指数型高通滤波

指数型高通滤波器的传递函数如下：

$H(u,v) = 1 - \exp(\ln(1/\sqrt{2})(D(u,v) / D_0)^n)$H(u,v)=1−exp(ln(1/2​)(D(u,v)/D0​)n)

Python语言实现如下：

def index_low_pass_kernel(img,D0,n=1):
    r,c = img.shape[1],img.shape[0]
    u = np.arange(r)
    v = np.arange(c)
    u, v = np.meshgrid(u, v)
    low_pass = np.sqrt( (u-r/2)**2 + (v-c/2)**2 )

    low_pass = np.exp(np.log(1 / np.sqrt(2)) * ((low_pass / D0)**n))

    # low_pass = np.clip(low_pass,0,1)
    return low_pass

def index_high_pass_filter(src,D0=5,n=1):
    assert src.ndim == 2
    kernel = 1 - index_low_pass_kernel(src,D0,n)
    gray = np.float64(src)
    gray_fft = np.fft.fft2(gray)
    gray_fftshift = np.fft.fftshift(gray_fft)
    dst = np.zeros_like(gray_fftshift)
    dst_filtered = kernel * gray_fftshift
    dst_ifftshift = np.fft.ifftshift(dst_filtered)
    dst_ifft = np.fft.ifft2(dst_ifftshift)
    dst = np.abs(np.real(dst_ifft))
    dst = np.clip(dst,0,255)
    return np.uint8(dst)

程序实现代码如下：