Fig 1.
Half-transparent 3D model of a cell featuring the shape of a prolate spheroid.
A is the cross-sectional surface area and d is the cell width, which is equal to the obscured third dimension due to the assumed rotational symmetry.
Fig 2.
Examples of cell cross sections with different coefficient of unellipticity (U).
(a) U > 1, (b) U < 1, (c) U = 1. Solid black silhouettes: cell cross sections; red dashed lines: regular ellipses having the same length and width as the cell cross section.
Fig 3.
Simple or composite geometric shapes used as models for testing the accuracy of the proposed method.
(a) prolate spheroid, (b) cylinder with hemispherical ends, (c) cylinder, (d) cylinder with conical ends, (e) cone, (f) cone with a hemispherical end, (g) Peridinium-like, (h) Ceratium-like. The latter two shapes are named after two common microalgae genera.
Fig 4.
3D model of Oxyphysis oxytoxoides, a heterotrophic dinoflagellate species common in temperate to subtropical waters.
(a) Scanning Electron Microscope picture of an individual of Oxyphysis oxytoxoides, (b) Binary picture obtained through image segmentation of a, and employed for the estimation of the cross-sectional surface area of the cell, (c) 3D reconstruction of a cell of O. oxytoxoides using a as a model.
Fig 5.
Box plots showing the errors caused by the new equation and the other tested methods in the estimation of the volume of four of the eight simple or composite geometric shapes (those yielding constant errors with the new equation and the prolate spheroid equation).
The median, as well as the 10th, 25th, 75th, and 90th percentiles are shown. Whiskers indicate the 10th percentile and 90th percentile, respectively; while the extent of outlying points (solid circles) identifies the data range (standard method is used to calculate percentile values).
Fig 6.
Box plots showing the errors caused by the new equation and the other tested methods in the estimation of the volume of four of the eight simple or composite geometric shapes (those yielding variable errors with the new equation and the prolate spheroid equation).
The median, as well as the 10th, 25th, 75th, and 90th percentiles are shown. Whiskers indicate the 10th percentile and 90th percentile, respectively; while the extent of outlying points (solid circles) identifies the data range (standard method is used to calculate percentile values).
Table 1.
Comparison between the “integration” method by Sieracki et al. (1998) and the newly proposed equation on a single sphere, a double sphere, or on a cylinder with hemispherical ends.
Table 2.
Percent errors obtained with the ‘integration’ algorithm (Sieracki et al. 1998) in the estimation of the biovolumes respectively of the solids of revolution a and b (see text).
Fig 7.
Box plots showing the errors caused by the new equation and the other tested methods in the estimation of the volume of the 3D shapes created with Cinema4D.
The median, as well as the 10th, 25th, 75th, and 90th percentiles are shown. Whiskers indicate the 10th percentile and 90th percentile, respectively, while the extent of outlying points (solid circles) identifies the data range (standard method is used to calculate percentile values). The * symbol denotes that values are off scale.