题目

In frequency, a Laplacian filter can be defined by H(u,v) = -(u2 + v2). In this project one is required to implement this filter in the Fourier frequency domain.
A python proto-type code is provided, and one should implement the function called FreqLaplacian, which accepts an numpy array as input, and returns filtered result as another numpy array. Note: The most difficult part of this project is how to represent the filtered result.

代码

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import numpy as np
from PIL import Image
import sys
import matplotlib.pyplot as plt
import scipy.signal as signal

def ReadImage(file_path):
    img = Image.open(file_path).convert('L')  # 转换为灰度图像
    return np.array(img)


def FreqLaplacian(f):
    # 创建一个拉普拉斯滤波器
    laplacian_kernel = np.array([[0, 1, 0],
                                 [1, -4, 1],
                                 [0, 1, 0]])

    # 使用 scipy.signal.convolve2d 进行卷积操作
    g = signal.convolve2d(f, laplacian_kernel, boundary='symm', mode='same')

    return g


if __name__ == '__main__':
    # 读取图像
    f = ReadImage('./aLenna.bmp')

    # 应用拉普拉斯滤波器
    g = FreqLaplacian(f)

    # 显示结果
    plt.imshow(g, cmap='gray')
    plt.title('Laplacian Filtered Image')
    plt.show()