MATLAB filter2/conv2 函数在 Python 语言中的等价函数

梦里梦外; 2022-01-06 11:03 314阅读 0赞

##  MATLAB filter2 和 conv2 函数说明 ##

在 MATLAB 中，**filter2** 函数实现二维数字滤波器．**conv2** 函数实现二维卷积．

**　　filter2(H, X, mode)** 等价于 **conv2(X, rot90(H,2), mode)**. 其中，**H** 表示有理传递函数的系数(Coefficients of rational transfer function)，即常说的滤波器核或卷积核．**X** 表示输入数据．**mode** 表示卷积或滤波所采用的模式，其决定了返回数据的长度，以及结果数据的不同部分．共有三种模式：'full', 'same', 'valid'，具体含义详见 filter2 函数的[ shape 参数文档说明][shape]，或查看我的博文[ 相关与卷积（数字信号处理）的数学原理及 Python 实现][Python] 的原理部分．

注：MATLAB 中，B = [rot90][](A, k) 将数组 A 逆时针旋转 k\*90 度，其中 k 为整数．

## Python 中的等价函数 ##

在 Python 中，MATLAB **filter2** 的等价函数是[ **scipy.signal.correlate2d**][_scipy.signal.correlate2d]；MATLAB **conv2** 的等价函数是 [**scipy.signal.convolve2d**][scipy.signal.convolve2d]．

具体来说，**filter2(H, X, mode)** 等价于 **scipy.signal.correlate2d(X, H, mode)**；**conv2(X, H, mode)** 等价于 **scipy.signal.convolve2d(X, H, mode)**．

注意，**filter2**(MATLAB) 与 **scipy.signal.correlate2d**的输入参数 H, X 的顺序是不一致的．

如果二维滤波或卷积结果采用常用的 'same' 模式，还可以使用 Python 中的 **cv2.filter2D** (OpenCV模块), **scipy.ndimage.correlate** 和 **scipy.ndimage.convolve** 替代．对于二维滤波（'same'模式）的具体用法为

[cv2.filter2D][](X, -1, H, borderType=cv2.BORDER\_CONSTANT)  
　　[scipy.ndimage.correlate][](X, H, mode='constant', cval=0.0)  
　　[scipy.ndimage.convolve][](X, [np.rot90][](H,2), mode='constant', cval=0.0)

## 示例 ##

MATLAB 代码

X = [1 2 3];  % input data H = [4 5 6];  % kernel % display filter2() results disp('filter2 results'); fprintf('full: '); disp(filter2(H, X, 'full')); fprintf('same: '); disp(filter2(H, X, 'same')); fprintf('valid: '); disp(filter2(H, X, 'valid')); fprintf('\n'); % display conv2() results disp('conv2 results'); fprintf('full: '); disp(conv2(H, X, 'full')); fprintf('same: '); disp(conv2(H, X, 'same')); fprintf('valid: '); disp(conv2(H, X, 'valid')); fprintf('\n');

Python 代码

import numpy as np import scipy.ndimage import scipy.signal import cv2 X = np.array([1, 2, 3]).reshape(1,3)  # input data
    H = np.array([4, 5, 6]).reshape(1,3)  # kernel
    
    # display scipy.signal.correlate2 results
    print ("scipy.signal.correlate2d results") print ("full: {}".format(scipy.signal.correlate2d(X, H, 'full'))) print ("same: {}".format(scipy.signal.correlate2d(X, H, 'same'))) print ("valid: {}".format(scipy.signal.correlate2d(X, H, 'valid'))) print ('') # display scipy.signal.convolve2 results
    print ("scipy.signal.convolve2d results") print ("full: {}".format(scipy.signal.convolve2d(X, H, 'full'))) print ("same: {}".format(scipy.signal.convolve2d(X, H, 'same'))) print ("valid: {}".format(scipy.signal.convolve2d(X, H, 'valid'))) # others
    print ("\nother filters in Python ('same' mode)") print ("cv2.filter2D: {}".format(cv2.filter2D(X.astype('float32'), -1, H, borderType=cv2.BORDER_CONSTANT))) print ("scipy.ndimage.correlate: {}".format(scipy.ndimage.correlate(X, H, mode='constant', cval=0.0))) print ("scipy.ndimage.convolve: {}".format(scipy.ndimage.convolve(X, np.rot90(H,2), mode='constant', cval=0.0)))

注：**cv2.filter2D** 在 **OpenCV 3.4.0** 中，不支持整数类型的输入数据，需要先转为浮点型如 'float32' 等，才能正确执行．

## 参考资料 ##

1. Equivalent of Matlab filter2(filter, image, 'valid') in python. [https://stackoverflow.com/questions/43270274/equivalent-of-matlab-filter2filter-image-valid-in-python ][https_stackoverflow.com_questions_43270274_equivalent-of-matlab-filter2filter-image-valid-in-python]

2. Equivalent function of matlabs filter2 in opencv.  [https://stackoverflow.com/questions/29212944/equivalent-function-of-matlabs-filter2-in-opencv][https_stackoverflow.com_questions_29212944_equivalent-function-of-matlabs-filter2-in-opencv]

3. What is the difference between conv2, filter2 and imfilter..? [https://www.mathworks.com/matlabcentral/answers/17529-what-is-the-difference-between-conv2-filter2-and-imfilter][https_www.mathworks.com_matlabcentral_answers_17529-what-is-the-difference-between-conv2-filter2-and-imfilter]

转载于:https://www.cnblogs.com/klchang/p/10427601.html

[shape]: https://www.mathworks.com/help/matlab/ref/filter2.html#bvjn16f-1-shape
[Python]: https://www.cnblogs.com/klchang/p/10012598.html
[rot90]: https://www.mathworks.com/help/matlab/ref/rot90.html
[_scipy.signal.correlate2d]: https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.correlate2d.html
[scipy.signal.convolve2d]: https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.convolve2d.html
[cv2.filter2D]: https://docs.opencv.org/master/d4/d86/group__imgproc__filter.html#ga27c049795ce870216ddfb366086b5a04
[scipy.ndimage.correlate]: https://docs.scipy.org/doc/scipy/reference/generated/scipy.ndimage.correlate.html
[scipy.ndimage.convolve]: https://docs.scipy.org/doc/scipy/reference/generated/scipy.ndimage.convolve.html
[np.rot90]: https://docs.scipy.org/doc/numpy/reference/generated/numpy.rot90.html
[https_stackoverflow.com_questions_43270274_equivalent-of-matlab-filter2filter-image-valid-in-python]: https://stackoverflow.com/questions/43270274/equivalent-of-matlab-filter2filter-image-valid-in-python%20
[https_stackoverflow.com_questions_29212944_equivalent-function-of-matlabs-filter2-in-opencv]: https://stackoverflow.com/questions/29212944/equivalent-function-of-matlabs-filter2-in-opencv
[https_www.mathworks.com_matlabcentral_answers_17529-what-is-the-difference-between-conv2-filter2-and-imfilter]: https://www.mathworks.com/matlabcentral/answers/17529-what-is-the-difference-between-conv2-filter2-and-imfilter