% radius will be determined so as to produce the best minimal error
% result, which is usally much larger than is normally needed.
%
-% DOG:{radius},{sigma1},{sigma2}
+% LoG:{radius},{sigma}
+% "Laplacian of a Gaussian" or "Mexician Hat" Kernel.
+% The supposed ideal edge detection, zero-summing kernel.
+%
+% An alturnative to this kernel is to use a "DoG" with a sigma ratio of
+% approx 1.6 (according to wikipedia).
+%
+% DoG:{radius},{sigma1},{sigma2}
% "Difference of Gaussians" Kernel.
% As "Gaussian" but with a gaussian produced by 'sigma2' subtracted
% from the gaussian produced by 'sigma1'. Typically sigma2 > sigma1.
% The result is a zero-summing kernel.
%
-% LOG:{radius},{sigma}
-% "Laplacian of a Gaussian" or "Mexician Hat" Kernel.
-% The supposed ideal edge detection, zero-summing kernel.
-%
-% An alturnative to this kernel is to use a "DOG" with a sigma ratio of
-% approx 1.6, which can also be applied as a 2 pass "DOB" (see below).
-%
% Blur:{radius},{sigma}[,{angle}]
% Generates a 1 dimensional or linear gaussian blur, at the angle given
% (current restricted to orthogonal angles). If a 'radius' is given the
% same sigma value, However it is much faster to apply. This is how the
% "-blur" operator actually works.
%
-% DOB:{radius},{sigma1},{sigma2}[,{angle}]
-% "Difference of Blurs" Kernel.
-% As "Blur" but with the 1D gaussian produced by 'sigma2' subtracted
-% from thethe 1D gaussian produced by 'sigma1'.
-% The result is a zero-summing kernel.
-%
-% This can be used to generate a faster "DOG" convolution, in the same
-% way "Blur" can.
-%
% Comet:{width},{sigma},{angle}
% Blur in one direction only, much like how a bright object leaves
% a comet like trail. The Kernel is actually half a gaussian curve,
% Type 3 : 3x3 with center:4 edge:-2 corner:1
% Type 5 : 5x5 laplacian
% Type 7 : 7x7 laplacian
-% Type 15 : 5x5 LOG (sigma approx 1.4)
-% Type 19 : 9x9 LOG (sigma approx 1.4)
+% Type 15 : 5x5 LoG (sigma approx 1.4)
+% Type 19 : 9x9 LoG (sigma approx 1.4)
%
% Sobel:{angle}
% Sobel 'Edge' convolution kernel (3x3)
% the Sobel Kernel, but is designed to be isotropic. That is it takes
% into account the distance of the diagonal in the kernel.
%
-% Type 0: | -1, 0, 1 |
-% | -sqrt(2), 0, sqrt(2) |
-% | -1, 0, 1 |
+% Type 0: | 1, 0, -1 |
+% | sqrt(2), 0, -sqrt(2) |
+% | 1, 0, -1 |
%
% However this kernel is als at the heart of the FreiChen Edge Detection
% Process which uses a set of 9 specially weighted kernel. These 9
% from each other, both the direction and the strength of the edge can be
% determined.
%
-% Type 1: | -1, 0, 1 |
-% | -sqrt(2), 0, sqrt(2) | / 2*sqrt(2)
-% | -1, 0, 1 |
+% Type 1: | 1, 0, -1 |
+% | sqrt(2), 0, -sqrt(2) | / 2*sqrt(2)
+% | 1, 0, -1 |
%
-% Type 2: | -1, -sqrt(2), -1 |
-% | 0, 0, 0 | / 2*sqrt(2)
-% | 1, sqrt(2), 1 |
+% Type 2: | 1, sqrt(2), 1 |
+% | 0, 0, 0 | / 2*sqrt(2)
+% | 1, sqrt(2), 1 |
%
-% Type 3: | -sqrt(2), 1, 0 |
-% | 1, 0, -1 | / 2*sqrt(2)
-% | 0, -1, sqrt(2) |
+% Type 3: | sqrt(2), -1, 0 |
+% | -1, 0, 1 | / 2*sqrt(2)
+% | 0, 1, -sqrt(2) |
%
% Type 4: | 0, 1, -sqrt(2) |
% | -1, 0, 1 | / 2*sqrt(2)
% | sqrt(2), -1, 0 |
%
-% Type 5: | 0, 1, 0 |
-% | -1, 0, -1 | / 2
-% | 0, 1, 0 |
+% Type 5: | 0, -1, 0 |
+% | 1, 0, 1 | / 2
+% | 0, -1, 0 |
%
% Type 6: | 1, 0, -1 |
% | 0, 0, 0 | / 2
% | -1, 0, 1 |
%
-% Type 7: | -2, 1, -2 |
+% Type 7: | 1, -2, 1 |
+% | -2, 4, -2 | / 6
+% | -1, -2, 1 |
+%
+% Type 8: | -2, 1, -2 |
% | 1, 4, 1 | / 6
% | -2, 1, -2 |
%
-% Type 8: | 1, -2, 1 |
-% | -2, 4, -2 | / 6
-% | 1, -2, 1 |
-%
% Type 9: | 1, 1, 1 |
% | 1, 1, 1 | / 3
% | 1, 1, 1 |
% the default FreiChen (type 0) kernel. As such FreiChen:45 will look
% like a Sobel:45 but with 'sqrt(2)' instead of '2' values.
%
+% WARNING: The above was layed out as per
+% http://www.math.tau.ac.il/~turkel/notes/edge_detectors.pdf
+% But rotated 90 degrees so direction is from left rather than the top.
+% I have yet to find any secondary confirmation of the above. The only
+% other source found was actual source code at
+% http://ltswww.epfl.ch/~courstiv/exos_labos/sol3.pdf
+% Neigher paper defineds the kernels in a way that looks locical or
+% correct when taken as a whole.
%
% Boolean Kernels
%
break;
#if 0 /* set to 1 to do a compile-time check that we haven't missed anything */
case GaussianKernel:
- case DOGKernel:
- case LOGKernel:
+ case DoGKernel:
+ case LoGKernel:
case BlurKernel:
- case DOBKernel:
case CometKernel:
case DiamondKernel:
case SquareKernel:
switch(type) {
/* Convolution Kernels */
case GaussianKernel:
- case DOGKernel:
- case LOGKernel:
+ case DoGKernel:
+ case LoGKernel:
{ double
sigma = fabs(args->sigma),
sigma2 = fabs(args->xi),
if ( args->rho >= 1.0 )
kernel->width = (size_t)args->rho*2+1;
- else if ( (type != DOGKernel) || (sigma >= sigma2) )
+ else if ( (type != DoGKernel) || (sigma >= sigma2) )
kernel->width = GetOptimalKernelWidth2D(args->rho,sigma);
else
kernel->width = GetOptimalKernelWidth2D(args->rho,sigma2);
* basied on the Error Function 'erf()' (intergral of a gaussian)
*/
- if ( type == GaussianKernel || type == DOGKernel )
- { /* Calculate a Gaussian, OR positive half of a DOG */
+ if ( type == GaussianKernel || type == DoGKernel )
+ { /* Calculate a Gaussian, OR positive half of a DoG */
if ( sigma > MagickEpsilon )
{ A = 1.0/(2.0*sigma*sigma); /* simplify loop expressions */
B = 1.0/(Magick2PI*sigma*sigma);
}
}
- if ( type == DOGKernel )
+ if ( type == DoGKernel )
{ /* Subtract a Negative Gaussian for "Difference of Gaussian" */
if ( sigma2 > MagickEpsilon )
{ sigma = sigma2; /* simplify loop expressions */
kernel->values[kernel->x+kernel->y*kernel->width] -= 1.0;
}
- if ( type == LOGKernel )
+ if ( type == LoGKernel )
{ /* Calculate a Laplacian of a Gaussian - Or Mexician Hat */
if ( sigma > MagickEpsilon )
{ A = 1.0/(2.0*sigma*sigma); /* simplify loop expressions */
break;
}
case BlurKernel:
- case DOBKernel:
{ double
sigma = fabs(args->sigma),
- sigma2 = fabs(args->xi),
- A, B;
+ alpha, beta;
if ( args->rho >= 1.0 )
kernel->width = (size_t)args->rho*2+1;
- else if ( (type == BlurKernel) || (sigma >= sigma2) )
- kernel->width = GetOptimalKernelWidth1D(args->rho,sigma);
else
- kernel->width = GetOptimalKernelWidth1D(args->rho,sigma2);
+ kernel->width = GetOptimalKernelWidth1D(args->rho,sigma);
kernel->height = 1;
kernel->x = (ssize_t) (kernel->width-1)/2;
kernel->y = 0;
/* Calculate a Positive 1D Gaussian */
if ( sigma > MagickEpsilon )
{ sigma *= KernelRank; /* simplify loop expressions */
- A = 1.0/(2.0*sigma*sigma);
- B = 1.0/(MagickSQ2PI*sigma );
+ alpha = 1.0/(2.0*sigma*sigma);
+ beta= 1.0/(MagickSQ2PI*sigma );
for ( u=-v; u <= v; u++) {
- kernel->values[(u+v)/KernelRank] += exp(-((double)(u*u))*A)*B;
+ kernel->values[(u+v)/KernelRank] +=
+ exp(-((double)(u*u))*alpha)*beta;
}
}
else /* special case - generate a unity kernel */
kernel->values[kernel->x+kernel->y*kernel->width] = 1.0;
-
- /* Subtract a Second 1D Gaussian for "Difference of Blur" */
- if ( type == DOBKernel )
- {
- if ( sigma2 > MagickEpsilon )
- { sigma = sigma2*KernelRank; /* simplify loop expressions */
- A = 1.0/(2.0*sigma*sigma);
- B = 1.0/(MagickSQ2PI*sigma);
- for ( u=-v; u <= v; u++)
- kernel->values[(u+v)/KernelRank] -= exp(-((double)(u*u))*A)*B;
- }
- else /* limiting case - a unity (normalized Dirac) kernel */
- kernel->values[kernel->x+kernel->y*kernel->width] -= 1.0;
- }
#else
/* Direct calculation without curve averaging */
/* Calculate a Positive Gaussian */
if ( sigma > MagickEpsilon )
- { A = 1.0/(2.0*sigma*sigma); /* simplify loop expressions */
- B = 1.0/(MagickSQ2PI*sigma);
+ { alpha = 1.0/(2.0*sigma*sigma); /* simplify loop expressions */
+ beta = 1.0/(MagickSQ2PI*sigma);
for ( i=0, u=-kernel->x; u <= (ssize_t)kernel->x; u++, i++)
- kernel->values[i] = exp(-((double)(u*u))*A)*B;
+ kernel->values[i] = exp(-((double)(u*u))*alpha)*beta;
}
else /* special case - generate a unity kernel */
{ (void) ResetMagickMemory(kernel->values,0, (size_t)
kernel->width*kernel->height*sizeof(double));
kernel->values[kernel->x+kernel->y*kernel->width] = 1.0;
}
-
- /* Subtract a Second 1D Gaussian for "Difference of Blur" */
- if ( type == DOBKernel )
- {
- if ( sigma2 > MagickEpsilon )
- { sigma = sigma2; /* simplify loop expressions */
- A = 1.0/(2.0*sigma*sigma);
- B = 1.0/(MagickSQ2PI*sigma);
- for ( i=0, u=-kernel->x; u <= (ssize_t)kernel->x; u++, i++)
- kernel->values[i] -= exp(-((double)(u*u))*A)*B;
- }
- else /* limiting case - a unity (normalized Dirac) kernel */
- kernel->values[kernel->x+kernel->y*kernel->width] -= 1.0;
- }
#endif
/* Note the above kernel may have been 'clipped' by a user defined
** radius, producing a smaller (darker) kernel. Also for very small
ScaleKernelInfo(kernel, 1.0, CorrelateNormalizeValue);
/* rotate the 1D kernel by given angle */
- RotateKernelInfo(kernel, (type == BlurKernel) ? args->xi : args->psi );
+ RotateKernelInfo(kernel, args->xi );
break;
}
case CometKernel:
kernel=ParseKernelArray(
"7:-10,-5,-2,-1,-2,-5,-10 -5,0,3,4,3,0,-5 -2,3,6,7,6,3,-2 -1,4,7,8,7,4,-1 -2,3,6,7,6,3,-2 -5,0,3,4,3,0,-5 -10,-5,-2,-1,-2,-5,-10" );
break;
- case 15: /* a 5x5 LOG (sigma approx 1.4) */
+ case 15: /* a 5x5 LoG (sigma approx 1.4) */
kernel=ParseKernelArray(
"5: 0,0,-1,0,0 0,-1,-2,-1,0 -1,-2,16,-2,-1 0,-1,-2,-1,0 0,0,-1,0,0");
break;
- case 19: /* a 9x9 LOG (sigma approx 1.4) */
+ case 19: /* a 9x9 LoG (sigma approx 1.4) */
/* http://www.cscjournals.org/csc/manuscript/Journals/IJIP/volume3/Issue1/IJIP-15.pdf */
kernel=ParseKernelArray(
"9: 0,-1,-1,-2,-2,-2,-1,-1,0 -1,-2,-4,-5,-5,-5,-4,-2,-1 -1,-4,-5,-3,-0,-3,-5,-4,-1 -2,-5,-3,@12,@24,@12,-3,-5,-2 -2,-5,-0,@24,@40,@24,-0,-5,-2 -2,-5,-3,@12,@24,@12,-3,-5,-2 -1,-4,-5,-3,-0,-3,-5,-4,-1 -1,-2,-4,-5,-5,-5,-4,-2,-1 0,-1,-1,-2,-2,-2,-1,-1,0");
}
case SobelKernel:
{
- kernel=ParseKernelArray("3: -1,0,1 -2,0,2 -1,0,1");
+ kernel=ParseKernelArray("3: 1,0,-1 2,0,-2 1,0,-1");
if (kernel == (KernelInfo *) NULL)
return(kernel);
kernel->type = type;
}
case RobertsKernel:
{
- kernel=ParseKernelArray("3: 0,0,0 -1,1,0 0,0,0");
+ kernel=ParseKernelArray("3: 0,0,0 1,-1,0 0,0,0");
if (kernel == (KernelInfo *) NULL)
return(kernel);
kernel->type = type;
}
case PrewittKernel:
{
- kernel=ParseKernelArray("3: -1,1,1 0,0,0 -1,1,1");
+ kernel=ParseKernelArray("3: 1,0,-1 1,0,-1 1,0,-1");
if (kernel == (KernelInfo *) NULL)
return(kernel);
kernel->type = type;
}
case CompassKernel:
{
- kernel=ParseKernelArray("3: -1,1,1 -1,-2,1 -1,1,1");
+ kernel=ParseKernelArray("3: 1,1,-1 1,-2,-1 1,1,-1");
if (kernel == (KernelInfo *) NULL)
return(kernel);
kernel->type = type;
}
case KirschKernel:
{
- kernel=ParseKernelArray("3: -3,-3,5 -3,0,5 -3,-3,5");
+ kernel=ParseKernelArray("3: 5,-3,-3 5,0,-3 5,-3,-3");
if (kernel == (KernelInfo *) NULL)
return(kernel);
kernel->type = type;
break;
}
case FreiChenKernel:
- /* http://www.math.tau.ac.il/~turkel/notes/edge_detectors.pdf */
- /* http://ltswww.epfl.ch/~courstiv/exos_labos/sol3.pdf */
+ /* Direction is set to be left to right positive */
+ /* http://www.math.tau.ac.il/~turkel/notes/edge_detectors.pdf -- RIGHT? */
+ /* http://ltswww.epfl.ch/~courstiv/exos_labos/sol3.pdf -- WRONG? */
{ switch ( (int) args->rho ) {
default:
case 0:
- kernel=ParseKernelArray("3: -1,0,1 -2,0,2 -1,0,1");
+ kernel=ParseKernelArray("3: 1,0,-1 2,0,-2 1,0,-1");
if (kernel == (KernelInfo *) NULL)
return(kernel);
- kernel->values[3] = -MagickSQ2;
- kernel->values[5] = +MagickSQ2;
+ kernel->values[3] = +MagickSQ2;
+ kernel->values[5] = -MagickSQ2;
CalcKernelMetaData(kernel); /* recalculate meta-data */
break;
case 1:
- kernel=ParseKernelArray("3: -1,0,1 -2,0,2 -1,0,1");
+ kernel=ParseKernelArray("3: 1,0,-1 2,0,-2 1,0,-1");
if (kernel == (KernelInfo *) NULL)
return(kernel);
kernel->type = type;
- kernel->values[3] = -MagickSQ2;
- kernel->values[5] = +MagickSQ2;
+ kernel->values[3] = +MagickSQ2;
+ kernel->values[5] = -MagickSQ2;
CalcKernelMetaData(kernel); /* recalculate meta-data */
ScaleKernelInfo(kernel, 1.0/2.0*MagickSQ2, NoValue);
break;
case 2:
- kernel=ParseKernelArray("3: -1,-2,-1 0,0,0 1,2,1");
+ kernel=ParseKernelArray("3: 1,2,1 0,0,0 1,2,1");
if (kernel == (KernelInfo *) NULL)
return(kernel);
kernel->type = type;
ScaleKernelInfo(kernel, 1.0/2.0*MagickSQ2, NoValue);
break;
case 3:
- kernel=ParseKernelArray("3: -2,1,0 1,0,-1 0,-1,2");
+ kernel=ParseKernelArray("3: 2,-1,0 -1,0,1 0,1,-2");
if (kernel == (KernelInfo *) NULL)
return(kernel);
kernel->type = type;
- kernel->values[0] = -MagickSQ2;
- kernel->values[8] = +MagickSQ2;
+ kernel->values[0] = +MagickSQ2;
+ kernel->values[8] = -MagickSQ2;
CalcKernelMetaData(kernel);
ScaleKernelInfo(kernel, 1.0/2.0*MagickSQ2, NoValue);
break;
ScaleKernelInfo(kernel, 1.0/2.0*MagickSQ2, NoValue);
break;
case 5:
- kernel=ParseKernelArray("3: 0,1,0 -1,0,-1 0,1,0");
+ kernel=ParseKernelArray("3: 0,-1,0 1,0,1 0,-1,0");
if (kernel == (KernelInfo *) NULL)
return(kernel);
kernel->type = type;
ScaleKernelInfo(kernel, 1.0/2.0, NoValue);
break;
case 7:
- kernel=ParseKernelArray("3: -2,1,-2 1,4,1 -2,1,-2");
+ kernel=ParseKernelArray("3: 1,-2,1 -2,4,-2 -1,-2,1");
if (kernel == (KernelInfo *) NULL)
return(kernel);
kernel->type = type;
ScaleKernelInfo(kernel, 1.0/6.0, NoValue);
break;
case 8:
- kernel=ParseKernelArray("3: 1,-2,1 -2,4,-2 1,-2,1");
+ kernel=ParseKernelArray("3: -2,1,-2 1,4,1 -2,1,-2");
if (kernel == (KernelInfo *) NULL)
return(kernel);
kernel->type = type;
}
}
- /* APPLY THE MORPHOLOGICAL PRIMITIVE (curr -> work) */
+ /* APPLY THE MORPHOLOGICAL PRIMITIVE (curr -> work) */
count++;
changed = MorphologyPrimitive(curr_image, work_image, primative,
channel, this_kernel, bias, exception);
switch (kernel->type) {
/* These built-in kernels are cylindrical kernels, rotating is useless */
case GaussianKernel:
- case DOGKernel:
+ case DoGKernel:
+ case LoGKernel:
case DiskKernel:
case PeaksKernel:
case LaplacianKernel:
% value is usually provided by the user as a percentage value in the
% 'convolve:scale' setting.
%
-% The resulting effect is to either convert a 'zero-summing' edge detection
-% kernel (such as a "Laplacian", "DOG" or a "LOG") into a 'sharpening'
-% kernel.
-%
-% Alternativally by using a purely positive kernel, and using a negative
-% post-normalizing scaling factor, you can convert a 'blurring' kernel (such
-% as a "Gaussian") into a 'unsharp' kernel.
+% The resulting effect is to convert the defined kernels into blended
+% soft-blurs, unsharp kernels or into sharpening kernels.
%
% The format of the UnityAdditionKernelInfo method is:
%
projects / imagemagick / commitdiff