Once we have computed  from the equation above, we can find its local maxima using gradient ascent or some other optimization technique. The problem with this "brute force" approach is that, for higher dimensions, it becomes computationally prohibitive to evaluate  over the complete search space. Instead, mean shift uses a variant of what is known in the optimization literature as multiple restart gradient descent.
Once we have determined  from the equation above, we can identify its local maxima using gradient ascent or another optimization method. Nevertheless, this "blind" approach has a significant limitation: for higher dimensions, it becomes computationally expensive to evaluate  over the entire search space. In contrast, mean shift uses a variant of multiple restart gradient descent.