What is the most effective way to access cv::Mat elements in a loop?

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You probably will get x10 speedup by switching order of your for loops. First loop rows, than (inner) loop columns.

According to the official documentations, they suggest that the most efficient way is to get the pointer to the row first, and then just use the plain C operator []. It also saves a multiplication for each iteration.

// compute sum of positive matrix elements
// (assuming that M isa double-precision matrix)
double sum=0;
for(int i = 0; i < M.rows; i++)
{
    const double* Mi = M.ptr<double>(i);
    for(int j = 0; j < M.cols; j++)
        sum += std::max(Mi[j], 0.);
}

For each, is the fastest access method using parallel CPU threads

jayrambhia's answer is approximately right, but it doesn't account for the step (also called the stride or pitch) of the Mat. You need to multiply by img.step, rather than img.cols. Also, if you're interested in speed, you want the per-colum loop nested inside the per-row loop. Something like the following. Even this assumes RGB color model in BGR component order, so it doesn't work for gray scale.

unsigned char *input = (unsigned char*)(img.data);
for(int j = 0;j < img.rows;j++){
    for(int i = 0;i < img.cols;i++){
        unsigned char b = input[img.step * j + i ] ;
        unsigned char g = input[img.step * j + i + 1];
        unsigned char r = input[img.step * j + i + 2];
    }
}

}

I'd say accessing it's data pointer.

Mat img = imread("filename.jpg",CV_LOAD_IMAGE_COLOR);
unsigned char *input = (unsigned char*)(img.data);

int i,j,r,g,b;
for(int i = 0;i < img.cols;i++){
    for(int j = 0;j < img.rows;j++){
        b = input[img.cols * j + i ] ;
        g = input[img.cols * j + i + 1];
        r = input[img.cols * j + i + 2];
        }
  }