A convex-hull based method with manifold projections for detecting cell protrusions.

Cell protrusions play an important role in a variety of cell physiological processes. In this paper, we propose a convex-hull based method, combined with manifold projections, to detect cell protrusions. A convex hull is generated based on the cell surface. We consider the cell surface and the boundary of its convex hull as two manifolds, which are diffeomorphic, and define a depth function based on the distance between the cell surface and its convex hull boundary. The extreme points of the depth function represent the positions of cell protrusions. To find the extreme points easily, we project the points on the cell surface onto the boundary of the convex hull and expand them in spherical polar coordinates. We conducted experiments on three types of cell protrusions. The proposed method achieved the average precision of 98.9%, 95.6%, and 94.7% on blebs, filopodia, and lamellipodia, respectively. Experiments on three datasets show that the proposed method has a robust performance.