TITLE: Geometric Method for Estimating Coral Surface Area Using Image Analysis
AUTHORS: Rowan Mclachlan, Andrea Grottoli

[DESCRIPTION]
<div class = "text-blocks"><div class = "text-block">This protocol outlines a non-destructive geometric method for estimating the surface area of Scleractinian coral samples with relatively simple morphologies (e.g., not densely branching). The geometric method was one of the earliest used for estimating the surface area of marine organisms (Odum et al. 1958). The basic principle of this method involves selecting geometric shapes or forms which closely resemble the morphology of a coral fragment (e.g., cylinders, cones, pyramids, hemispheres etc.), measuring the dimensional parameters of the coral, and applying the area equation for a given geometric shape to obtain the surface area estimate for the coral. This method has been commonly used in coral research previously (Szmant-Froelich 1985; Roberts and Ormond 1987; Babcock 1991; Bak and Meesters 1998; Naumann et al. 2009).</div><div class = "text-block"><span>In this protocol, two examples are given: one for a branching</span><span style = "font-style:italic;"> Porites compressa</span><span> colony, and one for a massive/mounding </span><span style = "font-style:italic;">Porites lobata </span><span>colony. There are three parts to estimating colony surface area: 1) photographing coral fragments, 2) image analysis, and 3) calculation of colony surface area using geometric equations.</span></div><div class = "text-block">This protocol was written by Rowan McLachlan and was reviewed by Dr. Andréa Grottoli.</div><div class = "text-block">Acknowledgments: I would like to thank Dr. Mia Hoogenboom and Dr. Allison Paley for introducing me to this geometric method at James Cook University, Queensland, Australia.</div><div class = "text-block"><span style = "font-weight:bold;">References:</span></div><div class = "text-block">- Babcock RC (1991) Comparative demography of three species of scleractinian corals using age- and size-dependent classifications. Ecol Monogr 61:225–244</div><div class = "text-block">- Bak RPM, Meesters EH (1998) Coral population structure: the hidden information of colony size-frequency distributions. Mar Ecol Prog Ser 162:301–306</div><div class = "text-block">- Naumann MS, Niggl W, Laforsch C, Glaser C, Wild C (2009) Coral surface area quantification-evaluation of established techniques by comparison with computer tomography. Coral Reefs 28:109–117</div><div class = "text-block">- Odum EP, Kuenzler EJ, Blunt MX (1958) Uptake of P32 and primary productivity in marine benthic algae. Limnol Oceanogr 3:340–345</div><div class = "text-block">- Roberts CM, Ormond RFG (1987) Habitat complexity and coral-reef fish diversity and abundance on Red-Sea fringing reefs. Mar Ecol Prog Ser 41:1–8</div><div class = "text-block">- Szmant-Froelich A (1985) The effect of colony size on the reproductive ability of the Caribbean coral Montastraea annularis (Ellis and Solander). Proc 5th Int Coral Reef Symp 4:295–300</div></div>

[STEPS]
?. [Photographing corals]
Prepare the photograph area. Setup a tripod so that the digital camera is pointing downward, parallel to the workbench as shown in Fig. 1. Place a metric ruler on two blocks of equal height (at least two inches) and make sure a section of the ruler is visible in the digital camera field of view. Arrange a light source so that coral fragments will be evenly lit. If a light source is not available, then the in-built camera flash is also suitable. It is important that all of the coral tissue on the uppermost surface is evenly illuminated (i.e., no dark shadows). Adjust the camera setting such that the ruler is clearly in focus (note: switch to manual focus if using a DSLR camera). If coral samples will be removed directly from experimental tanks (i.e., not frozen), then you may consider placing a waterproof sheet below the tripod, to protect the workbench from saltwater.
?. [Photographing corals]
Photograph coral colonies from multiple angles. Remove corals from experimental tanks and proceed to the photographing area. Note: It is essential that the photographs are taken relatively quickly (i.e., When all photographs have been taken, return coral colonies to the experimental tanks.
?. [Image analysis for branching morphology]
Import the first photo file. Open the first photo of either the front or the back of the coral (i.e., Fig. 2A or Fig. 2C) into the ImageJ software.
?. [Image analysis for branching morphology]
Set scale. By holding Ctrl + scrolling on your mouse, zoom into a region of the ruler (Fig. 5A). Using the straight-line tool (fifth button from the right in the ImageJ toolbar), carefully highlight a 2 cm region of the ruler (yellow line, Fig. 5B). Next click on Analyze > Set Scale, after which a dialogue box will appear (Fig. 5C). Set the known distance and unit of length to 2 and cm, respectively (Fig. 5C).
?. [Image analysis for branching morphology]
Draw isosceles trapezoid. An isosceles trapezoid has two parallel sides with equal angles from each of the parallel sides (i.e., green and orange angels in Fig. 6A). Using the polygon selection tool (third button from the right in the ImageJ toolbar), carefully draw an isosceles trapezoid as accurately as possible around the coral fragment (yellow lines Fig. 6B), and then press Ctrl + D to permanently draw this outline onto the image (black dotted line Fig. 6C).
?. [Image analysis for branching morphology]
Measure lengths & areas. Using the black dotted line guide that you drew in step 7 (Fig. 6C), measure the bottom width (Fig. 7A), top width (Fig. 7B), and height (Fig. 7C) of the coral fragment. Trace each line using the straight-line segment tool, then press Ctrl + M to measure the length. A dialogue box showing the results will appear on the right. If there are any dead tissue patches on the coral skeleton, trace around these using the polygon tool and measure (Fig. 7D). Note lengths will be listed under the "Length" column in the results dialogue box, whereas the dead tissue patch area is listed in the "Area" column.
?. [Image analysis for branching morphology]
Repeat for the second photo file. Import the second side photo into ImageJ (Fig. 8A), set the scale (Fig. 8B), draw a new trapezoid (Fig. 8C), and measure the widths, height, and dead tissue area (Fig. 8D–G) using the methods described in steps 5 through 8 above.
?. [Image analysis for branching morphology]
Measure top photo. Import the top-view photo into ImageJ (Fig. 9A), set the scale (Fig. 9B), and measure the 2-dimensional arial surface area (also known as dripline or crown area) using the polygon tool (Fig. 9C).
?. [Image analysis for branching morphology]
Download ImageJ. ImageJ can be downloaded for free from the NIH website: https://imagej.nih.gov/ij/download.html.
?. [Image analysis for branching morphology]
Overview of a geometric strategy for corals with simple branching morphology (details in steps 4–10). Several different geometric shapes can be used with this method of estimating the surface area of branching corals including rectangles or cylinders. However, for small fragments of Hawaiian corals species (e.g., Porites compressa and Pocilloproa meandrina), I have found that a truncated rectangular pyramid (Fig. 3A) most accurately approximates the surface area. This method involves measuring widths and heights from two perpendicular images of a coral fragment (Fig. 3B, C), and a 2-dimensional trace of the upper surface of the coral (Fig. 3D).
?. [Image analysis for mounding morphology]
Overview of a geometric strategy for corals with simple mounding morphology. Several different geometric shapes can be used in this method of estimating the surface area of mounding corals including circular domes or spheroids. However, for small mounds of Hawaiian corals species (e.g., Porites lobata and Porites evermanni), I have found that half a scalene ellipsoid (Fig. 10A) most accurately approximates the surface area. This method involves measuring widths and heights from two perpendicular images of a coral mound (Fig. 10B, C).
?. [Image analysis for mounding morphology]
Import photos, set scale, measure lengths a, b, and c in ImageJ using methods described above.
?. [Geometric equations]
Branching Morphology - Rectangular Pyramidal Frustum:The equation for the lateral* surface area of a rectangular pyramidal frustum was found on this website* Note the lateral surface area does not include the top or bottom surfaces, and instead only the sides. The dripline trace value is used for the upper surface area, and there is no bottom surface area, as the coral colony is attached to the ceramic frag plug. Equations may need to be adapted, depending upon the morphology of your coral samples.Lateral Surface Area of Rectangular Pyramidal Frustum (cm2) = (a+c) x √(1/4 x (b-d)2 + h2) + (b+d) x √(1/4 x (a-c)2 + h2)Calculate the surface area of the branching coral fragment using the a, b, c, d, and h values measured, and the equation shown above. Subtract any dead tissue areas, and add on the dripline area for the top of the fragment using the following equation:Branching Coral SA (cm2) = Lateral SA of Rectangular Pyramid + dripline area trace - dead tissue tracesMounding Morphology - Half Scalene Ellipsoid:The equation for the surface area of a scalene ellipsoid* was found on this website. * Note: this value needs to be divided by two, as the mounding coral represents only half a full scalene ellipsoid.Surface Area of a Half Scalene Ellipsoid (cm2) = 0.5 x 4π [(aZ x bZ + aZ x cZ + bZ x cZ)/3](1/Z), where Z = 1.6075Calculate the surface area of the mounding coral fragment using the a, b, and c values measured. Subtract any dead tissue areas using the following equation:Mounding Coral SA (cm2) = SA of Half Scalene Ellipsoid - dead tissue traces