CoDA: Interactive Segmentation and Morphological Analysis of Dendroid Structures Exemplified on Stony Cold-Water Corals

TL;DR

CoDA addresses the challenge of analyzing ontogenetic morphological development in dendroidal cold-water coral colonies from CT data by providing calyx-level segmentation, directed skeleton-tree reconstruction, and interactive visual analytics through CoDA.Graph. The method includes a parabola-based orientation heuristic to infer mother–daughter relationships, a refinement and proofreading workflow to correct segmentation and adjacencies, and a CSV-based linkage between Amira and CoDA.Graph for seamless exploration. Case studies on five specimens across three species demonstrate robust segmentation, skeleton-tree construction, and cross-species morphometric insights, enabling quantitative analyses of growth patterns and branching. The work advances reproducible, scalable analysis of complex dendroid structures and sets the stage for automated taxonomy and environmental-morphology studies in coral reef systems.

Abstract

Herein, we present CoDA, the Coral Dendroid structure Analyzer, a visual analytics suite that allows for the first time to investigate the ontogenetic morphological development of complex dendroid coral colonies, exemplified on three important framework-forming dendroid cold-water corals: Lophelia pertusa (Linnaeus, 1758), Madrepora oculata (Linnaeus, 1758), and Goniocorella dumosa (Alcock, 1902). Input to CoDA is an initial instance segmentation of the coral polyp cavities (calices), from which it estimates the skeleton tree of the colony and extracts classical morphological measurements and advanced shape features of the individual corallites. CoDA also works as a proofreading and error correction tool by helping to identify wrong parts in the skeleton tree and providing tools to quickly correct these errors. The final skeleton tree enables the derivation of additional information about the calices/corallite instances that otherwise could not be obtained, including their ontogenetic generation and branching patterns - the basis of a fully quantitative statistical analysis of the coral colony morphology. Part of CoDA is CoDAGraph, a feature-rich link-and-brush user interface for visualizing the extracted features and 2D graph layouts of the skeleton tree, enabling the real-time exploration of complex coral colonies and their building blocks, the individual corallites and branches. In the future, we expect CoDA to greatly facilitate the analysis of large stony corals of different species and morphotypes, as well as other dendroid structures, enabling new insights into the influence of genetic and environmental factors on their ontogenetic morphological development.

Figures (17)

• Figure 1: CoDA enables the analysis and visual exploration of the ontogenetic morphological development of dendroid cold-water corals. (a) The analysis starts with a computed-tomography (CT) image of the cold-water coral (CWC). (b, c) The polyp-cavity (calyx) segmentation 2021:schmitt2016:Baum2018:Titschack is the basis for the subsequent calyx/corallite instance segmentation. (d) Within the CoDA framework, a skeleton tree, describing the mother-daughter corallite relationship within a colony, is fitted to the corals. (e, f) The skeleton tree is visualized as graph layout in CoDA.Graph, our 2D visualization suite that augments CoDA with abstract, linked views, allowing the user to explore the colony and to focus on specific subsets of the tree during the analysis, e.g., on the descendants or ancestors of a calyx/corallite. (g, h) Traditional plots and views, e.g., scatter plot matrices (SPLOMs) and spreadsheets available in CoDA.Graph, complement CoDA's exploration and analysis capabilities.
• Figure 2: (a) The schematic depicts the typical parts of a cold-water coral colony (CC BY 4.0 Deed 2021:schmitt). The terms calyx and calice (in the schematic) can be used interchangeably and refer to the same part. We prefer calyx in the singular, while the plural is calices. (b) The photo shows the SaM-ID43148 (III) cold-water coral colony specimen. It is particularly large compared to other datasets and contains several colony fragments. Its dense structure makes the analysis and visual exploration particularly challenging without adequate tools. (c) The photo shows the NIWA-148046 (V) cold-water coral colony specimen. Its morphology differs from the other corals presented in this paper as the cavities resemble more a cylinder than a cone.
• Figure 3: (a) The initial contour-tree-based instance segmentation of the polyp-cavity (calyx) segmentation has 153 instances and involves a trade-off between the over-segmentation of large, adult corallites and the under-segmentation of small, young corallites. (b) The final, manually corrected instance segmentation contains only 114 calices.
• Figure 4: (a) The corallite mask is obtained by propagating the calyx instance segmentation onto the skeleton mask. (b) The region adjacency graph of the corallite instance segmentation (a) contains a vertex for each label (coral) and an edge for all labels sharing a border. Highlighted are edges that are not part of the colony tree and must be removed. (c) Parabolas are fitted to the calyx instance segmentation, allowing to orient each corallite from bottom to top. (d) The scatter plot shows the distribution of the voxel distances $\lVert \gamma \left( t_i \right) - x_i \rVert$ to the fitted parabola of a calyx and its skew that is used to orient it.
• Figure 5: (a) After orienting the edges and pruning daughter-daughter relationships, the graph is much cleaner compared to \ref{['fig:preprocessing steps tree computation']} but still contains some wrong edges, highlighted in red, and wrongly oriented edges, highlighted in green. In total, it has 115 edges. (b) The final result after manual refinement by the user is a graph consisting of five trees, each describing the ancestry in a single colony, and has 109 edges.