BoxBlur

procedure BoxBlur(img: TImage32; rect: TRect; radius, repeats: Integer);

With several repetitions and a smaller radius, BoxBlur can achieve a close approximation of GaussianBlur, and is much faster.
Empirically, using a radius about 1/4 that used in GaussianBlur together with 3 repeats, BoxBlur fairly closely approximates GaussianBlur. 

  uses Image32, Image32_Extra, Image32_PNG;
  ...
  var
    img: TImage32;
    rec: TRect;
    pt: TPoint;
  begin
    img := TImage32.Create(256, 256);

    rec := Rect(img.Width - 120, 0, img.Width, 120);
    pt := MidPoint(rec);
    DrawPoint(img, PointD(pt), 20, clNavy32);
    GaussianBlur(img, rec, 48);

    Windows.OffsetRect(rec, -120, 0);
    pt := MidPoint(rec);
    DrawPoint(img, PointD(pt), 20, clNavy32);
    GaussianBlur(img, rec, 24);

    rec := Rect(img.Width - 120, img.Height -125, 
      img.Width, img.Height-5);
    pt := MidPoint(rec);
    DrawPoint(img, PointD(pt), 20, clNavy32);
    BoxBlur(img, rec, 12, 3);

    Windows.OffsetRect(rec, -120, 0);
    pt := MidPoint(rec);
    DrawPoint(img, PointD(pt), 20, clNavy32);
    BoxBlur(img, rec, 6, 3);

    img.Free;

See Also

GaussianBlur