Segmentation of cellular structures is of primary interest in cell imaging for cell shape reconstruction and to provide crucial information about possible cell morphology changes during radiotherapy for instance. From the particular perspective of predictive oncology, this paper reports on a novel method for membrane segmentation from single channel actin tagged fluorescence confocal microscopy images, which remains a challenging task. Proposed method is based on the use of the Approximate Entropy formerly introduced by Pincus embedded within a Geodesic Active Contour approach. Approximate Entropy can be seen as an estimator of the regularity of a particular sequence of values and, consequently, can be used as an edge detector. In this prospective study, a preliminary study on Approximate Entropy as an edge detector function is first proposed with a particular focus on the robustness to noise, and some promising membrane segmentation results obtained on confocal microscopy images are also shown.