Measuring efficiency of segmentation algorithms using sensitivity and precision

To measure error rates of the segmentation algorithms in synthetic images, each 3D centroid obtained by the algorithm was matched with each true position based on the Euclidian distances between them. We adopted a particle-matching algorithm and minimized the cost function defined as the summation of Euclidian distances between assigned pairs [18]. The segmentation algorithm was judged to have detected the object correctly if a match was found between the true position of an object and the segmented position within a radius of 2 μm. A miss was scored when a true position was not paired with any of the segmented centroid positions or an object was under-segmented. When a segmented centroid was not paired with any true positions, we considered the segmentation algorithm had detected false signals (e.g. noise) as an object or over-segmented an object. We counted the number of real objects correctly detected by the algorithm N_ra and defined sensitivity as N_ra/N_r where N_r is the true number of objects in a synthetic image. We defined precision as N_ra/N_s where N_s is the total number of segmented objects.

Segmentation of the sparsely distributed h2AflV-gfp positive nuclei gave error-free positions that were compared to the segmentation results of the densely packed nuclei. Because the centroid of a correctly segmented transplanted nucleus in the dense channel should correspond to a ground truth data point from the sparse channel, we checked for matching centroid position of nuclei based on Euclidian distance from sparse and dense channels within 2 μm (a typical nuclear radius was 4 μm). Sensitivity was then defined as the ratio of the number of matches between dense and sparse (true positive) and the total number of nuclei in the sparse channel (true positive + false negative).