High-Throughput Segmentation of Tiled Biological Structures using Random-Walk Distance Transforms

Abstract

Various 3D imaging techniques are routinely used to examine biological materials, the results of which are usually a stack of grayscale images. In order to quantify structural aspects of the biological materials, however, they must first be extracted from the dataset in a process called segmentation. If the individual structures to be extracted are in contact or very close to each other, distance-based segmentation methods utilizing the Euclidean distance transform are commonly employed. Major disadvantages of the Euclidean distance transform, however, are its susceptibility to noise (very common in biological data), which often leads to incorrect segmentations (i.e., poor separation of objects of interest), and its limitation of being only effective for roundish objects. In the present work, we propose an alternative distance transform method, the random-walk distance transform, and demonstrate its effectiveness in high-throughput segmentation of three microCT datasets of biological tilings (i.e., structures composed of a large number of similar repeating units). In contrast to the Euclidean distance transform, the random-walk approach represents the global, rather than the local, geometric character of the objects to be segmented and, thus, is less susceptible to noise. In addition, it is directly applicable to structures with anisotropic shape characteristics. Using three case studies—tessellated cartilage from a stingray, the dermal endoskeleton of a starfish, and the prismatic layer of a bivalve mollusc shell—we provide a typical workflow for the segmentation of tiled structures, describe core image processing concepts that are underused in biological research, and show that for each study system, large amounts of biologically-relevant data can be rapidly segmented, visualized, and analyzed.

Architectural and ultrastructural features of tessellated calcified cartilage in modern and extinct chondrichthyan fishes

“…An arch is typically lined by a single series of voussoirs. A similar alignment of tesserae is sometimes present in elasmobranch TCC, here termed “voussoir tesserae.” Voussoir tesserae have not been explicitly documented before in modern or fossil chondrichthyans, although a short row of enlarged tesserae is illustrated in a hyomandibula of Urobatis (Baum et al ., 2019, Figure 3). The voussoir tesserae examined here are arranged in curved and rectilinear series and are associated with distinct morphological features such as ridges and the margins of foramina.…”

Endoskeletal mineralization in chimaera and a comparative guide to tessellated cartilage in chondrichthyan fishes (sharks, rays and chimaera)

“…unmineralized cartilage, perichondrium). Even a small skeletal element can be covered by thousands of tesserae, which also show regional differences in shape and size [ 45 , 73 ], making it challenging to draw general conclusions about tissue structure. However, despite immense variation observed in tesseral morphology and tiling pattern (e.g.…”

“…The great variation of tesserae sizes across ontogeny is owed at least partly to the fact that tesserae grow by accretion as the animals age and so smaller tesserae are likely more recently formed [ 21 , 23 ]. Shape variation of tesserae has also not been broadly characterized or quantified; however, on a 2 cm piece of skeleton from a stingray (the hyomandibula of U. halleri ), nearly 50% of the 2768 tesserae were six-sided, ranging from four- to eight-sided geometries [ 73 ]. Although tesserae are often depicted as polygonal, they can also be more stellate in their surface aspect [ 27 , 60 ] and can range from thin plates to cubes to tall columnar blocks in their vertical cross-sections ( figure 2 a–h ) [ 2 , 12 ].…”

“…500 µm and approx. 300 µm in width and height, respectively; [ 21 , 23 , 73 ]). The tesseral layer is often thicker or even multi-layered in skeletal regions that experience high loads (e.g.…”

“…[ 60 , 70 ]; Baum et al . [ 73 ]; Seidel et al . [ 13 ] multiple, layers of tessellated cartilage Dingerkus [ 74 ]; Maisey [ 6 ]; Dean et al .…”