Title: Measuring Shapes of Galaxy Images I: Ellipticity and Orientation

Abstract: 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.