When the mitochondrial network within the cell is in a fragmented state, it resembles a spatial distribution of prolate spheroids of various shapes, sizes and orientations. The cell is studied by making electron micrographs which amount to a series of planar slices through that spatial distribution. These micrographs exhibit sections of individual mitochondria, which have roughly elliptical shape. This paper uses a maximum-likelihood scheme to infer the distribution of spheroidal shapes, sizes and orientations from the observed distribution of elliptical sections.