In this paper, we present a new surface area estimator in local stereology. This new estimator is called the ‘Morse-type surface area estimator’ and is obtained using a two-stage sampling procedure. First a plane section through a fixed reference point of a three-dimensional structure is taken. In this section plane, a modification of the area tangent count method is used. The Morse-type estimator generalizes Cruz-Orive's pivotal estimator for convex objects to nonconvex objects. The advantages of the Morse-type estimator over existing local surface area estimators are illustrated in a simulation study. The Morse-type estimator is well suited for computer-assisted confocal microscopy and we demonstrate its practicability in a biological application: the surface area estimation of the nuclei of giant-cell glioblastoma from microscopy images. We also present an interactive software that allows the user to efficiently obtain the estimator.