Eroded Volume Fraction is a normalized measurement of the radial position of the center of an object.
It is similar to a shell analysis but continuous.
It has been described in Ballester, M., Kress, C., Hue-Beauvais, C., Kiêu, K., Lehmann, G., Adenot, P., & Devinoy, E. (2008). The nuclear localization of WAP and CSN genes is modified by lactogenic hormones in HC11 cells. Journal of cellular biochemistry, 105(1), 262–70. doi:10.1002/jcb.21823.
Here is the description given in the original article:
The EVF of a point within the nucleus is defined as the fraction of nuclear volume lying between a considered point and the nuclear membrane. The EVF rises from 0 at the nuclear periphery to 1 at the nuclear center. The EVF of points uniformly distributed within a nucleus is uniformly distributed between 0 and 1. This property holds for nuclei of any size and shape. It should be noted that the EVF changes more rapidly near the nuclear periphery than in the nuclear center. For instance, in a spherical nucleus with a radius of 5 mm, a point with an EVF equal to 0.5 lies only about 1 mm from the nuclear membrane. Standard erosion analyses Parada et al., 2004a were based on a discretized version of the EVF. EVFs were computed based on a Euclidean distance transform.
This implementation also allows to compute EVF from other segmented structure.
It also provides a normalization with nuclear intensity instead of volume.