Gaussian Blur in Delphi

Problem/Question/Abstract:

Gaussian Blur in Delphi

Answer:

The gaussian kernel exp(-(x^2 + y^2)) is of the form f(x)*g(y), which means that you can perform a two-dimensional convolution by doing a sequence of one-dimensional convolutions - first you convolve each row and then each column. This is much faster (an N^2 becomes an N*2). Any convolution requires some temporary storage - below the BlurRow routine allocates and frees the memory, meaning that it gets allocated and freed once for each row. Probably changing this would speed it up some, it's not entirely clear how much.

The kernel "size" is limited to 200 entries. In fact if you use radius anything like that large it will take forever - you want to try this with a radius = 3 or 5 or something. For a kernel with that many entries a straight convolution is the thing to do, while when the kernel gets much larger Fourier transform techniques will be better (I couldn't say what the actual cutoff is.)

One comment that needs to be made is that a gaussian blur has the magical property that you can blur each row one by one and then blur each column - this is much faster than an actual 2-d convolution.

Anyway, you can do this:


unit GBlur2;

interface

uses
  Windows, Graphics;

type
  PRGBTriple = ^TRGBTriple;
  TRGBTriple = packed record
    b: byte; {easier to type than rgbtBlue}
    g: byte;
    r: byte;
  end;
  PRow = ^TRow;
  TRow = array[0..1000000] of TRGBTriple;
  PPRows = ^TPRows;
  TPRows = array[0..1000000] of PRow;

const
  MaxKernelSize = 100;

type
  TKernelSize = 1..MaxKernelSize;
  TKernel = record
    Size: TKernelSize;
    Weights: array[-MaxKernelSize..MaxKernelSize] of single;
  end;
  {the idea is that when using a TKernel you ignore the Weights except
  for Weights in the range -Size..Size.}

procedure GBlur(theBitmap: TBitmap; radius: double);

implementation

uses
  SysUtils;

procedure MakeGaussianKernel(var K: TKernel; radius: double; MaxData, DataGranularity: double);
{makes K into a gaussian kernel with standard deviation = radius. For the current application
you set MaxData = 255 and DataGranularity = 1. Now the procedure sets the value of K.Size so
that when we use K we will ignore the Weights that are so small they can't possibly matter. (Small
Size is good because the execution time is going to be propertional to K.Size.)}
var
  j: integer;
  temp, delta: double;
  KernelSize: TKernelSize;
begin
  for j := Low(K.Weights) to High(K.Weights) do
  begin
    temp := j / radius;
    K.Weights[j] := exp(-temp * temp / 2);
  end;
  {now divide by constant so sum(Weights) = 1:}
  temp := 0;
  for j := Low(K.Weights) to High(K.Weights) do
    temp := temp + K.Weights[j];
  for j := Low(K.Weights) to High(K.Weights) do
    K.Weights[j] := K.Weights[j] / temp;
  {now discard (or rather mark as ignorable by setting Size) the entries that are too small to matter.
  This is important, otherwise a blur with a small radius will take as long as with a large radius...}
  KernelSize := MaxKernelSize;
  delta := DataGranularity / (2 * MaxData);
  temp := 0;
  while (temp < delta) and (KernelSize > 1) do
  begin
    temp := temp + 2 * K.Weights[KernelSize];
    dec(KernelSize);
  end;
  K.Size := KernelSize;
  {now just to be correct go back and jiggle again so the sum of the entries we'll be using is exactly 1}
  temp := 0;
  for j := -K.Size to K.Size do
    temp := temp + K.Weights[j];
  for j := -K.Size to K.Size do
    K.Weights[j] := K.Weights[j] / temp;
end;

function TrimInt(Lower, Upper, theInteger: integer): integer;
begin
  if (theInteger <= Upper) and (theInteger >= Lower) then
    result := theInteger
  else if theInteger > Upper then
    result := Upper
  else
    result := Lower;
end;

function TrimReal(Lower, Upper: integer; x: double): integer;
begin
  if (x < upper) and (x >= lower) then
    result := trunc(x)
  else if x > Upper then
    result := Upper
  else
    result := Lower;
end;

procedure BlurRow(var theRow: array of TRGBTriple; K: TKernel; P: PRow);
var
  j, n, LocalRow: integer;
  tr, tg, tb: double; {tempRed, etc}
  w: double;
begin
  for j := 0 to High(theRow) do
  begin
    tb := 0;
    tg := 0;
    tr := 0;
    for n := -K.Size to K.Size do
    begin
      w := K.Weights[n];
      {the TrimInt keeps us from running off the edge of the row...}
      with theRow[TrimInt(0, High(theRow), j - n)] do
      begin
        tb := tb + w * b;
        tg := tg + w * g;
        tr := tr + w * r;
      end;
    end;
    with P[j] do
    begin
      b := TrimReal(0, 255, tb);
      g := TrimReal(0, 255, tg);
      r := TrimReal(0, 255, tr);
    end;
  end;
  Move(P[0], theRow[0], (High(theRow) + 1) * Sizeof(TRGBTriple));
end;

procedure GBlur(theBitmap: TBitmap; radius: double);
var
  Row, Col: integer;
  theRows: PPRows;
  K: TKernel;
  ACol: PRow;
  P: PRow;
begin
  if (theBitmap.HandleType <> bmDIB) or (theBitmap.PixelFormat <> pf24Bit) then
    raise exception.Create('GBlur only works for 24-bit bitmaps');
  MakeGaussianKernel(K, radius, 255, 1);
  GetMem(theRows, theBitmap.Height * SizeOf(PRow));
  GetMem(ACol, theBitmap.Height * SizeOf(TRGBTriple));
  {record the location of the bitmap data:}
  for Row := 0 to theBitmap.Height - 1 do
    theRows[Row] := theBitmap.Scanline[Row];
  {blur each row:}
  P := AllocMem(theBitmap.Width * SizeOf(TRGBTriple));
  for Row := 0 to theBitmap.Height - 1 do
    BlurRow(Slice(theRows[Row]^, theBitmap.Width), K, P);
  {now blur each column}
  ReAllocMem(P, theBitmap.Height * SizeOf(TRGBTriple));
  for Col := 0 to theBitmap.Width - 1 do
  begin
    {first read the column into a TRow:}
    for Row := 0 to theBitmap.Height - 1 do
      ACol[Row] := theRows[Row][Col];
    BlurRow(Slice(ACol^, theBitmap.Height), K, P);
    {now put that row, um, column back into the data:}
    for Row := 0 to theBitmap.Height - 1 do
      theRows[Row][Col] := ACol[Row];
  end;
  FreeMem(theRows);
  FreeMem(ACol);
  ReAllocMem(P, 0);
end;

end.



Example:


procedure TForm1.Button1Click(Sender: TObject);
var
  b: TBitmap;
begin
  if not openDialog1.Execute then
    exit;
  b := TBitmap.Create;
  b.LoadFromFile(OpenDialog1.Filename);
  b.PixelFormat := pf24Bit;
  Canvas.Draw(0, 0, b);
  GBlur(b, StrToFloat(Edit1.text));
  Canvas.Draw(b.Width, 0, b);
  b.Free;
end;


Note that displaying 24-bit bitmaps on a 256-color system requires some special tricks - if this looks funny at 256 colors it doesn't prove the blur is wrong.