Difference of Gaussian Filter with numpy

DoG_filters.py

# http://fourier.eng.hmc.edu/e161/lectures/gradient/node9.html

"""
σ1 := width or std for first gussian distribution 
σ2 := width or std for second gussian distribution
"""
def DoG(σ1, σ2, shape): 
    if (σ1 == 0 or σ2 == 0):
        print("WARNING: Result Filter gonna be all zero. σ1 and σ2 must be non zero")
        return np.zeros(shape)
    def _(x, y):
        xy_exp = -0.5 * ((x-(shape[0]//2))**2 + (y-(shape[1]//2))**2)
        return (np.exp(xy_exp/σ1**2)/σ1 - np.exp(xy_exp/σ2**2)/σ2) / np.sqrt(2 * np.pi)
    return np.fromfunction(_, shape)
	
	
"""	
mechanistic-v1-model or gabor filter
λ := wavelength
θ := orientation
σ := standard deviation
γ := aspect ratio

np.meshgrid is tiny faster than our Gabor caused by alignment on L:32 
https://en.wikipedia.org/wiki/Gabor_filter
"""
def Gabor(λ, θ, σ, γ, shape):
    if (λ == 0 or σ == 0):
        print("WARNING: Result Filter gonna be all zero. λ and σ must be non zero")
        return np.zeros(shape)
    def _(x, y):
        _x, _y = x-(shape[0]//2), y-(shape[1]//2)
        X = _x*np.cos(θ) + _y*np.sin(θ)
        λ2Y2 = λ**2 * (-_x*np.sin(θ) + _y*np.cos(θ))**2
        return np.exp(-0.5*(X**2 + λ2Y2)/σ**2) * np.cos(2*np.pi*X/λ)
    return np.fromfunction(_, shape)