end;
end;

Which uses the the function to get the grayscale alpha mask:

class function TImageEffects.GetAlphaMask(image: TGPImage): TGPBitmap;
var
    imageAttributes: TGPImageAttributes;
    cm: TColorMatrix;
    graphics: TGPGraphics;
    Width, Height: UINT;
begin
    {
        Color transformations are of the form
    c =  (r, g, b, a)
    c' = (r, g, b, a)
    c' = c*M
        = (r, g, b, a, 1) * (0 0 0 0 0)
                            (0 0 0 0 0)
                            (0 0 0 0 0)
                            (1 1 1 1 0)
                            (0 0 0 0 1)
    }

    imageAttributes := TGPImageAttributes.Create;

{   cm := (
            ( 0,  0,  0, 0, 0),
            ( 0,  0,  0, 0, 0),
            ( 0,  0,  0, 0, 0),
            (-1, -1, -1, 1, 0),
            ( 1,  1,  1, 0, 1)
        );}
    cm[0, 0] :=  0; cm[0, 1] :=  0; cm[0, 2] :=  0; cm[0, 3] := 0; cm[0, 4] := 0;
    cm[1, 0] :=  0; cm[1, 1] :=  0; cm[1, 2] :=  0; cm[1, 3] := 0; cm[1, 4] := 0;
    cm[2, 0] :=  0; cm[2, 1] :=  0; cm[2, 2] :=  0; cm[2, 3] := 0; cm[2, 4] := 0;
    cm[3, 0] := -1; cm[3, 1] := -1; cm[3, 2] := -1; cm[3, 3] := 1; cm[3, 4] := 0;
    cm[4, 0] :=  1; cm[4, 1] :=  1; cm[4, 2] :=  1; cm[4, 3] := 0; cm[4, 4] := 1;


    imageAttributes.SetColorMatrix(
            cm,
            ColorMatrixFlagsDefault,
            ColorAdjustTypeBitmap);

    width := image.GetWidth;
    height := image.GetHeight;

    Result := TGPBitmap.Create(Integer(width), Integer(height));
    graphics := TGPGraphics.Create(Result);
   try
        graphics.DrawImage(
                image,
                MakeRect(0, 0, width, height), //destination rectangle
             0, 0, //source (x,y)
             width, height,
             UnitPixel,
                ImageAttributes);
   finally
        graphics.Free;
    end;
end;

The core is the gaussian blur:

class function TImageEffects.GaussianBlur(const bitmap: TGPBitmap;
  radius: Single): TGPBitmap;
var
    width, height: Integer;
    tempBitmap: TGPBitmap;
    bdSource: TBitmapData;
    bdTemp: TBitmapData;
    bdDest: TBitmapData;
    pSrc: PARGBArray;
    pTemp: PARGBArray;
    pDest: PARGBArray;
    stride: Integer;
    kernel: TKernel;
begin
//  kernel := MakeGaussianKernel2d(radius);
    kernel := MakeGaussianKernel1d(radius);
    try
//      Result := ConvolveBitmap(bitmap, kernel); brute 2d kernel

        width := bitmap.GetWidth;
        height := bitmap.GetHeight;

        // GDI+ still lies to us - the return format is BGR, NOT RGB.
        bitmap.LockBits(MakeRect(0, 0, width, height),
                ImageLockModeRead,
                PixelFormat32bppPARGB, bdSource);

        //intermediate bitmap
        tempBitmap := TGPBitmap.Create(width, height, PixelFormat32bppPARGB);
        tempBitmap.LockBits(MakeRect(0, 0, width, height),
                    ImageLockModeWrite,
                    PixelFormat32bppPARGB, bdTemp);

        //target bitmap
        Result := TGPBitmap.Create(width, height, PixelFormat32bppARGB);
        Result.LockBits(MakeRect(0, 0, width, height),
                    ImageLockModeWrite,
                    PixelFormat32bppPARGB, bdDest);

        pSrc := PARGBArray(bdSource.Scan0);
        pTemp := PARGBArray(bdTemp.Scan0);
        pDest := PARGBArray(bdDest.Scan0);
        stride := bdSource.Stride;

        ConvolveAndTranspose(kernel, pSrc^, pTemp^, width, height, stride, True, EdgeActionClampEdges);
        ConvolveAndTranspose(kernel, pTemp^, pDest^, height, width, stride, True, EdgeActionClampEdges);

        //Unlock source
       bitmap.UnlockBits(bdSource);
        tempBitmap.UnlockBits(bdTemp);
        Result.UnlockBits(bdDest);

        //get rid of temp
        tempBitmap.Free;
    finally
        kernel.Free;
    end;
end;

which requires a 1-D kernel:

class function TImageEffects.MakeGaussianKernel1d(radius: Single): TKernel;
var
    r: Integer;
    rows: Integer;
    matrix: TSingleDynArray;
    sigma: Single;
    sigma22: Single;
    sigmaPi2: Single;
    sqrtSigmaPi2: Single;
    radius2: Single;
    total: Single;
    index: Integer;
    row: Integer;
    distance: Single;
    i: Integer;
begin
    r := Ceil(radius);
    rows := r*2+1;

    SetLength(matrix, rows);
    sigma := radius/3.0;
    sigma22 := 2*sigma*sigma;
    sigmaPi2 := 2*pi*sigma;
    sqrtSigmaPi2 := Sqrt(sigmaPi2);
    radius2 := radius*radius;
    total := 0;

    Index := 0;
    for row := -r to r do
    begin
        distance := row*row;
        if (distance > radius2) then
            matrix[index] := 0
        else
        begin
            matrix[index] := Exp((-distance)/sigma22) / sqrtSigmaPi2;
            total := total + matrix[index];
            Inc(index);
        end;
    end;

    //Normalize the values
    for i := 0 to rows-1 do
        matrix[i] := matrix[i] / total;


    Result := TKernel.Create(rows, 1, matrix);
end;

And then the magic of the gaussian function is that it is separable into two 1D convolutions:

class procedure TImageEffects.convolveAndTranspose(kernel: TKernel;
  const inPixels: array of ARGB; var outPixels: array of ARGB; width,
  height, stride: Integer; alpha: Boolean; edgeAction: TEdgeAction);
var
    index: Integer;
    matrix: TSingleDynArray;
    rows: Integer; //number of rows in the kernel
    cols: Integer; //number of columns in the kernel
    rows2: Integer; //half row count
    cols2: Integer; //half column count

    x, y: Integer; //
    r, g, b, a: Single; //summed

Answer 1

The algorithm came from this blog entry: http://blog.ivank.net/fastest-gaussian-blur.html . It's implementing the last and fastest version, of course. :-)

It's copied directly from my working code, so the external assumptions might reflect that. The function returns a larger bitmap to accommodate the increase in size. In your code, you need to handle this accordingly, of course. It assumes a 32-bit alpha picture but can be easily modified to handle 24-bit only (CHANNELS constant and the PixelFormat values).

public static class DropShadow {
  const int CHANNELS = 4;

  public static Bitmap CreateShadow(Bitmap bitmap, int radius, float opacity) {
    // Alpha mask with opacity
    var matrix = new ColorMatrix(new float[][] {
            new float[] {  0F,  0F,  0F, 0F,      0F }, 
            new float[] {  0F,  0F,  0F, 0F,      0F }, 
            new float[] {  0F,  0F,  0F, 0F,      0F }, 
            new float[] { -1F, -1F, -1F, opacity, 0F },
            new float[] {  1F,  1F,  1F, 0F,      1F }
        });

    var imageAttributes = new ImageAttributes();
    imageAttributes.SetColorMatrix(matrix, ColorMatrixFlag.Default, ColorAdjustType.Bitmap);
    var shadow = new Bitmap(bitmap.Width + 4 * radius, bitmap.Height + 4 * radius);
    using (var graphics = Graphics.FromImage(shadow))
      graphics.DrawImage(bitmap, new Rectangle(2 * radius, 2 * radius, bitmap.Width, bitmap.Height), 0, 0, bitmap.Width, bitmap.Height, GraphicsUnit.Pixel, imageAttributes);

    // Gaussian blur
    var clone = shadow.Clone() as Bitmap;
    var shadowData = shadow.LockBits(new Rectangle(0, 0, shadow.Width, shadow.Height), ImageLockMode.ReadWrite, PixelFormat.Format32bppArgb);
    var cloneData = clone.LockBits(new Rectangle(0, 0, clone.Width, clone.Height), ImageLockMode.ReadWrite, PixelFormat.Format32bppArgb);

    var boxes = DetermineBoxes(radius, 3);
    BoxBlur(shadowData, cloneData, shadow.Width, shadow.Height, (boxes[0] - 1) / 2);
    BoxBlur(shadowData, cloneData, shadow.Width, shadow.Height, (boxes[1] - 1) / 2);
    BoxBlur(shadowData, cloneData, shadow.Width, shadow.Height, (boxes[2] - 1) / 2);

    shadow.UnlockBits(shadowData);
    clone.UnlockBits(cloneData);
    return shadow;
  }

  private static unsafe void BoxBlur(BitmapData data1, BitmapData data2, int width, int height, int radius) {
    byte* p1 = (byte*)(void*)data1.Scan0;
    byte* p2 = (byte*)(void*)data2.Scan0;

    int radius2 = 2 * radius + 1;
    int[] sum = new int[CHANNELS];
    int[] FirstValue = new int[CHANNELS];
    int[] LastValue = new int[CHANNELS];

    // Horizontal
    int stride = data1.Stride;
    for (var row = 0; row < height; row++) {
      int start = row * stride;
      int left = start;
      int right = start + radius * CHANNELS;

      for (int channel = 0; channel < CHANNELS; channel++) {
        FirstValue[channel] = p1[start + channel];
        LastValue[channel] = p1[start + (width - 1) * CHANNELS + channel];
        sum[channel] = (radius + 1) * FirstValue[channel];
      }
      for (var column = 0; column < radius; column++)
        for (int channel = 0; channel < CHANNELS; channel++)
          sum[channel] += p1[start + column * CHANNELS + channel];
      for (var column = 0; column <= radius; column++, right += CHANNELS, start += CHANNELS)
        for (int channel = 0; channel < CHANNELS; channel++) {
          sum[channel] += p1[right + channel] - FirstValue[channel];
          p2[start + channel] = (byte)(sum[channel] / radius2);
        }
      for (var column = radius + 1; column < width - radius; column++, left += CHANNELS, right += CHANNELS, start += CHANNELS)
        for (int channel = 0; channel < CHANNELS; channel++) {
          sum[channel] += p1[right + channel] - p1[left + channel];
          p2[start + channel] = (byte)(sum[channel] / radius2);
        }
      for (var column = width - radius; column < width; column++, left += CHANNELS, start += CHANNELS)
        for (int channel = 0; channel < CHANNELS; channel++) {
          sum[channel] += LastValue[channel] - p1[left + channel];
          p2[start + channel] = (byte)(sum[channel] / radius2);
        }
    }

    // Vertical
    stride = data2.Stride;
    for (int column = 0; column < width; column++) {
      int start = column * CHANNELS;
      int top = start;
      int bottom = start + radius * stride;

      for (int channel = 0; channel < CHANNELS; channel++) {
        FirstValue[channel] = p2[start + channel];
        LastValue[channel] = p2[start + (height - 1) * stride + channel];
        sum[channel] = (radius + 1) * FirstValue[channel];
      }
      for (int row = 0; row < radius; row++)
        for (int channel = 0; channel < CHANNELS; channel++)
          sum[channel] += p2[start + row * stride + channel];
      for (int row = 0; row <= radius; row++, bottom += stride, start += stride)
        for (int channel = 0; channel < CHANNELS; channel++) {
          sum[channel] += p2[bottom + channel] - FirstValue[channel];
          p1[start + channel] = (byte)(sum[channel] / radius2);
        }
      for (int row = radius + 1; row < height - radius; row++, top += stride, bottom += stride, start += stride)
        for (int channel = 0; channel < CHANNELS; channel++) {
          sum[channel] += p2[bottom + channel] - p2[top + channel];
          p1[start + channel] = (byte)(sum[channel] / radius2);
        }
      for (int row = height - radius; row < height; row++, top += stride, start += stride)
        for (int channel = 0; channel < CHANNELS; channel++) {
          sum[channel] += LastValue[channel] - p2[top + channel];
          p1[start + channel] = (byte)(sum[channel] / radius2);
        }
    }
  }

  private static int[] DetermineBoxes(double Sigma, int BoxCount) {
    double IdealWidth = Math.Sqrt((12 * Sigma * Sigma / BoxCount) + 1);
    int Lower = (int)Math.Floor(IdealWidth);
    if (Lower % 2 == 0)
      Lower--;
    int Upper = Lower + 2;

    double MedianWidth = (12 * Sigma * Sigma - BoxCount * Lower * Lower - 4 * BoxCount * Lower - 3 * BoxCount) / (-4 * Lower - 4);
    int Median = (int)Math.Round(MedianWidth);

    int[] BoxSizes = new int[BoxCount];
    for (int i = 0; i < BoxCount; i++)
      BoxSizes[i] = (i < Median) ? Lower : Upper;
    return BoxSizes;
  }

}

I assume it must be straighforward to convert it to Delphi.

Addendum: according to the comments on that blog, if you have an integer radius and three boxes, you can actually forget DetermineBoxes() and use:

BoxBlur(shadowData, cloneData, shadow.Width, shadow.Height, radius - 1);
BoxBlur(shadowData, cloneData, shadow.Width, shadow.Height, radius - 1);
BoxBlur(shadowData, cloneData, shadow.Width, shadow.Height, radius);

Its execution time is negligible compared to the bitmap itself but still...