I've been trying to learn math recently by implementing papers that I find related to projects I'm working on. Usually when I encounter a problem, I just google it, find the answer and continue on but this excerpt from a paper I'm reading is getting me really stuck. This is taken from a paper on edge detection in images compressed using the discrete cosine transform. I'm pretty sure I have a solid understanding of what the convolution operator is but the part about a row and column gradient operators is confusing me.
After googling around for it, I understand that it is supposed to essentially estimate the derivative, however I still don't understand what the specific row and column versions are supposed to be doing. Any help explaining what the row and column gradient operators are would be greatly appreciated.