Читать книгу Diatom Morphogenesis - Группа авторов - Страница 32

Each original image is masked to eliminate the background. From this, the masked image is used in entropy analysis. The number of rotations per image depends on identifiable regular occurring equally angularly spaced surface features such as rays, ocelli, rimoportulae, areolae, costae, chambers, ribbing, or slits. For example, in Asterolampra marylandica, there are large extended chambers on the surface resulting in a star-like shaped central area, and the number of these chambers dictates the number of rotations. Or, for Aulacodiscus, the number of rotations is equal to 360° divided by the number of ocelli or rimoportulae on the valve surface. If there are multiple images of the same species with a different number of the same identifiable feature, then the number of rotations is determined for each image, not each species. The number of rotations is based also on shape for non-circular valves. For example, Triceratium and Amphitetras would receive three and four rotations, respectively.

Number of rotations per image ranged from 3 to 64 as determined by the taxa used in this study (Table 2.1). A rotations test was used to determine if an optimal number of rotations was associated with the lowest possible entropy value for those circular-shaped taxa without distinct identifiable equally spaced surface features. For this test, Cyclotella meneghiniana was used.

Entropy is calculated as a cumulative quantity based on successive overlaying of rotated images while matching edges for each original image. After all rotations are completed, the final entropy value is the minimum amount of entropy left after successive subtractions of one image from the previous stack of rotated and overlain images. For entropy measurement, an equivalence between rotational and reflective symmetry also can be made. An equivalence between rotational and reflective symmetries was established as follows: two rotations represent one plane of reflective symmetry; three rotations represent two planes of reflective symmetry; and four rotations represent three planes of reflective symmetry. Rectangular taxa were rotated four times to represent four planes of reflective symmetry, and pentagonal taxa were rotated five times to represent five planes of reflective symmetry.