Fig. 3.

Fibril centroid detection. In (a), the color scale displays the distance field $D$ (unsmoothed) or $D_{\text{filt}}$ (smoothed with the indicated bandwidths $\sigma$). Local peaks in the field, plotted in red, are treated as candidate locations for the centroids of all the collagen fibrils in the image. (b) The number of centroids $N$ detected with different filter bandwidths $\sigma$. Circles denote actual results, while the plotted curve corresponds to the 5th-degree polynomial fit $p(\sigma )$. The optimal filter bandwidth (red) corresponds to the point at which $N$ is least sensitive (locally) to $\sigma$. (c) Equivalently, the optimal filter bandwidth corresponds to the lowest positive $\sigma$ where $(dp/d\sigma {)}^2$ reaches a local minimum, which is straightforward to compute.