Bayesian approach for predicting photogrammetric uncertainty in morphometric measurements derived from drones

Abstract

Increasingly, drone-based photogrammetry has been used to measure size and body condition changes in marine megafauna. A broad range of platforms, sensors, and altimeters are being applied for these purposes, but there is no unified way to predict photogrammetric uncertainty across this methodological spectrum. As such, it is difficult to make robust comparisons across studies, disrupting collaborations amongst researchers using platforms with varying levels of measurement accuracy. Here we built off previous studies quantifying uncertainty and used an experimental approach to train a Bayesian statistical model using a known-sized object floating at the water’s surface to quantify how measurement error scales with altitude for several different drones equipped with different cameras, focal length lenses, and altimeters. We then applied the fitted model to predict the length distributions and estimate age classes of unknown-sized humpback whales Megaptera novaeangliae, as well as to predict the population-level morphological relationship between rostrum to blowhole distance and total body length of Antarctic minke whales Balaenoptera bonaerensis. This statistical framework jointly estimates errors from altitude and length measurements from multiple observations and accounts for altitudes measured with both barometers and laser altimeters while incorporating errors specific to each. This Bayesian model outputs a posterior predictive distribution of measurement uncertainty around length measurements and allows for the construction of highest posterior density intervals to define measurement uncertainty, which allows one to make probabilistic statements and stronger inferences pertaining to morphometric features critical for understanding life history patterns and potential impacts from anthropogenically altered habitats.

Comparing Uncertainty Associated With 1-, 2-, and 3D Aerial Photogrammetry-Based Body Condition Measurements of Baleen Whales

“…We followed the Bayesian statistical framework described in Bierlich et al (2021) to incorporate TL and width measurements of each individual whale from single and multiple images. We used the freely available training data (Bierlich et al, 2020) used by Bierlich et al (2021) for the UAS hexacopters FreeFly Alta 6 and LemHex-44 (see section "Error Estimation" for description of these UAS platforms) of known-sized floating calibration objects collected in Monterey, CA (length = 1.27 m), Beaufort, NC (length = 1.48 m), and along the Western Antarctic Peninsula (WAP; length = 1.33 or 1.40 m), for a total of 110 images. We first estimated the posterior probability distribution of photogrammetric error parameters (θ) for each UAS platform used in data collection using the calibration data of the knownsized objects (x) via…”

“…We designed the likelihood function based on the ground sampling distance (GSD) and length measurement in pixels (L p ) described in Bierlich et al (2021), with the addition of including multiple measurements from single or multiple images to estimate body condition of individuals. We used the following photogrammetric equations,…”

“…of whale i in image j, and the exact, unknown Length k,i in meters of measurement k for whale i. Errors related to the object positioning within the image frame and lens distortion for the cameras used in this study (see section "Error Estimation" for description of UAS cameras) were found to be negligible by Bierlich et al (2021), and were thus not included in the model.…”

“…Recently, Bierlich et al (2021) developed a statistical model using training data of known-sized calibration objects to predict the length and associated uncertainty of unknown sized objects (e.g., whales). In the present study, we apply the model outputs from Bierlich et al (2021) to aerial imagery collected via UAS to predict and compare uncertainty associated with 1D, 2D, and 3D photogrammetry-based body condition measurements in three baleen whale species of different sizes: blue, humpback, and Antarctic minke whales (AMWs; Balaenoptera bonaerensis).…”

“…The four objectives of the present study are to: (1) apply methods described in Bierlich et al (2021) to incorporate uncertainty associated with multiple measurements of the same individual from image(s) to estimate the body condition of blue, humpback and minke whales; (2) compare how uncertainty scales across 1D, 2D, and 3D body condition measurements of these estimates; (3) compare precision in the posterior predictive distributions for each body condition estimate; and (4) compare how body condition indices are correlated for these species. The focus of our study is to shed light on how uncertainty scales across each body condition measurement to help guide other researchers to choose a method that best addresses their research objectives with the least uncertainty.…”