Spatial Variation in Coral Diversity and Reef Complexity in the Galápagos: Insights from Underwater Photogrammetry and New Data Extraction Methods

Abstract

Corals in the Galápagos present diverse reef configurations from biogenic coral reefs to coral communities growing on rocks and sand. These corals have experienced decades of disturbances including recurring El Niño and mass bleaching events. However, traditional methods in ecology have limited capacity in describing coral demographic trends across large spatial scales. Photogrammetry—a form of 3D imaging, has emerged over the past decade as a popular method for benthic surveys. However, the majority of protocols in the field utilize the 2D products of photogrammetry, ignoring overhangs and leaving significant information unexploited. We surveyed seven reef sites across the archipelago using underwater photogrammetry and developed new methods for 3D annotation and fractal dimension calculation. Our findings reveal variation in coral cover, diversity, and structural complexity across the archipelago. Our results align with previous studies in the region and add important information on reef structural complexity which was not measured here before. We release a unique dataset: Galápagos_3D, including seven 3D models and over 17,000 annotated images. This study establishes an important baseline for long-term monitoring, research, and conservation in the Galápagos, potentially informing evidence-based policies and advancing our understanding of coral resilience and recovery.

1. Introduction

The Galápagos archipelago, located in the Eastern Tropical Pacific approximately 1000 km west of Ecuador, is globally renowned for its biodiversity and unique ecological systems [1]. Among its marine ecosystems, coral communities range from those growing on volcanic rocks to fully developed biogenic reefs, such as Wellington Reef in Darwin [2,3]. Despite their relatively small size, these reefs play a crucial role in increasing regional marine connectivity and supporting diverse marine life [4]. However, Galápagos corals face numerous threats including climate change, oscillations in ocean currents, cold-water stress [5], warm-water bleaching events [6,7,8], urban development, tourism impacts [1], intense grazing pressure [9], coral diseases, pollution, habitat destruction [8], and invasive species [10].

Several studies have examined the coral communities in the Galápagos and their responses to environmental disturbances [11]. Over the past four decades, extreme climatic events such as the 1982–1983 and 1997–1998 El Niño events have caused severe coral bleaching and mortality, leading to long-term declines in reef cover and biodiversity [6,7,12]. Additionally, cold-water upwelling events, such as the 2007 La Niña, have further impacted these ecosystems [13,14,15]. More recently, marine heatwaves linked to consecutive El Niño years have raised concerns about the ability of Galápagos corals to withstand recurrent disturbances [13,16].

We started a long-term monitoring project using underwater photogrammetry in seven reef sites around the archipelago in order to document and study the adverse effects of such disturbances on the coral community and reef structural complexity. Photogrammetry is a form of 3D imaging that has been used extensively by marine ecologists in the past decade (e.g., [17,18,19]). Using a series of subsequent images as input, Structure-from-Motion photogrammetry builds a 3D model of the scene and estimates the relative camera locations. The 3D models capture the community structure together with the structural complexity of the site and are thus useful for ecological studies.

Traditionally, measuring coral reef structural complexity and biodiversity was done in situ by divers swimming along transect tapes [20,21,22], and later replaced and supplemented with photo quadrats [23,24], video surveys [22], and photogrammetric methods  [17,25,26,27]. Structural complexity was historically measured in situ using a chain draped over the reef surface and a measuring tape to compare surface contour versus planar distance within a quadrat [20,28], and later along transects [22,29,30,31]. These manual approaches inspired digital methods for calculating structural complexity from high-resolution 3D reconstructions [32]. The first predominant works replicated the rugosity metric in 2D and 3D [33,34,35], followed by more structural complexity metrics such as shelter space, vector dispersion, and fractal dimension [36,37,38,39,40].

Fractal dimension (FD) is a unitless measure of how a structure fills space, based on how spatial details change with measurement scale [41]. While FD has been measured in situ [31,42] and from photogrammetric models of coral colonies and reefs [27,38,39,43,44,45], earlier approaches often relied on top-down projections that neglect overhangs and crevices. Similarly, the majority of biodiversity measurements from photogrammetric models utilize photomosaics [46], which are 2D images generated from a single point of view. Despite offering large spatial coverage (commonly on the order of 100 m² at sub-centimeter resolution) and enabling advanced analyses via semantic segmentation [47,48], photomosaics overlook the three-dimensional complexity of reefs. Since many cryptic reef organisms inhabit hidden or vertical surfaces [21,49], we found it important to devise a methodology that operates in full 3D.

Our goal was to establish a baseline protocol for long-term monitoring based on photogrammetry in the region. Considering the need to improve cryptic species detection and overhang inclusion into structural complexity quantification, we chose to work with 3D models rather than their 2D counterparts, and introduce two novel analytical approaches:

1.

3D point-annotation for benthic classification: We used an image pair for each annotation point including the best camera view and a synthetic view providing the annotator 3D context (See Section 2.5).

2.

Fractal dimension calculation using directed geodesic walks: These follow a path along a slice of the 3D model without ignoring overhangs thus accounting for full 3D structure (See Section 2.8.2).

We applied these methods to assess coral community structure and reef complexity at seven sites across the Galápagos archipelago and we release our dataset Galápagos_3D (see Appendix A), that includes annotated 3D models useful for research in ecology, computer graphics, Artificial Intelligence (AI), and for informing conservation strategies in the region.

2. Materials and Methods

2.1. Study Sites

The locations are distributed throughout the archipelago (Figure 1 and Figure 2) and were selected based on the Charles Darwin Foundation team’s long-term monitoring sites [13] and earlier research in the area [2,4,8,9,12,50]. At each location, we began by examining the area to find a $10\times 10$ m² section featuring the highest coral density and species diversity at a depth of 8–12 m. Balancing these criteria is challenging, as the area with the most coral coverage is often not the most diverse. Additionally, the reef depth varies at each site, as outlined in

Table A1. Summary table of all counts, structural complexity measurements, GPS coordinates, and depth per site.

	Darwin-Wellington Reef	Española-Xarifa	Floreana-Tres Cuevitas	Floreana-Punta Cormorant	Marchena-Roca Espejo	Pinta-Cabo Ibetson	Wolf-Corales
Caulerpa	105	1	0	0	0	0	0
Dead Coral—Framework	66	31	11	16	90	332	40
Dead Coral—Rubble	1	65	12	0	38	39	0
Other	46	7	12	13	18	18	12
Pavona	566	0	731	351	35	3	812
Pocillopora	29	0	1	0	613	674	7
Porites	1108	584	0	16	361	10	961
Rock	855	353	1409	1317	1063	1423	580
Sand	177	800	463	485	265	64	93
Tubastraea	9	0	1	1	1	0	2
Unknown	129	8	130	51	74	71	101
Psammocora	0	1	8	1	19	18	0
Cube Counting FD	2.267	2.138	2.229	2.202	2.212	2.208	2.225
mean∖_slope	0.108951	0.035663	0.101956	0.074877	0.062882	0.062978	0.096196
lacunarity	1.495	1.626	1.998	1.615	1.458	1.536	1.684
Surface-Area	309	185	225	276	258	265	261
Lat	−91.995824	−89.644622	−90.408089	−90.419325	−90.401241	−90.720945	−91.815861
Lon	1.67824	−1.357863	−1.236136	−1.223949	0.312162	0.544216	1.386624
Depth	15	5	10	12	8	8	12

. Once the plot was selected and its boundaries marked using a transect tape and a compass, we installed permanent metal stakes at each corner of the plot.

2.2. Image Acquisition and Scene Set-Up

Before image acquisition, we placed a set of photogrammetric markers and color cards in the plot. These are used for scaling the map and assessing the quality of the images in terms of sharpness and illumination during image acquisition and also in post-processing. Moreover, the targets are placed in a way that helps the diver swim in a systematic manner while maintaining overlap between reciprocal legs.

Image acquisition was done using a Nikon D850 DSLR camera with a 35 mm NIKKOR (Nikon, Tokyo, Japan) lens and two Bigblue (Bigblue, Syosset, NY, USA) video lights. Images were acquired from a 2–3 m distance to the substrate at one frame per second. The diver holding the camera swam slowly and steadily while maintaining the camera mostly at a downward-looking angle. Nevertheless, the diver moved the camera around extensive 3D features to capture them from multiple angles of view. The diver swam in a boustrophedonic pattern (lawn mower pattern) across the plot to complete image acquisition from the first distance. Then the diver changed depth to a ∼5 m distance from the substrate and imaged the plot again. Imaging from two distances helps the image alignment process of the 3D reconstruction. For more details on image acquisition and scene set up please see our prior publication [19].

Figure 2. The 3D models from the Galápagos archipelago: Darwin, Wolf, Marchena, Pinta, Floreana, and Española. Each image shows the 3D model of a site. The models are $10\times 10{\mathrm{m}}^2$. A $1\times 1{\mathrm{m}}^2$ grid is shown in the background of each model.

Figure 2. The 3D models from the Galápagos archipelago: Darwin, Wolf, Marchena, Pinta, Floreana, and Española. Each image shows the 3D model of a site. The models are $10\times 10{\mathrm{m}}^2$. A $1\times 1{\mathrm{m}}^2$ grid is shown in the background of each model.

2.3. 3D Processing

Agisoft Metashape software (version 2.12) was used to reconstruct the 3D models from the series of subsequent images. We used the parameters described in Table S1.

We scaled the models using the photogrammetric targets as scale bars. 10–15 scale bars were defined per model in order to minimize the scaling error. For each scale bar we marked the points of known distance in several input images and entered the known distance value. We marked these points in several images until the scale errors were reduced to sub-centimeter values.

2.4. 3D Model Alignment and Export

After the models were constructed and scaled, we aligned them to the XY axis. This step is important for the structural complexity measurements as we do not want the effect of aspect (slope of the reef— differences in depth between corners of the plot) to affect the measurement. We first fit a plane to each model using the open3D python [51] package. The normal of this plane is used for finding the 3D rotation that aligns the model on the XY plane. We find the rotation matrix of the normal and rotate the model by the inverse. We then use the model’s bounding box to find a translation to the center of the axis (this is detailed in the supplementary code “orient model and set region limits”).

After rotating and translating the model, we build a point cloud from the 3D mesh using a distance-based sampling at 1 cm point density in Metashape. Finally, a $10{\mathrm{m}}^3$ region around the center of the axes was defined and the point clouds were exported for further analysis (cube counting and directed geodesic walks).

The point clouds are released as part of the dataset, please see Appendix A for more details.

2.5. 3D Annotation

We developed a novel approach for annotating 3D models using the best camera view and a synthetic image. First, we use the sparse point cloud generated in image alignment and read it using the open3D library [51]. We build a mesh from these points using the open3D alpha shapes surface reconstruction method. We sample points on this mesh using the open3D sample_points_poisson_disk method where each point has approximately the same distance to the neighbor points. Then we use a KD-tree to find the closest point in the sparse cloud to each of the points. We then read these points back as markers on the 3D model. The number of points per model is determined by measuring the surface area of the model in the region and multiplying it by ten in order to achieve approximately ten points per m².

For each marker, we extract the image with the smallest reprojection error. Reprojection error is measured by projecting the point from the 3D model (origin point) to the image and back to the 3D model (target point) and calculating the distance between them. After selecting the image with minimal error, it is cropped around the point in 1600 × 1600 pixels. Eventually we resized the images by half to enable their upload resulting in 800 × 800 pixels per image. We also extract a novel view for each point—a synthetic image of the 3D model using a top-down projection. This image is called synthetic because it was never taken by a camera. It is a rendering of the 3D model from a given viewpoint. We used Metashape’s functions to produce these images with each marker as the center of each image and a fixed size of 1600 × 1600 pixels (Figure 3). The advantage of using both images is that the close-up camera image helps to identify the class of the object while the synthetic view helps to put that in context. This is helpful for distinguishing corals such as Porites and Pavona which look similar from a close-up view, but the colonies have different 3D structures.

The pair of images (best camera view and synthetic image) per point was uploaded to Labelbox [52], an online platform for image annotation. The camera view is a close-up on the point while the synthetic image shows the 3D context of the point. Therefore, using the image pairs helps to annotate the points rapidly and accurately.

The annotations are released as part of the dataset, please see Appendix A for more details.

2.6. Classification

A total of 17,807 image pairs were annotated in 12 classes (results are detailed in Table A1): Pavona, Pocillopora, Porites, Psammocora, Rock, Sand, Tubastraea, Caulerpa, Dead Coral—Framework, Dead Coral—Rubble, Other, and Unknown. The class Dead Coral—Framework was used to describe biogenic substrate (coral skeletons that constitute a reef framework) found mostly in Darwin. The class Unknown was used for points where the images (best camera view and synthetic image) did not show the same point. The class Other was used for points that were not in any category such as photogrammetric targets.

The images were annotated by three members of the marine monitoring team of the Charles Darwin Foundation (W.I., F.T., and W.B.-S.) including reviewing all image pairs to validate the classifications. The three annotators were trained in benthic substrate classification and prior to the experiment reviewed different image examples together to achieve uniform classification.

We also used a classification: “Projection quality”, to describe the fit between the synthetic image and the best camera view. When both images showed the same point, we classify it as good, and when the synthetic view does not exactly align with the best camera view, we classify it as bad. This can happen if the 3D point is obscured by an overhang, since the synthetic views are generated only from a top-down view. We used this classification because in the future we aim to use these synthetic images together with the best camera view to train a neural network for coral identification, and using the synthetic views can increases the amount of training data almost twofold. Please see Appendix A for more information on using this data for training a classifier.

2.7. Community Metrics

We calculated the relative abundance of each class per site by dividing the number of observations from each genus by the total number of observations in the model. We calculated the Shannon Diversity index considering only the coral classes: Pavona, Pocillopora, Porites, and Psammocora. We used R Statistical Software (v4.1.2; R Core Team 2021) and the R package vegan [53,54]. Shannon Diversity is calculated as:

$$H=-\sum _{i=1}^S{p}_{i}ln\left(p_i\right)$$

(1)

where $p_i$ is the proportion of species i, and S is the number of species.

We calculated percent coral cover calculating the proportions of four coral classes—Pavona, Pocillopora, Porites, and Psammocora, out of all classes.

We used Principal Component Analysis (PCA) to visualize the difference in community structure on two axes. We omitted the classes Unknown, Other, and Caulerpa from this analysis, thus reducing nine dimensions to two. PCA is a method that identifies the axes (principal components) along which the data has the greatest variance, projecting the data onto these components.

2.8. Structural Complexity Metrics

2.8.1. Fractal Dimension from Cube Counting

We previously worked on cube-counting for assessing fractal dimension of coral reefs and detailed the method extensively [39]. In short, the cube-counting method [55] enables to calculate the fractal dimension of objects as:

$$FD=\underset{ϵ\to 0}{lim}{\displaystyle \frac{logN\left(ϵ\right)}{log(1/(ϵ\left)\right)}},$$

(2)

where $ϵ$ is the length of the cube and N($ϵ$) is the number of cubes required to cover the object at a given length. N($ϵ$) is calculated for several cube-lengths ($ϵ$) and the fractal dimension is calculated as the slope of the fitted line between log(N($ϵ$)) and log(1/$ϵ$).

We take each point cloud and bound it with a minimal bounding cube (∼10 m³). The cube is then divided into 8 equal cubes by dividing each axis. In each iteration, cubes that contain a part of the point cloud are counted (Equation (2)) and used in the next iteration.

For flat shapes, the size of the cube should not affect the measurement while in complex shapes more surface detail is revealed with smaller cube sizes, and the number of cubes increase exponentially when decreasing the cube length. Flat reefs are expected to have lower values close to two, and reefs that are rich in structural features—i.e., structurally complex reefs, are expected to have values closer to three [39].

2.8.2. Fractal Dimension from Directed Geodesic Walks

To calculate structural complexity, we developed an automatic method that takes an input mesh and returns fractal dimension. This is a novel method that elaborates the classic rugosity metric and applies a similar measurement over multiple scales (resolutions) across the full model.

$$\mathtt{Fractal\; dimension\; from\; geodesic\; walks}=\underset{ϵ\to 0}{lim}{\displaystyle \frac{log(Walk ratio)}{log(1/(Step size\left)\right)}}$$

(3)

$$\mathtt{Walk\; ratio}\left(\mathtt{Step\; size}\left(\mathtt{r}\right)\right)={\displaystyle \frac{\mathtt{Distance}\mathtt{traveled}}{\mathtt{Geodesic}\mathtt{Distance}}}$$

(4)

The steps below are automatic and do not require intervention. The full code for conducting this analysis is available online. We first construct a mesh from the point cloud using the Open3D Python package (version 0.18). The mesh is then cropped into 5 cm-wide slices with 5 cm intervals along both axes, resulting in approximately 200 slices per site. To measure the structural complexity of these slices we simulate a walk along each slice over a range of step sizes (we used the following step sizes given in meters: = 0.01, 0.02, 0.03, 0.05, 0.07, 0.1, 0.2, 0.3, 0.4, 0.6, 0.8, 0.99, 1.1, 1.2, 1.4, 1.5, 1.7, 2, 2.5, 3, 5). The starting and ending points of the walk are defined as the minimal and maximal coordinates along the slice. Using PyVista [56] python package (version 0.44.1) we calculate the geodesic path: the shortest path along the mesh surface between these points. This path determines the order of points for subsequent walks, therefore we call this method directed geodesic walks. We use the recorded vertices of the geodesic path as a baseline for building a new point cloud by densifying these points. This enab*les us to maintain the order of points rather than just their coordinates for the walk algorithm.

It is crucial to balance the slice width: too wide, and the walk avoids the actual terrain, underestimating complexity; too thin, and the mesh fragments, making the walk ineffective. Moreover, we had several cases (57 out of 29,343) where the walk did not work because the algorithm was unable to find points in the specified step size. We excluded these from the FD assessment.

The algorithm follows two key rules: avoid revisiting previous points (using point indices rather than coordinates), and choose the minimal point on the axis of the walk, for example if the walk is along the x-axis, choose the point with the minimal x coordinate (see Figure 4). For each slice, the walk is conducted twice per step-size: once from start to finish and then in reverse. The average number of steps is recorded, and the walk ratio is calculated as the distance traveled divided by the geodesic path length. A linear model is then fitted to the log relationship between walk ratio and step size for each slice, with the overall score per site being the mean of these measurements.

This method captures structural complexity by observing how the walk ratio decreases with increasing step size (Figure 4). For flat surfaces, step size has little effect, as both small and large steps cover similar distances. For complex surfaces, however, smaller steps traverse more intricate paths, highlighting structural complexity. This difference provides an estimate of the dimension and complexity of the reef structure. The idea is that for complex structures the walk ratio will decrease when increasing the step size. For flat surfaces, the step size r has no influence on the distance of the walk. To portray this, imagine an ant, a horse, and an elephant crossing a surface from start to end. If the surface is flat, they will all travel the same distance. If the surface is wavy, rugged, and complex, the ant will travel a larger distance than the horse and elephant. Measuring how the distance traveled changes by step size gives an estimation of the dimension of the surface and the structural complexity of the reef.

2.9. Estimation of Required Resources

The aforementioned tasks of data collection and analysis include manual labor and computer processing. Image acquisition requires two dives including scene set up and recollection of photogrammetric targets. We dedicated a laptop for this project (ASUS-TEK ROG G18, with intel i9 processor, 64 RAM, and Nvidia RTX 4080 laptop GPU). Building a model on this laptop takes less than 24 h, enabling to view the results rapidly and evaluate if more dives are required for a given site. This is especially important when working in remote areas that require dedicated cruises to reach.

Image annotation was done on the Labelbox online platform [52], that automatically records annotation statistics. Although the full process took us several weeks to complete, the average time per label is between eight and 12 s. A main bottleneck is the internet speed and the time it takes the website to load the image pair for annotation. Given a faster connection, we believe that the average time can be reduced to less than five seconds. Reloading the annotations back to Metashape is done automatically using a python script deployed in Metashape after exporting and parsing the annotations from Labelbox.

The workflow for structural analysis is fully automated, apart from a few manual actions in Metashape software (building point cloud from model and exporting the point cloud). We provide a set of scripts that take the input point cloud and return the FD score from cube counting and geodesic walks.

3. Results

We studied seven reefs using 3D point annotations and structural complexity metrics. All results are summarized in Table A1.

3.1. Community Metrics from 3D Annotations

First, we examined the relative abundance of each class. The results (Figure 5A) show that Darwin (n = 3091) is dominated by Porites (36%) and Pavona (18%). Española (n = 1850) is characterized by Sand (43%) and Porites (32%). Fl_cormorant_pt (n = 2251) is dominated by rock (58%) with contributions from Sand (21%) and Pavona (15%). Fl_tres_Cuevas (n = 2778) shows a high abundance of rock (51%) and Pavona (26%). Marchena (n = 2577) is characterized by rock (41%) and Pocillopora (24%), with higher evenness among coral classes. Pinta (n = 2652) has substantial rock cover (54%) and Pocillopora (25%). Wolf (n = 2608) is dominated by Porites (37%) and Pavona (31%).

Coral diversity (Figure 5B) was calculated based on the coral classes Pavona, Pocillopora, Porites, and Psammocora. The results show that Marchena has the highest diversity (0.87), followed by Darwin and Wolf (0.71/0.72). Española and Fl_tres_cuevas have the lowest diversity. When examining the relative abundance of coral classes, it shows that Española is dominated by Porites, while Fl_cormorant_pt and Fl_tres_cuevas are dominated by Pavona. In contrast, Marchena, Darwin, and Wolf exhibit higher evenness among coral classes.

The results of coral cover per site (Figure 5C) varied from 14% in Fl_cormorant_pt to 42% in Wolf. Darwin had 38% coral cover, while Fl_tres_cuevas, Pinta, and Española had 21–24%. Marchena showed 29% coral cover.

3.2. Multidimensional Scaling

We performed a Principal Component Analysis (PCA) to reduce the dimensionality of the data (Figure 5D) and visualize site similarity and class contributions. The first and second PCs explain 49% and 25% of the variation in the data. Caulerpa class was only apparent in Darwin and Unknown and Other classes are points that were not identified and therefore we dropped them from the PCA.

The PCA biplot (Figure 5D) shows that Darwin and Wolf are close due to their higher proportions of Porites and Pavona. Floreana sites (Fl_tres_cuevas and Fl_cormorant_pt) cluster together and are affected by Pavona, Sand, and Rock. Pinta and Marchena group together due to higher proportions of Pocillopora, and Psammocora, Española is separate from all sites due to the high proportion of Sand.

3.3. Structural Complexity from Cube Counting and Walk Ratios

The results of these two metrics show similar trends. To compare them we normalized them using min-max scaling and plotted them against each other (Figure 6C). Darwin, Fl_tres_cuevas, Wolf, and Espanola maintain their ranks of structural complexity in both methods. However, the sites Marchena and Pinta have the same cube counting results and slightly different walk results. Fl_cormorant_pt has higher Geodesic walk scores than these two sites, but lower FD from cube counting.

These findings emphasize the importance of using complementary metrics to understand reef structural complexity.

4. Discussion

Our results reveal significant variation in coral cover and diversity across sites and differences in structural complexity. Northern sites, such as Darwin and Wolf, exhibited the highest coral cover, primarily dominated by Porites and Pavona species. In contrast, Marchena demonstrated the highest coral diversity, with more evenness among Pavona, Pocillopora, Psammocora, and Porites. Floreana sites had relatively lower coral cover but exhibited high structural complexity, suggesting that these reefs may still provide essential habitat for reef-associated organisms despite their lower coral abundance.

Our findings align with previous research that documented higher coral cover in northern sites and patchier distributions in central and southern locations. Moreover, our study expands upon prior work by incorporating 3D structural complexity assessments that provide a more comprehensive understanding of reef habitat variation. This suggests that our new methods are reliable and valuable for research and monitoring in the region. Moreover, in situ surveys by divers can be biased by the diver. The main advantage of photogrammetry is the ability to analyze the results from the lab in an objective manner.

The results suggest that both geographical location and depth significantly influence coral community composition, although this was not directly tested. The Galápagos archipelago can be divided into five distinct bio-regions based on fish and macro invertebrate community composition [57]. The differences in coral cover and diversity can be linked to their geographic locations as each of these regions is characterized by different physical and biological regimes that can help to explain the observed variation between sites [3]. Importantly, we surveyed only seven plots across the archipelago and more surveys are needed to shed light on the differences within and between islands.

Protocols for annotating photogrammetric models from underwater environments usually use the photomosaic [47,48] which is a 2D representation of the 3D model. We aimed to segment the 3D model in order to obtain samples that are obscured in the photomosaic such as from overhangs and crevices. A similar method for point cloud annotation was previously presented [58,59,60]; however, it requires additional software. Our workflow operates in Metashape and the annotations can be distributed online, e.g., on Labelbox [52]. Moreover, using the synthetic image (the 3D model view) improves the annotation accuracy and speed because it enables to view the point in context while the close-up images facilitate precise identification. Previous research on 3D semantic segmentation of coral reef models was done via deep learning and multi-view images (e.g., [61,62,63,64]). In this work, we have taken the first step toward semantic segmentation of 3D models from the region by compiling a large dataset of annotations (see Appendix A). An important follow up study will focus on training a deep neural net based on the image pairs presented here and testing if including the novel views in training increases the accuracy in predicting benthic classes.

Calculating fractal dimension from geodesic walks is a novel method developed for analyzing wide-scale reef models. Cube counting for fractal dimension was implemented by us previously on smaller models [39]; however, it is less effective for large area models because of their extensive lateral extent and relatively shallow vertical features, which result in larger cube sizes being mostly empty. In Figure 6, A and B appear different primarily due to the range on the y-axis. Darwin, Fl_tres_cuevas, and Wolf exhibit the highest fractal dimension from cube counting and geodesic walks. Española has the lowest slope, suggesting a flatter reef structure. Geodesic walks enable to depict structural complexity in large area models effectively. This is evident in the results (Figure 6C) where geodesic walks maintain similar rank orderings among sites as cube counting. Nevertheless, there are some discrepancies, most notably between Pinta/Marchena and Fl_cormorant_pt. Here, cube counting overestimates structural complexity. The first two are relatively flat models abundant in Pocillopora. On the other hand, Fl_cormorant_pt has an abundance of Pavona colonies scattered across the substrate in different sizes (Figure 2). Cube counting rated these sites high probably because of differences between the small box sizes and the larger ones.

The amount of human input required in this study is relatively low as the majority of methods are automated. Image acquisition is done by divers in situ, taking 1−2 scuba dives. Constructing the models and analyzing them for structural complexity is done automatically with a set of custom python scripts. The image annotation scheme is efficient because it takes only a few seconds for an annotator to classify the image pair in question. Replicating this study in other regions would require basic knowledge of underwater photogrammetry to enable 3D reconstruction and basic proficiency in Python to run the code provided in this work.

Establishing permanent monitoring plots and tracking the fate of single coral colonies over large spatial and temporal extents is one of the crucial next steps in coral reef monitoring and ecology. Expanding our baseline surveys to a continuous monitoring scheme necessitates 3D registration of models from the same site, which is challenging to achieve in the underwater domain [65]. We placed metal stakes in the corners of the plots that can be used as reference points for future surveys and 3D model matching. Once corresponding models of the same site over time are registered (superimposed), the 3D annotation points can be examined in consecutive models, tracking the same point over time. Such direct temporal comparisons can be further automated and facilitated using deep learning. As mentioned above, the dataset generated here (see Appendix A) can be used to train a classifier for classifying the same points over time or new points from more 3D models in the region.

Photogrammetry is becoming one of the most popular tools in the benthic ecology toolbox, with more and more groups adopting 3D imaging protocols to study coral reefs. Nevertheless, the majority of methods use the 2D data: Digital Elevation Models (DEMs) and photomosaics. Considering advances in 3D imaging technologies it is paramount to develop new ways for scientific analysis of 3D data. However, at this point analyzing photomosaics is more pragmatic than analyzing 3D models as there is a plethora of solutions for automatic 2D image segmentation, however there are hardly any tools for 3D segmentation. Moreover, current methods in benthic mosaic analysis enable measuring the sizes of single colonies and how they changes over time [47] (object-based analysis), which our method is lacking (point-based analysis). We believe that in the near future tools will be developed for 3D instance segmentation, which represents the highest level of detail that can be extracted from photogrammetric surveys of the seabed. With regards to structural complexity analysis, in our opinion the method presented here is superior to a DEM based measurement as it accounts for the full 3D structure of the reef as captured by the model rather than reducing a dimension (Z). With this in mind, image acquisition should aim to capture multiple angles of view on the reef rather than having the camera facing only downwards. This helps to ensure that cryptic reef features will show in the 3D reconstruction.

5. Conclusions

Our application of novel photogrammetric techniques represents a significant methodological advancement in Galápagos coral research. Implementing fractal dimension analysis through directed geodesic walks quantifies fine-scale reef complexity across multiple spatial scales, enhancing our ability to compare reefs with different structural compositions and providing a robust metric for monitoring long-term changes in habitat complexity. We release a new dataset: Galápagos_3D, including the 3D models used in this study together with 3D annotations and classified image pairs. This data is useful for studies in ecology and computer graphics such as 3D segmentation from sparse labels via region growing [66].

Additionally, while we documented spatial variation in reef complexity, temporal monitoring is needed to assess long-term resilience. Repeated surveys, particularly following extreme climatic events, will be crucial in understanding whether certain coral communities are developing adaptive responses to recurring stressors. Given the increasing frequency of marine heatwaves and El Niño events, understanding which coral communities are most resilient and why will be critical for conservation planning. Conservation efforts should prioritize sites with high coral cover and structural heterogeneity, as these areas may serve as ecological strongholds in the face of climate change.

Future studies should focus on longitudinal assessments, combining photogrammetry with genetic and physiological analyses to identify potential resilience mechanisms in corals of the Galápagos. Additionally, integrating satellite remote sensing data with underwater photogrammetry could enhance large-scale monitoring efforts, providing a more comprehensive picture of the state of coral ecosystems.

In conclusion, this work demonstrates the application of photogrammetry for coral reef ecology and sets a new standard for reef monitoring in the Galápagos. We report new methods for structural complexity and community composition analysis, and release a new dataset of annotated 3D models. We aim to continue this long-term research effort and contribute to evidence-based conservation policies, ensuring the preservation of these vital ecosystems for future generations.