Fig 1.
Method for filming 2 x 2 m underwater quadrat.
A diver followed a lawnmower pattern (dotted line) over the quadrat, making 5–6 passes over each 2 m span of the quadrat and keeping the camera’s height and orientation consistent.
Fig 2.
Objects of known dimensions 3D modelled inside 2 x 2 m quadrat.
Two example dimensions, the quadrat length and the length of a standard SCUBA cylinder, are shown. Inset is a photo of the in-water scene. Objects of muted colors roughly matching the tones of the surrounding reef were chosen, representing a range of sizes and shapes. The 10 objects were: (1) pyramid-shaped mould, (2) pyramid-shaped tile, (3) natural-shaped mould, (4) brick, (5) pyramid-shaped tile, (6) transect tape, (7) dive weight (8) dive fin, (9) weight belt, and (10) SCUBA cylinder.
Fig 3.
Methods for quantifying linar rugosity on 3D model.
Six virtual chains with link length 2 cm were laid in a grid pattern over 3D modelled quadrats. A: The extendible-chain method determines how long a chain would need to be to cover the input curve. RN is the draped length of the chain. RDn is the undraped length of chain n. B: The fixed-length chain method determines how far a chain of a set length (1 m was used) would reach over the curve; this method more closely resembles traditional chain-and-tape measurements, although it can miss details because of the chain’s limited length. RNn is the draped length of chain n. RDn is the undraped length of the chain.
Fig 4.
D describes the relationship between a model’s resolution, or minimum pixel size, (δ) and its surface area S(δ). Above, the same patch of coral reef is rendered at five resolutions. The grid below each rendering is composed of squares, each of width δ, that are projected onto the original surface. Surface area always increases with finer resolution. D is 2—the slope logS(δ)/log(δ).
Fig 5.
Process for computing vector dispersion (1/k).
A: The user positions the scaled 3D model such that the quadrat lays flat along the X-Y plane or, if the quadrat was tilted underwater, tilted at the appropriate angle. The script then performs steps B-D. B: Project grid of points spaced 1 cm apart (as in [54]) onto the model such that each point falls on the highest point of the model. C: Connect adjacent points with triangles, creating i triangles. D: Compute the directional cosines of each triangle’s normal vector (cosx, cosy, and cosz labelled a, b, and c in the inset), and combine them as in Eq 3 for 1/k. Diagram D modified from material available through Creative Commons License.
Fig 6.
Accuracy of 3D model in terms of point-to-point distances.
The root mean square errors (RMSE) of our models were 1.48 cm in X-Y and 1.35 cm in Z, with models underestimating dimensions in both X-Y and Z.
Fig 7.
In-situ chain-and-tape measurements compared to those taken with a virtual chain on a 3D model.
Method I is the extendible-chain method and Method II is the fixed-length chain method. The extendible chain method had an accuracy of 85.7 ± 22.8% and the fixed length chain method had an accuracy of 86.8 ± 7.8%.
Fig 8.
Fractal Dimension (D) of underwater 3D-printed objects at five spacial scales compared to ground truths.
3D printed structures were placed underwater and 3D modelled. Their surface areas were computed at five spatial scales (60, 30, 15, 5, and 1 cm) to compute D, which is the slope of model’s resolution versus model’s surface area on logarithmic scales. Surface areas at the 60 and 30 cm resolutions matched nearly perfectly between the ground-truth structures (top row) and the underwater 3D models (UW 3DM), while the 3D models slightly underestimated surface area at finer resolutions.
Table 1.
Accuracies of Underwater 3D Models (UW 3DM) in terms of fractal Dimension (D) and vector dispersion (1/k).
Accuracies computed using Eq 2 for D and Eq 1 for 1/k. Sets I, II, and III are pictured in Fig 8.
Table 2.
Models showed low variation in terms of rugosity (R), vector dispersion (1/k) and fractal Dimension (D). Eight quadrats were each modelled three times. The coefficient of variation (CV) was the average standard deviation of measurements divided by the average measurement.