Object Segmentation and Ground Truth in 3D Embryonic Imaging
Fig 2
Post-processing steps to separate under-segmented objects.
Top panel is a result of the DS algorithm and the bottom panel are the results obtained after post-processing steps for the single stack shown in Fig 1. (a) Stem plot of the volumes of segmented objects obtained after DS algorithm. The black dashed vertical line (at 237 voxels) indicates the empirically calculated ‘Fused object volume’ threshold value above which the objects (with volumes > 160 μm3) were subjected to post-processing steps. Position of the dashed line depends upon the DS algorithm and noise filter parameters and volumes of segmented objects (S1 Text). (b) A 3D rendered object from the left side of the black dashed line in (a) correctly segmented by the DS algorithm as indicated with the centroid position in red. (c) An example of 3D rendering of a fused object, as indicated by the position of the centroid in red, from the right side of the black dashed line in (a). (d) Frequency distribution of voxels in x, y and z direction for the correctly segmented nucleus in (b) obtained after DS algorithm. Note that a single nucleus has a unimodal distribution of voxels in each direction. (e) Frequency distribution of voxels in x, y and z direction for the fused case in (c). The distribution in the z-direction indicates 3 peaks marked by asterisks (*), suggesting three nuclei fused in the z-direction. (f) 3D rendered object shown in (b) is post-processed with K-means (centroid position in blue) and GMM (centroid position in green). All the three methods give the same centroid position. (g) 3D rendered object shown in (c) is post-processed with K-means and GMM that find 3 new centroid positions indicated in blue and green thus segregating fused nuclei. (h) Stem plot after DS with post-processing steps. Blue and green stem plots represent segmented volumes after DS with K-means and DS with GMM, respectively. Post-processing steps tend to reduce under-segmentation. (i) Dependence of the average processing time of post-processing steps GMM and K-means on the maximum number of local peaks mnp. Processing time was measured for each single object with a given mnp value. The error bars indicate standard deviations.