Measure egg volume and surface area

Our research into egg camouflage resulted in hundreds of egg photographs that needed cutting out from their backgrounds. I searched for a simple tool or equation that would let us do this easily, but the equations didn’t fit our eggs very well, or were difficult to solve from a few points. So I came up with a new mathematical formula that describes the shape of an egg, and can be fitted to a few anchor points. The tool fitted egg shapes so well that I developed the script to work out the surface area and volume of the eggs with a greater precision than the traditional length and breadth method. This tool is described and tested in my publication (download PDF).

Installation

• Make sure you’ve got ImageJ (a great open source image editor).
• Download the zip file here
• Unzip and copy the “Egg Tools” folder into your imagej plugins folder (e.g. C:/Program Files/ImageJ/plugins for windows).
• Restart ImageJ and the tool will be loaded.

Instructions

• Photograph your egg(s) side-on with a scale-bar in the photo at the same height as the centre of the egg. Make sure there is no lens distortion (e.g. when you photograph a flat chequerboard all the lines come out straight in the photo. If you do have barrel or pincushion distortion you can correct it (e.g. with RAWTherapee or Photoshop).
• Open the image in ImageJ, select the multi-point tool. Place a point on the tip and base of the egg, and three or more extra points around the edge on each side (8 points in total, as in the above photo).
• Go Plugins>Egg Tools>Egg Measurement and follow the instructions, or see the video below.

Video Walkthrough

Why is this useful?

The geometrical properties of eggs – such as volume and surface area – have uses ranging from ecological, physiological and morphological studies in birds, to predictions of chick condition in the poultry industry. Although measurements of an egg’s length and breadth can be used to approximate an egg’s geometry, the coefficients used in these models are specific to the original test population, and within-species variation in egg shape means these methods cannot be used reliably outside of that original test population. The mathematical formula here describes the curvature of a bird’s egg, and it can be used to calculate the shape, volume and surface area of an egg precisely from digital images. Using data from a number of species I demonstrated that the model has a greater level of accuracy than length and breadth-based methods.

How it works

The equation is essentially an ellipse that has a normal distribution added. The variable a describes the width of the ellipse, b describes where the centre of the ellipse bulge sits, and c describes how acute/pointed that bulge is.

Citation:

Troscianko, J. (2014). A simple tool for calculating egg shape, volume and surface area from digital images. Ibis, 156(4), 874-878 https://doi.org/10.1111/ibi.12177