Before we start computing the seams, we need to find out what metric we will be using to compute these seams. We need a way to assign "importance" to each pixel so that we can find out the paths that are least important. In computer vision terminology, we say that we need to assign an energy value to each pixel so that we can find the path of minimum energy. Coming up with a good way to assign the energy value is very important because it will affect the quality of the output.

One of the metrics that we can use is the value of the derivative at each point. This is a good indicator of the level of activity in that neighborhood. If there is some activity, then the pixel values will change rapidly. Hence the value of the derivative at that point would be high. On the other hand, if the region were plain and uninteresting, then the pixel values wouldn't change as rapidly. So, the value of the derivative at that point in the grayscale image would be low.

For each...