Automated image-based analysis methods for filament networks structures in two and three dimensions

Among natural organisms with a morphology resembling filament networks, notable examples include mycorrhizal networks, which are filamentous structures formed by underground growing fungi that establish symbiotic relationships with plant roots: in these relationships, the fungus obtains sugar in exchange for nutrients, and they can build connectivity among multiple plants. These fungi have attracted ample interest from the research community due to their importance in maintaining ecosystem resilience and suggesting sustainable crop management strategies. Fungal filaments, called hyphae, grow from multiple apices or tips of a mycelium assuming topologies that can reach a high level of complexity due to possible high rate of branching, filaments overlapping, and irregular network morphologies. Controlled laboratory experiments are fundamental to understanding how these networks are established and evolve. In these experiments, typically the fungi are cultivated in a transparent medium, allowing its observation through an optical microscope. However, interpreting these complex network structures can be a highly laborious process. Therefore, several image analysis software tools have been developed in recent years to automatically obtain quantitative measures from microscope images of fungal samples. The typical workflow adopted by such tools is 1) detecting the filaments and obtaining a skeleton representation of the structure, 2) computing a morphological graph, where each node represents an apex, or a branch point and each edge represents the filament connecting the points of interest. Under certain conditions, the problem of approximating the network structure of a filamentous fungus can be well approximated as two-dimensional (2D), however, it is inherently three-dimensional (3D). Advanced techniques for imaging 3D volumes (e.g., Laser Scanning Confocal Microscopy), rely on complex sample preparation protocols. Instead, acquiring images at different focal depths (i.e., Z-stack) using a common brightfield microscope allows for observing the sample as it is. Another aspect that is difficult to capture in the analysis of a 2D image is that the biological filaments frequently overlap with each other, which, if not accounted for, typically causes an overestimation of the connectivity by about 20%. In this context, this PhD thesis proposes new algorithms for improved, automated reconstruction of filament networks from images that have been demonstrated to work effectively and robustly across various types of networks and images with different characteristics and noise levels. The validation of the algorithm’s adequacy as measurement method showed moderate concordance with manual measurements. First, a detection algorithm for filaments with ridge-like features is developed and tested on multiple image sets. It is shown that detection performance is on par with the state of the art, with more intuitive tuning parameters that depend directly on the image length scale. Then, a method for detecting and quantifying spores in a 3D Z-stacked sample, based on detection in each plane, followed by clustering, is proposed and validated. The method has an average relative error of 3.25%, showing that, for large samples, the 3D method significantly outperforms the single-frame 2D option. Furthermore, this thesis provides a method for correcting the filament network topology for errors introduced through occlusions by spores: given a correct detection as input, the proposed method does not produce any error. Once the filaments have been detected, two ways to represent the structure are considered in this thesis: 1) as a sparse matrix where filaments are indicated as integers, 2) as a sparse homeomorphic graph where each node has a coordinate. Depending on the type of representation, two methods for identifying filament overlaps and connecting the correct parts of the overlapping filaments to each other are proposed. Both methods rely on geometrically analyzing the detected filaments in the neighborhood of potential overlaps. The first relies on extracting a patch around each branch point and isolating the intersection arms, and it achieves an overlap detection F1-score of 0.89. The second relies on using steerable filters and archives F1=0.91-0.92. Additionally, given the graph representation, an algorithm for merging graphs from different focal planes is proposed, yielding a single representation with information from multiple focal planes, including filaments that are potentially only detectable in a subset of the considered planes. Using the shape-from-focus approach, this resulting representation can be turned into a 3D model of the structure. The 3D reconstruction is validated quantitatively using 3D-printed prototypes. Finally, several derivative and qualitative results are presented. The morphological graphs with and without overlaps are compared. Different ways to visualize distributions of filament properties throughout the network are tested, and 3D reconstructions of real fungal samples are shown. To sum up, this PhD thesis proposes performant solutions to the following key issues in automated analysis of filament networks: filament detection, spore detection, correction for occlusion caused by spores, correction for filament overlaps, and 3D reconstruction of the filaments. The proposed solutions were validated following different procedures for each challenge and provided results suggesting significant steps towards a fully automated analysis of filament network images. Future perspectives of this study include further improving the accuracy in filament detection, since it represents the main source of errors in the current analyses, and utilizing the developed techniques to decode the networking strategies of mycorrhizal fungi.