Function logfilter

Synopse

Laplacian of Gaussian filter.

g = logfilter(f, sigma)
- g: Image.
- f: Image. input image
- sigma: Double. scaling factor

Description

Filters the image f by the Laplacian of Gaussian (LoG) filter with parameter sigma. This filter is also known as the Marr-Hildreth filter. Obs: to better efficiency, this implementation computes the filter in the frequency domain.



In [1]:

    
import numpy as np
def logfilter(f, sigma):
    import ia898.src as ia
    
    f = np.array(f)

    if len(f.shape) == 1: f = f[newaxis,:]
    x = (np.array(f.shape)//2).astype(int)
    
    h = ia.log(f.shape, (np.array(f.shape)//2).astype(int), sigma)
    h = ia.dftshift(h)
    H = np.fft.fft2(h)
    if not ia.isccsym(H):
        raise ValueError('log filter is not symmetrical')        
    G = np.fft.fft2(f) * H
    g = np.fft.ifft2(G).real
    
    return g

Examples



In [2]:

    
testing = (__name__ == "__main__")
if testing:
    ! jupyter nbconvert --to python logfilter.ipynb
    import numpy as np
    import sys,os
    ia898path = os.path.abspath('../../')
    if ia898path not in sys.path:
        sys.path.append(ia898path)
    import ia898.src as ia









    



[NbConvertApp] Converting notebook logfilter.ipynb to python
[NbConvertApp] Writing 2015 bytes to logfilter.py

Example 1



In [3]:

    
if testing:
    %matplotlib inline
    import matplotlib.pyplot as plt
    import matplotlib.image as mpimg

    f = mpimg.imread('../data/cameraman.tif')

    g07 = ia.logfilter(f, 0.7)

    nb = ia.nbshow(3)
    nb.nbshow(f, 'Imagem original')
    nb.nbshow(ia.normalize(g07), 'LoG filter')
    nb.nbshow(g07 > 0, 'positive values')
    nb.nbshow()









    




                                    
                    Imagem original                     
                    LoG filter                     
                    positive values

Example 2



In [4]:

    
if testing:
    g5 = ia.logfilter(f, 5)
    g10 = ia.logfilter(f, 10)

    nb = ia.nbshow(2,2)
    nb.nbshow(ia.normalize(g5), 'sigma=5')
    nb.nbshow(g5 > 0, 'positive, sigma=5')
    nb.nbshow(ia.normalize(g10), 'sigma=10')
    nb.nbshow(g10 > 0, 'positive, sigma=10')
    nb.nbshow()









    




                                    
                    sigma=5                     
                    positive, sigma=5
                    
                    sigma=10                     
                    positive, sigma=10



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