  We suggest a set of morphological measures that we believe can help in
quantifying the shapes of two-dimensional cosmological images such as galaxies,
clusters, and superclusters of galaxies. The method employs non-parametric
morphological descriptors known as the Minkowski functionals in combination
with geometric moments widely used in the image analysis. For the purpose of
visualization of the morphological properties of image contour lines we
introduce three auxiliary ellipses representing the vector and tensor Minkowski
functionals. We study the discreteness, seeing, and noise effects on elliptic
contours as well as their morphological characteristics such as the ellipticity
and orientation. In order to reduce the effect of noise we employ a technique
of contour smoothing. We test the method by studying simulated elliptic
profiles of toy spheroidal galaxies ranging in ellipticity from E0 to E7. We
then apply the method to real galaxies, including eight spheroidals, three disk
spirals and one peculiar galaxy, as imaged in the near-infrared $K_s$-band (2.2
microns) with the Two Micron All Sky Survey (2MASS). The method is numerically
very efficient and can be used in the study of hundreds of thousands images
obtained in modern surveys.
