Image-based Morphological Characterization of Filamentous Biological Structures with Non-constant Curvature Shape Feature

TL;DR

The paper tackles 3D morphological analysis of tendrils with non-constant curvature under mechano-stimulation, addressing marker-based tracking limitations. It introduces a marker-free stereo pipeline combined with a 3D Piece-Wise Clothoid (PWC) model, leveraging Frenet–Serret rigidity and Fréchet-distance mapping to produce accurate centerline reconstructions described by curvature $\kappa(s)$ and torsion $\tau(s)$. Key contributions include end-to-end processing from pre-processing to automatic curvature–torsion fitting, validated by $R^2>0.99$ and sub-23-pixel projection errors across views, plus a grid-search strategy for robust penalty selection. The approach yields biomechanical insights into tendril sensitivity along the length and offers a foundation for tendon-inspired robotics and marker-free morphological analysis of slender filaments.

Abstract

Tendrils coil their shape to anchor the plant to supporting structures, allowing vertical growth toward light. Although climbing plants have been studied for a long time, extracting information regarding the relationship between the temporal shape change, the event that triggers it, and the contact location is still challenging. To help build this relation, we propose an image-based method by which it is possible to analyze shape changes over time in tendrils when mechano-stimulated in different portions of their body. We employ a geometric approach using a 3D Piece-Wise Clothoid-based model to reconstruct the configuration taken by a tendril after mechanical rubbing. The reconstruction shows high robustness and reliability with an accuracy of R2 > 0.99. This method demonstrates distinct advantages over deep learning-based approaches, including reduced data requirements, lower computational costs, and interpretability. Our analysis reveals higher responsiveness in the apical segment of tendrils, which might correspond to higher sensitivity and tissue flexibility in that region of the organs. Our study provides a methodology for gaining new insights into plant biomechanics and offers a foundation for designing and developing novel intelligent robotic systems inspired by climbing plants.

Figures (14)

• Figure 1: Biological experiment setup and data collection procedure. $\mathbf{A}.$ Definition of the portions of the tendril stimulated in the experiments. In this work, we subdivided each tendril into four segments and stimulated only one using a wooden stick. $\mathbf{B}.$ Measurements of the applied force during the experiments. To verify the intensity of the applied stimulus, we measured the interaction with a precision load cell and replicated the same motion over the selected portion for all the tendrils. $\mathbf{C}.$ Experimental setup. After the stimulation, the plant main stem was taped on a panel, leaving the tendril hanging free. On the panel, markers are used to facilitate the data processing and identify common features in the three views used for the 3D reconstruction. $\mathbf{D}.$ Schematic representation of the stimuli-induced morphological changes that occurred over time in the four experimental sets.
• Figure 2: Steps of the pre-possessing applied to each captured video. $\mathbf{A}.$ The first frame of each video, $\mathcal{I}^0_i$ ($i=1, 2, 3$), is processed in a semi-automatic fashion. The user is asked to select a ROI that contains the element to be analyzed (i.e., a tendril). The ArUco markers are attached to the background, serving as global correspondence between the images captured by the three cameras and retrieving the camera parameters. $\mathbf{B}.$ The RGB image is then converted to HSV color space (left) and thresholded to extract the foreground (i.e., the selected tendril) from the background (right). Again, we ask the user to select the connection point between the main stem and the tendril to avoid the segmentation algorithm further selecting points not belonging to the tendril. $\mathbf{C}.$ Using the connected components algorithm, each set of pixels is labeled according to its connections with the neighboring ones. Then, the centroid, $\mathbb{C}^0_i$ ($i$ is the $i$-th camera), for the pixels contained in the ROI is computed and stored to automate the extraction of the pixels belonging to the tendril in successive frames. $\mathbf{D}.$ The results of the automatic extraction of the tendril using the updated centroid, $\mathbb{C}^{t-1}_i$ (where $t-1$ is the time frame and $i$ is the $i$-th camera), and considering only the portion of the image contained in the ROI defined in $\mathcal{I}^0_i$.
• Figure 3: Illustration of the sorting algorithm steps for off-plane morphing where the distance between the self-intersection point and tendril tip is negligible. $\mathbf{A}.$ Example of tendril configuration. $\mathbf{B}.$ The skeleton points are split into two sets divided by the self-intersection point ($\mathbf{p}_{c}$). $\mathbf{C}.$ Ordering the first set, $\mathcal{S}_1$, up to the self-intersection point, which is removed. The remaining points are collected in a new set with two ordering directions: clockwise ($\mathcal{S}^*_2$) and counterclockwise ($\mathcal{S}_2$). $\mathbf{D}.$ For each set, we fit a line using $N_i$ points ($i =1,2$). $\mathbf{E}.$ The correct ordering direction is selected by considering the angles between the lines pairs $\langle\mathbf{L}_{N_1}, \mathbf{L}_{N_2} \rangle$ and $\langle\mathbf{L}_{N_1}, \mathbf{L}_{N^*_2} \rangle$. $\mathbf{F}.$ Final, ordered set of points.
• Figure 4: Illustration of the sorting algorithm steps for off-plane morphing where the distance between the self-intersection point and tendril tip is not negligible. $\mathbf{A}.$ Example of tendril configuration. $\mathbf{B}.$ Unordered points of the skeleton. $\mathbf{C}.$ The ordering starts from $\mathbf{p}_{s}$ until reaching the point of intersection $\mathbf{p}_{c}$ that is then removed. The first set of ordered points is generated ($\mathcal{S}_1$). The remaining points are grouped according to their connectivity and sorted, obtaining three sets: one containing the tip ($\mathcal{S}_3$) and two on the ring having reversed order ($\mathcal{S}_2$, $\mathcal{S}^*_2$). $\mathbf{D}.$ Each set is labeled according to the distance between $\mathbf{p}_{c}$ and the last point in the set. The one with the biggest distance (i.e., $\mathcal{S}_3$) is removed. $\mathbf{E}.$ The correct set between $\mathcal{S}_2$ and $\mathcal{S}^*_2$ is selected by considering the angles between the lines pairs $\langle\mathbf{L}_{N_1}, \mathbf{L}_{N_2} \rangle$ and $\langle\mathbf{L}_{N_1}, \mathbf{L}_{N^*_2} \rangle$. $\mathbf{F}.$ Final ordered set of points.
• Figure 5: The process of mapping the points between the views. $\mathbf{A}.$ Homographic transformation between the views to position all the points with respect to a single reference frame. $\mathbf{B}.$ Application of the Fréchet distance to map the extracted set of points. When a set of correspondence has been found, the triangulation of the points can be applied to retrieve the three-dimensional shape of the curve.