Algorithm 4.

Moving Window Smoothing

Let x1 ≤ x2, ≤ … ≤ xn be the n ordered data points, with corresponding intensity measurements y1 ≤ y2 ≤ … ≤yn. Let w ≥ 0 be the window size, which defines the neighborhood about the data point. for i = 1 to n do Let l = max(l,i − w) be the left boundary of the window. Let r = min(n,i + w) be the right boundary of the window. Let f(·) be the smoothing function. For the mean, this would be $$f(x)=\frac{1}{r-l+1}{\displaystyle \sum _{j=l}^r}{x}_j$$ and for the median this would be $$f(x)=\{\begin{array}{ll}{x}_{\lfloor (r-l+1)/2+1\rfloor },\hfill & (r-l+1)\text{odd},\hfill \\ \frac{1}{2}\left(x_{\lfloor (r-l+1)/2\rfloor }+x_{\lfloor (r-l+1)/2+1\rfloor }\right),\hfill & (r-l+1)\text{even},\hfill \end{array}$$ where [·] denotes the floor function. Compute the estimate ŷj = f(xj). end for