# -*- coding: utf-8 -*-
"""
FilterKernel
=============
Implementation of various volumetric filter kernels.
.. _FilterTypes:
Filter Type
-----------
Filter types defined by the ``ftype`` key include:
=============== =====================================
Type Descrition
=============== =====================================
``mean`` uniform averaging filter
``gaussian`` Gaussian filter
``log`` Laplacian of Gaussian filter (LoG)
``dog`` Difference of Gaussians filter (DoG)
``sphere`` Sphere filter
``disk`` Disk filter
=============== =====================================
"""
__author__ = 'Christoph Kirst <christoph.kirst.ck@gmail.com>'
__license__ = 'GPLv3 - GNU General Pulic License v3 (see LICENSE.txt)'
__copyright__ = 'Copyright © 2020 by Christoph Kirst'
__webpage__ = 'http://idisco.info'
__download__ = 'http://www.github.com/ChristophKirst/ClearMap2'
import numpy as np
import math
import ClearMap.ImageProcessing.Filter.StructureElement as se
###############################################################################
### Filter kernel
###############################################################################
[docs]def filter_kernel(ftype = 'Gaussian', shape = (5,5), radius = None, sigma = None, sigma2 = None):
"""Creates a filter kernel of a special type
Arguments
---------
ftype : str
Filter type, see :ref:`FilterTypes`.
shape : array or tuple
Shape of the filter kernel.
radius : tuple or float
Radius of the kernel (if applicable).
sigma : tuple or float
Std for the first gaussian (if applicable).
sigma2 : tuple or float
Std of a second gaussian (if present).
Returns
-------
krenel : array
Filter kernel.
"""
ndim = len(shape);
if ndim == 2:
return filter_kernel_2d(ftype=ftype, shape=shape, sigma=sigma, sigma2=sigma2, radius=radius);
elif ndim == 3:
return filter_kernel_3d(ftype=ftype, shape=shape, sigma=sigma, sigma2=sigma2, radius=radius);
else:
raise ValueError('Kernel for %d dimensions not implemented !' % ndim);
[docs]def filter_kernel_2d(ftype = 'Gaussian', shape = (5,5), sigma = None, sigma2 = None, radius = None):
"""Creates a 2d filter kernel of a special type
Arguments
---------
ftype : str
Filter type, see :ref:`FilterTypes`.
shape : array or tuple
Shape of the filter kernel.
radius : tuple or float
Radius of the kernel (if applicable).
sigma : tuple or float
Std for the first gaussian (if applicable).
sigma2 : tuple or float
Std of a second gaussian (if present).
Returns
-------
krenel : array
Filter kernel.
"""
ftype = ftype.lower();
o = se.structure_element_offsets(shape);
mo = o.min(axis=1);
shape = np.array(shape);
if ftype == 'mean': # unifrom
return np.ones(shape)/ shape.prod();
elif ftype == 'gaussian':
if sigma == None:
sigma = shape / 2. / math.sqrt(2 * math.log(2));
sigma = np.array(sigma);
if len(sigma) < 3:
sigma = np.array((sigma[0], sigma[0]));
else:
sigma = sigma[0:2];
g = np.mgrid[-o[0,0]:o[0,1], -o[1,0]:o[1,1]];
add = ((shape + 1) % 2) / 2.;
x = g[0,:,:,:] + add[0];
y = g[1,:,:,:] + add[1];
ker = np.exp(-(x * x / 2. / (sigma[0] * sigma[0]) + y * y / 2. / (sigma[1] * sigma[1])));
return ker/ker.sum();
elif ftype == 'sphere':
if radius == None:
radius = mo;
radius = np.array(radius);
if len(radius) < 3:
radius = np.array((radius[0], radius[0]));
else:
radius = radius[0:2];
g = np.mgrid[-o[0,0]:o[0,1], -o[1,0]:o[1,1]];
add = ((shape + 1) % 2) / 2.;
x = g[0,:,:,:] + add[0];
y = g[1,:,:,:] + add[1];
ker = 1 - (x * x / 2. / (radius[0] * radius[0]) + y * y / 2. / (radius[1] * radius[1]));
ker[ker < 0] = 0.;
return ker / ker.sum();
elif ftype == 'disk':
if radius == None:
radius = mo;
radius = np.array(radius);
if len(radius) < 3:
radius = np.array((radius[0], radius[0]));
else:
radius = radius[0:2];
g = np.mgrid[-o[0,0]:o[0,1], -o[1,0]:o[1,1]];
add = ((shape + 1) % 2) / 2.;
x = g[0,:,:,:] + add[0];
y = g[1,:,:,:] + add[1];
ker = 1 - (x * x / 2. / (radius[0] * radius[0]) + y * y / 2. / (radius[1] * radius[1]));
ker[ker < 0] = 0.;
ker[ker > 0] = 1.0;
return ker / ker.sum();
elif ftype == 'log': # laplacian of gaussians
if sigma == None:
sigma = shape / 4. / math.sqrt(2 * math.log(2));
sigma = np.array(sigma);
if len(sigma) < 3:
sigma = np.array((sigma[0], sigma[0]));
else:
sigma = sigma[0:2];
g = np.mgrid[-o[0,0]:o[0,1], -o[1,0]:o[1,1]];
add = ((shape + 1) % 2) / 2.;
x = g[0,:,:,:] + add[0];
y = g[1,:,:,:] + add[1];
ker = np.exp(-(x * x / 2. / (radius[0] * radius[0]) + y * y / 2. / (radius[1] * radius[1])));
ker /= ker.sum();
arg = x * x / math.pow(sigma[0], 4) + y * y/ math.pow(sigma[1],4) - (1/(sigma[0] * sigma[0]) + 1/(sigma[1] * sigma[1]));
ker = ker * arg;
return ker - ker.sum()/len(ker);
elif ftype == 'dog':
if sigma2 == None:
sigma2 = shape / 2. / math.sqrt(2 * math.log(2));
sigma2 = np.array(sigma2);
if len(sigma2) < 3:
sigma2 = np.array((sigma2[0], sigma2[0]));
else:
sigma2 = sigma2[0:2];
if sigma == None:
sigma = sigma2 / 1.5;
sigma = np.array(sigma);
if len(sigma) < 3:
sigma = np.array((sigma[0], sigma[0]));
else:
sigma = sigma[0:2];
g = np.mgrid[-o[0,0]:o[0,1], -o[1,0]:o[1,1]];
add = ((shape + 1) % 2) / 2.;
x = g[0,:,:,:] + add[0];
y = g[1,:,:,:] + add[1];
ker = np.exp(-(x * x / 2. / (sigma[0] * sigma[0]) + y * y / 2. / (sigma[1] * sigma[1])));
ker /= ker.sum();
sub = np.exp(-(x * x / 2. / (sigma2[0] * sigma2[0]) + y * y / 2. / (sigma2[1] * sigma2[1])));
return ker - sub / sub.sum();
else:
raise ValueError('Filter type %r not valid!' % ftype);
[docs]def filter_kernel_3d(ftype = 'Gaussian', shape = (5,5,5), sigma = None, sigma2 = None, radius = None):
"""Creates a 3d filter kernel of a special type
Arguments
---------
ftype : str
Filter type, see :ref:`FilterTypes`.
shape : array or tuple
Shape of the filter kernel.
radius : tuple or float
Radius of the kernel (if applicable).
sigma : tuple or float
Std for the first gaussian (if applicable).
sigma2 : tuple or float
Std of a second gaussian (if present).
Returns
-------
krenel : array
Filter kernel.
"""
ftype = ftype.lower();
o = se.structure_element_offsets(shape);
mo = o.min(axis=1);
shape = np.array(shape);
if ftype == 'mean': # differnce of gaussians
return np.ones(shape)/ shape.prod();
elif ftype == 'gaussian':
if sigma == None:
sigma = shape / 2. / math.sqrt(2 * math.log(2));
sigma = np.array(sigma);
if len(sigma) < 3:
sigma = np.array((sigma[0], sigma[0], sigma[0]));
else:
sigma = sigma[0:3];
g = np.mgrid[-o[0,0]:o[0,1], -o[1,0]:o[1,1], -o[2,0]:o[2,1]];
add = ((shape + 1) % 2) / 2.;
x = g[0,:,:,:] + add[0];
y = g[1,:,:,:] + add[1];
z = g[2,:,:,:] + add[2];
ker = np.exp(-(x * x / 2. / (sigma[0] * sigma[0]) + y * y / 2. / (sigma[1] * sigma[1]) + z * z / 2. / (sigma[2] * sigma[2])));
return ker/ker.sum();
elif ftype == 'sphere':
if radius == None:
radius = mo;
radius = np.array(radius);
if len(radius) < 3:
radius = np.array((radius[0], radius[0], radius[0]));
else:
radius = radius[0:3];
g = np.mgrid[-o[0,0]:o[0,1], -o[1,0]:o[1,1], -o[2,0]:o[2,1]];
add = ((shape + 1) % 2) / 2.;
x = g[0,:,:,:] + add[0];
y = g[1,:,:,:] + add[1];
z = g[2,:,:,:] + add[2];
ker = 1 - (x * x / 2. / (radius[0] * radius[0]) + y * y / 2. / (radius[1] * radius[1]) + z * z / 2. / (radius[2] * radius[2]));
ker[ker < 0] = 0.;
return ker / ker.sum();
elif ftype == 'disk':
if radius == None:
radius = mo;
radius = np.array(radius);
if len(radius) < 3:
radius = np.array((radius[0], radius[0], radius[0]));
else:
radius = radius[0:3];
g = np.mgrid[-o[0,0]:o[0,1], -o[1,0]:o[1,1], -o[2,0]:o[2,1]];
add = ((shape + 1) % 2) / 2.;
x = g[0,:,:,:] + add[0];
y = g[1,:,:,:] + add[1];
z = g[2,:,:,:] + add[2];
ker = 1 - (x * x / 2. / (radius[0] * radius[0]) + y * y / 2. / (radius[1] * radius[1]) + z * z / 2. / (radius[2] * radius[2]));
ker[ker < 0] = 0.;
ker[ker > 0] = 1.0;
return ker / ker.sum();
elif ftype == 'log': # laplacian of gaussians
if sigma == None:
sigma = shape / 4. / math.sqrt(2 * math.log(2));
sigma = np.array(sigma);
if len(sigma) < 3:
sigma = np.array((sigma[0], sigma[0], sigma[0]));
else:
sigma = sigma[0:3];
g = np.mgrid[-o[0,0]:o[0,1], -o[1,0]:o[1,1], -o[2,0]:o[2,1]];
add = ((shape + 1) % 2) / 2.;
x = g[0,:,:,:] + add[0];
y = g[1,:,:,:] + add[1];
z = g[2,:,:,:] + add[2];
ker = np.exp(-(x * x / 2. / (radius[0] * radius[0]) + y * y / 2. / (radius[1] * radius[1]) + z * z / 2. / (radius[2] * radius[2])));
ker /= ker.sum();
arg = x * x / math.pow(sigma[0], 4) + y * y/ math.pow(sigma[1],4) + z * z / math.pow(sigma[2],4) - (1/(sigma[0] * sigma[0]) + 1/(sigma[1] * sigma[1]) + 1 / (sigma[2] * sigma[2]));
ker = ker * arg;
return ker - ker.sum()/len(ker);
elif ftype == 'dog':
if sigma2 == None:
sigma2 = shape / 2. / math.sqrt(2 * math.log(2));
sigma2 = np.array(sigma2);
if len(sigma2) < 3:
sigma2 = np.array((sigma2[0], sigma2[0], sigma2[0]));
else:
sigma2 = sigma2[0:3];
if sigma == None:
sigma = sigma2 / 1.5;
sigma = np.array(sigma);
if len(sigma) < 3:
sigma = np.array((sigma[0], sigma[0], sigma[0]));
else:
sigma = sigma[0:3];
g = np.mgrid[-o[0,0]:o[0,1], -o[1,0]:o[1,1], -o[2,0]:o[2,1]];
add = ((shape + 1) % 2) / 2.;
x = g[0,:,:,:] + add[0];
y = g[1,:,:,:] + add[1];
z = g[2,:,:,:] + add[2];
ker = np.exp(-(x * x / 2. / (sigma[0] * sigma[0]) + y * y / 2. / (sigma[1] * sigma[1]) + z * z / 2. / (sigma[2] * sigma[2])));
ker /= ker.sum();
sub = np.exp(-(x * x / 2. / (sigma2[0] * sigma2[0]) + y * y / 2. / (sigma2[1] * sigma2[1]) + z * z / 2. / (sigma2[2] * sigma2[2])));
return ker - sub / sub.sum();
else:
raise ValueError('Filter type %r not valid!' % ftype);
###############################################################################
### Tests
###############################################################################
def _test():
"""Tests"""
import ClearMap.ImageProcessing.Filter.FilterKernel as fk
import ClearMap.Visualization.Plot3d as p3d
k = fk.filter_kernel(ftype='dog', shape=(15,15,15), sigma=None, radius=None, sigma2=None);
p3d.plot(k)
Source
