Features Calculated Using the Convex Hull of the Protein Fluorescence

The convex hull of the protein localization image was calculated using the convhull function in Matlab and converted to a binary image.

The fraction of the convex hull area occupied by protein fluorescence

The roundness of the convex hull

$$\frac{(Perimeter)^2}{4\pi Area}$$ (3.6)

The eccentricity of the convex hull

The eccentricity of the ellipse equivalent, based on second order moments, to the protein image convex hull was calculated using [49]

$$\frac{\sqrt{(Semimajor Axis)^2 - (Semiminor Axis)^2}}{(Semimajor Axis)}$$ (3.7)

where

$$Semimajor Axis = \sqrt\frac{2[\mu_{20}+\mu_{02}+ \sqrt{(\mu_{20}-\mu_{02})^2 + 4\mu_{11}^2}]}{\mu_{00}}$$ (3.8)

and

$$Semiminor Axis = \sqrt\frac{2[\mu_{20}+\mu_{02}- \sqrt{(\mu_{20}-\mu_{02})^2 + 4\mu_{11}^2}]}{\mu_{00}}$$ (3.9)

(The $\mu_{xy}$ above are the central moments of the image intensity function).