Cost and time-effective method for multiscale measures of rugosity, fractal dimension, and vector dispersion from coral reef 3D models

Abstract

We present a method to construct and analyse 3D models of underwater scenes using a single cost-effective camera on a standard laptop with (a) free or low-cost software, (b) no computer programming ability, and (c) minimal man hours for both filming and analysis. This study focuses on four key structural complexity metrics: point-to-point distances, linear rugosity (R), fractal dimension (D), and vector dispersion (1/k). We present the first assessment of accuracy and precision of structure-from-motion (SfM) 3D models from an uncalibrated GoPro™ camera at a small scale (4 m2) and show that they can provide meaningful, ecologically relevant results. Models had root mean square errors of 1.48 cm in X-Y and 1.35 in Z, and accuracies of 86.8% (R), 99.6% (D at scales 30-60 cm), 93.6% (D at scales 1-5 cm), and 86.9 (1/k). Values of R were compared to in-situ chain-and-tape measurements, while values of D and 1/k were compared with ground truths from 3D printed objects modelled underwater. All metrics varied less than 3% between independently rendered models. We thereby improve and rigorously validate a tool for ecologists to non-invasively quantify coral reef structural complexity with a variety of multi-scale metrics.