Fig 1.
Tessellated cartilage of the stingray Urobatis, at multiple levels of structural organization.
(A) The skeleton is visible in CT scans due to the mineralization of the cartilage. (B,C) The hyomandibula, a skeletal element connecting cranium and jaws. (D) Transverse section of the hyomandibula—the outer layer of mineralized, tessellated cartilage (tesserae, t) is visible, surrounding an inner core of unmineralized, radiolucent cartilage (uc). (E) Surface view of the hyomandibula; note the variation in the shape of tesserae and the size of pores (p). Tesserae can be demarcated by connecting the pores between adjacent tesserae. Specimens: (A) Urobatis concentricus (USNM87539), medical CT; (B-E) Urobatis halleri, μCT.
Fig 2.
μCT images of tesserae acquired with different resolutions.
Images (A) and (B) show a single tessera surrounded by neighboring tesserae. (A) Synchrotron μCT image with voxel size 0.678 μm. In the center of the tessera, many cell lacunae (cl) are visible. The close-up shows an inter-tesseral joint consisting of inter-tesseral contact zones (icz) with direct contact between adjacent tesserae and fibrous zones (fz) without direct contact. (B) Voxel size: 4.89 μm. This image shows the native resolution of the μCT scans used in this paper, before being downsampled for analysis to 9.78 μm (see ‘Input Data’ below). Note that the inter-tesseral contact zones and small fibrous zones cannot be seen since the resolution is not high enough. Hence we use the following terminology throughout this paper: Inter-tesseral connection (co) for the entire connection between tesserae, including both contact and fibrous zones and appearing as areas of high intensity (high gray values) between tesserae, unmineralized pores (p) for areas of low intensity between tesserae, and tessera center (c) for the region around the center of a tessera.
Fig 3.
Overview of the segmentation pipeline.
(A) Volume rendering of input μCT image; (B) Preprocessing result: volume rendering of input image smoothed with anisotropic diffusion to maintain edges. Differences to (A) are not visible here, but smoothing the image improves the segmentation significantly; (C) Surface representation of foreground segmentation, now tesserae are separated from the background using local thresholding; (D) 2D distance map measuring distances to pores between tesserae; (E) Segmentation result after applying hierarchical watershed transform; (F) Postprocessing result: segmentation after manual error corrections, the arrows in (E) and (F) highlight a segmentation error due to a hole inside a tessera which is corrected by merging two segments.
Fig 4.
Neighborhood for local thresholding.
(A) Slice through smoothed image Is with S highlighted in yellow and B(x, l) in red, the blue point denotes the voxel x; (B) Close-up of box in (A) with N(x) ≔ B(x, l) ∩ S highlighted in orange.
Fig 5.
Plane approximation for 2D distance map computation.
(A) The red point shows the position of the voxel x for which the plane approximation should be computed. The mineralized cartilage (foreground) is shown as transparent surface. (B) Rays starting from x and intersection points . (C) Rotated view showing the best fitting plane Hx (green) for the points shown in (B). The mineralized cartilage has been cut in order to visualize the orientation of the plane.
Fig 6.
Illustration of the hierarchical watershed segmentation results.
Different persistence thresholds were used: 0 (A); 10 (B); 30 (C); 50 (D). While (A) shows an oversegmentation, (B) represents an almost perfect segmentation. In (C) and (D), the chosen persistence thresholds were too large, resulting in undersegmented regions that comprise several tesserae.
Fig 7.
Graph representation of the segmentation.
(A) Transparent surface and graph; (B) Only the graph. In the close-ups, the layer of vertices on the backside has been removed.
Fig 8.
Example for manual error correction using a combination of merge and split operations.
Additionally, the graph representation is shown with vertices inside a transparent surface. (A) There are three tesserae without pores between them, this leads to a bad watershed segmentation result; (B) Merge the three labels into one large label; (C) Use spectral-clustering-based split to resolve the error. Note how the corrected graph is more regular regarding edge lengths and vertex positions compared to (A) and (B).
Fig 9.
Number of labels created by hierarchical watershed segmentations plotted against persistence values.
Computations are done for three hyomandibula datasets with increasing hyomandibula size for persistence values from 0 to 100. The green lines indicate the persistence value we chose for the hierarchical watershed segmentations (A: 10, B: 18, C: 20). Note how the values increase with hyomandibula size.
Table 1.
Hyomandibula dataset information.
Fig 10.
Manual landmarks for evaluation.
(A) Isosurface of dataset I with one manually placed landmark per tessera but without landmarks on low mineralized areas. (B) Rotated close-up of the region where the tendon is connected to the hyomandibula. Here, no landmarks were created because it is very difficult or impossible to distinguish the tesserae in this region. (C) Same close-up as in (B) but without the low mineralized regions. The backside of the hyomandibula was removed for this image.
Table 2.
Number of tesserae in 2D distance map-based final pipeline segmentations.
Fig 11.
Precision-recall plots for datasets I, II and III.
Persistence values range from 0 to 80 in single steps. Each fifth persistence value is written at the top right position next to the respective green dot in case of the 2D distance map and at the bottom left position of a yellow triangle in case of the 3D distance map. The final pipeline segmentation is highlighted with a red star (I: precision 0.9888, recall 0.9964; II: 0.9899, 0.9987; III: 0.9898, 0.995), the watershed segmentation used to generate this final pipeline segmentation is highlighted with a magenta star (I: precision 0.9786, recall 0.9822; II: 0.9643, 0.9949; III: 0.9583, 0.9864).
Fig 12.
Precision-recall plots for datasets I, II, and III with and without preprocessing (anisotropic diffusion).
Each fifth persistence value is written at the top right position next to the respective green dot in case of a 2D distance map with preprocessing and at the bottom left position of a yellow triangle in case of a 2D distance map without preprocessing. The final pipeline segmentation is highlighted with a red star, the watershed segmentation used to generate this final pipeline segmentation is highlighted with a magenta star.
Fig 13.
Selected regions for manual segmentations.
(1) Flat regularly-shaped tesserae with bounding box size of 120 x 84 x 178 taken from dataset I containing 99 tesserae; (2) Edge region with bounding box size 94 x 195 x 254 taken from dataset I containing 83 tesserae; (3) Flat region with thin, irregularly-shaped tesserae, perforated by large pores and intra-tesseral holes with bounding box size 215 x 126 x 228 taken from dataset II containing 85 tesserae.
Table 3.
VI / RAND values for region 1 consisting of flat regularly-shaped tesserae.
Table 4.
VI / RAND values for region 2 (edge region).
Table 5.
VI / RAND values for region 3 consisting of flat tesserae with thin, irregularly-shaped tesserae, perforated by large pores and intra-tesseral holes.
Fig 14.
Close-up showing the worst VI label pair for region 1 (A/B) and region 3 (C/D).
(A) Final pipeline segmentation of region 1; (B) Manual segmentation 1 of region 1; (C) Final pipeline segmentation of region 3; (D) Manual segmentation 1 of region 3.
Fig 15.
Comparison of results without (top row) and with (bottom row) anisotropic diffusion.
(A,E) Volume rendering of original scalar field (A) and scalar field after anisotropic diffusion (E). (B,F) Surfaces of binary segmentations using the same parameters for local thresholding. The red arrow indicates intra-tesseral holes that appear in the binary segmentation if no anisotropic diffusion is applied. (C,G) Maximum intensity projections of 2D distance maps generated from binary segmentations. (D,H) Surfaces of segmentation results using comparable persistence parameters. Wrong segmentations are highlighted with outlines. In rare cases, the application of anisotropic diffusion might break tesserae (H), but these broken tesserae are usually easy to fix with a simple manual merge operation.
Fig 16.
Illustration of segmentation problems: 3D distance map (top row) compared to 2D distance map (bottom row).
(A-C) Segmentation based on 3D distance map for different cross sections. Only for (A) it is possible to generate the desirable segmentation. (B) The 3D distance map has only one maximum, hence no separation is possible. (C) The 3D distance map has several maxima but the separation appears at the wrong place, that is, where the object is thinnest. (D-E) Segmentation based on 2D distance map. Segmentation is successful for all three cross sections.
Fig 17.
Comparison of 3D (A) and 2D (B) distance maps and resulting hierarchical watershed segmentations (C, D).
(A) and (B) show maximum intensity projections of the 3D and 2D distance maps, respectively. Two zoom-in levels are provided to better illustrate the differences. (A) The 3D distance map tends to create large plateaus (i.e. areas with equal values), in particular in the regions of inter-tesseral connections, where projections of mineralized tissue are narrow in two dimensions. (C) These plateaus can span inter-tesseral joints, leading to inaccurate separation of individual tesserae. (B) By comparison with the 3D distance map, the 2D distance map has much more gradual contours and does not show any plateaus. Instead, the distance values decrease toward the inter-tesseral connections, allowing tesserae to be accurately separated well from one another, even when joint spaces are not evident (D).