仅使用Numpy即可卷积2d [英] Convolve2d just by using Numpy

问题描述

我正在研究使用Numpy进行的图像处理，并且面临卷积滤波的问题.

I am studying image-processing using Numpy and facing a problem with filtering with convolution.

我想对灰度图像进行卷积. (将2d数组与较小的2d数组进行卷积)

有人有优化我的方法的想法吗?

Does anyone have an idea to refine my method ?

我知道 scipy 支持convolve2d但是我只想通过使用Numpy来进行卷积.

I know that scipy supports convolve2d but I want to make a convolve2d only by using Numpy.

首先，我将2d数组作为子矩阵.

First, I made a 2d array the submatrices.

a = np.arange(25).reshape(5,5) # original matrix

submatrices = np.array([
     [a[:-2,:-2], a[:-2,1:-1], a[:-2,2:]],
     [a[1:-1,:-2], a[1:-1,1:-1], a[1:-1,2:]],
     [a[2:,:-2], a[2:,1:-1], a[2:,2:]]])

子矩阵看起来很复杂，但是下图显示了我正在做的事情.

the submatrices seems complicated but what I am doing is shown in the following drawing.

接下来，我将每个子矩阵乘以一个过滤器.

Next, I multiplied each submatrices with a filter.

conv_filter = np.array([[0,-1,0],[-1,4,-1],[0,-1,0]])
multiplied_subs = np.einsum('ij,ijkl->ijkl',conv_filter,submatrices)

并对它们求和.

np.sum(np.sum(multiplied_subs, axis = -3), axis = -3)
#array([[ 6,  7,  8],
#       [11, 12, 13],
#       [16, 17, 18]])

因此该过程可以称为我的convolve2d.

Thus this procudure can be called my convolve2d.

def my_convolve2d(a, conv_filter):
    submatrices = np.array([
         [a[:-2,:-2], a[:-2,1:-1], a[:-2,2:]],
         [a[1:-1,:-2], a[1:-1,1:-1], a[1:-1,2:]],
         [a[2:,:-2], a[2:,1:-1], a[2:,2:]]])
    multiplied_subs = np.einsum('ij,ijkl->ijkl',conv_filter,submatrices)
    return np.sum(np.sum(multiplied_subs, axis = -3), axis = -3)

但是，我发现这个my_convolve2d麻烦的原因有3个.

However, I find this my_convolve2d troublesome for 3 reasons.

1. 子矩阵的生成太笨拙，难以读取，只能在过滤器为3 * 3的情况下使用
2. 可变子矩阵的大小似乎太大，因为它比原始矩阵大约9倍.
3. 求和似乎有点不直观.简单地说，很丑.

感谢您阅读本文.

种类的更新.我为自己写了一个conv3d.我将其保留为公共领域.

Kind of update. I wrote a conv3d for myself. I will leave this as a public domain.

def convolve3d(img, kernel):
    # calc the size of the array of submatracies
    sub_shape = tuple(np.subtract(img.shape, kernel.shape) + 1)

    # alias for the function
    strd = np.lib.stride_tricks.as_strided

    # make an array of submatracies
    submatrices = strd(img,kernel.shape + sub_shape,img.strides * 2)

    # sum the submatraces and kernel
    convolved_matrix = np.einsum('hij,hijklm->klm', kernel, submatrices)

    return convolved_matrix

推荐答案

您可以使用as_strided 要摆脱第二个丑陋"的总和，请更改您的einsum，以便输出数组仅包含j和k.这意味着您需要进行第二次求和.

To get rid of your second "ugly" sum, alter your einsum so that the output array only has j and k. This implies your second summation.

conv_filter = np.array([[0,-1,0],[-1,5,-1],[0,-1,0]])
m = np.einsum('ij,ijkl->kl',conv_filter,sub_matrices)

# [[ 6  7  8]
#  [11 12 13]
#  [16 17 18]]

这篇关于仅使用Numpy即可卷积2d的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！