Three-Dimensional Graph Reconstruction of Filamentous Structures from z-Stack Images

Automated analysis of images containing complex filament network structures has several interesting applications in both two-dimensional (2D) and three-dimensional (3D) environments, including the analysis of filamentous fungi. In this context, both morphology and topology are important features for the characterization of biological samples. Brightfield microscopy Z-stacks is one of the simplest techniques for imaging samples characterized by a given depth, and it consists of acquiring images at different focal depths. It allows simpler sample preparation, reduces acquisition system complexity, and performs non-invasive analysis compared to other techniques. In this study, we propose an algorithm that, given a Z-stack image of a filamentous structure, 1) detects the filaments in each focal plane producing a binary skeleton, 2) smoothes the resulting graph into a less dense homeomorphic graph, 3) identifies the corresponding nodes from the different focal planes by solving an optimal matching problem, 4) estimates the relative depth of the filament at each node coordinate through a shape-from-focus approach, and 5) identifies shallow overlaps through a criterion based on steerable filters. The resulting output is a graph where each node has a 3D coordinate representing the 3D filament network’s morphology and topology. The algorithm’s 3D reconstruction capabilities are tested on 3D-printed structures used as ground truth with a filament radius of 0.5 mm, obtaining a Root Mean Square Error (RMSE) lower than the filament radius for most cases. The approach is then tested on images of the real filamentous fungus Rhizophagus irregularis. First, the overlap detection is assessed on six manually annotated 2D images of the fungus (F 1 =0.91–0.92). Then, we show the potential of the provided solution for the automated 3D reconstructions of Z-stack images of the fungus with different complexities of the grown network, and the robustness of the proposed method is assessed through a sensitivity analysis.