  The detection of objects that are multi-oriented is a difficult pattern
recognition problem. In this paper, we propose to evaluate the performance of
different families of descriptors for the classification of galaxy
morphologies. We investigate the performance of the Hu moments, Flusser
moments, Zernike moments, Fourier-Mellin moments, and ring projection
techniques based on 1D moment and the Fourier transform. We consider two main
datasets for the performance evaluation. The first dataset is an artificial
dataset based on representative templates from 11 types of galaxies, which are
evaluated with different transformations (noise, smoothing), alone or combined.
The evaluation is based on image retrieval performance to estimate the
robustness of the rotation invariant descriptors with this type of images. The
second dataset is composed of real images extracted from the Galaxy Zoo 2
project. The binary classification of elliptical and spiral galaxies is
achieved with pre-processing steps including morphological filtering and a
Laplacian pyramid. For the binary classification, we compare the different set
of features with Support Vector Machines (SVM), Extreme Learning Machine, and
different types of linear discriminant analysis techniques. The results support
the conclusion that the proposed framework for the binary classification of
elliptical and spiral galaxies provides an area under the ROC curve reaching
99.54%, proving the robustness of the approach for helping astronomers to study
galaxies.
