Convolution kernels to implement as filters (image operators)

Low pass filters

• Average

  double arAverage3x3[] = {
    1.0/9.0,  1.0/9.0,  1.0/9.0,
    1.0/9.0,  1.0/9.0,  1.0/9.0,
    1.0/9.0,  1.0/9.0,  1.0/9.0 
  };
  double arAverage5x5[] = {
    1.0/25.0, 1.0/25.0, 1.0/25.0, 1.0/25.0, 1.0/25.0,
    1.0/25.0, 1.0/25.0, 1.0/25.0, 1.0/25.0, 1.0/25.0,
    1.0/25.0, 1.0/25.0, 1.0/25.0, 1.0/25.0, 1.0/25.0,
    1.0/25.0, 1.0/25.0, 1.0/25.0, 1.0/25.0, 1.0/25.0,
    1.0/25.0, 1.0/25.0, 1.0/25.0, 1.0/25.0, 1.0/25.0
  };
  

• Smooth Strong

  double arSmoothStrong3x3(
    1.0/10.0, 1.0/10.0, 1.0/10.0,
    1.0/10.0, 2.0/10.0, 1.0/10.0,
    1.0/10.0, 1.0/10.0, 1.0/10.0 );
  

• Smooth Medium

  double arSmoothMedium3x3(
    1.0/16.0, 2.0/16.0, 1.0/16.0,
    2.0/16.0, 4.0/16.0, 2.0/16.0,
    1.0/16.0, 2.0/16.0, 1.0/16.0 );
  

• Smooth Soft

  double arSmoothSoft3x3(
    1.0/16.0, 1.0/16.0, 1.0/16.0,
    1.0/16.0, 8.0/16.0, 1.0/16.0,
    1.0/16.0, 1.0/16.0, 1.0/16.0 );
  

High pass filters

• Sharp Boost

  double arSharpBoost3x3(
     0.0,       -1.0/16.0,  0.0,
    -1.0/16.0,  20.0/16.0, -1.0/16.0,
     0.0,       -1.0/16.0,  0.0 );
  

• Sharp Strong

  double arSharpStrong3x3(
     0.0,     -1.0/6.0,  0.0,
    -1.0/6.0, 10.0/6.0, -1.0/6.0,
     0.0,     -1.0/6.0,  0.0 );
  

• Sharp Medium

  double arSharpMedium3x3(
     0.0, -1.0,  0.0,
    -1.0,  5.0, -1.0,
     0.0, -1.0,  0.0 );
  

• Sharp Soft

  double arSharpSoft3x3(
     1.0,  -2.0,   1.0,
    -2.0,   5.0,  -2.0,
     1.0,  -2.0,   1.0 );
  

Gaussian & Laplacian filters

• Gaussian

  double arGaussian3x3(
    1.0/16.0, 2.0/16.0, 1.0/16.0,
    2.0/16.0, 4.0/16.0, 2.0/16.0,
    1.0/16.0, 2.0/16.0, 1.0/16.0 );
  

• Laplacian

  double arLaplacian3x3(
    -1.0,  -1.0,  -1.0,
    -1.0,   9.0,  -1.0,
    -1.0,  -1.0,  -1.0 );
  

Compass edges detection

enum ECompassDirection
{
  CD_North,
  CD_NorthEast,
  CD_East,
  CD_SouthEast,
  CD_South,
  CD_SouthWest,
  CD_West,
  CD_NorthWest
};

Oriented compass edges detection: Given north kernel, we compute east one by a rotation of 90° right. For each pixels we compute:

• Gx = Apply north kernel
• Gy = Apply east kernel

Then resulting pixel is compute as:

• G = sqrt(Gx*Gx + Gy*Gy) for full precision or
• G = |Gx| + |Gy| for a quick approximation.

virtual bool DetectEdges(AbstractImage& ioImage,
  const elxKerneld& iNorthKernel,
  ECompassDirection iDirection,
  bool ibQuick=false,
  ProgressNotifier& iNotifier) const = 0;

Compass edges detection: Given compass kernel, we compute a set of 8 kernels by 45° right rotation. For each pixels we compute:

• G0 = apply north kernel
• G1 = apply north East kernel
• G2 = apply East kernel
• G3 = apply SouthEast kernel
• G4 = apply South kernel
• G5 = apply SouthWest kernel
• G6 = apply West kernel
• G7 = apply NorthWest kernel

Then we compute G as: G = max(G0,G1,G2,G3,G4,G2,G6,G7)

virtual bool DetectEdges(AbstractImage& ioImage,
  const elxKerneld& iNorthKernel,
  ProgressNotifier& iNotifier) const = 0;

• Sobel

  double arSobelNorth3x3(
     1.0,   2.0,   1.0,
     0.0,   0.0,   0.0,
    -1.0,  -2.0,  -1.0 );
  

• Prewitt

  double arPrewittNorth3x3(
    1.0, 0.0, -1.0,
    1.0, 0.0, -1.0,
    1.0, 0.0, -1.0 );
  

• Robinson

  double arRobinsonNorth3x3(
    1.0, 0.0, -1.0,
    1.0, 0.0, -1.0,
    1.0, 0.0, -1.0 );
  

• Kirsch

  double arKirschNorth3x3(
    -5.0, 3.0, 3.0,
    -5.0, 0.0, 3.0,
    -5.0, 3.0, 3.0 );
  

• Freeman

  double arFreemanNorth3x3(
    -5.0, 3.0, 3.0,
    -5.0, 0.0, 3.0,
    -5.0, 3.0, 3.0 );
  

• FreiChen

  double arFreiChenNorth3x3(
    -1.0,   0.0, 1.0,
    -sqrt2, 0.0, sqrt2,
    -1.0,   0.0, 1.0 );
  

Other edges detection

• Robert Cross edges detector
• Canny edges detector
• Zero crossing detector
• Marr-Hildreth

  double arMarrHildreth3x3[] = {
    1.0/sqrt2,       1.0,      1.0/sqrt2,
    1.0,       -4.0-2.0*sqrt2, 1.0,
    1.0/sqrt2,       1.0,      1.0/sqrt2 
  };