Gabor Filter

01_gabor_filter.py

# (reference) https://ja.wikipedia.org/wiki/ガボールフィルタ

%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
import scipy.stats as st
import math

plt.style.use('fivethirtyeight')

def gabor_filter(sigma_x, sigma_y, theta, lamb, psi, gamma):
    
    sz_x = math.floor(6 * sigma_x)
    if (sz_x % 2) == 0:
        sz_x = sz_x + 1

    sz_y = math.floor(6 * sigma_y)
    if (sz_y %2)==0:
        sz_y=sz_y+1

    xx = np.linspace(-math.floor(sz_x/2), math.floor(sz_x/2), 100)
    yy = np.linspace(math.floor(-sz_y/2), math.floor(sz_y/2), 100)
    X, Y = np.meshgrid(xx, yy)

    # Rotation 
    x_theta =  X*np.cos(theta) + Y*np.sin(theta)
    y_theta = -X*np.sin(theta) + Y*np.cos(theta)
    
    x_theta2 = np.array(map(lambda x : x**2 / sigma_x**2, x_theta))
    x_theta3 = np.array(map(lambda x : 2*np.pi/lamb*x + psi, x_theta))
    y_theta2 = np.array(map(lambda y : gamma**2 * y**2 / sigma_y**2, y_theta))
    
    return np.exp(-.5*(x_theta2 + y_theta2))*np.cos(x_theta3)

def draw_digit(data, size):
    #print n
    #size = 17
    Z = data.reshape(size,size)   # convert from vector to 28x28 matrix
    Z = np.array(Z[::-1,:]).T                # flip vertical
    plt.xlim(0,size-1)
    plt.ylim(0,size-1)
    plt.pcolor(Z)
    plt.gray()
    plt.tick_params(labelbottom="off")
    plt.tick_params(labelleft="off")

#\lambda は波長のコサイン成分、\theta はガボール関数の縞模様の方向、\psi は位相オフセット、\gamma は空間アスペクト比
data = gabor_filter(90., 90., theta=np.pi/4, lamb=400, psi=0., gamma=.5)
plt.figure(figsize=(3,3))
draw_digit(data, data.shape[0])

02_cos_filter.py

def cos_filter(size, theta=0, freq=1, phase=0):
    
    if (size %2) != 0:
        tuning = 0.5
    else:
        tuning = 0

    _min = size - math.floor(size/2) - tuning
    _max = size + math.floor(size/2) + tuning
    
    xx = np.linspace(_min, _max, size)
    yy = np.linspace(_min, _max, size)
    X, Y = np.meshgrid(xx, yy)

    # Rotation 
    x_theta =  (X*freq+phase)*np.cos(theta) + (Y*freq+phase)*np.sin(theta)
    
    return np.cos(x_theta)




data = cos_filter(17, theta=np.pi/4, freq=.346, phase=-1.5)
plt.figure(figsize=(3,3))
draw_digit(data, data.shape[0])