matlab - matlab中的二维卷积——代码优化

Question

这是我们练习图像处理的作业。我的代码工作正常。我想在代码优化方面获得一些帮助。

function C = convolve_slow(A,B)
(file name is accordingly convolve_slow.m ) 
This routine performs convolution between an image A and a mask B.
Input:      A - a grayscale image (values in [0,255]) 
            B - a grayscale image (values in [0,255]) serves as a mask in the convolution.
Output:     C - a grayscale image (values in [0,255]) - the output of the convolution. 
                      C is the same size as A.

Method:  Convolve A with mask B using zero padding. Assume the origin of B is at 
     floor(size(B)/2)+1.
Do NOT use matlab convolution routines (conv,conv2,filter2 etc). 
Make the routine as efficient as possible: Restrict usage of for loops which are expensive (use matrix multiplications and matlab routines such as dot etc).
To simplify and reduce ifs, you should pad the image with zeros before starting your convolution loop.
Do not assume the size of A nor B (B might actually be larger than A sometimes).

这是我们的解决方案

function [ C ] = convolve_slow( A,B )
%This routine performs convolution between an image A and a mask B.
% Input:      A - a grayscale image (values in [0,255])
%             B - a grayscale image (values in [0,255]) serves as a mask in the convolution.
% Output:     C - a grayscale image (values in [0,255]) - the output of the convolution. 
%             C is the same size as A.
% 
% Method:  Convolve A with mask B using zero padding. Assume the origin of B is at floor(size(B)/2)+1.
% init C to size A with zeros
C = zeros(size(A));
% make b xy-reflection and vector
vectB = reshape(flipdim(flipdim(B,1),2)' ,[] , 1);
% padding A with zeros
paddedA = padarray(A, [floor(size(B,1)/2) floor(size(B,2)/2)]);
% Loop over A matrix:
for i = 1:size(A,1)
    for j = 1:size(A,2)
        startAi = i;
        finishAi = i + size(B,1) - 1;
        startAj = j;
        finishAj = j + size(B,2) - 1;
        vectPaddedA = reshape(paddedA(startAi :finishAi,startAj:finishAj)',1,[]);
        C(i,j) = vectPaddedA* vectB;
    end
end
end  

因为我是图像处理和 Matlab 的新手。你能帮我优化代码吗，特别是基于矩阵的操作。可以不使用循环吗？

Answer 1

无需显式写出代码，我可以找到一种将其归结为一个主 for 循环的方法。基本上，通过将 A 和 B 的每一列展开为一个向量(这就是它在 MATLAB 中的内部存储方式)，将矩阵 A 和 B 视为列向量。然后 A 的每个 (i,j) 坐标可以映射到线性索引 k(使用函数 sub2ind 例如)。然后，对于 A 主体内的每个线性索引(忽略填充)，计算与该线性索引周围的子矩阵对应的线性索引列表(这可能是这里最难的部分)。然后计算 A( theseIndices ) 和 B(:) 的点积。使用此方法，您只需遍历 A 的每个线性索引。